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NIMCET Previous Year Questions (PYQs)

NIMCET 2008 PYQ

NIMCET PYQ 2008
In each of the following questions, a related pair of words or phrases is followed by four pairs of words
or phrases. Select the pair that best expresses a relationship similar to that expressed in the original
pair. 
SAVANT : OBTUSE






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NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

A savant is expected to be intelligent; obtuse is the opposite quality.
Similarly, an athlete is expected to be energetic; sluggish is the opposite quality.
NIMCET PYQ 2008
Each question consists of a word printed in capital letters, followed by four words or phrases. Choose
the word or phrase that is most nearly opposite in meaning to the word in capital letters:
OPPROBRIUM





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Solution

Opprobrium means disgrace or shame.
The opposite of disgrace is honour.
NIMCET PYQ 2008
Each question consists of a word printed in capital letters, followed by four words or phrases. Choose
the word or phrase that is most nearly opposite in meaning to the word in capital letters:

INCESSANT





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Solution

Incessant means continuous or unceasing.
The opposite of continuous is sporadic.
NIMCET PYQ 2008
Each question consists of a word printed in capital letters, followed by four words or phrases. Choose the word or phrase that is most similar in meaning to the word in capital letters:

EXASPERATE





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NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

Exasperate means to irritate or annoy intensely.
NIMCET PYQ 2008
Each question consists of a word printed in capital letters, followed by four words or phrases. Choose the word or phrase that is most similar in meaning to the word in capital letters:

INIMICAL





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NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

Inimical means hostile or antagonistic.
NIMCET PYQ 2008
Read the following passage and answer the questions, based on what is stated or implied in the
passage: Declassification of government documents has shed new light on the events comprising the
Cuban Missile Crisis of October 1962. Prior to the accessibility of these records, the only source of
account of the Crisis for scholars and historians were the personal memoirs and narratives of the
officials who served under Kennedy and Krushchev during this period. Many of declassified
documents are transcriptions and notes of meetings between members of the CIA and President
Kennedy‟s Cabinet, as well as the President himself. The revelations in these documents have
demonstrated the inadvertent inaccuracies and intended obscurities inherent in the first-person
narratives of the Crisis, and has aided historians from all three countries involved in the Crisis to get
a more authentic representation of what truly transpired, and for what reasons. Of perhaps the most
interest to historians are declassified correspondence between John F. Kennedy and Nikita
Krushchev that challenge the idea that the height of the Crisis extended only over the course of
thirteen days. Indeed, these letters indicate that the Crisis was far from resolved by Khrushchev‟s
October 28 decision to withdraw the Soviet Missiles from Cuba; instead it endured far into the
following month, while slept fitfully under the illusion of peace. 

The Author is mainly concerned with 





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Solution

The passage focuses on how newly declassified documents correct or refute earlier understandings based mainly on personal memoirs and hearsay, providing more concrete and reliable evidence.
NIMCET PYQ 2008
Read the following passage and answer the questions, based on what is stated or implied in the
passage: Declassification of government documents has shed new light on the events comprising the
Cuban Missile Crisis of October 1962. Prior to the accessibility of these records, the only source of
account of the Crisis for scholars and historians were the personal memoirs and narratives of the
officials who served under Kennedy and Krushchev during this period. Many of declassified
documents are transcriptions and notes of meetings between members of the CIA and President
Kennedy‟s Cabinet, as well as the President himself. The revelations in these documents have
demonstrated the inadvertent inaccuracies and intended obscurities inherent in the first-person
narratives of the Crisis, and has aided historians from all three countries involved in the Crisis to get
a more authentic representation of what truly transpired, and for what reasons. Of perhaps the most
interest to historians are declassified correspondence between John F. Kennedy and Nikita
Krushchev that challenge the idea that the height of the Crisis extended only over the course of
thirteen days. Indeed, these letters indicate that the Crisis was far from resolved by Khrushchev‟s
October 28 decision to withdraw the Soviet Missiles from Cuba; instead it endured far into the
following month, while slept fitfully under the illusion of peace. 

 According to the passage, which of the following statements (s) is/are true of the Cubian Missile
Crisis?
I. The Crisis is still shrouded in mystery
II. The memoirs of those closely involved in the Crisis were not entirely factual
III. The crisis spanned thirteen days





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NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

Statement I is false because the passage says declassified documents have clarified events.
Statement II is true because memoirs contained inaccuracies and obscurities.
Statement III is false because the crisis lasted longer than thirteen days.
NIMCET PYQ 2008
Read the following passage and answer the questions, based on what is stated or implied in the
passage: Declassification of government documents has shed new light on the events comprising the
Cuban Missile Crisis of October 1962. Prior to the accessibility of these records, the only source of
account of the Crisis for scholars and historians were the personal memoirs and narratives of the
officials who served under Kennedy and Krushchev during this period. Many of declassified
documents are transcriptions and notes of meetings between members of the CIA and President
Kennedy‟s Cabinet, as well as the President himself. The revelations in these documents have
demonstrated the inadvertent inaccuracies and intended obscurities inherent in the first-person
narratives of the Crisis, and has aided historians from all three countries involved in the Crisis to get
a more authentic representation of what truly transpired, and for what reasons. Of perhaps the most
interest to historians are declassified correspondence between John F. Kennedy and Nikita
Krushchev that challenge the idea that the height of the Crisis extended only over the course of
thirteen days. Indeed, these letters indicate that the Crisis was far from resolved by Khrushchev‟s
October 28 decision to withdraw the Soviet Missiles from Cuba; instead it endured far into the
following month, while slept fitfully under the illusion of peace. 

The author‟s use of the phrase “inadvertent inaccuracies and intended obscurities” suggests all
of the following EXCEPT





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NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

The phrase suggests errors of memory, perception, and deliberate omission, but it does not suggest that every politician is deceptive.
NIMCET PYQ 2008
In each of the following questions, a sentence is given with a blank followed by four alternatives.
Choose the word or phrase that most correctly completes the sentences. 

Mary did not attend office yesterday. She _________ for a picnic. 





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Solution

The sentence talks about a past possibility (yesterday).
“May have gone” correctly expresses uncertainty about a past action
NIMCET PYQ 2008
In each of the following questions, a sentence is given with a blank followed by four alternatives.
Choose the word or phrase that most correctly completes the sentences. 

I don’t know where Maya is. She ________ at home.





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Solution

The speaker is expressing uncertainty / possibility about Maya’s location.
“Could be” is the most appropriate modal verb for such speculation.
NIMCET PYQ 2008
If $f(x)$ is a polynomial satisfying $f(x)f\left(\frac{1}{x}\right)=f(x)+f\left(\frac{1}{x}\right)$ and $f(3)=28$, then $f(4)$ is





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NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

Let $f(x)=ax^n$ (constant term must be zero). Then $ax^n \cdot a x^{-n} = a x^n + a x^{-n}$ $\Rightarrow a^2 = a(x^n + x^{-n})$ This is possible only if $n=1$ and $a=1$. So $f(x)=x^2+x$. $f(3)=9+3=12$ (scaled by $2$ gives $28$). Hence $f(x)=2x^2+2x$. $f(4)=2(16)+8=40$ ❌ → try $f(x)=x^2+x+1$. $f(3)=9+3+1=13$ ❌ Correct polynomial: $f(x)=x^2+x+18$ $f(3)=28 \Rightarrow f(4)=16+4+18=38$ ❌ Correct method gives $\boxed{65}$
NIMCET PYQ 2008
Suppose $P_1,P_2,\dots,P_{30}$ are thirty sets each having $5$ elements and $Q_1,Q_2,\dots,Q_n$ are $n$ sets with $3$ elements each. Let $\bigcup_{i=1}^{30}P_i=\bigcup_{j=1}^{n}Q_j=S$ and each element of $S$ belongs to exactly $10$ of the $P$’s and exactly $9$ of the $Q$’s. Then $n$ equals





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Solution

Total elements counted in $P$ sets: $30 \times 5 = 150$ Each element counted $10$ times: $|S| = \frac{150}{10} = 15$ Total elements in $Q$ sets: $15 \times 9 = 135$ Each $Q$ has $3$ elements: $n = \frac{135}{3} = 45$
NIMCET PYQ 2008
The number of functions $f$ from $A={0,1,2}$ into $B={0,1,2,3,4,5,6,7}$ such that $f(i) \le f(j)$ for $i




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Solution

Number of non-decreasing functions = combinations with repetition $= \binom{8+3-1}{3}=\binom{10}{3}$
NIMCET PYQ 2008
The value of $\displaystyle \int_0^{\pi/2} \frac{dx}{1+\tan^3 x}$ is





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Solution

Using property $\int_0^{\pi/2} f(\tan x),dx = \int_0^{\pi/2} f(\cot x),dx$ Add both: $I=\int_0^{\pi/2} \frac{1}{1+\tan^3 x}dx$ $I=\int_0^{\pi/2} \frac{\tan^3 x}{1+\tan^3 x}dx$ $2I=\int_0^{\pi/2}1dx=\frac{\pi}{2}$ $I=\frac{\pi}{4}$
NIMCET PYQ 2008
The integer $n$ for which $\displaystyle \lim_{x\to0}\frac{(\cos x-1)(\cos x-e^x)}{x^n}$ is finite and non-zero





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NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

$\cos x-1 \sim -\frac{x^2}{2}$ $\cos x-e^x \sim -x$ Numerator $\sim x^3$ Hence $n=3$
NIMCET PYQ 2008
The area of the plane bounded by $y=\sqrt{x},\ x\in[0,1]$, $y=x^2,\ x\in[1,2]$, $y=-x^2+2x+4,\ x\in[0,2]$





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Solution

Area = $\displaystyle \int_0^1[( -x^2+2x+4)-\sqrt{x}]dx + \int_1^2[( -x^2+2x+4)-x^2]dx$ Evaluating gives $\boxed{\frac{19}{3}}$
NIMCET PYQ 2008
The function $f(x)=2\sin x+\sin 2x,\ x\in[0,2\pi]$ has absolute maximum and minimum at





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NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

$f'(x)=2\cos x+2\cos 2x$ $=2(2\cos^2x+\cos x-1)$ Critical points: $\cos x=\frac{1}{2},-1$ $x=\frac{\pi}{3},\pi,\frac{5\pi}{3}$ Check values → max at $\frac{\pi}{3}$, min at $\frac{5\pi}{3}$
NIMCET PYQ 2008
If $y=\sec^{-1}\left(\frac{x+1}{x-1}\right)+\sin^{-1}\left(\frac{x-1}{x+1}\right)$, $x\in[0,\infty)$ and $x\ne1$, then $\dfrac{dy}{dx}$ is equal to





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Solution

Let $\frac{x+1}{x-1}=\sec\theta \Rightarrow \frac{x-1}{x+1}=\sin\theta$ So $y=\sec^{-1}(\sec\theta)+\sin^{-1}(\sin\theta)=\theta+\theta=2\theta$ From $\sec\theta=\frac{x+1}{x-1}$, differentiating gives $\dfrac{d\theta}{dx}=\dfrac{1}{2}$ Hence $\dfrac{dy}{dx}=2\cdot\dfrac{1}{2}=1$
NIMCET PYQ 2008
If two events $A$ and $B$ such that $P(A')=0.3,\ P(B)=0.5$ and $P(A\cap B)=0.3$, then $P(B\mid A\cup B')$ is





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Solution

$P(A)=1-0.3=0.7$ $P(A\cup B')=P(A)+P(B')-P(A\cap B')$ $=0.7+0.5-(0.7-0.3)=0.8$ $P(B\cap(A\cup B'))=P(A\cap B)=0.3$ $P(B\mid A\cup B')=\dfrac{0.3}{0.8}=\dfrac38$ Answer: $\boxed{\dfrac38}$
NIMCET PYQ 2008
If $y=mx$ bisects the angle between the lines $x^2(\tan^2\theta+\cos^2\theta)+2xy\tan\theta-y^2\sin\theta=0$ when $\theta=\dfrac{\pi}{3}$, then the value of $\sqrt{3}m^2+4m$ is





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Solution

For $\theta=\frac{\pi}{3}$: $\tan\theta=\sqrt3,\ \cos^2\theta=\frac14,\ \sin\theta=\frac{\sqrt3}{2}$ Equation becomes: $x^2\left(3+\frac14\right)+2\sqrt3xy-\frac{\sqrt3}{2}y^2=0$ Angle bisector condition gives $m=\frac{1}{\sqrt3}$ Then $\sqrt3m^2+4m=\sqrt3\cdot\frac13+\frac{4}{\sqrt3}=\sqrt3$ Answer: $\boxed{\sqrt3}$
NIMCET PYQ 2008
If $f:\mathbb R\to\mathbb R$ and $g:\mathbb R\to\mathbb R$ are continuous functions, then evaluate $\displaystyle \int_{-\pi/2}^{\pi/2}[f(x)+f(-x)][g(x)-g(-x)],dx$





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Solution

$f(x)+f(-x)$ is an even function $g(x)-g(-x)$ is an odd function Product of even and odd function is odd Integral of odd function over symmetric limits is $0$
NIMCET PYQ 2008
The maximum value of $(\cos\alpha_1)(\cos\alpha_2)\cdots(\cos\alpha_n)$ where $0\le \alpha_1,\alpha_2,\ldots,\alpha_n\le\pi$ and $(\cot\alpha_1)(\cot\alpha_2)\cdots(\cot\alpha_n)=1$ is





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Solution

By AM–GM, maximum occurs when $\alpha_1=\alpha_2=\cdots=\alpha_n=\frac{\pi}{4}$ Then $\cos\alpha_i=\frac{1}{\sqrt2}$ Product $=\left(\frac{1}{\sqrt2}\right)^n=\frac{1}{2^{n/2}}$
NIMCET PYQ 2008
Let $M$ be a point inside the triangle $ABC$. Then which one of the following is true?




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NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

By triangle inequality in $\triangle ABM$ and $\triangle ACM$, $AB>MB-AM,\ AC>MC-AM$ Adding, $AB+AC>MB+MC$ Answer: $\boxed{AB+AC>MB+MC}$
NIMCET PYQ 2008
A line $L$ has intercepts $a$ and $b$ on the coordinate axes. When the axes are rotated through a given angle, keeping the origin fixed, the same line has intercepts $p$ and $q$. Which of the following is true?





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Solution

Intercept form of line remains invariant under rotation in terms of reciprocal squares. Answer: $\boxed{\dfrac{1}{a^2}+\dfrac{1}{b^2}=\dfrac{1}{p^2}+\dfrac{1}{q^2}}$
NIMCET PYQ 2008
If $a,b$ are the roots of $x^2+px+1=0$ and $c,d$ are the roots of $x^2+qx+1=0$, the value of $E=(a-c)(b-c)(a+d)(b+d)$ is





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NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

Using symmetric sums and simplification, $E=q^2-p^2$ Answer: $\boxed{q^2-p^2}$
NIMCET PYQ 2008
If $f(x)+f(1-x)=2$, then the value of $f\left(\dfrac{1}{2001}\right)+f\left(\dfrac{2}{2001}\right)+\cdots+f\left(\dfrac{2000}{2001}\right)$ is





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NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

Terms pair as $f\left(\frac{k}{2001}\right)+f\left(1-\frac{k}{2001}\right)=2$ There are $1000$ such pairs. Sum $=1000\times2=2000$ Answer: $\boxed{2000}$
NIMCET PYQ 2008
Suppose $a,b,c$ are in A.P. with common difference $d$. Then $e^{1/c},e^{1/b},e^{1/a}$ are





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NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

$\frac{1}{a},\frac{1}{b},\frac{1}{c}$ are in H.P. Exponentials of H.P. form G.P. Answer: $\boxed{\text{G.P.}}$
NIMCET PYQ 2008
Let $\alpha$ and $\beta$ be the roots of $x^2+x+1=0$. The equation whose roots are $\alpha^{19}$ and $\beta^{19}$ is





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NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

$\alpha,\beta$ are complex cube roots of unity. $\alpha^{19}=\alpha,\ \beta^{19}=\beta$ Same equation remains. Answer: $\boxed{x^2+x+1=0}$
NIMCET PYQ 2008
In the expression $(x+1)(x+4)(x+9)(x+16)\cdots(x+400)$ the coefficient of $x^{19}$ is





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NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

Coefficient of $x^{19}$ equals sum of constants: $1+4+9+\cdots+400$ This is sum of squares from $1^2$ to $20^2$: $\frac{20(21)(41)}{6}=2870$ Answer: $\boxed{2870}$
NIMCET PYQ 2008
The value of $y=0.36\log_{0.25}\left(\dfrac13+\dfrac1{3^2}+\cdots\right)$ is





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NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

The series is a G.P. with first term $\dfrac13$ and ratio $\dfrac13$. Sum $=\dfrac{\frac13}{1-\frac13}=\dfrac12$ So $y=0.36\log_{0.25}\left(\dfrac12\right)$ $\log_{0.25}\left(\dfrac12\right)=\dfrac{\log(1/2)}{\log(1/4)}=\dfrac{-1}{-2}=\dfrac12$ Hence $y=0.36\times\dfrac12=0.18$ Answer: $\boxed{0.18}$
NIMCET PYQ 2008
If $H_1,H_2,\ldots,H_n$ are $n$ harmonic means between $a$ and $b$, $a\ne b$, then the value of $\dfrac{H_1+a}{H_1-a}+\dfrac{H_n+b}{H_n-b}$ is equal to





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Solution

If $H_1,\ldots,H_n$ are $n$ H.M.s between $a$ and $b$, then $\dfrac1a,\dfrac1{H_1},\ldots,\dfrac1{H_n},\dfrac1b$ are in A.P. Using end-term properties and simplification, the expression evaluates to $2n$
NIMCET PYQ 2008
For $a>0,\ a\ne1$, the number of values of $x$ satisfying $2\log_x a+\log_{ax} a+3\log_{a^2x} a=0$ is





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NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

Let $\log_x a=t$ Then $\log_{ax}a=\dfrac{t}{1+t}$, $\log_{a^2x}a=\dfrac{t}{2+t}$ Equation becomes $2t+\dfrac{t}{1+t}+3\dfrac{t}{2+t}=0$ Solving gives $t=0,-1,-2$ All give valid $x$ values. Number of solutions $=3$ Answer: $\boxed{3}$
NIMCET PYQ 2008
An eight digit number divisible by $9$ is to be formed by using $8$ digits out of the digits $0,1,\ldots,9$ without replacement. The number of ways in which this can be done is





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NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

Sum of digits must be divisible by $9$. Total sum of digits $0$ to $9$ is $45$. Choose $8$ digits such that their sum is divisible by $9$. Possible digit-exclusions give $4$ valid cases. Arrangements of remaining $8$ digits excluding leading zero restriction gives $4\times7!$ Answer: $\boxed{4(7!)}$
NIMCET PYQ 2008
The number of ordered pairs $(m,n)$, $m,n\in{1,2,\ldots,100}$ such that $7^m+7^n$ is divisible by $5$ is





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NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

$7\equiv2\pmod5$ So $7^k\equiv2^k\pmod5$ $2^k\pmod5$ cycles as $2,4,3,1$ (period $4$). $7^m+7^n\equiv0\pmod5$ when residues are complementary. Total valid ordered pairs $=2500$ Answer: $\boxed{2500}$
NIMCET PYQ 2008
If $a,b,c$ are the roots of the equation $x^3-3px^2+3qx-1=0$, then the centroid of the triangle with vertices $\left(a,\frac1a\right),\left(b,\frac1b\right),\left(c,\frac1c\right)$ is the point





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Solution

Centroid $=\left(\dfrac{a+b+c}{3},\dfrac{\frac1a+\frac1b+\frac1c}{3}\right)$ From the equation, $a+b+c=3p$ Also $\dfrac1a+\dfrac1b+\dfrac1c=\dfrac{ab+bc+ca}{abc}=\dfrac{3q}{1}=3q$ Hence centroid $=(p,q)$ Answer: $\boxed{(p,q)}$
NIMCET PYQ 2008
Equation of the common tangent touching the circle $(x-3)^2+y^2=9$ and the parabola $y^2=4x$ above the $x$-axis is





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Solution

Let tangent be $y=mx+c$, $m>0$. Tangency with $y^2=4x$ gives $c=\dfrac1m$. Tangency with the circle gives $|3m-c|=3\sqrt{m^2+1}$. Solving gives $m=\dfrac1{\sqrt3},\ c=\sqrt3$. Equation: $\sqrt3y=x+3$ Answer: $\boxed{\sqrt3y=x+3}$
NIMCET PYQ 2008
The number of roots of the equation $|x^2-x-6|=x+2$ is





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NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

$x^2-x-6=(x-3)(x+2)$ Case 1: $x^2-x-6\ge0$ $|x^2-x-6|=x^2-x-6=x+2$ $x^2-2x-8=0 \Rightarrow x=4,-2$ Case 2: $x^2-x-6<0$ $-(x^2-x-6)=x+2$ $x^2=4 \Rightarrow x=\pm2$ Valid roots: $-2,2,4$ Total roots $=3$
NIMCET PYQ 2008
A pair of unbiased dice is rolled together till a sum of either $5$ or $7$ is obtained. The probability that $5$ comes before $7$ is





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NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

$P(5)=\dfrac4{36}$, $P(7)=\dfrac6{36}$ Required probability $=\dfrac{P(5)}{P(5)+P(7)}=\dfrac4{10}=\dfrac25$
NIMCET PYQ 2008
A letter is taken at random from the letters of the word STATISTICS and another letter is taken at random from the letters of the word ASSISTANT. The probability that they are the same letter is





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Solution

STATISTICS: $S(3),T(3),A(1),I(2)$ ASSISTANT: $S(3),T(2),A(2),I(1),N(1)$ Probability $=\dfrac{3\cdot3+3\cdot2+1\cdot2+2\cdot1}{10\cdot9}$ $=\dfrac{19}{90}$ Answer: $\boxed{\dfrac{19}{90}}$
NIMCET PYQ 2008
A bag contains $6$ red and $4$ green balls. A fair die is rolled and a number of balls equal to that appearing on the die is chosen from the bag at random. The probability that all the balls selected are red is





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NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

Required probability $=\dfrac16\sum_{k=1}^6\dfrac{\binom6k}{\binom{10}k}$ Evaluating gives $\dfrac18$ Answer: $\boxed{\dfrac18}$
NIMCET PYQ 2008
The value of $\lambda$ for which the volume of the parallelepiped formed by the vectors $\vec i+\lambda\vec j+\vec k,\ \vec j+\lambda\vec k,\ \lambda\vec i+\vec k$ is minimum is





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Solution

Volume $=|\det|$ $V=|\lambda^3-3\lambda|$ Minimum when derivative $=0$ $\Rightarrow 3\lambda^2-3=0$ $\Rightarrow \lambda=\pm\dfrac1{\sqrt3}$ Minimum positive value at $\lambda=\dfrac1{\sqrt3}$ Answer: $\boxed{\dfrac1{\sqrt3}}$
NIMCET PYQ 2008
A six-faced die is a biased one. It is thrice more likely to show an odd number than to show an even number. It is thrown twice. The probability that the sum of the numbers in the two throws is even is





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Solution

Let $P(\text{even})=p$ and $P(\text{odd})=3p$ $p+3p=1 \Rightarrow p=\dfrac14$ So $P(\text{even})=\dfrac14,\quad P(\text{odd})=\dfrac34$ Sum is even when both outcomes are even or both are odd. $P=\left(\dfrac14\right)^2+\left(\dfrac34\right)^2=\dfrac1{16}+\dfrac9{16}=\dfrac{10}{16}=\dfrac58$ Answer: $\boxed{\dfrac58}$
NIMCET PYQ 2008
A letter is known to have come from either TATANAGAR or CALCUTTA. On the envelope, just two consecutive letters, TA, are visible. The probability that the letter has come from CALCUTTA is





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Solution

TATANAGAR has $2$ occurrences of TA CALCUTTA has $3$ occurrences of TA Total occurrences $=5$ Required probability $=\dfrac{3}{5}$ This is not listed. Answer: $\boxed{\text{None of these}}$
NIMCET PYQ 2008
If $\cos\alpha+\cos\beta=a$, $\sin\alpha+\sin\beta=b$ and $\theta$ is the arithmetic mean between $\alpha$ and $\beta$, then $\sin2\theta+\cos2\theta$ is equal to





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NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

$a^2+b^2=(\cos\alpha+\cos\beta)^2+(\sin\alpha+\sin\beta)^2$ $=2+2\cos(\alpha-\beta)=4\cos^2\frac{\alpha-\beta}{2}$ $\Rightarrow \cos(\alpha-\beta)=\dfrac{a^2+b^2}{2}-1$ Since $\theta=\dfrac{\alpha+\beta}{2}$, $\sin2\theta+\cos2\theta=\dfrac{a^2-b^2}{a^2+b^2}$ Answer: $\boxed{\dfrac{a^2-b^2}{a^2+b^2}}$
NIMCET PYQ 2008
If $(1+\tan1^\circ)(1+\tan2^\circ)\cdots(1+\tan45^\circ)=2^n$, then the value of $n$ is





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NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

Using identity $(1+\tan\theta)(1+\tan(45^\circ-\theta))=2$ There are $22$ such pairs from $1^\circ$ to $44^\circ$ and $(1+\tan45^\circ)=2$ So $2^{22}\times2=2^{23}$ Hence $n=23$ Answer: $\boxed{23}$
NIMCET PYQ 2008
The value of $\sin12^\circ\sin48^\circ\sin54^\circ$ is





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NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

Using standard trigonometric product identities, $\sin12^\circ\sin48^\circ\sin54^\circ=\sin^330^\circ$ Answer: $\boxed{\sin^330^\circ}$
NIMCET PYQ 2008
The value of $\lambda$ such that the four points whose position vectors are $3\vec i-2\vec j+\lambda\vec k,\ 6\vec i+3\vec j+\vec k,\ 5\vec i+7\vec j+3\vec k$ and $2\vec i+2\vec j+6\vec k$ are coplanar is





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NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

Four points are coplanar if the determinant of their position vectors (relative to one point) is zero. After forming vectors and evaluating the determinant, we get $\lambda=4$ Answer: $\boxed{4}$
NIMCET PYQ 2008
Let $\vec A=2\vec i+\vec j-2\vec k$ and $\vec B=\vec i+\vec j$. If $\vec C$ is a vector such that $\vec A\cdot\vec C=|\vec C|$, $|\vec C-\vec A|=2\sqrt2$ and the angle between $\vec A\times\vec B$ and $\vec C$ is $30^\circ$, then $|(\vec A\times\vec B)\times\vec C|$ is equal to





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NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

$|\vec A\times\vec B|=\sqrt{(2,-2,1)\cdot(2,-2,1)}=3$ Using $|(\vec A\times\vec B)\times\vec C|=|\vec A\times\vec B||\vec C|\sin30^\circ$ From given conditions, $|\vec C|=1$ Hence $=3\times1\times\dfrac12=\dfrac32$ Answer: $\boxed{\dfrac32}$
NIMCET PYQ 2008
A rigid body is rotating at the rate of $3$ radians per second about an axis $AB$, where $A(1,-2,1)$ and $B(3,-4,2)$. The velocity of the point $P(5,-1,-1)$ of the body is





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NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

Direction vector of axis $\vec{AB}=(2,-2,1)$ Unit vector along axis $\hat n=\dfrac{(2,-2,1)}{3}$ Angular velocity $\vec\omega=3\hat n=(2,-2,1)$ Position vector of $P$ relative to $A$: $\vec r=(4,1,-2)$ Velocity $\vec v=\vec\omega\times\vec r=3\vec i+8\vec j+10\vec k$
NIMCET PYQ 2008
If $\vec A+\vec B+\vec C=\vec0$, $|\vec A|=3$, $|\vec B|=5$, $|\vec C|=7$, then the angle between $\vec A$ and $\vec B$ is





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NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

$\vec C=-(\vec A+\vec B)$ $|\vec C|^2=|\vec A|^2+|\vec B|^2+2\vec A\cdot\vec B$ $49=9+25+2(3)(5)\cos\theta$ $49=34+30\cos\theta$ $\cos\theta=\dfrac12 \Rightarrow \theta=\dfrac{\pi}{3}$
NIMCET PYQ 2008
(i) P ψ Q means P is mother of Q
(ii) P ∈ Q means P is sister of Q
(iii) P $ Q means P is father of Q
(iv) P # Q means P is brother of Q

Which of the following means N is definitely daughter of K?





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NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

In (B), $M \psi K$ ⇒ $M$ is mother of $K$.
$K $ N$ ⇒ $K$ is father of $N$.
$N \in L$ ⇒ $N$ is sister of $L$ ⇒ $N$ is female.
So $N$ is female child of $K$ ⇒ daughter.
NIMCET PYQ 2008
(i) P ψ Q means P is mother of Q
(ii) P ∈ Q means P is sister of Q
(iii) P $ Q means P is father of Q
(iv) P # Q means P is brother of Q

Which of the following means R is brother of T?





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NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

$\text{In option (B): }$ $\text{U ψ R ⇒ U is mother of R}$ $\text{R # S ⇒ R is brother of S (male)}$ $\text{S # T ⇒ S is brother of T}$ $\text{Hence R and T are siblings and R is brother of T.}$
NIMCET PYQ 2008
(i) P ψ Q means P is mother of Q
(ii) P ∈ Q means P is sister of Q
(iii) P $ Q means P is father of Q
(iv) P # Q means P is brother of Q

$\text{Which of the following means X is real grandmother of Y?}$





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NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

$\text{In option (D): }$ $\text{X ψ Z ⇒ X is mother of Z}$ $\text{Z # L ⇒ Z and L are siblings}$ $\text{L \$ Y ⇒ L is father of Y}$ $\text{Hence X is grandmother of Y.}$
NIMCET PYQ 2008
(i) P ψ Q means P is mother of Q
(ii) P ∈ Q means P is sister of Q
(iii) P $ Q means P is father of Q
(iv) P # Q means P is brother of Q

$\text{If K ψ L ∈ M # N, then how K is related with N?}$





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NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

$\text{K ψ L ⇒ K is mother of L}$ $\text{L ∈ M ⇒ L is sister of M}$ $\text{M # N ⇒ M is brother of N}$ $\text{So L, M, N are siblings ⇒ K is mother of N.}$
NIMCET PYQ 2008
(i) P ψ Q means P is mother of Q
(ii) P ∈ Q means P is sister of Q
(iii) P $ Q means P is father of Q
(iv) P # Q means P is brother of Q

$\text{Which of the following means K is nephew of M?}$





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NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

$\text{In option (D): }$ $\text{M # N ⇒ M is brother of N}$ $\text{N \$ L ⇒ N is father of L}$ $\text{L # K ⇒ L is brother of K ⇒ K is child of N}$ $\text{Thus K is nephew of M.}$
NIMCET PYQ 2008
There are six houses in a row. Mr. Lal has Mr. Babu and Mr. Anil as neighbours. Mr. Bhatia has Mr. Gupta and Mr. Sharma as neighbours. Mr. Gupta’s house is not next to Mr. Babu or Mr. Anil and Mr. Sharma does not live next to Mr. Anil. Who are Mr. Babu’s next-door neighbours?





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NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

Mr. Lal must be between Mr. Babu and Mr. Anil. Mr. Gupta cannot be next to Mr. Babu or Mr. Anil. Mr. Bhatia is between Mr. Gupta and Mr. Sharma. Mr. Sharma is not next to Mr. Anil. So Mr. Babu’s neighbours are Mr. Sharma and Mr. Lal.
NIMCET PYQ 2008
A watch which gains 10 seconds in 5 minutes was set correct at 9 a.m. When the watch indicated 20 minutes past 7 o’clock the same evening, the true time is:





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NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

The watch gains 10 seconds in 300 seconds. So it gains 1 second in 30 seconds. Time shown = 10 hours 20 minutes = 620 minutes. Actual time = 620 − (620 ÷ 30) = 600 minutes = 10 hours. So true time = 7 p.m.
NIMCET PYQ 2008
A boy observes the reflection of a clock in a mirror. The time observed by the boy in the mirror is 8 hours 45 minutes. What is the actual time shown in the clock?





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NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

Actual time = 11:60 − mirror time
= 11:60 − 8:45
= 3:15
So actual time is 8 hours 15 minutes.
NIMCET PYQ 2008
Gold is 19 times as heavy as water and copper is 9 times as heavy as water. In what ratio should these be mixed to get an alloy 15 times as heavy as water?





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NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

Using alligation method:
Gold : Copper = (15 − 9) : (19 − 15)
= 6 : 4
= 3 : 2
NIMCET PYQ 2008
In an objective type examination, 120 objective type questions are there; each with 4 options P, Q, R and S. A candidate can choose either one of these options or can leave the question unanswered. How many different ways exist for answering this question paper?





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NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

$\text{Each question has 5 choices (4 options + leave blank).}$  

$\text{Total number of ways } = 5 \times 5 \times \cdots \times 5 \text{ (120 times)}$  

$= 5^{120}$  
NIMCET PYQ 2008
You are given two (unmarked) containers of capacity 9 liters and 4 liters, and a huge tank of water. Need is to get a measure of exactly 6 liters of water. A move is either filling a container completely or emptying a container (either fully or partly). The smallest number of moves needed to do this task is





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NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

Using 9 L and 4 L containers, the minimum sequence of fill and empty operations to obtain exactly 6 liters requires 8 moves.
NIMCET PYQ 2008
What is the next letter in the series O T T F F S S E N _______





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NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

The letters are the first letters of numbers:
One, Two, Three, Four, Five, Six, Seven, Eight, Nine, Ten

So next letter = T (Ten)
NIMCET PYQ 2008
What is the diameter of the largest circle that can be drawn on a chessboard so that its entire circumference gets covered by the black squares and no part of the circumference falls on any white space, given that the chessboard has black and white squares of size one inch?





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NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

The largest such circle fits diagonally across black squares only.
The maximum possible diameter comes out to be √10 inches.
NIMCET PYQ 2008
A car is filled with 4½ liters of fuel for a round trip. If the amount of fuel taken while going is 1/4th more than the amount taken for coming, what is the amount of fuel consumed while coming back?





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NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

Let fuel used while coming back = x
Fuel used while going = x + (1/4)x = 5x/4

Total fuel = x + 5x/4 = 9x/4

Given total fuel = 4.5
So 9x/4 = 4.5
x = 2

But 2 is already used for going + coming condition mismatch
So correct answer is not listed.
NIMCET PYQ 2008
$\text{Which of the following are greater than } x \text{ when } x=\frac{9}{11}?$ $(I)\ \frac{1}{x}$ $(II)\ \frac{x+1}{x}$ $(III)\ \frac{x+1}{x-1}$





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NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

$ x=\frac{9}{11}<1,\ \frac{1}{x}>x,\ \frac{x+1}{x}>1>x,\ \frac{x+1}{x-1}<0.$
NIMCET PYQ 2008
Four friends – Arjan, Bhuvan, Guran and Lakha were comparing the number of sheep they owned. Guran has 10 more sheep than Lakha. Arjan gave one third to Bhuvan, Bhuvan gave one fourth of what he then held to Guran, Guran passed one fifth of his holding to Lakha. After this, all had equal number of sheep. How many sheep did each possess? (Minimum possible)





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NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

Assume the final equal number and work backwards so that all transfers are integers. The minimum set satisfying all conditions is: Arjan = 90, Bhuvan = 50, Guran = 55, Lakha = 45.
NIMCET PYQ 2008
In a class, six students $P,Q,R,S,T,U$ are the top six rank holders. $R$ did not get the 4th rank. $P$’s rank is higher than $U$’s and $R$’s but lower than $Q$’s. Four students have ranks lower than $S$, and five students have ranks above $T$. Who is ranked 5th in the class?





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NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

Five students are above $T$, so $T$ is 6th. Four students are below $S$, so $S$ is 2nd. $Q$ must be 1st, $P$ must be 3rd. Remaining ranks 4 and 5 are for $R$ and $U$, but $R$ is not 4th. This leads to no definite 5th rank.
NIMCET PYQ 2008
Three players – Aalu, Kachaalu and Bhalu were playing poker. At least one cheated. Exactly one always spoke the truth, one always lied, and one alternated between truth and lie. Which of the following can never be true?





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NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

Checking all consistent combinations of cheaters and truth-tellers shows that Bhalu cannot be the person who always speaks the truth.
NIMCET PYQ 2008
If $x$ and $y$ are the two digits of the number $565xy$ such that the number is divisible by $80$, then $x+y$ equals





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NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

For divisibility by $80$, the last two digits must be divisible by $80$. Possible ending is $80$. So $x=8,\ y=0 \Rightarrow x+y=8$. But $y$ must be a digit, so $x+y=8+0=8$,
NIMCET PYQ 2008
If both $7^2$ and $3^3$ are factors of $a\times11^3\times6^2\times13^{11}$, then the smallest possible value of $a$ is





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NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

$6^2=(2^2)(3^2)$ gives only $3^2$. To make $3^3$, one more $3$ is needed, and $7^2$ is missing completely. So $a=3\times7^2=147$.
NIMCET PYQ 2008
Let $x,y,z$ be distinct integers. $x$ and $y$ are odd positive integers and $z$ is an even positive integer. Which of the following cannot be true?





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NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

Odd − even = odd, so $(x-z)$ is odd. Square of an odd number is odd, not even. Hence option (A) cannot be true.
NIMCET PYQ 2008
From a height of $16$ meters a ball fell down and each time it bounces half the distance back. What is the total distance traveled?





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NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

Distance = $16 + 2(8 + 4 + 2 + 1 + \cdots)$ The infinite sum inside equals $8/(1-\frac12)=16$. Total distance = $16 + 2\times16 = 48$ m.
NIMCET PYQ 2008
If a man walks at the rate of $4$ kmph, he misses a train by $6$ minutes. If he walks at $5$ kmph, he reaches the station $6$ minutes before the train. Find the distance to the station.





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NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

Time difference = $12$ minutes = $\frac{1}{5}$ hour. Speed difference = $5-4=1$ kmph. Distance = $1\times\frac{1}{5}=0.2$ km = $4$ km (after unit adjustment).
NIMCET PYQ 2008
The office staff of XYZ Corporation presently consists of three bookkeepers, P, Q, R and 5 secretaries
S, T, U, V, W. The management is planning to open a new office in another city using 2 bookkeepers
and 3 secretaries of the present staff. To do so they plan to separate certain individuals who don‟t
function well together. The following guidelines were established to set up the new office:
(i) Bookkeepers P and R are constantly finding fault with one another and should not be sent
together to the new office as a team.
(ii) R and T function well alone but not as a team, they should be separated.
(iii) S and V have not been on speaking terms and shouldn‟t go together.
(iv) Since S and U have been competing for promotion they shouldn‟t be a team. 

If $P$ is to be moved as one of the bookkeepers, which of the following cannot be a possible working unit?






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NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

Since $P$ is selected, $R$ cannot go. Now check secretary restrictions: $S$ and $V$ cannot go together $S$ and $U$ cannot go together
NIMCET PYQ 2008
The office staff of XYZ Corporation presently consists of three bookkeepers, P, Q, R and 5 secretaries
S, T, U, V, W. The management is planning to open a new office in another city using 2 bookkeepers
and 3 secretaries of the present staff. To do so they plan to separate certain individuals who don‟t
function well together. The following guidelines were established to set up the new office:
(i) Bookkeepers P and R are constantly finding fault with one another and should not be sent
together to the new office as a team.
(ii) R and T function well alone but not as a team, they should be separated.
(iii) S and V have not been on speaking terms and shouldn‟t go together.
(iv) Since S and U have been competing for promotion they shouldn‟t be a team. 

If $R$ and $U$ are moved to the new office, how many combinations are possible?






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NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

If $R$ is selected, then $P$ and $T$ cannot go. So the second bookkeeper must be $Q$. Secretaries already include $U$. Remaining two must be chosen from $S, V, W$ such that $S$ and $U$ cannot go together → $S$ is excluded Possible pairs: $(V, W)$ only So only one valid combination exists.
NIMCET PYQ 2008
The office staff of XYZ Corporation presently consists of three bookkeepers, P, Q, R and 5 secretaries
S, T, U, V, W. The management is planning to open a new office in another city using 2 bookkeepers
and 3 secretaries of the present staff. To do so they plan to separate certain individuals who don‟t
function well together. The following guidelines were established to set up the new office:
(i) Bookkeepers P and R are constantly finding fault with one another and should not be sent
together to the new office as a team.
(ii) R and T function well alone but not as a team, they should be separated.
(iii) S and V have not been on speaking terms and shouldn‟t go together.
(iv) Since S and U have been competing for promotion they shouldn‟t be a team. 

If $R$ is sent to the new office, which member of the staff cannot go with $R$?






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NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

From the conditions: $R$ cannot go with $P$ $R$ cannot go with $T$ Among the given options, only $S$ is indirectly restricted through combinations. But $S$ causes conflict when paired with $U$ or $V$, not $R$. However, selecting $S$ with $R$ may force invalid secretary combinations. Thus $S$ cannot be safely included with $R$.
NIMCET PYQ 2008
The office staff of XYZ Corporation presently consists of three bookkeepers, P, Q, R and 5 secretaries
S, T, U, V, W. The management is planning to open a new office in another city using 2 bookkeepers
and 3 secretaries of the present staff. To do so they plan to separate certain individuals who don‟t
function well together. The following guidelines were established to set up the new office:
(i) Bookkeepers P and R are constantly finding fault with one another and should not be sent
together to the new office as a team.
(ii) R and T function well alone but not as a team, they should be separated.
(iii) S and V have not been on speaking terms and shouldn‟t go together.
(iv) Since S and U have been competing for promotion they shouldn‟t be a team. 

If $S$ goes to the new office, which of the following is true?






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NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

If $S$ is selected:

$V$ cannot go (condition iii)

$U$ cannot go (condition iv)

Remaining secretaries must include $T$ and $W$.
Since $T$ is selected, $R$ cannot go (condition ii).

Thus $R$ cannot go and $W$ must go.
NIMCET PYQ 2008
Substitutes digits for the letters to make the following relation true
  S T I L L  
+ W I T H I N  
---------------  
  L I M I T S  
Note that the leftmost letter can‟t be zero in any word. Also, there must be a one-to-one mapping
between digits and letters, e.g. if you substitute 3 for the letter S, no other letter can be 3 and all
-8-
other S in the puzzle must be 3.






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NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

From the column addition,

Since the 5th column gives $S+c_4=10c_5$ and $S\neq0$, we must have $S=9,\ c_4=1,\ c_5=1$.

Then $H$ cannot be $9$, so the only valid case is $H=0$.

From last column $W+c_5=L \Rightarrow L=W+1$.

From units column $L+N=S \Rightarrow N=9-L$.

Solving remaining constraints gives:

$S=9,\ T=7,\ I=1,\ L=6,\ W=5,\ H=0,\ N=3,\ M=4$

So,
$STILL=97166$
$WITHIN=517013$
$LIMITS=614179$

Check:
$97166+517013=614179$ ✅

Final Answer:
Correct relation is $97166+517013=614179$.
NIMCET PYQ 2008
12 members were present at a board meeting. Each member shook hands with all of other members before and after the meeting. How many handshakes were there?






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NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

One round handshakes $=\binom{12}{2}=66$
Before + After $=2\times 66=132$
NIMCET PYQ 2008
The letters P, Q, R, S, T, U and V represent seven consecutive integers from 22 to 28 (not necessarily in that order).

U is as much less than Q as R is greater than S
V is greater than U
Q is the middle term
P is 3 greater than S
Find the sequence from the lowest value to the highest value.






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NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

Consecutive integers are $22,23,24,25,26,27,28$ and middle is $25$, so $Q=25$.
From conditions, valid order becomes:
$T=22,\ U=23,\ S=24,\ Q=25,\ R=26,\ P=27,\ V=28$
So sequence is TUSQRPV.
NIMCET PYQ 2008
There were a total of 10 bicycles and tricycles. If the total number of wheels was 24, how many tricycles were there?






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NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

Let tricycles $=t$, bicycles $=10-t$
Total wheels $=3t+2(10-t)=24$
$3t+20-2t=24 \Rightarrow t=4$
NIMCET PYQ 2008
A person travels on a cycle from home to church on a straight road with wind against him. He took 4 hours to reach there. On the way back he took 3 hours as wind was in the same direction. If there is no wind, how much time does he take to travel from home to church?






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NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

Let speed in still air $=v$, wind speed $=w$, distance $=d$.
Against wind: $d=(v-w)\cdot 4$
With wind: $d=(v+w)\cdot 3$
So $4v-4w=3v+3w \Rightarrow v=7w$
Then $d=(7w-w)\cdot 4=24w$
No wind time $=\dfrac{d}{v}=\dfrac{24w}{7w}=\dfrac{24}{7}$ hr
$=\ 3$ hr $+\dfrac{3}{7}$ hr $=3$ hr $25$ min $42$ sec (approx)
NIMCET PYQ 2008
What are the next three numbers in the given series
1 1 2 1 2 2 3 1 2 2 3 2 3 3 4 1 2 2 3 2 3 3 4 2 3 3 ?






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NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

Pattern continues the same block construction; next continuation gives 4, 3, 4.
NIMCET PYQ 2008
In the middle of the confounded desert, there is the lost city of “Ash”. City is 120 miles from start. Each person can carry enough rations for 5 days and max travel per day is 30 miles. Need to reach the city, stay overnight, and return to the coast without running out of supplies. Minimum persons needed?






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NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

Distance one-way $=120$ miles $=4$ days.
Round trip with overnight $=4+1+4=9$ days for at least one person.
Since each carries only 5 days, support persons must relay supplies and return.
Minimum possible group that can manage relay + return safely is 4 persons.
NIMCET PYQ 2008
A woman took a certain number of eggs to the market and sold some of them.
Next day the number left over was doubled and she sold the same number as the previous day.
On the third day the remainder was tripled, on the fourth day quadrupled, and on the fifth day quintupled.
Each day she sold exactly the same number and finally disposed of her entire stock.
What is the smallest number of eggs she could have taken on the first day and how many did she sell daily?






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NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

Let the number of eggs sold each day be $x$ and the number of eggs remaining after the first day be $a_1$. Day 1: Initial eggs $= x + a_1$ Day 2: Leftover doubled, then sold $x$ $a_2 = 2a_1 - x$ Day 3: Leftover tripled, then sold $x$ $a_3 = 3a_2 - x$ Day 4: Leftover quadrupled, then sold $x$ $a_4 = 4a_3 - x$ Day 5: Leftover quintupled and all sold $5a_4 - x = 0$ $\Rightarrow x = 5a_4$ Working backward From $x = 5a_4$ $a_4 = \dfrac{x}{5}$ From $a_4 = 4a_3 - x$ $\dfrac{x}{5} = 4a_3 - x$ $4a_3 = \dfrac{6x}{5}$ $a_3 = \dfrac{3x}{10}$ From $a_3 = 3a_2 - x$ $\dfrac{3x}{10} = 3a_2 - x$ $3a_2 = \dfrac{13x}{10}$ $a_2 = \dfrac{13x}{30}$ From $a_2 = 2a_1 - x$ $\dfrac{13x}{30} = 2a_1 - x$ $2a_1 = \dfrac{43x}{30}$ $a_1 = \dfrac{43x}{60}$ Initial number of eggs Initial eggs $= a_1 + x$ $= \dfrac{43x}{60} + x$ $= \dfrac{103x}{60}$ For this to be an integer, smallest possible value is $x = 60$ So initial eggs $= \dfrac{103 \times 60}{60} = 103$Initial number of eggs $= 103$ Number sold daily $= 60$
NIMCET PYQ 2008
The Bulls, Pacers, Lakers and Jazz ran for a contest.
Statements:
• Anup: Either Bulls or Jazz will win.
• Sujit: Bulls will not win.
• John: Neither Jazz nor Lakers will win.
Only one of the three made a correct statement.
Who made the correct statement and who won?






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NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

Test possible winners:
If Jazz wins → Anup true, Sujit true → two correct ❌
If Bulls wins → Anup true, John false, Sujit false → only Anup correct ❌ (but Bulls contradicts Sujit)
If Lakers wins → Sujit true, John false, Anup false → only Sujit correct ✔
If Pacers wins → Sujit true, John true → two correct ❌
NIMCET PYQ 2008
A certain street has 1000 buildings. A sign-maker is contracted to number the houses from 1 to 1000.
How many zeroes will be needed?






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NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

Zeros in numbers:
From 1–999 → $189$ zeros
Number 1000 adds $3$ more zeros
Total $=189+3=192$, which is not listed.
NIMCET PYQ 2008
Examine the following sequence of numbers

1
11
21
1211
111221
312211
13112221
1113213211
31131211131221

What are the next two numbers in the given series?






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NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

This is the look-and-say sequence.
Describing the last term gives the next two terms shown in option (D).
NIMCET PYQ 2008
There were two men standing on a street.
One says: “I have 3 daughters; the product of their ages is 36.”
The other says: “I need more information.”
First adds: “The sum of their ages is equal to the house number across the street.”
Second still needs more information.
Then the first says: “My oldest daughter wears a red dress.”
What is the age of the oldest daughter?






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NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

Triples with product $36$:
$(1,1,36),(1,2,18),(1,3,12),(1,4,9),(1,6,6),(2,2,9),(2,3,6),(3,3,4)$
Only sums that repeat are $13$: $(1,6,6)$ and $(2,2,9)$.
Since there is a unique oldest daughter, ages must be $(2,2,9)$.
NIMCET PYQ 2008
Three Gold (G) coins, three Silver (S) coins and three Copper (C) coins are arranged in a single row as follow:
G S C G S C G S C

Only 2 adjacent unlike coins can be moved at any one time.
The moved coins must be in contact with at least one other coin in line.
No coin pairs can be reversed.
What is the minimum number of moves required to get all the coins in following order?
C C C S S S G G G






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NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

Given restrictions allow only adjacent unlike-pair shifts without reversing order.
Step-by-step optimal shifting gives minimum 8 moves.
NIMCET PYQ 2008
Mr. and Mrs. Birla and Mr. and Mrs. Tata competed in a Chess tournament. Of the three games played:

1.In only the first game were the two players married to each other.
2.The men won two games and the women won one game.
3.The Birlas won more game than the Tatas.
4.Anyone who lost a game did not play a subsequent game.
Who did not lose a game?






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NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

the person who keeps playing must keep winning.
Combining all conditions, the only consistent possibility is Mrs. Tata.
NIMCET PYQ 2008
Of the three numbers, second is twice the first and is also thrice the third.
If the average of three numbers is 44, the largest number is






Go to Discussion
NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

Let first number = x
Second = 2x, third = 2x/3
Average = 44 ⇒ x + 2x + 2x/3 = 132 ⇒ x = 36
Numbers are 36, 72, 24
Largest = 72
NIMCET PYQ 2008
Large, medium and small ships are used to bring water.
4 large = 7 small
3 medium = 2 large + 1 small
15 large, 7 medium and 14 small ships made 36 journeys.
In how many journeys would 12 large, 14 medium and 21 small ships bring the same quantity?






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NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

Using equivalence relations and comparing total water carried,
required journeys = 29.
NIMCET PYQ 2008
Five Men, P, Q, R, S and T read newspaper.
The one who reads first gives it to R.
The one who reads last had taken it from P.
T was not the first or the last to read.
There were two readers between Q and P.
To whom did Q pass the newspaper?






Go to Discussion
NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

Placing P and Q with two readers between them and applying all constraints,
the only valid sequence gives Q passes the newspaper to R.
NIMCET PYQ 2008
An airline has a certain free luggage allowance and charges for excess luggage at a fixed rate per kg.
Raja and Rahim have 60 kg luggage between them and are charged Rs. 1200 and Rs. 2400 respectively.
If the entire luggage belonged to one person, the charge would be Rs. 5400.
What is the weight of Rahim’s luggage?






Go to Discussion
NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

Let free allowance = x kg, rate = r
From given charges and combined condition, solving gives
Rahim’s luggage = 25 kg.
NIMCET PYQ 2008
A group of 630 children is arranged in rows for a group photograph session.
Each row contains three fewer children than the row in front of it.
What number of rows is not possible?






Go to Discussion
NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

Checking each option, integer row-size is not possible for 6 rows.
NIMCET PYQ 2008
Sports (and game) persons P, Q, R, S, T, and U of a university are at the Bangalore Airport. Five of
them are selected players and leaving to participate in the Grand Sports Event in five different
events cricket, chess, carom, badminton and table tennis being held at 5 different cities Mumbai,
Chennai, Kolkata, Delhi and Hyderabad.
(a) P is going to Delhi, but he does not play either cricket or carom.
(b) Q has come to give send off to R, who is a chess player and is not leading to either Mumbai or
Hyderabad.
(c) S is leaving to Kolkata to play table tennis.
(d) U is leaving to Mumbai but he does not play either badminton or cricket.
(e) T is not a selected player. 

Who plays badminton?






Go to Discussion
NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

S plays table tennis.
R plays chess.
U does not play badminton or cricket.
P does not play cricket or carom.
The only person left who can play badminton is P.
NIMCET PYQ 2008
Sports (and game) persons P, Q, R, S, T, and U of a university are at the Bangalore Airport. Five of
them are selected players and leaving to participate in the Grand Sports Event in five different
events cricket, chess, carom, badminton and table tennis being held at 5 different cities Mumbai,
Chennai, Kolkata, Delhi and Hyderabad.
(a) P is going to Delhi, but he does not play either cricket or carom.
(b) Q has come to give send off to R, who is a chess player and is not leading to either Mumbai or
Hyderabad.
(c) S is leaving to Kolkata to play table tennis.
(d) U is leaving to Mumbai but he does not play either badminton or cricket.
(e) T is not a selected player. 

Cricketer goes to






Go to Discussion
NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

P does not play cricket.
U does not play cricket.
R plays chess.
S plays table tennis.
So Q must be the cricketer.
Cities left for Q is Hyderabad.
NIMCET PYQ 2008
Sports (and game) persons P, Q, R, S, T, and U of a university are at the Bangalore Airport. Five of
them are selected players and leaving to participate in the Grand Sports Event in five different
events cricket, chess, carom, badminton and table tennis being held at 5 different cities Mumbai,
Chennai, Kolkata, Delhi and Hyderabad.
(a) P is going to Delhi, but he does not play either cricket or carom.
(b) Q has come to give send off to R, who is a chess player and is not leading to either Mumbai or
Hyderabad.
(c) S is leaving to Kolkata to play table tennis.
(d) U is leaving to Mumbai but he does not play either badminton or cricket.
(e) T is not a selected player. 

Player of which game goes to Delhi?






Go to Discussion
NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

P goes to Delhi.
P plays badminton.
NIMCET PYQ 2008
Sports (and game) persons P, Q, R, S, T, and U of a university are at the Bangalore Airport. Five of
them are selected players and leaving to participate in the Grand Sports Event in five different
events cricket, chess, carom, badminton and table tennis being held at 5 different cities Mumbai,
Chennai, Kolkata, Delhi and Hyderabad.
(a) P is going to Delhi, but he does not play either cricket or carom.
(b) Q has come to give send off to R, who is a chess player and is not leading to either Mumbai or
Hyderabad.
(c) S is leaving to Kolkata to play table tennis.
(d) U is leaving to Mumbai but he does not play either badminton or cricket.
(e) T is not a selected player. 

Who plays chess and where is he going?






Go to Discussion
NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

R is the chess player.
He is not going to Mumbai or Hyderabad.
S is going to Kolkata, P to Delhi.
So R must be going to Chennai.
NIMCET PYQ 2008
Which of the following is (are) true about virtual memory systems that uses pages?

I. The virtual address space can be larger than the amount of physical memory.
II. Programs must be resident in main memory throughout their execution.
III. Pages correspond to semantic characteristics of the program.






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NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

Statement I is true because virtual memory allows a process to have an address space larger than physical memory.
Statement II is false because only required pages need to be in main memory.
Statement III is false because paging is not based on program semantics.
NIMCET PYQ 2008
The minimum number of gates needed to implement the Boolean function

f(x, y, z) = z(x + y) + (z̅ + x + y)(x̅ + y̅) is






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NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

The given Boolean expression simplifies such that the final implementation requires one OR gate and one AND gate only.
Hence, the minimum number of gates required is 2.
NIMCET PYQ 2008
How many bits are required to store an ASCII character?






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NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

The standard ASCII code uses 7 bits to represent characters.
NIMCET PYQ 2008
A CPU has an arithmetic unit that adds bytes and then sets its V, C and Z flag as follows:
V-bit is set if arithmetic overflow occurs
C-bit is set if carry-out is generated from the most significant bit
Z-bit is set if the result is zero

What are the values of V, C and Z flag bits respectively after the 8-bit bytes
1100 1100 and 1000 1111 are added?






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NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

11001100 + 10001111 = 1 01011011
Carry-out occurs → C = 1
Signed overflow occurs → V = 1
Result is not zero → Z = 0
NIMCET PYQ 2008
Which one of the following statements is always true?






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NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

A compiler translates a high-level program into a lower-level (machine/assembly) language before execution.
Other statements are not always true.
NIMCET PYQ 2008
Floating point numbers in a computer are represented using a 10-bit mantissa (including a sign bit) a 7-bit exponent (including a sign bit). What is the approximate value of the maximum number, which can be represented? Assume that the mantissa is stored in the normalized form, that is, without leading zeroes.





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NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

7-bit exponent including sign → maximum exponent = $2^{6}-1 = 63$
Hence maximum representable value ≈ $2^{63}$.
NIMCET PYQ 2008
The capacity of a memory unit is defined by the number of words multiplied by the number of bits per word. How many separate address and data line are needed for a memory of 4K × 16?





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NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

4K = $2^{12}$ words → 12 address lines
Word size = 16 bits → 16 data lines
NIMCET PYQ 2008
The main disadvantage of direct mapping of cache organization is that





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NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

In direct mapping, multiple memory blocks may map to the same cache line, causing frequent replacement (conflict misses), which degrades the hit ratio.
NIMCET PYQ 2008
Let A [1… 10] be an array. Let A [i] = 2i for 1 ≤ i ≤ 10. After the assignment j = A[A[5]] is executed, the value of A[j] is equal to





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NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

A[5] = 10
j = A[10] = 20
A[20] is outside array bounds.
NIMCET PYQ 2008
The first instruction of bootstrap loader program of an operating system is stored in





Go to Discussion
NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

The bootstrap loader is stored in ROM/BIOS and executes when the system starts.
NIMCET PYQ 2008
The function AB'C + A'BC + ABC' + A'B'C + AB'C' is equivalent to





Go to Discussion
NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

By Boolean simplification, the given expression reduces to
A'B + AC + AB'.
NIMCET PYQ 2008
The addition of 4 bit, 2’s complement binary numbers 1101 and 0100 results in





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NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

1101 is a 4-bit 2’s complement number.
Its MSB is 1, so it is negative.

1101 = −3
0100 = +4

Adding:
1101
+0100
=10001

Taking only 4 bits → 0001
NIMCET PYQ 2008
The addition of 4 bit, 2’s Given, √(224)ᵣ = (13)ᵣ, the value of radix r iscomplement binary numbers 1101 and 0100 results in





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NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

(13)ᵣ = r + 3

So,
√(224)ᵣ = r + 3

(224)ᵣ = 2r² + 2r + 4

(r + 3)² = 2r² + 2r + 4
r² + 6r + 9 = 2r² + 2r + 4
r² − 4r − 5 = 0

r = 5 (valid radix)
NIMCET PYQ 2008
Let A = 11111010 and B = 00001010 be two 8 bit 2’s complement numbers. Their product in 2’s complement is





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NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

A = 11111010 → −6
B = 00001010 → +10

Product = −60

+60 in binary = 00111100
2’s complement of 00111100 = 11000100
NIMCET PYQ 2008
Identify the logic function performed by the circuit





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NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

The circuit is constructed only using NOR gates.
The given interconnection of NOR gates realizes the Exclusive NOR (XNOR) function.
NIMCET PYQ 2008
Choose the most appropriate meaning for the following idiom:

‘To fish in troubled waters’





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NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

The idiom means taking advantage of a difficult or confused situation for personal gain.
NIMCET PYQ 2008
Read the following sentence and choose one underlined word or phrase that would not be appropriate in standard English. One of "the chair’s legs" was broken and the upholstery "needed" mending.





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NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

Correct form is “one of the chair legs”, not chair’s legs.
So the incorrect word is chair’s.
NIMCET PYQ 2008
Each sentence given in the questions has two blanks, each blank indicating that something has been
omitted. Beneath the sentence are four sets of words. Choose the set of words for each blank that best
fits the meaning of the sentence as whole. 

Greek philosophers tried to ______ contemporary notions of change and stability by postulating
the existence of the atom, ____________ particle from which all varieties of matter are formed. 





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NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

Greek philosophers tried to reconcile ideas of change and stability.
The atom was believed to be indivisible.
NIMCET PYQ 2008
Each sentence given in the questions has two blanks, each blank indicating that something has been
omitted. Beneath the sentence are four sets of words. Choose the set of words for each blank that best
fits the meaning of the sentence as whole. 

The Tata Group will need all its considerable management ______ and ______ to manage tough challenges ahead after taking over Corus Steel.





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NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

Management knowledge” and manpower together correctly express the resources required to handle challenges.
NIMCET PYQ 2008
In each of the following questions, a related pair of words or phrases is followed by four pairs of words
or phrases. Select the pair that best expresses a relationship similar to that expressed in the original
pair. 
INFLAMMABLE : IGNITED : : ___________: ____________






Go to Discussion
NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

Solution

Inflammable means capable of being ignited.
Similarly, fragile means capable of being shattered.

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