MCA NIMCET 2018 Previous Year Question Paper and Solution with PDF

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MCA NIMCET Previous Year Questions (PYQs)

MCA NIMCET 2018 PYQ

Qus : 1 MCA NIMCET PYQ 2018

$$ \frac{d^{2}x}{dy^{2}} \; = \; ? $$

$ (a) -\left(\dfrac{d^{2}y}{dx^{2}}\right)^{-1}\left(\dfrac{dy}{dx}\right)^{-3} $

$ (b) \left(\dfrac{d^{2}y}{dx^{2}}\right)\left(\dfrac{dy}{dx}\right)^{-2} $

$ (c) -\left(\dfrac{d^{2}y}{dx^{2}}\right)\left(\dfrac{dy}{dx}\right)^{-3} $

$ (d) \left(\dfrac{d^{2}y}{dx^{2}}\right)^{-1} $

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MCA NIMCET Mathematics PYQ MCA NIMCET Differentiation (Disha JEE) PYQ

Solution

Qus : 2 MCA NIMCET PYQ 2018

If $\lim_{x\to\infty}\left(1+\frac{a}{x}+\frac{b}{x^2}\right)^{2x}=e^2$ then the values of a and b are:

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MCA NIMCET Mathematics PYQ MCA NIMCET Limit Continuity Differentiability (Disha JEE) PYQ

Solution

Qus : 3 MCA NIMCET PYQ 2018

Consider the equation (43)_x = (y3)₈ where x and y are unknown. The number of possible solutions is

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 4 MCA NIMCET PYQ 2018

Let the memory access time is 10 milliseconds and cache access time is 10 microseconds. Assume the cache hit ratio 15%. The effective memory access time is

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Incorrect Answer

Qus : 5 MCA NIMCET PYQ 2018

What are the values of R₁ and R₂ respectively in the expression (235)_R1 = (565)₁₀ = (1065)_R2

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 6 MCA NIMCET PYQ 2018

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 7 MCA NIMCET PYQ 2018

In order to store floating numbers in computer using the normalized representation and 32-bit single precision, the number of bits used for exponent and fraction are __________, __________ respectively.

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 8 MCA NIMCET PYQ 2018

Change the speech : "If you don't keep quite I shall shoot you", he said to her in a calm voice.

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 9 MCA NIMCET PYQ 2018

Choose the correct spelling fol the word given below.

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 10 MCA NIMCET PYQ 2018

Select the pair of words, which are related in the same way as the capitalized words are related to each other.
BUTTERFLY : FREEDOM

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 11 MCA NIMCET PYQ 2018

Which of the following is the closest in meaning to the word, CLOWN?

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 12 MCA NIMCET PYQ 2018

Fill in the blank choosing the correct word.

The vote will have to be laid______ until next week.

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 13 MCA NIMCET PYQ 2018

Fill in the blank choosing the correct question tag.

He has done his duty,______

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 14 MCA NIMCET PYQ 2018

Choose one of the options that is most nearly same as meaning of the word Epitome.

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 15 MCA NIMCET PYQ 2018

Which collocation goes with the word AWARE?

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 16 MCA NIMCET PYQ 2018

Identify the underlined part which has an error.

He couldn't cope up with the hot climate of the place any longer

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 17 MCA NIMCET PYQ 2018

The _________ pittance the widow receives from the government cannot keep her from poverty.

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 18 MCA NIMCET PYQ 2018

The other boys or Henry_______to blame.

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 19 MCA NIMCET PYQ 2018

In the question, the word "Echo" is usual in four different ways, numbered A to D.

Choose the option in which the usage of the word is inappropriate.

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 20 MCA NIMCET PYQ 2018

The sentences given below when properly sequenced form a coherent paragraph. Each sentence is labeled with a letter. Choose the most logical order of sentences from the given choices to construct a coherent paragraph.

P : It refers to those times when there is no war or fight among nations.

Q : Many people argue that war is a necessary evil and the only process of solving international disputes.

R: Peace means complete freedom from disturbance.

S : Once the world starts believing that wars are unnecessary, they decide to abolish war completely.

T : But in reality, war happens only because people are not ready to settle disputes in a peaceful manner.

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 21 MCA NIMCET PYQ 2018

I do not wish to cast aspersions on the corporate takeover. On the contrary, it is a key facilitator of creative destruction and doubtless the most effective remaining means by which shareholder voices can mold a corporation. But while change in management is often necessary, you cannot effectively run a corporation with differing authoritative i voices espousing opposing corporate goals. It has to be one or the other. If the board s riven with conflicting interests, corporate governance will suffer. If directors cannot agree with the CEO's strategy, they should replace him. Corporate dissonance, of course, is unavoidable in periods of transition. But it is not a value to be pursued for its own sake. A cacophony produces only red ink.

What according to the author facilitates creative destruction?

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 22 MCA NIMCET PYQ 2018

Which of the following words used in the passage reinforces the idea contained in the word, 'DISSONANCE'?

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 23 MCA NIMCET PYQ 2018

What according to the author makes corporate governance suffer?

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 24 MCA NIMCET PYQ 2018

Find the synonym that is most nearly similar in meaning to the word : DEBACLE.

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 25 MCA NIMCET PYQ 2018

Choose the phrasal verb that means

"To spend time doing unimportant things instead of doing necessary things".

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 26 MCA NIMCET PYQ 2018

Which of the following is close to the meaning of the word, IMPOLITIC?

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 27 MCA NIMCET PYQ 2018

Choose an option to replace the phrase given in bold.

The bank has hired a consultant who will look into any issues which arise during the merger.

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 28 MCA NIMCET PYQ 2018

$6 + \log_{1/4} \dfrac{1}{\sqrt{2}} \left[ \sqrt{1 - \dfrac{1}{\sqrt{2}}} \sqrt{1 - \dfrac{1}{\sqrt{2}}} \sqrt{1 - \dfrac{1}{\sqrt{2}}} \cdots \right] =$

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 29 MCA NIMCET PYQ 2018

The function $f(x) = \log\left(x + \sqrt{x^2 + 1}\right)$ is

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 30 MCA NIMCET PYQ 2018

Two person A and B agree to meet 20 april 2018 between 6pm to 7pm with understanding that they will wait no longer than 20 minutes for the other. What is the probability that they meet?

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 31 MCA NIMCET PYQ 2018

Three numbers a,b and c are chosen at random (without replacement) from among the numbers 1, 2, 3, ..., 99. The probability that $a^3+b^2+c^2-3abc$ is divisible by 3 is,

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 32 MCA NIMCET PYQ 2018

A and B play a game where each is asked to select a number from 1 to 25. If the two number match, both of them win a prize. The probability that they will not win a prize in a single trial is :

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

The total number of ways in which numbers can be choosed =25 x 25=625 The number of ways in which either players can choose same numbers = 25

Probability that they win a prize = 25/625 = 1/25

Thus, the probability that they will not win a prize in a single trial = 1 - 1/25 = 24/25

Qus : 33 MCA NIMCET PYQ 2018

The quadratic equation whose roots are $\sin^218^o$ and $\cos^236^o$ is

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Roots:

$\alpha = \sin^2 18^\circ = \left(\frac{\sqrt{5} - 1}{4}\right)^2 = \frac{3 - \sqrt{5}}{8}$

$\beta = \cos^2 36^\circ = \left(\frac{\sqrt{5} + 1}{4}\right)^2 = \frac{3 + \sqrt{5}}{8}$

Sum of roots ($S$):

$S = \alpha + \beta = \frac{(3 - \sqrt{5}) + (3 + \sqrt{5})}{8} = \frac{6}{8} = \frac{3}{4}$

Product of roots ($P$): $P = \alpha\beta = \left(\frac{(\sqrt{5} - 1)(\sqrt{5} + 1)}{16}\right)^2 = \left(\frac{4}{16}\right)^2 = \frac{1}{16}$

Equation: $x^2 - Sx + P = 0$ $x^2 - \frac{3}{4}x + \frac{1}{16} = 0 \implies 16x^2 - 12x + 1 = 0$

Qus : 34 MCA NIMCET PYQ 2018

Sum to infinity of a geometric is twice the sum of the first two terms. Then what are the possible values of common ratio?

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Let first term $= a$ and common ratio $= r$, where $|r| < 1$

Sum to infinity: $S_{\infty} = \dfrac{a}{1-r}$

Sum of first two terms: $S_2 = a + ar = a(1+r)$

Step 2: Set up the equation
Given: $S_{\infty} = 2 \times S_2$

$\dfrac{a}{1-r} = 2 \cdot a(1+r)$

Step 3: Simplify
Dividing both sides by $a$ (since $a \ne 0$):

$\dfrac{1}{1-r} = 2(1+r)$

$1 = 2(1+r)(1-r)$

$1 = 2(1 - r^2)$

$1 = 2 - 2r^2$

$2r^2 = 1$

$r^2 = \dfrac{1}{2}$

$r = \pm\dfrac{1}{\sqrt{2}}$

Qus : 35 MCA NIMCET PYQ 2018

Suppose that m and n are fixed numbers such that the mth term of an HP is equal to n and the nth term is equal to m, (m ≠ n). Then the (m + n)th term is:

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Given: The sequence is in H.P. with $a_m = n$ and $a_n = m$ $(m \ne n)$.

In an H.P., reciprocals of terms form an A.P. So, $\tfrac{1}{a_m} = \tfrac{1}{n}$ and $\tfrac{1}{a_n} = \tfrac{1}{m}$.

This A.P. leads to common difference $d = \tfrac{1}{mn}$ and first term $A = \tfrac{1}{mn}$.

Thus, the reciprocal of the $(m+n)$th term is:

$b_{m+n} = \tfrac{m+n}{mn}$

Hence, the $(m+n)$th term of H.P. is:

$a_{m+n} = \dfrac{mn}{m+n}$

Final Answer: $ \dfrac{mn}{m+n} $

Qus : 36 MCA NIMCET PYQ 2018

If A is an invertible skew-symmetric matrix, then

is a

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 37 MCA NIMCET PYQ 2018

If the mean of the squares of first n natural numbers be 11, then n is equal to?

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Given: Mean of squares of first n natural numbers is 11.

Use the identity for sum of squares: $$\sum_{k=1}^{n} k^2=\frac{n(n+1)(2n+1)}{6}$$

Mean $=$ (sum) $ \div n \Rightarrow $ $$\frac{1}{n}\sum_{k=1}^{n}k^2=\frac{(n+1)(2n+1)}{6}=11$$

Solve for $n$: $$(n+1)(2n+1)=66 $$ $$\;\Rightarrow\; 2n^2+3n+1=66 \;\Rightarrow\; $$ $$n=\frac{-3\pm\sqrt{9+520}}{4}=\frac{-3\pm 23}{4}$$

Only positive integer solution: $$n=\frac{20}{4}=5$$

Answer: $n=5$.

Qus : 38 MCA NIMCET PYQ 2018

The set of points, where $f(x)=\frac{x}{1+|x|}$ is differentiable in

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 39 MCA NIMCET PYQ 2018

$\int_0^{\pi} x\, f(\sin x)\, dx$ is equal to

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 40 MCA NIMCET PYQ 2018

Let $f: R \rightarrow R$ be defined by $f(x) = \begin{cases} x + 2 & \text{if } x < 0 \\ |x - 2| & \text{if } x \geq 0 \end{cases}$. Find $\int_{-2}^{3} f(x)\, dx$

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 41 MCA NIMCET PYQ 2018

The slope of two-lines $6x^2-xy-2y^2=0$ differ by

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Equation:

$6x^2 - xy - 2y^2 = 0$

Compare with: $ ax^2 + 2hxy + by^2 = 0 $

$a = 6$

$2h = -1 \;\;\Rightarrow\;\; h = -\tfrac{1}{2}$

$b = -2$

Slopes satisfy:

$bm^2 + 2hm + a = 0$

$-2m^2 - m + 6 = 0$

$\Rightarrow 2m^2 + m - 6 = 0$

Solving quadratic:

$m = \dfrac{-1 \pm \sqrt{49}}{4}$

$m = \dfrac{-1 \pm 7}{4}$

Therefore:

$m_1 = \tfrac{3}{2}, \quad m_2 = -2$

Answer: $ \tfrac{7}{2} $

Qus : 42 MCA NIMCET PYQ 2018

If the radius of the circle changes at the rate of $-\dfrac{2}{\pi}$ m/s, at what rate does the circle's area change when the radius is 10m?

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 43 MCA NIMCET PYQ 2018

The point of intersection os circle $x^2+y^2+10x-12y+51=0$ and the line $3y+x=3$ is

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 44 MCA NIMCET PYQ 2018

The number of solutions of the equation sinx + sin5x = sin3x lying in the interval $[0, \pi]$ is

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 45 MCA NIMCET PYQ 2018

In an acute-angled ΔABC the least value of secA+secB+secC is

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 46 MCA NIMCET PYQ 2018

Let $P = \{\theta : \sin\theta - \cos\theta = \sqrt{2}\cos\theta \}$ and $Q = \{\theta : \sin\theta + \cos\theta = \sqrt{2}\sin\theta \}$ be two sets. Then

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 47 MCA NIMCET PYQ 2018

If $\dfrac{\tan x}{2} = \dfrac{\tan y}{3} = \dfrac{\tan z}{5}$ and $x + y + z = \pi$, then the value of $\tan^2 x + \tan^2 y + \tan^2 z$ is

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 48 MCA NIMCET PYQ 2018

The circles whose equations are $x^2+y^2+c^2=2ax$ and $x^2+y^2+x^2-2by=0$ will touch one another externally, if

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 49 MCA NIMCET PYQ 2018

The locus of the orthocentre of the triangle formed by the lines (1+p)x-py+p(1+p)=0, (1+p)(x-q)+q(1+ q)=0 and y=0 where p≠q is

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Straight Line

Qus : 50 MCA NIMCET PYQ 2018

Equation of the common tangents with a positive slope to the circle $x^2+y^2-8x=0$ and$\dfrac{x^2}{9}-\dfrac{y^2}{4}=1$ is

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 51 MCA NIMCET PYQ 2018

The area enclosed between the curves $y^2=x$ and $y=|x|$ is

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 52 MCA NIMCET PYQ 2018

Equation of the line perpendicular to x-2y=1 and passing through (1,1) is

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 53 MCA NIMCET PYQ 2018

If $A = \begin{bmatrix} 0 & 5 \\ 0 & 0 \end{bmatrix}$ and $f(x) = 1 + x + x^2 + \cdots + x^{16}$, then $f(A) =$

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 54 MCA NIMCET PYQ 2018

9 balls are to be placed in 9 boxes and 5 of the balls cannot fit into 3 small boxes. The number of ways of arranging one ball in each of the boxes is

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

First off all select 5 boxes out 6 boxes in which 5 big ball can fit then arrange these ball in these 5 boxes and then put remaining 4 ball in any remaining box.

So Ans is [(6C5)5!](4!) = 6!4! = 17280

Qus : 55 MCA NIMCET PYQ 2018

Which of the following function is the inverse of itself?

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 56 MCA NIMCET PYQ 2018

A student council has 10 members. From this one President, one Vice-President, one Secretary, one Joint-Secretary and two Executive Committee members have to be elected. In how many ways this can be done?

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 57 MCA NIMCET PYQ 2018

In a survey where 100 students reported which subject they like, 32 students in total liked Mathematics, 38 students liked Business and 30 students liked Literature. Moreover, 7 students liked both Mathematics and Literature, 10 students liked both Mathematics and Business. 8 students like both Business and Literature, 5 students liked all three subjects. Then the number of people who liked exactly one subject is

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Given totals: $|M|=32,\ |B|=38,\ |L|=30$

Intersections (inclusive): $|M\cap L|=7,\ |M\cap B|=10,\ |B\cap L|=8,\ |M\cap B\cap L|=5$.

Compute “only” counts:

$\displaystyle |M\ \text{only}|=|M|-|M\cap B|-|M\cap L|+|M\cap B\cap L|=32-10-7+5=20$
$\displaystyle |B\ \text{only}|=|B|-|M\cap B|-|B\cap L|+|M\cap B\cap L|=38-10-8+5=25$
$\displaystyle |L\ \text{only}|=|L|-|M\cap L|-|B\cap L|+|M\cap B\cap L|=30-7-8+5=20$

Exactly one subject: $20+25+20=\boxed{65}$.

Qus : 58 MCA NIMCET PYQ 2018

If A and B are two events and $P(A \cup B) = \dfrac{5}{6}$, $P(A \cap B) = \dfrac{1}{2}$, the A and B are two events which are

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 59 MCA NIMCET PYQ 2018

If $a_1, a_2,...a_n$ are positive real numbers whose product is a fixed number c, then the minimum of $a_1, a_2, ....2a_n$ is

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Key Concept: AM-GM Inequality
$\dfrac{a_1 + a_2 + \cdots + a_n}{n} \geq (a_1 \cdot a_2 \cdots a_n)^{1/n}$

Step 1: Rewrite the sum
$a_1 + a_2 + \cdots + a_{n-1} + 2a_n$

This has $n$ terms: $(a_1, a_2, \ldots, a_{n-1}, 2a_n)$

Step 2: Apply AM-GM
$\dfrac{a_1 + a_2 + \cdots + a_{n-1} + 2a_n}{n} \geq (a_1 \cdot a_2 \cdots a_{n-1} \cdot 2a_n)^{1/n}$

$\geq (2 \cdot a_1 a_2 \cdots a_n)^{1/n}$

$\geq (2c)^{1/n}$

Step 3: Find minimum
$a_1 + a_2 + \cdots + 2a_n \geq n(2c)^{1/n}$

Minimum value $= n(2c)^{1/n}$

Equality holds when $a_1 = a_2 = \cdots = a_{n-1} = 2a_n$

Answer: Minimum value $= \boxed{n(2c)^{1/n}}$

Qus : 60 MCA NIMCET PYQ 2018

If $a, b, c$ are the roots of the equation $x^3 - 3x^2 + 3x + 7 = 0$, then the value of\[\begin{vmatrix}2bc - a^2 & c^2 & b^2 \\c^2 & 2ac - b^2 & a^2 \\b^2 & a^2 & 2ab - c^2\end{vmatrix}\]is

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 61 MCA NIMCET PYQ 2018

The coefficient of $x^n$ in the expansion of $(1 - 2x + 3x^2 - 4x^3 + \cdots \text{ to } \infty)^{-n}$ is

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 62 MCA NIMCET PYQ 2018

Let $\alpha$ and $\beta$ be the roots of the equation $x^2 - px + r = 0$ and $\dfrac{\alpha}{2}, 2\beta$ are the roots of the equation $x^2 - qx + r = 0$, then the value of $r$,

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 63 MCA NIMCET PYQ 2018

How many natural numbers smaller than $2 \times 10^8$ can be formed using the digits 1 and 2 only?

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 64 MCA NIMCET PYQ 2018

and

, then the value of

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 65 MCA NIMCET PYQ 2018

Differential coefficient of $\log_{10} x$ with respect to $\log_{x} 10$ to

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 66 MCA NIMCET PYQ 2018

$f(x) = x + |x|$ is continuous for

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 67 MCA NIMCET PYQ 2018

If $\vec{a}, \vec{b}$ and $\vec{c}$ are unit vectors, then $|\mathbf{a} - \mathbf{b}|^2 + |\mathbf{b} - \mathbf{c}|^2 + |\mathbf{c} - \mathbf{a}|^2$ does not exceeds

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 68 MCA NIMCET PYQ 2018

The vector $\vec{a} = \alpha\hat{i} + 2\hat{j} + \beta\hat{k}$ lies in the plane of the vector $\vec{b} = \hat{i} + \hat{j}$ and $\vec{c} = \hat{j} + \hat{k}$ and bisects the angle between $\vec{b}$ and $\vec{c}$. Then which of the following gives possible values of $\alpha$ and $\beta$? \begin{enumerate}

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 69 MCA NIMCET PYQ 2018

Forces $4\hat{i} - 3\hat{j} + 7\hat{k}$ and $-2\hat{i} + 2\hat{j} - 8\hat{k}$ are acting on a particle and displaced it from the point $(5, 7, 1)$ to $(2, 5, -6)$, then the work done by the force is

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Incorrect Question

Qus : 70 MCA NIMCET PYQ 2018

A bird is flying in a straight line with velocity vector 10i+6j+k, measured in km/hr. If the starting point is (1,2,3), how much time does it to take to reach a point in space that is 13m high from the ground?

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 71 MCA NIMCET PYQ 2018

The value of $\cot\!\left(cosec^{-1}\dfrac{5}{3} + \tan^{-1}\dfrac{2}{3}\right)$ is

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 72 MCA NIMCET PYQ 2018

If $\sin\theta = 3\sin(\theta + 2\alpha)$, then value of $\tan(\theta + \alpha) + 2\tan\alpha$ is

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 73 MCA NIMCET PYQ 2018

In a triangle ABC, angle A=90° and D is the midpoint of AC. What is the value of

equal to?

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 74 MCA NIMCET PYQ 2018

Through any point (x, y) of a curve which passes through the origin, lines are drawn parallel to the coordinate axes. The curve, given that it divides the rectangle formed by the two lines and the axes into two areas, one of which is twice the other, represents a family of

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 75 MCA NIMCET PYQ 2018

A line passing through (4, 2) meets the x and y-axis at P and Q respectively. If O is the origin, then the locus of the centre of the circumcircle of ΔOPQ is -

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 76 MCA NIMCET PYQ 2018

In a city 40% of the adults are illiterate while 85% of the children are literate If the ratio of the adults to that of the children is 2:3 then what percent of the population is literate?

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Let the number of adults and children be 2x and 3x

∴

Literate population = 60% of 2x + 85% of 3x =

\frac{1 5}{4} x

∴

Required % =

\frac{1 5}{4} x

\times

\frac{1}{5 x}

\times

100% = 75 %

Qus : 77 MCA NIMCET PYQ 2018

There are 50 students admitted to a nursery class. Some students can speak only English and some can speak only Hindi. Ten students can speak both English and Hindi. If the number of students who can speak English is 21, then how many students can speak Hindi, only Hindi and only English.

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Total No of students = 50

No of students who can speak both English and Hindi = 10

No of students who can speak Hindi = 50−21 = 29 + 10 = 39

No of students who can speak only Hindi = 50 − 21 = 29

No of students who can speak only English = 21 − 10 = 11

Qus : 78 MCA NIMCET PYQ 2018

The last digit of the number obtained by multiplying the numbers 81 x 82 x 83 x 84 x 85 x 86 x 87 x 88 x 89 is

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Last digit of 82 x 85 = 0

Qus : 79 MCA NIMCET PYQ 2018

It has been reported in recent years that a very large number of seats in the engineering colleges in the country remain vacant at the end of the admission session.

Which of the following may be probable cause of the above effect ?

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 80 MCA NIMCET PYQ 2018

At what time, in minutes, between 3 o'clock and 4 o'clock, both the needles will coincide each other?

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 81 MCA NIMCET PYQ 2018

If $\log_3 2,\ \log_3(2^x - 5),\ \log_3\!\left(2^x - \dfrac{7}{2}\right)$ are in arithmetic progression, then the value of $x$ is equal to

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 82 MCA NIMCET PYQ 2018

Let n be the number of different 5 digit numbers, divisible by 4 that can be formed with the digits 1,2, 3, 4, 5 and 6, with no digit being repeated. What is the value of n ?

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

We have to make 5 digit no. And also divisible by 4 using digits (1,2,3,4,5,6) To be divisible by 4 last two digit of 5 digits no should be divisible by 4 so we choose last two digits st they are divisible by 4 and rest with remaining four digits. Last two digits only can be 12,16,24,32,36,52,56,64 as all are divisible by 4. So total no of ways= no ways of choosing first 3 digits* no ways of choosing last two digits Total= (4*3*2)*(8) =192

Abhijeet Kushwaha

Qus : 83 MCA NIMCET PYQ 2018

Let S be the set of integers x such that

(i) 100 ≤ x ≤ 200

(ii) x is odd and

(iii) x is divisible by 3 but not 7

How many elements does S contain?

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 84 MCA NIMCET PYQ 2018

Two pipes A and B can fill a cistern in 37.5 and 45 min, respectively. Both pipes are opened. The cistern will be filled in just half an hour, if pipe B is turned off after

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 85 MCA NIMCET PYQ 2018

At what time, in minutes, between 3 o'clock and 4 o' clock, both the needles will coincide each other?

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2
3
4
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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 86 MCA NIMCET PYQ 2018

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 87 MCA NIMCET PYQ 2018

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 88 MCA NIMCET PYQ 2018

In the below series, you will be looking at the letter pattern, diagram pattern or number pattern. Fill the blank in the end of the series.

JAK, KBL, LCM, MDN, ____

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 89 MCA NIMCET PYQ 2018

A caterpillar crawls up a pole of 75 inches high, starting from the ground. Each day, it crawls up 5 inches and each night it slides down 4 inches. When will it reach the top of the pole?

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 90 MCA NIMCET PYQ 2018

The time on the watch is a quarter to three. If the minute hand points of North - East, in which direction does the hour hand point?

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 91 MCA NIMCET PYQ 2018

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 92 MCA NIMCET PYQ 2018

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 93 MCA NIMCET PYQ 2018

Decide which of the given conclusions logically follow from the given statement(s).

Statements :

Some codes are secrets.

All secrets are puzzles.

Conclusions :

I. All secrets being codes is a possibility.

II. Atleast some puzzles are codes.

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 94 MCA NIMCET PYQ 2018

Decide which of the given conclusions logically follow from the given statement(s).

Statements :

Some metals are alloys.

No metal is a stone.

Conclusions :

I. No alloy is stone.

II. Atleast some alloys are metals.

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 95 MCA NIMCET PYQ 2018

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 96 MCA NIMCET PYQ 2018

Statements :

All mangoes are golden in colour.

No golden-coloured things are cheap.

Conclusions :

I) All mangoes are cheap.

II) Golden-coloured mangoes are not cheap.

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 97 MCA NIMCET PYQ 2018

By selling an article, what is the profit percent gained?

I) 5% discount is given on list price.

II) If discount is not given, 20% profit is gained.

III) The cost price of the articles is Rs. 5,000.

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 98 MCA NIMCET PYQ 2018

Decide which of the given conclusions logically follows from the given statement(s).

Statements :

All politicians are honest.

All honest are fair.

Conclusions :

I) Some honest are politicians

II) No honest is politician

III) Some fair are politicians

IV) All fair are politicians

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 99 MCA NIMCET PYQ 2018

Forty students watched films A, B and C over a week. Each student watched either only one film or all three. Thirteen students watched film A, sixteen students watched film B and nineteen students watched film C. How many students watched all three films?

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 100 MCA NIMCET PYQ 2018

Two bus tickets from city A to B and three tickets from city A to C cost Rs. 77, but three tickets from city A to B and two tickets from city A to C cost Rs. 73. What are the fares for cities B and C from A?

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 101 MCA NIMCET PYQ 2018

Decide which of the assumptions is implicit in the statement and choose your answer accordingly.

Statement :

"Buy pure and natural honey of company X." - An advertisement in a newspaper.

Assumptions :

I. Artificial honey can be prepared.

II. People do not mind paying more for pure and natural honey.

III. No other company supplies pure honey.

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 102 MCA NIMCET PYQ 2018

Choose the conclusion which logically follows from the given statement(s).

Statement :

All scientists working in America are talented.

Some Indian scientists are working in America.

Conclusions :

1. None of Indian scientists is talented.

2. Some talented Indian scientists have migrated to America.

3. All talented scientists are Indians.

4. Some Indian scientists are talented.

The conclusion(s) correctly drawn is/are

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 103 MCA NIMCET PYQ 2018

One New York publisher has estimated that 50,000 to 60,000 people in the United States want an anthology that includes the complete works of William Shakespeare. And what accounts for this renewed interest in Shakespeare? As scholars point out, his psychological insights into both male and female characters are amazing even today. This paragraph best supports the statement that

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 104 MCA NIMCET PYQ 2018

A runs 1 2/3 times as fast as B. If A gives B a start of 80 m, how far must the winning 3 post be so that A and B might reach it at the same time?

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 105 MCA NIMCET PYQ 2018

Two men and three boys can do a piece of work in ten days; while three men and two boys can do the same work in eight days. In how many days can two men and one boy do the work?

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 106 MCA NIMCET PYQ 2018

How many numbers between 1 and 1000 are divisible by all numbers 2, 3, 4, 5 and 6?

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 107 MCA NIMCET PYQ 2018

There are 8436 steel balls, each with a radius of 1 centimeter, stacked in a pile, with 1 ball on top, 3 balls in the second layer, 6 in the third layer, 10 in the fourth and so on. The number of horizontal layers in the pile is

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 108 MCA NIMCET PYQ 2018

A body travels from A to B in 10s with a speed of 50 km/h and returns with a speed of 100 km/h in 5s. The average speed and the average velocity for the whole journey is

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 109 MCA NIMCET PYQ 2018

Find the odd one out.

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 110 MCA NIMCET PYQ 2018

Find out the wrong number in the following series.

15, 16, 34, 105, 424, 2124, 12756

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 111 MCA NIMCET PYQ 2018

My mother is twice as old as my brother. I am five years younger to my brother but three years older to my sister. If my sister is twelve years of age, how old is my mother?

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 112 MCA NIMCET PYQ 2018

Find the missing term in the series.

3, 20, 63, 144, 275, ___

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 113 MCA NIMCET PYQ 2018

Nine individuals Z, Y, X, W, V, U, T, S and R are the only candidates who can serve on three Committees A, B and C and each candidate should serve on exactly one of the Committees. Committee A should consist of exactly one member more than Committee B. It is possible that there are no members of Committee C. Among Z, Y and X none can serve on Committee A. Among W, V and U none can serve on Committee B. Among T, S and R none can serve on Committee C.

In case T and Z are the individuals serving on Committee B, how many of the nine individuals should serve on Committee C ?

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 114 MCA NIMCET PYQ 2018

In case T, S and X are the only individuals serving on Committee B, the membership of Committee C should be

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 115 MCA NIMCET PYQ 2018

In case R is the only individual serving on Committee B, which among the following should serve on Committee A?

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 116 MCA NIMCET PYQ 2018

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 117 MCA NIMCET PYQ 2018

Which one of the following expression does NOT represent exclusive NOR of x and y?

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 118 MCA NIMCET PYQ 2018

If a signal passing through a gate is initiated by sending a low into one of the inputs and the output is high, the gate is

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 119 MCA NIMCET PYQ 2018

Given $\sqrt{(224)_r} = (13)_r$, then the value of the radix is

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 120 MCA NIMCET PYQ 2018

What type of errors are not detected by assembler?

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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

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