NIMCET 2015 Previous Year Question Paper and Solution with PDF

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NIMCET Previous Year Questions (PYQs)

NIMCET 2015 PYQ

Qus : 1 NIMCET PYQ 2015

If $\vec{a}=4\hat{j}$ and $\vec{b}=3\hat{j}+4\hat{k}$ , then the vector form of the component of $\vec{a}$ alond $\vec{b}$ is

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NIMCET Previous Year PYQ NIMCET NIMCET 2015 PYQ

Solution

Qus : 2 NIMCET PYQ 2015

If $\vec{a}$ and $\vec{b}$ in space, given by $\vec{a}=\frac{\hat{i}-2\hat{j}}{\sqrt{5}}$ and $\vec{b}=\frac{2\hat{i}+\hat{j}+3\hat{k}}{\sqrt{14}}$ , then the value of $(2\vec{a}+\vec{b}).[(\vec{a} \times \vec{b}) \times (\vec{a}-2\vec{b})]$ is

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NIMCET Previous Year PYQ NIMCET NIMCET 2015 PYQ

Solution

Qus : 3 NIMCET PYQ 2015

The letters of English alphabet from A to M were written, leaving space for one letter between every two letters and then the remaining letters were inserted beginning with N and ending the series with Z after M.

Which letter would be 3rd to the right of the 7th letter from the left

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NIMCET Previous Year PYQ NIMCET NIMCET 2015 PYQ

Solution

Arrangement:

1 A, 2 N, 3 B, 4 O, 5 C, 6 P, 7 D, 8 Q, 9 E, 10 R, 11 F, 12 S, 13 G, 14 T, 15 H, 16 U, 17 I, 18 V, 19 J, 20 W, 21 K, 22 X, 23 L, 24 Y, 25 M, 26 Z

Step:

7th letter from the left = D (position 7)

3rd letter to the right of D = position 10 = R

Answer: R

Qus : 4 NIMCET PYQ 2015

Which letter would be exactly in the middle of eighteenth letter from the beginning and fifteenth from the end?

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NIMCET Previous Year PYQ NIMCET NIMCET 2015 PYQ

Solution

Qus : 5 NIMCET PYQ 2015

How many 3-digit numbers divisible by 5, can be formed using the digits 2 3 5 6 7 and 9, without repetition of digits?

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NIMCET Previous Year PYQ NIMCET NIMCET 2015 PYQ

Solution

A number divisible by 5 must end in 5.

Fix the units digit as 5.

Remaining digits for hundreds and tens places: 2, 3, 6, 7, 9 (5 digits).

Number of ways to choose hundreds and tens digits = 5 × 4 = 20.

Answer: 20

Qus : 6 NIMCET PYQ 2015

Using only 2, 5,10, 25 and 50 paise coins, what is the smallest number of coins required to pay exactly 78 paise, 69 paise and Rs. 1.01 to three different persons?

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NIMCET Previous Year PYQ NIMCET NIMCET 2015 PYQ

Solution

1) 78 paise

Take highest coin:
50 → remaining = 28
28 = 10 + 10 + 2 + 2 + 2 + 2

Coins used:
50, 10, 10, 2, 2, 2, 2
Number of coins = 7

2) 69 paise

50 → remaining = 19
19 = 10 + 5 + 2 + 2

Coins used:
50, 10, 5, 2, 2
Number of coins = 5

3) Rs. 1.01 = 101 paise

50 + 25 = 75 → remaining = 26
26 = 10 + 10 + 2 + 2 + 2

Coins used:
50, 25, 10, 10, 2, 2, 2
Number of coins = 7

Total minimum coins:

78 paise → 7 coins
69 paise → 5 coins
101 paise → 7 coins

Total = 7 + 5 + 7 = 19 coins

Answer: 19 coins

Qus : 7 NIMCET PYQ 2015

Which of the following two patterns will fit in the blanks of the series ZA₅ ,Y₄B, XC₆, W₃D, _________ , _________?

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NIMCET Previous Year PYQ NIMCET NIMCET 2015 PYQ

Solution

1) First letter pattern:

Z, Y, X, W → letters are moving backward by 1.
Next letters: V, U

2) Number pattern:

5, 4, 6, 3
Odd positions: 5, 6 → increasing by 1 → next = 7
Even positions: 4, 3 → decreasing by 1 → next = 2

3) Last letter pattern:

A, B, C, D → increasing alphabetically.
Next letters: E, F

So the missing terms are:

VE7, U2F

Answer: VE7, U2F

Qus : 8 NIMCET PYQ 2015

Which of the following numbers comes next in the two-digit decimal number sequence 61, 52, 63, 94, ______?

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NIMCET Previous Year PYQ NIMCET NIMCET 2015 PYQ

Solution

One-line Exam Shortcut:

Look at the movement of digits:
61 → 52 → 63 → 94

First digit changes: −1, +1, +3
Second digit changes: +1, +1, +1

Continue the pattern:
First digit: 9 − 5 = 4
Second digit: 4 + 2 = 6

Next number = 46

Correct Answer: 46

Qus : 9 NIMCET PYQ 2015

Three ladies X, Y and Z marry three men A, B and C. X is married to A, Y is not married to an engineer. Z is not married to a doctor, C is not a doctor and A is a lawyer. Then which of the following statements is correct?

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Solution

Given: X is married to A. A is a lawyer. C is not a doctor. Y is not married to an engineer. Z is not married to a doctor.

Step 1 (Professions):

A is a lawyer.
So the remaining two professions are doctor and engineer for B and C.
Given C is not a doctor ⇒ C must be an engineer.
Therefore, B must be a doctor.

Step 2 (Marriages):

X is married to A (fixed).
Remaining men for Y and Z are B and C.
Z is not married to a doctor, and B is the doctor ⇒ Z cannot marry B ⇒ Z is married to C.
So Y is married to B.

Final Matches:

X – A (Lawyer)
Y – B (Doctor)
Z – C (Engineer)

Qus : 10 NIMCET PYQ 2015

There are five books A, B, C, D and E placed on table. If A is placed blow E, C is placed above D, B is placed below A and D is placed between A and E, then which of the following books can be on the top?

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NIMCET Previous Year PYQ NIMCET NIMCET 2015 PYQ

Solution

Given: A is below E, B is below A, D is between A and E, and C is above D.

Arrangement (fixed order):

E is above D, D is above A, A is above B
So: E > D > A > B

Now place C:

C must be above D, so C can be:
1) Above E → C becomes the top book
2) Between E and D → E becomes the top book

Therefore, the book(s) that can be on the top: C or E

Qus : 11 NIMCET PYQ 2015

Among five children A, B, C, D and E, B is taller than E but shorter than D. A is shorter than C but taller than D. If all the children stand in a line according to their heights, then who would be the fourth if counted from the tallest one?

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Solution

Given:

B is taller than E but shorter than D → D > B > E
A is shorter than C but taller than D → C > A > D

Combined order (tallest to shortest):

C > A > D > B > E

4th from the tallest: B

Qus : 12 NIMCET PYQ 2015

In a family of six-person A, B, C, D, E, and F there are two married couples.
D is the grandmother of A and mother of B.
C is the wife of B and mother of F
F is the granddaughter of E

What is C to A?

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NIMCET Previous Year PYQ NIMCET NIMCET 2015 PYQ

Solution

Given:

D is the grandmother of A and mother of B ⇒ B is A’s parent.
C is the wife of B ⇒ C is spouse of A’s parent.

Therefore, C is A’s mother.

Answer: Mother

Qus : 13 NIMCET PYQ 2015

In a family of six-person A, B, C, D, E, and F there are two married couples.
D is the grandmother of A and mother of B.
C is the wife of B and mother of F
F is the granddaughter of E

How many male members are there in the family?

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NIMCET Previous Year PYQ NIMCET NIMCET 2015 PYQ

Solution

From the statements:
• C is wife of B ⇒ B is male, C is female.
• D is grandmother/mother ⇒ D is female.
• F is granddaughter ⇒ F is female.

So far, confirmed genders:
Male: B
Female: C, D, F

The problem says there are two married couples.
One couple is clearly (B, C).
The second couple could be:
• (D, E) ⇒ E male, or
• (A, E) ⇒ A male, or
• (A, someone) depending on relations not specified.

Since the gender of A and E is not fixed by the data, the total number of male members can vary.

Therefore, the exact number of male members cannot be uniquely determined.

Correct conclusion: Cannot be determined

Qus : 14 NIMCET PYQ 2015

In a family of six-person A, B, C, D, E, and F there are two married couples.
D is the grandmother of A and mother of B.
C is the wife of B and mother of F
F is the granddaughter of E

Who among the following is one of the couples?

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NIMCET Previous Year PYQ NIMCET NIMCET 2015 PYQ

Solution

• One married couple is clearly B–C (given: C is the wife of B).
• The problem states there are two married couples.
• D is a grandmother and mother → D is female.
• F is the granddaughter of E → E must be older than F and can be male.

There is no condition contradicting D being married to E. Hence, D–E can be the second couple.

Answer: D and E

Qus : 15 NIMCET PYQ 2015

In a family of six-person A, B, C, D, E, and F there are two married couples.
D is the grandmother of A and mother of B.
C is the wife of B and mother of F
F is the granddaughter of E

Which of the following is true?

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NIMCET Previous Year PYQ NIMCET NIMCET 2015 PYQ

Solution

C is wife of B ⇒ B is male, C is female.
D is grandmother ⇒ D is female.
F is granddaughter ⇒ F is female.
Gender of A is not given.

So A cannot be surely brother/sister of F, and B having two daughters is also not sure.

Answer: 4) None of these

Qus : 16 NIMCET PYQ 2015

A, B, C, D, E, F and G are seven girls having different amount of money from among Rs. 10, 20, 40,60, 80, 120 and 200 with them. They had 3 chocolates, 2 toffees, and 2 lollipops together, each one having one of these seven items.

B and F do not have chocolates and they have Rs. 200 and Rs. 80 respectively.
C has Rs. 60 with her and G has an amount which is neither Rs. 40 nor Rs. 120.
A has Rs. 10 and does not have a toffee.
The girl having Rs. 40 with her is the only one other than A to have the same type of item.
E and the girl having Rs. 20 with her have the same kind of item.

How much amount does G have with her?

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NIMCET Previous Year PYQ NIMCET NIMCET 2015 PYQ

Solution

Girl	Amount (Rs.)	Item
A	10	Lollipop
B	200	Toffee
C	60	Chocolate
D	40	Lollipop
E	120	Chocolate
F	80	Toffee
G	20	Chocolate

Final Answer: G has Rs. 20

Qus : 17 NIMCET PYQ 2015

B and F do not have chocolates and they have Rs. 200 and Rs. 80 respectively.
C has Rs. 60 with her and G has an amount which is neither Rs. 40 nor Rs. 120.
A has Rs. 10 and does not have a toffee.
The girl having Rs. 40 with her is the only one other than A to have the same type of item.
E and the girl having Rs. 20 with her have the same kind of item.

Which of the following girls have chocolates with them?

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NIMCET Previous Year PYQ NIMCET NIMCET 2015 PYQ

Solution

Girl	Amount (Rs.)	Item
A	10	Lollipop
B	200	Toffee
C	60	Chocolate
D	40	Lollipop
E	120	Chocolate
F	80	Toffee
G	20	Chocolate

Final Answer: G has Rs. 20

Qus : 18 NIMCET PYQ 2015

B and F do not have chocolates and they have Rs. 200 and Rs. 80 respectively.
C has Rs. 60 with her and G has an amount which is neither Rs. 40 nor Rs. 120.
A has Rs. 10 and does not have a toffee.
The girl having Rs. 40 with her is the only one other than A to have the same type of item.
E and the girl having Rs. 20 with her have the same kind of item.

Which of the following combination is definitely correct?

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NIMCET Previous Year PYQ NIMCET NIMCET 2015 PYQ

Solution

Girl	Amount (Rs.)	Item
A	10	Lollipop
B	200	Toffee
C	60	Chocolate
D	40	Lollipop
E	120	Chocolate
F	80	Toffee
G	20	Chocolate

Final Answer: G has Rs. 20

Qus : 19 NIMCET PYQ 2015

B and F do not have chocolates and they have Rs. 200 and Rs. 80 respectively.
C has Rs. 60 with her and G has an amount which is neither Rs. 40 nor Rs. 120.
A has Rs. 10 and does not have a toffee.
The girl having Rs. 40 with her is the only one other than A to have the same type of item.
E and the girl having Rs. 20 with her have the same kind of item.

Which girl has Rs. 40 with her?

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NIMCET Previous Year PYQ NIMCET NIMCET 2015 PYQ

Solution

Girl	Amount (Rs.)	Item
A	10	Lollipop
B	200	Toffee
C	60	Chocolate
D	40	Lollipop
E	120	Chocolate
F	80	Toffee
G	20	Chocolate

Final Answer: G has Rs. 20

Qus : 20 NIMCET PYQ 2015

P, Q, R, S, T, U and V are sitting in a row facing North. In order to determine, who is sitting exactly in the middle of the row, which of the following information is needed?

T and U are sitting at extreme ends of the row
S is third to the right of T
Q is four places to the left of R and P is two places to the left of V

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NIMCET Previous Year PYQ NIMCET NIMCET 2015 PYQ

Solution

We need to find who sits in the middle (position 4) among 7 persons.

Using I + II:

T and U are at the extreme ends. If T is at the right end, S cannot be 3rd to the right (out of row). So T must be at the left end, and S becomes position 4 (middle).
Middle = S

Using I + III:

With T and U fixed at the ends, Q must be 4 places left of R, so only possible is Q at position 2 and R at position 6. Also P is 2 places left of V, so P at position 3 and V at position 5. The remaining person S automatically comes at position 4.
Middle = S

Conclusion: Statement I along with either II or III is sufficient.

Correct Option: 3) I and either II or III are sufficient

Qus : 21 NIMCET PYQ 2015

How many times do the hour and the minute hands of a clock overlap in 24 hours?

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NIMCET Previous Year PYQ NIMCET NIMCET 2015 PYQ

Solution

In 12 hours, the hour and minute hands overlap 11 times.

So in 24 hours, they overlap 11 × 2 = 22 times.

Qus : 22 NIMCET PYQ 2015

In a certain code, TOGETHER is coded as RQEGRJCT. In the same code, PAROLE will be written as:

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Solution

Given: TOGETHER → RQEGRJCT

Rule: Letters are shifted alternately: −2, +2, −2, +2, ...

PAROLE:

P → N (−2)
A → C (+2)
R → P (−2)
O → Q (+2)
L → J (−2)
E → G (+2)

Answer: NCPQJG

Qus : 23 NIMCET PYQ 2015

A drawer contains 10 black and 10 brown socks which are all mixed up. What is the smallest number of socks to be taken from the drawer to decide without seeing them, to be sure that there is atleast one pair of socks of the same colour?

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Solution

There are only 2 colours (black and brown).
If you pick 2 socks, they could be 1 black and 1 brown.
On picking the 3rd sock, it must match the colour of one of the first two socks.

Answer: 3 socks

Qus : 24 NIMCET PYQ 2015

Find the missing number in the series: 4, 7, 25, 10, __________, 20, 16, 19

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Solution

Qus : 25 NIMCET PYQ 2015

A circular field with inner radius of 10 meters and outer radius of 20 meters is divided into 5 successive stages for ploughing, The ploughing at each stage, with starting points P1, P2, P3, P4 and P5, was allotted to one of the five farmers F1, F2, F3, F4 and F5, not necessarily in that order.

F was allotted the stage starting at point P4.
The stage from P5 to P3 was not the first Stage.
F4 was allotted the work of the fourth stage.
Finishing point of stage 3 was P1 and the work was not allotted to F1.
F3 was allotted the work of stage 3 was P1 and the work was not allotted to F1.

Which of the following is the finish point for farmer F2?

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Solution

Qus : 26 NIMCET PYQ 2015

F was allotted the stage starting at point P4.
The stage from P5 to P3 was not the first Stage.
F4 was allotted the work of the fourth stage.
Finishing point of stage 3 was P1 and the work was not allotted to F1.
F3 was allotted the work of stage 3 was P1 and the work was not allotted to F1.

Which stage was ploughed by F5?

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Solution

Qus : 27 NIMCET PYQ 2015

F was allotted the stage starting at point P4.
The stage from P5 to P3 was not the first Stage.
F4 was allotted the work of the fourth stage.
Finishing point of stage 3 was P1 and the work was not allotted to F1.
F3 was allotted the work of stage 3 was P1 and the work was not allotted to F1.

What are the starting and ending points of the field ploughed by F4?

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NIMCET Previous Year PYQ NIMCET NIMCET 2015 PYQ

Solution

Qus : 28 NIMCET PYQ 2015

F was allotted the stage starting at point P4.
The stage from P5 to P3 was not the first Stage.
F4 was allotted the work of the fourth stage.
Finishing point of stage 3 was P1 and the work was not allotted to F1.
F3 was allotted the work of stage 3 was P1 and the work was not allotted to F1.

What is the starting point for stage?

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Solution

Qus : 29 NIMCET PYQ 2015

If Tuesday falls on the fourth of a month then which day will fall three days after 24th of the same month?

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NIMCET Previous Year PYQ NIMCET NIMCET 2015 PYQ

Solution

Day Calculation The 4th of the month is a Tuesday.

Step 1: Find the day on the 24th of the month:

4th (Tuesday) → 11th (Tuesday + 7 days = 1 week)
11th → 18th (Tuesday + 7 days = 1 more week)
18th → 24th (Tuesday + 6 days = 6 days ahead, so 24th is a Monday)

Step 2: Now, calculate 3 days after the 24th (Monday):

Monday → Tuesday (1 day)
Tuesday → Wednesday (2 days)
Wednesday → Thursday (3 days)

Answer: 3 days after the 24th is a Thursday.

Qus : 30 NIMCET PYQ 2015

If the statements “All chickens are birds”, “Some chickens are hens” and “Female birds lay eggs”, are all facts, then which of the following must also be a fact?
I. All birds lay eggs

II. Some hens are birds

III. Some chickens are not hens

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Solution

Qus : 31 NIMCET PYQ 2015

There is a family of six members A, B, C, D, E and F
There are two married couples in the family and the family members represent three generations.
Each member has a distinct choice of a colour amongst Green, Yellow, Black, Red, White and Pink
No lady member likes either Green or White.
C, who likes Black colour, is the daughter-in-law of E.
B is the brother of F and son of D and likes Pink
A is the grandmother of F and F does not like Red.
Wife of the husband having a choice for Green colour, likes Yellow.

Which of the following is the colour preference of A?

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Solution

Qus : 32 NIMCET PYQ 2015

There is a family of six members A, B, C, D, E and F
There are two married couples in the family and the family members represent three generations.
Each member has a distinct choice of a colour amongst Green, Yellow, Black, Red, White and Pink
No lady member likes either Green or White.
C, who likes Black colour, is the daughter-in-law of E.
B is the brother of F and son of D and likes Pink
A is the grandmother of F and F does not like Red.
Wife of the husband having a choice for Green colour, likes Yellow.

Which of the following could be the colour combination of one of the couples?

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Solution

Qus : 33 NIMCET PYQ 2015

There is a family of six members A, B, C, D, E and F
There are two married couples in the family and the family members represent three generations.
Each member has a distinct choice of a colour amongst Green, Yellow, Black, Red, White and Pink
No lady member likes either Green or White.
C, who likes Black colour, is the daughter-in-law of E.
B is the brother of F and son of D and likes Pink
A is the grandmother of F and F does not like Red.
Wife of the husband having a choice for Green colour, likes Yellow.

Which of the following is one of the married couples?

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Solution

Qus : 34 NIMCET PYQ 2015

There is a family of six members A, B, C, D, E and F
There are two married couples in the family and the family members represent three generations.
Each member has a distinct choice of a colour amongst Green, Yellow, Black, Red, White and Pink
No lady member likes either Green or White.
C, who likes Black colour, is the daughter-in-law of E.
B is the brother of F and son of D and likes Pink
A is the grandmother of F and F does not like Red.
Wife of the husband having a choice for Green colour, likes Yellow.

Which of the following is true about F?

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Solution

Qus : 35 NIMCET PYQ 2015

If the English word “EXAMINATION” is coded as 56149512965, then the word “GOVERNMENT” is coded as

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Solution

Qus : 36 NIMCET PYQ 2015

Gopal starts from his house towards West. After walking a distance of 30 meters, he turned towards right and walked 20 meters. He turned left and after moving a distance of 10 meters, turned to his left again and walked 40 meters. He then turned left and walked 5 meters. Finally, he turns to his left. In which direction is he walking now?

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NIMCET Previous Year PYQ NIMCET NIMCET 2015 PYQ

Solution

Qus : 37 NIMCET PYQ 2015

Read the conclusion and then decide which of the given conclusions logically follows from the two given statements, (i) and (ii) disregarding commonly known facts.

Statements:

(i) No woman teacher can play.

(ii) Some woman teachers are athletes.

Conclusions:

I. Male athletes can play.

II. Some athletes can play

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Solution

Qus : 38 NIMCET PYQ 2015

Which of the following numbers come next in the series 8, 6, 9, 23, 87, ________?

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Solution

Qus : 39 NIMCET PYQ 2015

In an examination, there are 100 questions divided into 3 parts A, B, C, and each part should contain at least one question. Each question in parts A, B, and C carry 1, 2 and 3 marks respectively. Part A is for at least 60% of the total marks and part B should contain 23 questions. How many questions must be set in part C?

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Solution

Given: Total questions = 100, Part B = 23 questions (2 marks each).

Let Part A = $a$ questions (1 mark), Part C = $c$ questions (3 marks).

So, $a + 23 + c = 100 \Rightarrow a + c = 77$.
Total marks = $a + 46 + 3c$.
Part A marks ≥ 60% total marks:
$\Rightarrow a \geq 0.6(a + 46 + 3c)$
$\Rightarrow a \geq 0.6a + 27.6 + 1.8c$
$\Rightarrow 0.4a \geq 27.6 + 1.8c$
$\Rightarrow a \geq 69 + 4.5c$.

Using $a = 77 - c$:
$77 - c \geq 69 + 4.5c \Rightarrow 8 \geq 5.5c \Rightarrow c \leq 1.45$.
So, $c = 1$.

Answer: Part C has 1 question.

Qus : 40 NIMCET PYQ 2015

If ÷ means addition, – means division, × means subtraction and + means multiplication, then the value of $\frac{(36 \times 4)-(8 \times 4)}{4+8 \times 2 +16\div 1}$

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Solution

Qus : 41 NIMCET PYQ 2015

Which letter in the word CYBERNETICS occupies the same position as it does in the English alphabet?

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NIMCET Previous Year PYQ NIMCET NIMCET 2015 PYQ

Solution

Qus : 42 NIMCET PYQ 2015

The remainder when 2³¹ is divided by 5 is

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NIMCET Previous Year PYQ NIMCET NIMCET 2015 PYQ

Solution

Remainder of 2³¹ Divided by 5

To find the remainder of 2³¹ divided by 5, we look at the cycle of powers of 2 mod 5: 2, 4, 3, 1 (repeats every 4 terms).

31 mod 4 = 3, so 2³¹ corresponds to the 3rd term, which is 3.

Answer: 3

Qus : 43 NIMCET PYQ 2015

Let $\vec{a}$ and $\vec{b}$ be two vectors, which of the following vectors are not perpendicular to each other?

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NIMCET Previous Year PYQ NIMCET NIMCET 2015 PYQ

Solution

Qus : 44 NIMCET PYQ 2015

If $A=\begin{bmatrix} a &b &c \\ b & c & a\\ c& a &b \end{bmatrix}$ , where $a, b, c$ are real positive numbers such that $abc = 1$ and $A^{T}A=I$ then the equation that not holds true among the following is

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NIMCET Previous Year PYQ NIMCET NIMCET 2015 PYQ

Solution

Qus : 45 NIMCET PYQ 2015

The equation of the tangent at any point of the curve $x=acos2t$, $y=2\sqrt{2}a sint$ with $m$ as its slope is

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NIMCET Previous Year PYQ NIMCET NIMCET 2015 PYQ

Solution

Qus : 46 NIMCET PYQ 2015

The locus of the mid points of all chords of the parabola $y^{2}=4x$ which are drawn through its vertex, is

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NIMCET Previous Year PYQ NIMCET NIMCET 2015 PYQ

Solution

Qus : 47 NIMCET PYQ 2015

The value of $\lim_{x\to a} \frac{\sqrt{a+2x}-\sqrt{3x}}{\sqrt{3a+x}-2\sqrt{x}}$

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NIMCET Previous Year PYQ NIMCET NIMCET 2015 PYQ

Solution

Qus : 48 NIMCET PYQ 2015

The value of $\int_{-\pi/3}^{\pi/3} \frac{x sinx}{cos^{2}x}dx$

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NIMCET Previous Year PYQ NIMCET NIMCET 2015 PYQ

Solution

Qus : 49 NIMCET PYQ 2015

The foci of the ellipse $\frac{x^{2}}{16}+\frac{y^{2}}{b^{2}}=1$ and the hyperbola $\frac{x^{2}}{144}-\frac{y^{2}}{{81}}=\frac{1}{25}$ coincide, then the value of $b^{2}$ is

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NIMCET Previous Year PYQ NIMCET NIMCET 2015 PYQ

Solution

Qus : 50 NIMCET PYQ 2015

If $a+b+c=\pi$ , then the value of $\begin{vmatrix} sin(A+B+C) &sinB &cosC \\ -sinB & 0 &tanA \\ cos(A+B)&-tanA &0 \end{vmatrix}$ is

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NIMCET Previous Year PYQ NIMCET NIMCET 2015 PYQ

Solution

Qus : 51 NIMCET PYQ 2015

If the mean deviation of the numbers 1, 1 + d, 1 + 2d, ....., 1 + 100d from their mean is 255, then the value of d is

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NIMCET Previous Year PYQ NIMCET NIMCET 2015 PYQ

Solution

Given AP: $1,\,1+d,\,1+2d,\,\ldots,\,1+100d$ (total $101$ terms). The mean is the middle term $1+50d$.

Mean Deviation (about mean): For $2n+1$ terms $a,a+d,\ldots,a+2nd$, $$\text{MD}=\frac{d\,n(n+1)}{2n+1}.$$

Here $2n+1=101 \Rightarrow n=50$. So $$\text{MD}=\frac{d\cdot 50\cdot 51}{101}=\frac{2550}{101}\,d.$$

Given $\text{MD}=255$. Solve for $d$: $$\frac{2550}{101}\,d=255 \;\Rightarrow\; d=\frac{255\times 101}{2550}=10.1.$$

Answer: $d=10.1$.

Qus : 52 NIMCET PYQ 2015

If $P=sin^{20} \theta + cos^{48} \theta $ then the inequality that holds for all values of is

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NIMCET Previous Year PYQ NIMCET NIMCET 2015 PYQ

Solution

Qus : 53 NIMCET PYQ 2015

If a, b, c are in geometric progression, then $log_{ax}^{a}, log_{bx}^{a}$ and $log_{cx}^{a}$ are in

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NIMCET Previous Year PYQ NIMCET NIMCET 2015 PYQ

Solution

Qus : 54 NIMCET PYQ 2015

The value of the sum $\frac{1}{2\sqrt{1}+1\sqrt{2}}+\frac{1}{3\sqrt{2}+2\sqrt{3}}+\frac{1}{4\sqrt{3}+3\sqrt{4}}+...+\frac{1}{25\sqrt{24}+24\sqrt{25}}$ is

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NIMCET Previous Year PYQ NIMCET NIMCET 2015 PYQ

Solution

Qus : 55 NIMCET PYQ 2015

If $\vec{a}=\hat{i}-\hat{k},\, \vec{b}=x\hat{i}+\hat{j}+(1-x)\hat{k}$ and $\vec{c}=y\hat{i}+x\hat{j}+(1+x-y)\hat{k}$ , then $[\vec{a} , \vec{b}, \vec{c}]$ depends on

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NIMCET Previous Year PYQ NIMCET NIMCET 2015 PYQ

Solution

Qus : 56 NIMCET PYQ 2015

If $42 (^nP_2)=(^nP_4)$ then the value of n is

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NIMCET Previous Year PYQ NIMCET NIMCET 2015 PYQ

Solution

Qus : 57 NIMCET PYQ 2015

The foot of the perpendicular from the point (2, 4) upon $x + y = 1$ is

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NIMCET Previous Year PYQ NIMCET NIMCET 2015 PYQ

Solution

Qus : 58 NIMCET PYQ 2015

The value of k for which the equation $(k-2)x^{2}+8x+k+4=0$ has both real, distinct and negative roots is

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NIMCET Previous Year PYQ NIMCET NIMCET 2015 PYQ

Solution

Qus : 59 NIMCET PYQ 2015

If (2, 1), (–1, –2), (3, 3) are the midpoints of the sides BC, CA, AB of a triangle ABC, then equation of the line BC is

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NIMCET Previous Year PYQ NIMCET NIMCET 2015 PYQ

Solution

Qus : 60 NIMCET PYQ 2015

If a fair dice is rolled successively, then the probability that 1 appears in an even numbered throw is

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NIMCET Previous Year PYQ NIMCET NIMCET 2015 PYQ

Solution

Qus : 61 NIMCET PYQ 2015

Let $\vec{a}=\hat{i}+\hat{j}+\hat{k}, \vec{b}=\hat{i}-\hat{j}+\hat{k}$ and $\vec{c}=\hat{i}-\hat{j}-\hat{k}$ be three vectors. A vector $\vec{v}$ in the plane of $\vec{a}$ and $\vec{b}$ whose projection on $\frac{\vec{c}}{|\vec{c}|}$ is $\frac{1}{\sqrt{3}}$, is

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NIMCET Previous Year PYQ NIMCET NIMCET 2015 PYQ

Solution

Qus : 62 NIMCET PYQ 2015

The number of bit strings of length 10 that contain either five consecutive 0’s or five consecutive 1’s is

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NIMCET Previous Year PYQ NIMCET NIMCET 2015 PYQ

Solution

We count bit strings of length 10 that contain at least one run of five identical bits.

Case 1: Exactly one block of five consecutive 0’s.
The block $00000$ can start at positions 1 to 6, so 6 choices.
The remaining 5 positions can be filled freely with 0 or 1, except they should not create another block of five 0’s.
Valid fillings = $2^5 - 1 = 31$.
So number of strings with exactly one block of five 0’s is
$6 \times 31 = 186$

Case 2: Exactly one block of five consecutive 1’s.
By symmetry, the count is the same.
$186$

Case 3: One block of five 0’s and one block of five 1’s.
This is possible only when the blocks do not overlap.
The only such strings are
$0000011111$ and $1111100000$

So total such strings = $2$.
Using inclusion–exclusion principle:
$186 + 186 + 2 = 222$
Final Answer: $222$

Qus : 63 NIMCET PYQ 2015

If $0 < x < \pi $ and $cos x + sin x = \frac{1}{2}$ , then the value of tan x is

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NIMCET Previous Year PYQ NIMCET NIMCET 2015 PYQ

Solution

Qus : 64 NIMCET PYQ 2015

If $\vec{a}, \vec{b}$ and $\vec{c}$ are the position vectors of the vertices A, B, C of a triangle ABC, then the area of the triangle ABC is

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NIMCET Previous Year PYQ NIMCET NIMCET 2015 PYQ

Solution

Qus : 65 NIMCET PYQ 2015

If $\int e^{x}(f(x)-f'(x))dx=\phi(x)$ , then the value of $\int e^x f(x) dx$ is

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NIMCET Previous Year PYQ NIMCET NIMCET 2015 PYQ

Solution

Qus : 66 NIMCET PYQ 2015

If $3x + 4y + k = 0$ is a tangent to the hyperbola ,$9x^{2}-16y^{2}=144$ then the value of $K$ is

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NIMCET Previous Year PYQ NIMCET NIMCET 2015 PYQ

Solution

Qus : 67 NIMCET PYQ 2015

$a, b, c$ are positive integers such that $a^{2}+2b^{2}-2bc=100$ and $2ab-c^{2}=100$. Then the value of $\frac{a+b}{c}$ is

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NIMCET Previous Year PYQ NIMCET NIMCET 2015 PYQ

Solution

Qus : 68 NIMCET PYQ 2015

If $(– 4, 5)$ is one vertex and $7x – y + 8 = 0$ is one diagonal of a square, then the equation of the other diagonal is

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NIMCET Previous Year PYQ NIMCET NIMCET 2015 PYQ

Solution

Qus : 69 NIMCET PYQ 2015

Out of $2n + 1$ tickets, which are consecutively numbered, three are drawn at random. Then the probability that the numbers on them are in arithmetic progression is

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NIMCET Previous Year PYQ NIMCET NIMCET 2015 PYQ

Solution

Qus : 70 NIMCET PYQ 2015

A circle touches the X-axis and also touches another circle with centre at (0, 3) and radius 2. Then the locus of the centre of the first circle is

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NIMCET Previous Year PYQ NIMCET NIMCET 2015 PYQ

Solution

Qus : 71 NIMCET PYQ 2015

Let $\bar{P}$ and $\bar{Q}$ denote the complements of two sets P and Q. Then the set $(P-Q)\cup (Q-P) \cup (P \cap Q)$ is

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NIMCET Previous Year PYQ NIMCET NIMCET 2015 PYQ

Solution

Expression: $(P - Q) \cup (Q - P) \cup (P \cap Q)$

Recall: $P - Q = P \cap \bar{Q}$ and $Q - P = Q \cap \bar{P}$.

Thus the union consists of three mutually exclusive parts:

Elements only in $P$: $P \cap \bar{Q}$
Elements only in $Q$: $Q \cap \bar{P}$
Elements in both: $P \cap Q$

The union of these three pieces is precisely all elements that are in $P$ or $Q$:

$(P - Q) \cup (Q - P) \cup (P \cap Q) = P \cup Q$.

Qus : 72 NIMCET PYQ 2015

With the usual notation $\frac{d^{2}x}{dy^{2}}$

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NIMCET Previous Year PYQ NIMCET NIMCET 2015 PYQ

Solution

Qus : 73 NIMCET PYQ 2015

The radius of the circle passing through the foci of the ellipse $\frac{x^2}{16}+\frac{y^2}{9}$and having it centre at (0, 3) is

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NIMCET Previous Year PYQ NIMCET NIMCET 2015 PYQ

Solution

Qus : 74 NIMCET PYQ 2015

A function $f : (0,\pi) \to R$ defined by $f(x) = 2 sin x + cos 2x$ has

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NIMCET Previous Year PYQ NIMCET NIMCET 2015 PYQ

Solution

Qus : 75 NIMCET PYQ 2015

A matrix $M_r$ is defined as $M_r=\begin{bmatrix} r &r-1 \\ r-1&r \end{bmatrix} , r \in N$ then the value of $det(M_1) + det(M_2) +...+ det(M_{2015})$ is

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NIMCET Previous Year PYQ NIMCET NIMCET 2015 PYQ

Solution

Qus : 76 NIMCET PYQ 2015

If $\vec{AC}=2\hat{i}+\hat{j}+\hat{k}$ and $\vec{BD}=-\hat{i}+3\hat{j}+2\hat{k}$ then the area of the quadrilateral ABCD is

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NIMCET Previous Year PYQ NIMCET NIMCET 2015 PYQ

Solution

Qus : 77 NIMCET PYQ 2015

The value of $sin^{-1}\frac{1}{\sqrt{2}}+sin^{-1}\frac{\sqrt{2}-\sqrt{1}}{\sqrt{6}}+sin^{-1}\frac{\sqrt{3}-\sqrt{2}}{\sqrt{12}}+...$ to infinity , is equal to

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NIMCET Previous Year PYQ NIMCET NIMCET 2015 PYQ

Solution

Qus : 78 NIMCET PYQ 2015

If two circles $x^{2}+y^{2}+2gx+2fy=0$ and $x^{2}+y^{2}+2g'x+2f'y=0$ touch each other then whichof the following is true?

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NIMCET Previous Year PYQ NIMCET NIMCET 2015 PYQ

Solution

Qus : 79 NIMCET PYQ 2015

$\int_0^\pi [cotx]dx$ where [.] denotes the greatest integer function, is equal to

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NIMCET Previous Year PYQ NIMCET NIMCET 2015 PYQ

Solution

Qus : 80 NIMCET PYQ 2015

In a right angled triangle, the hypotenuse is four times the perpendicular drawn to it from the opposite vertex. The value of one of the acute angles is

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NIMCET Previous Year PYQ NIMCET NIMCET 2015 PYQ

Solution

Qus : 81 NIMCET PYQ 2015

A is targeting B, B and C are targeting A. Probability of hitting the target by A, B and C are $\frac{2}{3}, \frac{1}{2}$ and $\frac{1}{3}$ respectively. If A is hit then the probability that B hits the target and C does not, is

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NIMCET Previous Year PYQ NIMCET NIMCET 2015 PYQ

Solution

Qus : 82 NIMCET PYQ 2015

If the angles of a triangle are in the ratio 2 : 3 : 7, then the ratio of the sides opposite to these angles is

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NIMCET Previous Year PYQ NIMCET NIMCET 2015 PYQ

Solution

Qus : 83 NIMCET PYQ 2015

Suppose that A and B are two events with probabilities $P(A) =\frac{1}{2} \, P(B)=\frac{1}{3}$ Then which of the following is true?

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NIMCET Previous Year PYQ NIMCET NIMCET 2015 PYQ

Solution

Qus : 84 NIMCET PYQ 2015

The number of one-to-one functions from {1, 2, 3} to {1, 2, 3, 4, 5} is

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NIMCET Previous Year PYQ NIMCET NIMCET 2015 PYQ

Solution

Qus : 85 NIMCET PYQ 2015

A harbour lies in a direction 60° South of West from a fort and at a distance 30 km from it, a ship sets out from the harbour at noon and sails due East at 10 km an hour. The time at which the ship will be 70 km from the fort is

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NIMCET Previous Year PYQ NIMCET NIMCET 2015 PYQ

Solution

Qus : 86 NIMCET PYQ 2015

If $x, y, z$ are three consecutive positive integers, then $log (1 + xz)$ is

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NIMCET Previous Year PYQ NIMCET NIMCET 2015 PYQ

Solution

Qus : 87 NIMCET PYQ 2015

A professor has 24 text books on computer science and is concerned about their coverage of the topics (P) compilers, (Q) data structures and (R) Operating systems. The following data gives the number of books that contain material on these topics: $n(P) = 8, n(Q) = 13, n(R) = 13, n(P \cap R) = 3, n(P \cap R) = 3, n(Q \cap R) = 3, n(Q \cap R) = 6, n(P \cap Q \cap R) = 2 $ where $n(x)$ is the cardinality of the set $x$. Then the number of text books that have no material on compilers is

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NIMCET Previous Year PYQ NIMCET NIMCET 2015 PYQ

Solution

Given: Total books = 24, and books with compilers $n(P)=8$.

Asked: Number of books with no material on compilers = $|P'|$.

\[ |P'| = \text{Total} - |P| = 24 - 8 = \boxed{16}. \]

Note: The other intersection counts aren’t needed since “no compilers” depends only on $n(P)$.

Qus : 88 NIMCET PYQ 2015

The value of $tan(\frac{7\pi}{8})$ is

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NIMCET Previous Year PYQ NIMCET NIMCET 2015 PYQ

Solution

Qus : 89 NIMCET PYQ 2015

If $\vec{a}$ and $\vec{b}$ are vectors such that $|\vec{a}|=13$, $|\vec{b}|=5$ and $\vec{a} . \vec{b} =60$then the value of $|\vec{a} \times \vec{b}|$ is

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NIMCET Previous Year PYQ NIMCET NIMCET 2015 PYQ

Solution

Qus : 90 NIMCET PYQ 2015

Two towers face each other separated by a distance of 25 meters. As seen from the top of the first tower, the angle of depression of the second tower’s base is 60° and that of the top is 30°. The height (in meters) of the second tower is

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NIMCET Previous Year PYQ NIMCET NIMCET 2015 PYQ

Solution

Two Towers – Height of the Second Tower

Distance between towers’ bases = 25 m

Let the first tower be $AB$ (top $A$, base $B$) and the second tower be $CD$ (top $C$, base $D$). The bases $B$ and $D$ are 25 m apart.

From the top $A$: angle of depression to base $D$ is $60^\circ$ and to top $C$ is $30^\circ$.

From right $\triangle ABD$: \[ \tan 60^\circ=\frac{AB}{BD}=\frac{AB}{25}\;\Rightarrow\; AB=25\sqrt{3}. \]
From right $\triangle ACD$: vertical difference $=AB-CD$ and horizontal $=25$. \[ \tan 30^\circ=\frac{AB-CD}{25}=\frac{1}{\sqrt{3}} \;\Rightarrow\; AB-CD=\frac{25}{\sqrt{3}}. \]
Substitute $AB=25\sqrt{3}$: \[ 25\sqrt{3}-CD=\frac{25}{\sqrt{3}} \;\Rightarrow\; CD=25\!\left(\sqrt{3}-\frac{1}{\sqrt{3}}\right) =\frac{50}{\sqrt{3}}\;\text{m}. \]

Answer: $ \displaystyle CD=\frac{50}{\sqrt{3}} \approx 28.87\ \text{m} $

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Given: Total questions = 100, Part B = 23 questions (2 marks each).

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Remainder of 231 Divided by 5

Answer: 3

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Remainder of 2³¹ Divided by 5