NIMCET 2015 Previous Year Question Paper and Solution with PDF

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Previous Year Questions

NIMCET Previous Year Questions (PYQs)

NIMCET 2015 PYQ

Qus : 1

$\vec{a}=4\hat{j}$ 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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Solution

Qus : 2

$\vec{a}$ 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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Solution

Qus : 3

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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Solution

Qus : 4

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

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Solution

Qus : 5

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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Solution

Qus : 6

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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Solution

Qus : 7

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

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Solution

Qus : 8

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

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Solution

Qus : 9

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

Qus : 10

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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Solution

Qus : 11

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

Qus : 12

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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Solution

Qus : 13

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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Solution

Qus : 14

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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Solution

Qus : 15

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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Solution

Qus : 16

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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Solution

Qus : 17

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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Solution

Qus : 18

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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Solution

Qus : 19

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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Solution

Qus : 20

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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Solution

Qus : 21

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

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Solution

Qus : 22

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

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Solution

Qus : 23

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

Sock Drawer Problem: Minimum Socks to Guarantee a Pair of Same Color

Given:

10 black socks
10 brown socks
All socks are mixed up in the drawer

Goal: Find the smallest number of socks to pick without seeing so that at least one pair of same color socks is guaranteed.

Reasoning:

Worst case: you pick one black sock and one brown sock → no pair yet.
So after picking 2 socks, you may have no pair.
Picking one more sock (3rd sock) ensures that at least two socks must be of the same color (by Pigeonhole Principle).

Answer: The smallest number of socks to pick to guarantee at least one pair of the same color is 3.

Qus : 24

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

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Solution

Qus : 25

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

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

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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Solution

Qus : 28

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

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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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

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

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

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

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

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

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

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Solution

Qus : 36

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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Solution

Qus : 37

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

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

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Solution

Qus : 39

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

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

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

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Solution

Qus : 42

The remainder when 2³¹ is divided by 5 is

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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

Let

$\vec{a}$ and

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

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Solution

Qus : 44

$A=\begin{bmatrix} a &b &c \\ b & c & a\\ c& a &b \end{bmatrix}$ , 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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Solution

Qus : 45

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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Solution

Qus : 46

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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Solution

Qus : 47

The value of

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

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Solution

Qus : 48

The value of

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

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Solution

Qus : 49

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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Solution

Qus : 50

$a+b+c=\pi$ , 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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Solution

Qus : 51

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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Solution

Qus : 52

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

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Solution

Qus : 53

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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Solution

Qus : 54

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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Solution

Qus : 55

$\vec{a}=\hat{i}-\hat{k},\, \vec{b}=x\hat{i}+\hat{j}+(1-x)\hat{k}$ 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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Solution

Qus : 56

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

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Solution

Qus : 57

The foot of the perpendicular from the point (2, 4) upon

$x + y = 1$ is

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Solution

Qus : 58

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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Solution

Qus : 59

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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Solution

Qus : 60

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

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Solution

Qus : 61

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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Solution

Qus : 62

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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Solution

Qus : 63

$0 < x < \pi$ and

$cos x + sin x = \frac{1}{2}$ , then the value of tan x is

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Solution

Qus : 64

$\vec{a}, \vec{b}$ 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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Solution

Qus : 65

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

$\int e^x f(x) dx$ is

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Solution

Qus : 66

$3x + 4y + k = 0$ is a tangent to the hyperbola ,

$9x^{2}-16y^{2}=144$ then the value of

$K$ is

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Solution

Qus : 67

$a, b, c$ 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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Solution

Qus : 68

$(– 4, 5)$ 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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Solution

Qus : 69

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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Solution

Qus : 70

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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Solution

Qus : 71

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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Solution

Qus : 72

With the usual notation

$\frac{d^{2}x}{dy^{2}}$

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Solution

Qus : 73

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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Solution

Qus : 74

A function

$f : (0,\pi) \to R$ defined by

$f(x) = 2 sin x + cos 2x$ has

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Solution

Qus : 75

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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Solution

Qus : 76

$\vec{AC}=2\hat{i}+\hat{j}+\hat{k}$ and

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

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Solution

Qus : 77

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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Solution

Qus : 78

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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Solution

Qus : 79

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

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Solution

Qus : 80

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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Solution

Qus : 81

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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Solution

Qus : 82

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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Solution

Qus : 83

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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Solution

Qus : 84

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

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Solution

Qus : 85

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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Solution

Qus : 86

$x, y, z$ are three consecutive positive integers, then

$log (1 + xz)$ is

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4
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Solution

Qus : 87

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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Solution

Qus : 88

The value of

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

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4
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Solution

Qus : 89

$\vec{a}$ 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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4
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Solution

Qus : 90

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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Solution

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Sock Drawer Problem: Minimum Socks to Guarantee a Pair of Same Color

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Day Calculation

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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