CUET PG MCA Mathematics Previous Year Question Paper and Solution with PDF

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CUET PG MCA
Previous Year Questions

CUET PG MCA Previous Year Questions (PYQs)

CUET PG MCA Mathematics PYQ

Qus : 1

$A=\begin{bmatrix}{\cos B} & {-\sin B} \\ {\sin B} & {\cos B}\end{bmatrix}$ then

$A+{A}^T=I$ for B equal to

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Solution

Qus : 2

The number of 7-digit numbers whose sum of the digits equals to 10 and which is formed by using the digits 1, 2, and 3 only is:

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Solution

Qus : 3

If from each of the three boxes containing 3 white and 1 black, 2 white and 2 black, 1 white and 3 black balls, one ball is drawn at random, then the probability that 2 white and 1 black balls will be drawn is:

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Solution

Qus : 4

Let

$f(x)=\, \vert{|x|}-1\vert$ , then point(s) where

$f(x)$ is not differentiable is (are):

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Solution

Qus : 5

Letf

$f:[2,\infty)\rightarrow R$ be the function defined by

$f(x)=x^2-4x+5$ , then the range of

$f$

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Solution

Qus : 6

The function

$f(x)= \frac{[ln(1+ax)-ln(1-b x)]}{x}$ is not defined at

$x=0$ . What value may be assigned to

$f$ at

$x=0$ , so that it is continuous?

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Solution

Qus : 7

The are enclosed between the graphs of

$y=x^3$ and the lines

$x=0$ ,

$y=1$ ,

$y=8$ is:

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Solution

Qus : 8

If the vertices of a triangle are O(0,0), A(a,0) and B(0,a). Then, the distance between its circumcenter and orthocenter is:

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Solution

Qus : 9

The straight lines x+y-4=0, 3x+y-4=0 and x+3y-4=0 form a triangle which is:

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Solution

Qus : 10

If one of the lines of

$ax^2+2hxy+by^2=0$ bisects the angle between the axes in the first quadrant, the

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Solution

Qus : 11

What is the value of :

$[tan^2(90-\theta)-sin^2(90-\theta)] cosec^2(90-\theta) cot^2 (90-\theta)$

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Solution

Qus : 12

$A+B=45{^{\circ}}$ , then

$(1+tanA)(1+tanB)$ is equal to:

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Solution

Qus : 13

$\vec{a}$ and

$\vec{b}$ are two unit vectors such that

$\vec{a}+2\vec{b}$ and

$5\vec{a}-4\vec{b}$ are perpendicular to each other, then the angle between

$\vec{a}$ and

$\vec{b}$ is:

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Solution

Solution:

Given two unit vectors

$\vec{a}$ and

$\vec{b}$ , and the vectors

$\vec{a} + 2\vec{b}$ and

$5\vec{a} - 4\vec{b}$ are perpendicular, we use the condition for perpendicular vectors:

$(\vec{a} + 2\vec{b}) \cdot (5\vec{a} - 4\vec{b}) = 0$ Expanding the dot product:

$(\vec{a} + 2\vec{b}) \cdot (5\vec{a} - 4\vec{b}) = \vec{a} \cdot 5\vec{a} + \vec{a} \cdot (-4\vec{b}) + 2\vec{b} \cdot 5\vec{a} + 2\vec{b} \cdot (-4\vec{b})$ Using properties of dot products and knowing

$\vec{a}$ and

$\vec{b}$ are unit vectors (

$\vec{a} \cdot \vec{a} = 1$ and

$\vec{b} \cdot \vec{b} = 1$ ):

$5(\vec{a} \cdot \vec{a}) - 4(\vec{a} \cdot \vec{b}) + 10(\vec{b} \cdot \vec{a}) - 8(\vec{b} \cdot \vec{b}) = 0$ Simplifying:

$5(1) - 4(\vec{a} \cdot \vec{b}) + 10(\vec{a} \cdot \vec{b}) - 8(1) = 0$

$5 - 8 + 6(\vec{a} \cdot \vec{b}) = 0$

$-3 + 6(\vec{a} \cdot \vec{b}) = 0$

$6(\vec{a} \cdot \vec{b}) = 3$

$\vec{a} \cdot \vec{b} = \frac{1}{2}$ The dot product

$\vec{a} \cdot \vec{b} = \cos \theta$ , where

$\theta$ is the angle between

$\vec{a}$ and

$\vec{b}$ :

$\cos \theta = \frac{1}{2}$ Therefore, the angle

$\theta$ is:

$\theta = \cos^{-1} \left( \frac{1}{2} \right) = 60^\circ$
Final Answer:

$\boxed{60^\circ}$

Qus : 14

Let

$\vec{a}=\hat{i}-\hat{j}$ and

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

$\vec{c}$ be a vector such that

$(\vec{a} \times \vec{c})+\vec{b}=0$ and

$\vec{a}.\vec{c}=4$ , then

$|\vec{c}|^2$ is equal to

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Solution

Solution:

Given vectors:

$\vec{a} = \hat{i} - \hat{j}$
$\vec{b} = \hat{i} + \hat{j} + \hat{k}$
And $(\vec{a} \times \vec{c}) + \vec{b} = 0$
$\vec{a} \cdot \vec{c} = 4$

From

$(\vec{a} \times \vec{c}) + \vec{b} = 0$ , we get:

$\vec{a} \times \vec{c} = -\vec{b}$ Let

$\vec{c} = x\hat{i} + y\hat{j} + z\hat{k}$ . The cross product

$\vec{a} \times \vec{c}$ is:

$\vec{a} \times \vec{c} = \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \\ 1 & -1 & 0 \\ x & y & z \end{vmatrix}$ Expanding this determinant:

$\vec{a} \times \vec{c} = (z \hat{i} + z \hat{j} + (x + y) \hat{k})$ Setting

$\vec{a} \times \vec{c} = -\vec{b}$ , we get:

$z = -1, \quad z = -1, \quad x + y = -1$ Therefore:

$x + y = -1$ Now, from

$\vec{a} \cdot \vec{c} = 4$ :

$\vec{a} \cdot \vec{c} = 1 \cdot x + (-1) \cdot y = 4$ Simplifying:

$x - y = 4$ Solving the system of equations:

$x + y = -1$

$x - y = 4$ Adding the two equations:

$2x = 3 \quad \Rightarrow \quad x = \frac{3}{2}$ Substituting into

$x + y = -1$ :

$\frac{3}{2} + y = -1 \quad \Rightarrow \quad y = -\frac{5}{2}$ Now,

$\vec{c} = \frac{3}{2} \hat{i} - \frac{5}{2} \hat{j} - \hat{k}$ . To find

$|\vec{c}|^2$ , we compute:

$|\vec{c}|^2 = \left( \frac{3}{2} \right)^2 + \left( -\frac{5}{2} \right)^2 + (-1)^2 = \frac{9}{4} + \frac{25}{4} + 1$

$|\vec{c}|^2 = \frac{9 + 25 + 4}{4} = \frac{38}{4} = 9.5$
Final Answer:

$\boxed{9.5}$

Qus : 15

$\vec{a}$ ,

$\vec{b}$ ,

$\vec{c}$ and

$\vec{d}$ are the unit vectors such that

$(\vec{a} \times \vec{b}).(\vec{c} \times \vec{d})=1$ and

$(\vec{a}.\vec{c})=\frac{1}{2}$ , then

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Solution

Qus : 16

Let A ={1,2,3} and consider the relation R= {(1,1), (2,2), (3,3), (1,2), (2,3), (1,3)} then R is:

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Solution

Qus : 17

A spring is being moved up and down. An object is attached to the end of the spring that undergoes a vertical displacement. The displacement is given by the equation

$y = 3.50 sint + 1.20 sin2t$ . Find the first two values of t (in seconds) for which y =0.

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Solution

Qus : 18

A ball is thrown off the edge of a building at an angle of 60° and with an initial velocity of 5 meters per second. The equation that represents the horizontal distance of the ball x is

$x={{\nu}}_0(\cos \theta)t$ , where

${{\nu}}_0$ is the initial velocity.

$\theta$ is the angle at which it is thrown and

$t$ is the time in seconds. About how far will the ball travel in 10 seconds?

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Solution

Qus : 19

Let

$n$ be a positive integer and

$R=\{(a,b) \in Z\times Z\, |\, a-b\, =nm\, for\, \, some\, \, m\ne0\in Z\}$

Then R is:

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Solution

Qus : 20

The a, b, c and d are in GP and are in ascending order such that a+d = 112 and b+c 48. If the GP is continued with a as the first term, then the sum of the first six terms is:

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Solution

Qus : 21

Given below are two statements:

Statement I : If

$A\subset B$ then B can be expressed as

$B=A\cup(\overline{A}\cap B)$ and P(A) > P(B).

Statement II : If A and B are independent events, then (

$A$ and

$\overline{B}$ ), (

$\overline{A}$ and

$B$ ) and (

$\overline{A}$ and

$\overline{B}$ ) are also independent

In the light of the above statements, choose the most appropriate answer from the options given below:

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Solution

Qus : 22

$\vec{a}$ ,

$\vec{b}$ and

$\vec{c}$ are unit vectors, then

$|\vec{a}-\vec{b}|^2+|\vec{b}-\vec{c}|^2+|\vec{c}-\vec{a}|^2$ does not exceed

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Solution

Qus : 23

$\vec{a}=\hat{i}+\hat{j}+\hat{k}$ ,

$\vec{a}.\vec{b}=1$ and

$\vec{a} \times \vec{b}=\hat{j}-\hat{k}$ , then

$\vec{b}$ is equal to

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Solution

Qus : 24

Consider the diagram given below and the following two statements:

Statement I: Events A and B can be expressed as:

$\begin{array}{ll}{A=(A\cap\overline{B})\cup Y} \\ {B=(A\cap B)\cup Z}\, \end{array}$

Statement II: Events A and B can be expressed as:

$A= X-Y$

$B=Y+Z$

In the light of the above statements, choose the most appropriate answer from the options given below:

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Solution

Qus : 25

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.

Assertion A : In a class of 40 students. 22 drink Sprite, 10 drink Sprite but not Pepsi. Then the number of students who drink both Sprite and Pepsi is 15.

Reason R: For any two finite sets A and B,

$n(A) = n(A - B) + n (A \cup B)$

In the light of the above statements, choose the most appropriate answer from the options given below:

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Solution

Qus : 26

Match the list

LIST 1	LIST 2
A. If 4th term of a G.P. is square of its second term, and its first term is 3, then common ratio is _______	I. 5
B. The first term of an AP is 5 and the last term is 45 and the sum of the terms is 400. The number of terms is_____	II. -5/2
C. The sum of three numbers which are in AP is 27 and sum of their squares is 293. Then the common difference is ______	III. 16
D. The fourth and 54th terms of an AP are, respectively, 64 and -61. The common difference is ______	IV. 3

choose the correct answer from the options given below:

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Solution

Qus : 27

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R

Assertion A : The system of equations x + y + z = 4, 2x - y + 2z = 5, x - 2y - z = 3 has unique solution.

Reason R: If A is 3 x 3 matrix and B is a 3 x 1 non-zero column matrix. then the equation AX = B has unique solution if A is non-singular.

In the light of the above statements, choose the most appropriate answer from the options given below:

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Solution

Qus : 28

There are 200 students in a school out which 120 students play football, 50 students play cricket and 30 students play both football and cricket. The number of students who play one game only is:

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Solution

Qus : 29

Which of the following are true:

(A) Ogive graph is used to measure the median of the collection of datas.

(B) Two events A and B are such that P(A) = 1/2 and P(B) = 7/12 and P(not A not B) = 1/4 then A and B are independent events.

(D) The number of two–digits even number formed from digits 1,2,3,4,5 is 10

Choose the correct answer from the options given below:

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Solution

Qus : 30

There are 15 points in a plane such that 5 points are collinear and no three of the remaining points are collinear then total number of straight lines formed are:

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Solution

Qus : 31

Match List I with List II

List - I (Domain)	List - II (Range)
A. $y=\frac{1}{2-\sin 3x}$	I. $\Bigg{(}1,\frac{7}{3}\Bigg{]}$
B. $y=\frac{{x}^2+x+2}{{x}^2+x+1},\, x\in R$	II. $\Bigg{[}\frac{\pi}{2},\pi\Bigg{)}\cup(\pi,\frac{3\pi}{2}\Bigg{]}$
C. $y=\sin x-\cos x$	III. $\Bigg{[}\frac{1}{3},1\Bigg{]}$
D. $y={\cot }^{-1}(-x)-{\tan }^{-1}x+{sec}^{-1}x$	IV. $[-\sqrt[]{2},\sqrt[]{2}]$

Choose the correct answer from the options given below:

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Solution

Qus : 32

An equilateral triangle is inscribed in a parabola

$y^2=8x$ whose one vertix is at the vertex of the parabola then the length of the side of the triangle is:

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Solution

Qus : 33

$x_1, x_2, x_3$ as well as

$y_1, y_2, y_3$ are in G.P. with the same common ratio, then the points

$(x_1, y_1)$ ,

$(x_2, y_2)$ and

$(x_3, y_3)$

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Solution

Qus : 34

Match List – I with List – II

List - I	List - II
(A) Eccentricity of the conic $x^2-4x+4y+4y^2=12$	(I) 10/3
(B) Latus rectum of conic $5x^2+9y^2=45$	(II) 1
(C) The straight line x+y=a touches the curve $y=x-x^2$ then value of a	(III) 2
(D) Eccentricity of conic $3x^2-y^2=4$	(IV) $\sqrt{3}/2$

Choose the correct answer from the options given below:

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Solution

Qus : 35

The area of the region bounded by the curve

$y^2=4x$ and

$x^2=4y$ is

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Solution

Qus : 36

The value of x satisfies the inequality

$|x-1|+|x-2|\geq4$ if

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Solution

Qus : 37

If the parametric equation of a curve is given by

$x=e^t cost$ and

$y=e^t sint$ then the tangent to the curve at the point

$t=\frac{\pi}{4}$ makes the angle with the axis of x is

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Solution

Given parametric equations:

$x = e^t \cos t,\quad y = e^t \sin t$ To find the angle of the tangent at

$t = \frac{\pi}{4}$ , compute the slope:

$\frac{dy}{dx} = \frac{\frac{dy}{dt}}{\frac{dx}{dt}} = \frac{e^t(\sin t + \cos t)}{e^t(\cos t - \sin t)} = \frac{\sin t + \cos t}{\cos t - \sin t}$ At

$t = \frac{\pi}{4}$ ,

$\sin\left(\frac{\pi}{4}\right) = \cos\left(\frac{\pi}{4}\right) = \frac{\sqrt{2}}{2}$ So,

$\frac{dy}{dx} = \frac{\frac{\sqrt{2}}{2} + \frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2} - \frac{\sqrt{2}}{2}} = \frac{\sqrt{2}}{0}$ The slope is undefined, which means the tangent is vertical.

Final Answer: The angle with the x-axis is

$\boxed{90^\circ}$

Qus : 38

$f(a+b-x)=f(x)$ then

$\int ^b_axf(x)dx$ is equal to

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Solution

Qus : 39

${x}^2+\frac{1}{{x}^2}=2$ then the value of

${x}^{256}+\frac{1}{{x}^{256}}$

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Solution

Qus : 40

Consider the system of linear equations as 2x + 2y + z = 1, 4x + ky + 2z = 2 and kx + 4y + z = 1 then choosethe correct statement(s) from blow

(A) The system of equation has a unique solution if k≠4 and k≠2

(B) The system of equations is inconsistent for every real number k

(D) The system of equations have infinite number of solutions if k = 2

Choose the correct answer from the options given below

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Solution

Qus : 41

The function

$f(x)=[x]^n$ , integer n>=2 (where [y] is the greatest integer less than or equal to y), is discontinuous at all point of

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Solution

Qus : 42

If the roots of the equation

$x^2+4x+a^2-3a$ are real then the value of a (is / are)

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Solution

Qus : 43

Match List – I with List – II

List - I	List - II
(A) $\int ^{\pi/2}_0\frac{{\sin }^4x}{{\sin }^4x+{\cos }^4x}dx$	(I) 0
(B) $\int ^{\pi/3}_{\pi/6}\frac{1}{1+\sqrt[]{\tan x}}dx$	(II) 0
(C) $\int ^1_0x{e}^xdx$	(III) $\frac{\pi}{12}$
(D) $\int ^1_{-1}{x}^{109}{\cos }^{88}xdx$	(IV) $\frac{\pi}{4}$

Choose the correct answer from the options given below:

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Solution

Qus : 44

Which of the following statement sare TRUE?

(A) A equation

$ax^2+bx+c=0$ has real and distinct roots if

$b^2-4ac>=0$ and

$a\ne0$ .

(B) The unit digit in

$49^{18}$ is 1.

(D) The line bx – ay = 0 meet the hyperbola

$\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$

Choose the correct answer from the options given below:

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Solution

Qus : 45

The line passes through a point (2, 3) such that sum of its intercepts on the axes is 12 then equation of line/s is/are given by

(A) 3x+y=9

(B) x+3y=9

(D) 5x+7y=35

Choose the correct answer from the options given below:

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Solution

Qus : 46

$\lim _{{x}\rightarrow0}\frac{\sqrt[]{1-\cos 2x}}{x}$

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Solution

Qus : 47

If permutaiton of the letters of the word ‘AGAIN’ are arranged in the order as in a dictionary then 49th word i

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Solution

Qus : 48

The mean of 5 data is 5.2 and their variance is 27.296. If there of the data are 1, 3 and 6 then other two data are

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Solution

Qus : 49

If the vertices of a triangle are (1, 2), (2, 5) and (4, 3) then the area of the triangle is:

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Solution

Qus : 50

Which of the following statements are TRUE?

(A) If each element in a row is a constant multiplier of corresponding element of another row of a determinant, then the value of the determinant is always non-zero.

(B) If each element on one side of the principal diagonal of a determinant is zero, then the value of the determinants the product of the diagonal elements.

(D) If A is non-singular matrix of order three, then

$adj A=|A|^2$

Choose the correct answer from the options given below:

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Solution

Qus : 51

A function f(x) is defined as

$f(x)=\begin{cases}{\frac{1-\cos 4x}{{x}^2}} & {;x{\lt}0} \\ {a} & {;x=0} \\ {\frac{\sqrt[]{x}}{\sqrt[]{(16+\sqrt[]{x})-4}}} & {;x{\gt}0}\end{cases}$ if the function f(x) is continuous at x = 0, then the value of a is:

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Solution

Qus : 52

The equation of a circle that passes through the points (3, 0) and (0, –2) and its lies on a line 2x + 3y = 3 then equation of the cicle is given by:

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Solution

Qus : 53

Consider the diagram given below and the following two statements:

Statement I: Regions X, Y and Z can be expressed as

$A\cap\overline{B},\, A\cap B$ and

$\, \overline{A}\cap B$ respectively

Statement II: P(Y) = P (A) - P (X) = P (B) - P (Z)

In the light of the above statements, choose the correct answer from the options given below:

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Solution

Qus : 54

Let

$\alpha >2$ is an integer. If there are only 10 positive integers satisfying the inequality

$(x-\alpha)(x-2\alpha)(x-\alpha^2)<0$ then the value/s of

$\alpha$ is

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Solution

Qus : 55

$\int \frac{({x}^5-x{)}^{1/5}}{{x}^6}dx=$
(where C is an arbitrary constant)

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Solution

Qus : 56

In a class there are 400 students, the following table shows the number of students studying one or more of the subjects:

Subject	Number of Students
Mathematics	250
Physics	150
Chemistry	100
Mathematics and Physics	100
Mathematics and Chemistry	60
Physics and Chemistry	40
Mathematics, Physics and chemistry	30

A. The number of students who study only Mathematics is 100.

B. The number of students who study only Physics is 40.

C. The number of students who study only Chemistry is 40.

D. The number of students who do not study Mathematics, Physics and Chemistry is 70.

Choose the correct answer from the options given below:

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Solution

Qus : 57

The arithmetic means of two observations is 125 and their geometric mean is 60. Find the harmonic mean of the two observations.

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Solution

Qus : 58

The arithmetic mean and standard deviation of series of 20 items were calculated by a student as 20 cm and 5 cm respectively. But while calculating them an item 15 was misread as 30. Find the correct standard deviation.

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Solution

Qus : 59

Given the marks of 25 students in the class as

$\{m_1,m_2,m_3,..m_{25}\}$ . Marks lie in the range of [1-100] and

$\overline{m}$ is the mean. Which of the following quantity has the value zero?

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Solution

Qus : 60

A equation of conic is

$ax^2+2hxy+by^2+2gx+2fy+c=0$ , where

$a, b, c, f, g$ and

$h$ are constants. Then which of the following statement are true?

(A) The given conic is circle if a = 0 and b = 0.

(B) The given conic is circle if

$a=b\ne0$ and h = 0.

$a=b=\ne0$ and

$h\ne0$ .

(D) The given conic represents a pair of real and distinct straight lines if f = g = c = 0 and

$h^2-ab>0$ .

Choose the correct answer from the options given below:

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Solution

Qus : 61

Match List – I with List – II

List - I	List - II $f(0)$
(A) $f(x)=\frac{log(1+4x)}{x}$	(I) $\frac{1}{4}$
(B) $f(x)=\frac{log(4+x)-log4}{x}$	(II) 1
(C) $f(x)=\frac{x}{sinx}$	(III) 4
(D) $\frac{1-cos^3x}{x sin2x}$	(IV) $\frac{3}{4}$

Choose the correct answer from the options given below:

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Solution

Qus : 62

The terms

$1,\, \log _y(x),\, \log _z(y)\, and\, 15\log _x(z)$ are in AP.

Based on this information answer the following questions.

The Common difference of AP is

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Solution

Qus : 63

The terms

$1,\, \log _y(x),\, \log _z(y)\, and\, 15\log _x(z)$ are in AP.

Based on this information answer the following questions.

The value of xy is:

1
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Solution

Qus : 64

The terms

$1,\, \log _y(x),\, \log _z(y)\, and\, 15\log _x(z)$ are in AP.

Based on this information answer the following questions.

yz is equal to :

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Solution

Qus : 65

Which of the following statements are NOT TRUE?

(A) If A and B are symmetric matrices, then AB – BA is a skew symmetric matrix.

(B) Multiplying a determinant by k means multiply elements of one column by k.

$A^2-A+I=0$ , then

$A^-1$ is equal to A + I.

(D) If A and B are invertible matrices of same order, then

$(A+B)^{-1}=B^{-1}+A^{-1}$ .

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Solution

Qus : 66

Consider n events

${{E}}_1,{{E}}_2\ldots{{E}}_n$ with respective probabilities

${{p}}_1,{{p}}_2\ldots{{p}}_n$ . If

$P\Bigg{(}{{E}}_1,{{E}}_2\ldots{{E}}_n\Bigg{)}=\prod ^n_{i=1}{{p}}_i$ , then

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Solution

Qus : 67

Given a set of events

${{E}}_1,{{E}}_2\ldots{{E}}_n$ defined on the sample space S such that :

(i)

$\forall\, i\, and\, j,\, i\ne j,\, {{E}}_i\cap{{E}}_j=\phi$

(ii)

$\begin{matrix}\overset{{n}}{\bigcup } \\ ^{i=1}\end{matrix}{{E}}_i=S$

(iii)

$P({{E}}_i){\gt}0,\, \forall$

Then the events are

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Solution

Qus : 68

4 Indians, 3 Americans and 2 Britishers are to be arranged around a round table. Answer the following questions.

The number of ways arranging them is :

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Solution

Qus : 69

4 Indians, 3 Americans and 2 Britishers are to be arranged around a round table. Answer the following questions.

The number of ways arranging them so that the two Britishers should never come together is:

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Solution

Qus : 70

4 Indians, 3 Americans and 2 Britishers are to be arranged around a round table. Answer the following questions.

The number of ways of arranging them so that the three Americans should sit together is:

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Solution

Short Solution:

Total people = 4 Indians + 3 Americans + 2 Britishers = 9
Since arrangement is around a circular table, we fix one position ⇒ remaining to arrange: 8 positions

Group the 3 Americans together as a single unit ⇒ total units = 4 Indians + 1 American group + 2 Britishers = 7 units
Circular arrangement of 7 units =

$(7 - 1)! = 6!$

Internal arrangements of 3 Americans =

$3!$

Total arrangements =

$6! \times 3! = 720 \times 6 = \boxed{4320}$

Qus : 71

Given three identical boxes B₁ B₂ and B₃ each containing two balls. B₁ containstwo golden balls. B₂ contains two silver balls and B₃ contains one silver and onegolden ball. Conditional probabilities that the golden ball is drawn from B₁, B₂, B₃are ____,______,______ respectively

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Solution

Qus : 72

Math List I with List II:

LIST I	LIST 2
A. In a GP, the third term is 24 and 6th term is 192. The common ratio is _____	I. 78
B. Let S_n denotes the sum of first n terms of an AP. If S_2n=3S_n, then S_3n/S_n equals to _______	II. 6
C. The sum of 3 terms of a GP is 13/12 and their product is -1. The first term is ______	III. -1
D. The least value of n for which the sum 3+6+9+...+n is greater than 1000 is	IV. 2

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Solution

Qus : 73

Math List I with List II :

$\omega \ne1$ is a cube root of unity.

LIST I	LIST II
A. The value of $\frac{1}{9}(1-\omega)(1-{\omega}^2)(1-{\omega}^4)(1-{\omega}^8)\,$ is	I. 0
B. $\omega{(1+\omega-{\omega}^2)}^7$ ________ is equal to	II. 1
C. The least positive integer n such that ${(1+{\omega}^2)}^n={(1+{\omega}^4)}^n$ is	III. -128
D. $(1+\omega+{\omega}^2)$ is equal to	IV. 3

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Solution

Qus : 74

Math List I with List II :

$\omega \ne1$ is a cube root of unity.

LIST I	LIST II
A. $\log _4(\log _3(81))=$	I. 0
B. ${3}^{4\log _9(7)}={7}^k$ , then k =	II. 3
C. ${2}^{\log _3(5)}-{5}^{\log _3(2)}=$	III. 1
D. $\log _2[\log _2(256)]=$	IV. 2

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Solution

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