CUET (PG) Mathematics Medium Questions

Which of the following statements are false about the region bounded by $|x-y|\le 2$ and $|x+y|\le 2$

A. rhombus of area $8\sqrt{2}$ sq. units.
B. square of area 16 sq. units.
C. square of side length $2\sqrt{2}$ units.
D. rhombus of side length 2 units.

The circumcentre of the triangle whose sides are $3x-y+3=0$, $3x+4y+3=0$, and $x+3y+11=0$ is

Match the LIST-I with LIST-II

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

Assertion A: The value of the integral ${\int }_{\pi /6}^{\pi /3}\frac{dx}{1+\sqrt{\tan x}}$ is equal to $\frac{\pi }{6}$.

Reason R: ${\int }_a^{b}f(x)dx={\int }_a^{b}f(a+b-x)dx$

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

Let $S=\{x\in \mathbb{R}:x\ge 0\text{ and }2|\sqrt{x}-3|+\sqrt{x}(\sqrt{x}-6)+6=0\}$. Then which of the following statements are false about S?

A. S is an empty set.

B. S contains exactly one element.

C. S contains exactly two elements.

D. S contains exactly four elements.

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The value of the expression $\left(\genfrac{}{}{0ex}{}{47}{4}\right)+{\sum }_{j=1}^5\left(\genfrac{}{}{0ex}{}{52-j}{3}\right)$ is

Match the LIST-I with LIST-II

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For any natural number $a$, define $aN=\{ax:x\in N\}$.

If $b,c,d\in N$ such that $bN\cap cN=dN$, then what is d?

The area of the region $\{(x,y):x^2+y^2\le 1\le x+y\}$ is given by

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

Let A be 2 $\times$ 2 matrix with real entries. Let I be the 2 $\times$ 2 identity matrix. Denote by $tr(A)$, the sum of diagonal entries of A. Assume that $A^2=I$.

Assertion A: If $A\ne I$ and $A\ne -I$, then $\det (A)=-1$

Reason R: If $A\ne I$ and $A\ne -I$, then $tr(A)\ne 0$

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

Arrange the following ellipses in increasing order the length of their latus - rectum:

A. $4x^2+9y^2=1$ B. $5x^2+4y^2=1$ C. $4x^2+3y^2=1$ D. $25x^2+16y^2=1600$

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If [.] denotes the greatest integer function, then arrange the following values in increasing order.

How many even numbers of 4-digit numbers that can be formed using the digits 1, 2, 3, 4, 5 if no digit is repeated?

Match the LIST-I with LIST-II

LIST-I

A. ${\lim }_{x\to 2}\frac{x^5-2^5}{x-2}$

B. ${\lim }_{x\to 0}\frac{1-\cos 2x}{x^2}$

C. ${\lim }_{x\to 0}\frac{1-\cos 2x}{x}$

D. ${\lim }_{x\to 0}\frac{1-\cos x}{x^2}$

LIST-II

I. $\frac{1}{2}$

II. $80$

III. $2$

IV. $0$

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The quadratic curve $y=f(x)$ if it touches the line $y=x$ at the point $x=1$ and passes through the point $(-1,0)$ is given by

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

Assertion A: The number of ways of distributing 11 identical balls in 5 distinct boxes such that no box is empty is $\left(\genfrac{}{}{0ex}{}{10}{4}\right)$.

Reason R: The number of ways of choosing any 4 places from 10 different places is $\left(\genfrac{}{}{0ex}{}{10}{4}\right)$.

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

The LCM of the two numbers is 280 and their ratio is 7:8. The two numbers are:

A. 70
B. 80
C. 35
D. 40

Choose the correct answer from the options given below:

If a, b, c are all positive and are $p^{th}$, $q^{th}$ and $r^{th}$ terms of a G.P, then value of

$\left|\begin{array}{ccc}\log a& p& 1\\ \log b& q& 1\\ \log c& r& 1\end{array}\right|$

Let n be an odd natural number such that the variance of $1,2,3,4,\dots ,n$ is 14. Then n is equal to

Which of the following statements are true about the two circles whose equations are given below:

$x^2+y^2-10x-10y-41=0$, and

$x^2+y^2-16x-10y+80=0$

A. Distance between two centres is the average of radii of both the circles.
B. Both circle's centres lie inside region of one another.
C. Both circles pass through the centre of each other.
D. Circles have two intersection points.

Choose the correct answer from the options given below: