List of top Questions asked in CUET (PG)

When a coin is tossed twice, which of the following is the probability of getting both tails?

In a small factory one supervisor and four labourers work. The labourers draw salary of \(\rupee 5000\) per month each while supervisor gets \(\rupee 15000\) per month. Which of the following are mean and mode of the salaries?

Match List-I with List-II. A. Domain of \(f(x)=\dfrac{1{\sqrt{x^2-1}}\),
B. Range of \(f(x)=\dfrac{1}{\sqrt{x^2-1}}\),
C. Domain of \(f(x)=\sqrt{x-2}\),
D. Range of \(f(x)=\sqrt{x-2}\).}

Which of the following statements are true? A. \(2^{4n}-1\) is divisible by \(15\).
B. \(5,12\) and \(13\) is Pythagorean triplet.
C. \(n^7-n\) is divisible by \(42\).
D. \(1^2+2^2+3^2+\cdots+n^2=\left[\dfrac{n(n+1){2}\right]^2\).}

Which of the following statements are true? A. For any two vectors \(\vec{a}\) and \(\vec{b}\), \(|\vec{a}+\vec{b}|\leq |\vec{a}|+|\vec{b}|\).
B. Scalar product of two non-zero vectors might be zero.
C. For any two vectors \(\vec{a}\) and \(\vec{b}\), \(|\vec{a}\cdot \vec{b}|\leq |\vec{a}||\vec{b}|\).
D. Cross product of two vectors is not a vector.
E. Dot product of two vectors is a scalar.

Which of the following is/are solution of the LPP? \[ \text{Min }Z=12x+9y \] Subject to \[ x+2y\leq 40,\quad 3x+y\geq 30,\quad 4x+3y\geq 60,\quad x,y\geq 0 \] A. \((15,0)\),
B. \((40,0)\),
C. \((4,18)\),
D. \((6,12)\),
E. \((10.5,6)\).

The function \(f(x)=|x-2|+|x|+|x+2|\) is not differentiable at which points?

Arrange the following in ascending order based on their values:
A. \(\displaystyle \int_0^{\frac{\pi}{2}}\frac{1}{1+\sin x}\,dx\),
B. \(\displaystyle \int_1^2 x^2\,dx\),
C. \(\displaystyle \int_0^{\frac{\pi}{2}}\sin x\,dx\),
D. \(\displaystyle \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\sin^3x\,dx\).

If one of the roots of equation \(ax^4+bx^3+cx^2+dx+e=0\) is \(\sqrt{2}+\sqrt{-3}\), then arrange the following in non-decreasing order \((a\neq 0)\). A. \(a\),
B. \(b\),
C. \(c\),
D. \(d\),
E. \(e\).

Arrange the following in increasing order as per the last digit:
A. \(2^{444}\),
B. \(17^{10}\),
C. \(13^{10}+2\),
D. \(1^1+2^2+3^3+\cdots+100^{100}\),
E. \(11!+2\).

Given below are two statements:

Assertion (A):
A function \(f:N\to N\), defined as \[ f(x)= \begin{cases} x+1, & \text{if } x \text{ is odd}\\ x-1, & \text{if } x \text{ is even}\\ \end{cases} \] is not surjective.
Reason (R):
A function \(f:X\to Y\) is said to be surjective if every element of \(Y\) is the image of some element of \(X\) under \(f\), i.e., for every \(y\in Y\), there exists \(x\in X\), such that \(f(x)=y\).

Which of the following is equation of hyperbola with vertices \((\pm 2,0)\) and foci \((\pm 3,0)\)?

Given below are two statements:

Assertion (A):
The function \(f(x)=x|x|\) is continuous at \(x=0\) and derivative of \(f\) also exists at \(x=0\).
Reason (R):
It is necessary and sufficient that every continuous function is derivable at any point.

Given below are two statements:

Assertion (A):
The angle between the pair of lines \[ \frac{x+3}{3}=\frac{y-1}{5}=\frac{z+3}{4} \quad \text{and} \quad \frac{x+1}{1}=\frac{y-4}{1}=\frac{z-5}{2} \] is \(\cos^{-1}\left(\frac{8\sqrt{3}}{15}\right)\).
Reason (R):
The angle between the two lines is \[ \cos\theta=\frac{a_1a_2+b_1b_2+c_1c_2}{\sqrt{a_1^2+b_1^2+c_1^2}\sqrt{a_2^2+b_2^2+c_2^2}}. \]

If each side of a rectangle is increased by \(10\%\), then which of the following will represent the increased area of a rectangle?

On adding any three consecutive even numbers, the summation result would always be divisible by which of the following?

The normal at the point \((1,1)\) on the curve \(2y+x^2=3\) is?

If \[ x=e^{\tan^{-1}\left(\frac{y-x^2}{x}\right)} \] then \(\dfrac{dy}{dx}=?\)

Evaluate the determinant:
\[ \left| \begin{array}{ccc} b+c & a-b & a\\ c+a & b-c & b\\ a+b & c-a & c\\ \end{array} \right| \]

If \(a,b,c\) are in arithmetic progression, then find the value of \[ \left| \begin{array}{ccc} x+2 & x+3 & x+2a\\ x+3 & x+4 & x+2b\\ x+4 & x+5 & x+2c\\ \end{array} \right|. \]

If \(y=e^{m\sin^{-1}x}\) and \(y_n\) indicates \(n^{th}\) derivative of \(y\) with respect to \(x\), then which of the following relation is true?

Which of the following is derivative of \(\sqrt{a^{\sqrt{x}}}\) with respect to \(x\)?

Which of the following represents the slope of the line passing through points (3, −2) and (3, 4)?

In a randomized block design with one factor having 5 levels and another factor having 5 levels, the degree of freedom for the error sum of squares are equal to

To test whether two different skin creams A and B have different effects on the human body, $n$ persons were enrolled in a clinical trial. Then cream A was applied to one arm and cream B to the other arm of each of the $n$ randomly selected persons. What type of design is this?