List of top Questions asked in CUET (UG)

The general solution of differential equation \(\frac{dy}{dx} - xy = e^{\frac{x^2}{2}}\)

Match List I with List II

List I	List II
\(A.\ [1 + (\frac{dy}{dx})^2] = \frac{d^2y}{dx^2}\)	I. order 2, degree 3
\(B. \ (\frac{d^3y}{dx^2})^2 - 3\frac{d^2y}{dx^2} + 2(\frac{dy}{dx})^4 = y^4\)	II. order 2, degree 1
\(C. \ (\frac{dy}{dx})^2 + (\frac{d^2y}{dx^2})^3 = 0\)	III. order 1, degree 2
\(D.\ (\frac{dy}{dx})^2 + 6y^3 = 0\)	IV. order 3, degree 2

Choose the correct answer from the options given below:

The area bounded by x = 1, x = 2, xy = 1 and x-axis is:

The value of the integral \(\int e^x (logx + \frac{1}{x})dx\) is:

The interval on which the function \(f(x)=2x^3 +12x^2 +18x-7\) is decreasing, is:

The points on the curve \(\frac{x^2}{9} + \frac{y^2}{16} = 1\) at which the tangents are parallel to x-axis:

If \(e^y(x+2)=10\), then \(\frac{d^2y}{dx^2}\) is equal to:

If, \(f(x) = \begin{bmatrix}0 & x-a & x-b \\[0.3em]x+a&o & x-c \\[0.3em]x+b & x+c & 0\\[0.3em] \end{bmatrix}\), then \(f(0)\) is:

If, A is a square matrix of order 3 and |A| = -2 then. \(|-2 \ A^{-1}|\) is:

A. \(\begin{bmatrix}1& 2& 3   \\[0.3em]2 & 4 & 5   \\[0.3em]3 & 5&6   \\[0.3em] \end{bmatrix}\) is a Symmetric matrix. 
B. \(\begin{bmatrix}0 &0 &0   \\[0.3em]0& 0&0   \\[0.3em] \end{bmatrix}\) is a Null matrix.
C. \(\begin{bmatrix}1& 0& 0   \\[0.3em]0 & 2 & 0\\[0.3em]0 & 0&3\\[0.3em] \end{bmatrix}\) is an Identity matrix.
D. \(\begin{bmatrix}0& 1&2   \\[0.3em]-1 & 0 & 3   \\[0.3em]-2 & 3&0\\[0.3em] \end{bmatrix}\) is a Skew symmetric matrix.
E. \(\begin{bmatrix}\sqrt{3} &0& 0\\[0.3em]0 & \sqrt{3} & 0   \\[0.3em]0 & 0&\sqrt{3}   \\[0.3em] \end{bmatrix}\) is a Scalar matrix
Choose the correct answer from the options given below:

If, A is a square matrix of order \(3 \times 3\) such that \(A^2 = A\) and I is the unit matrix of order \(3 \times 3\), then the value of \((I-A)^3+A^2+I\) is:

A random variable X has the following probability distribution

then value of E(X) is:

Name the famous European painter, who was deeply inspired by the Mughal court paintings.

The value of b for which the function f(x) = sinx - bx + C, where b and e are constants is decreasing for \(x \in R\) is given by

The radius of a spherical ball is increasing at the rate of 1 m/sec. At the radius equal to 3m, the volume of the ball is increasing at the rate given by:

The absolute maximum value of the function f(x)=sinx + cosx, x \(\in\)[0, \(\pi\)] is:

\(\int \frac{cos x - sin x}{1 + sin2x} dx\) is equal to:

The value of \(\int_0^{\frac{\pi}{2}} log (\frac{5 + 4 sinx}{5 + 4 cosx})dx\) is:

The area of the region enclosed between the parabolas \(y^2 = x + 1\) and \(y^2 = x + 1\) is:

The area of the region bounded by the curves \(x^2=4y\), the line x = 3 and x axis is:

The solution of the differential equation cosx siny dx + sinx cosy dy = 0 is:

For any two non zero vectors \(\vec{a}\) and \(\vec{b}\)
A. If \(|\vec{a}| = |\vec{b}|\)then \(\vec{a} = \vec{b}\)
B. If \(\vec{a} = \vec{b}\) then \(|\vec{a}| = |\vec{b}|\)
C. \(\vec{a} . \vec{b}=\vec{b} . \vec{a}\)
D. \(\vec{a} \times \vec{b}=\vec{b} \times \vec{a}\)
E. area of the parallelogram = \(\frac{1}{2} |\vec{a} \times \vec{b}|\). where \(\vec{a}\) and \(\vec{b}\) represent resent the diagonals of the parallelogram.
Choose the correct answer from the options given below:

The value of \(\lambda\), for which the projection of \(\vec{a} = \lambda \hat{i} + \hat{j} +4 \hat{k}\) on \(\vec{b} =2\hat{i} +6 \hat{j} +3\hat{k}\) is 4 units

The straight line \( \frac{x+2}{3} = \frac{z-3}{ -2}, y-2 \) is

If the lines \(\frac{x-1}{-3} = \frac{y-2}{2 \lambda} = \frac{z-3}{2}\) and \(\frac{x-1}{3 \lambda} = \frac{y-1}{2} = \frac{z-6}{-5}\) are perpendicular. Then the value of \(\lambda\) is: