List of top Questions asked in CUET (UG)

for which value of \(\lambda\) is the function ,\(f(x) = \begin{cases} \lambda(x^2-2x) & \text{if } x \leq 0 \\ 4x+1& \text{if } x > 0 \end{cases}\) continuous at \(x=0 ?\)

The derivative \(\frac{\mathrm dy}{\mathrm d x}\) ,if \(x=a(\theta -sin\theta),y=a(1+cos\theta)\) is :

If \(y=sin^{-1}x \) and \((1-x^2)\frac{d^2y}{dx^2} -x \frac{dy}{dx}=K\),then value of K is:

If \(y=log[\frac{x^2}{e^2}]\) then value of \(\frac{d^2y}{dx^2}\) is:

The condition on a and b, such that for \(y = \frac{a}{x}-\frac{b}{x²}\), \(\frac{dy}{dx} =0\) at x=1 is:

The interval in which the function \(f(x) = 10-6x-2x²\) is decreasing is:

Area of the region bounded by the curve |x|+|y|=1 and x-axis is :

The value of the integral \(\int\limits_2^4 \frac{x}{x^2+1} dx\) is:

The sum of order and degree of the differential equation\[\frac{\{1+(\frac{dy}{dx})^2\}^\frac{5}{2}}{\frac{d^2y}{dx^2}}=p\]is:

The solution of the differential equation\(\frac{dy}{dx}= \frac{6}{x^2}; y(1) = 3\) is:

The mean of the number of heads in a simultaneous toss of three coins is :

For the LPP
Maximise z=x+y
subject to x-y≤-1, x+y≤2, x, y≥0, z has:

Choose the wrong statement from the following:

Let f: R→R defined by f(x)=2x³-7 for x∈R. Then:
(A) f is one-one function
(B) f is many to one function
(C) f is bijective function
(D) f is into function
Choose the correct answer from the options given below:

Match List I with List II

Choose the correct answer from the options given below:

Let \(tan^{-1}y=tan^{-1}x+tan^{-1}(\frac{2x}{1-x^2})\). Then y is:

The value of 2y-3x, if
\(2\begin {bmatrix}x &5\\ 7&y-3\end{bmatrix}+\begin{bmatrix}3&-4\\ 1&2\end{bmatrix}=\begin{bmatrix}7&6 \\15&14\end{bmatrix}\) is:

Match List - I with List II. If \(A = \begin{vmatrix}3&-2&3 \\2 &1 &-1 \\4 &-3 &2\end{vmatrix}\)

Choose the correct answer from the options given below:

The number of square matrices of order 2 using numbers 1 and -1 exactly once and the number 0 twice is:

Let \(\begin{vmatrix}3x&-7\\1&4\end{vmatrix}=\begin{vmatrix}3&2\\ 4&x\end{vmatrix}\), then value of x is:

The value of the determinant \(\begin{vmatrix}acosθ&bsinθ&0 \\-bsinθ&acosθ&0\\ 0&0&c\end{vmatrix}\) is:

The points of discontinuity of the function \(f\) defined by \(f(x) = \begin{cases} x+2 & x≤1 \\ x-2 &1<x<2\\ 0& x≥2\end{cases}\) are:

The dissolution of Partnership may take place due to:
A. Retirement of Partner
B. Death of Partner
C. Insolvency of Partner
D. Admission of New Partner
E. Completion of Venture, if partnership formed for that purpose
Choose the correct answer from the options given below:

Identify the statement which are not true for the natural ecosystem
(A) Grassland and desert are example of terrestrial ecosystem. 
(B) Oceans and rivers are man-made ecosystems. 
(C) Wetland and estuary are examples of aquatic ecosystem. 
(D) Crop fields and aquarium are natural ecosystems.
Choose the correct answer from the option given below

The greatest biodiversity on the earth is seen in