List of top Questions asked in CUET (UG)

The coordinates of the foot of the perpendicular drawn from origin to the plane \(2x - 3y + 4z - 6 = 0\) is :

If \(\frac{x+y}{x-y}+\frac{x-y}{x+y}=\frac{10}{3}\),then \(\frac xy=\)

\((6:30+19:50), \)in 24 hours clock is :

The mean of Binomial distribution \(B(4,\frac13) \) is : 

If the planes \(\overrightarrow{r}.(2\hat{i}-\lambda\hat{j}+3\hat{k})=0\) and \(\overrightarrow{r}.(\lambda\hat{i}+5\hat{j}-\hat{k})=5\) are perpendicular to each other ,then value \(\lambda^2+\lambda \) is :

In a box containing 100 bulbs, 10 are defective. The probability that out of a sample of 5 bulbs none is defective, is :

The lines \(\frac{x-2}{1}=\frac{y-3}{1}=\frac{z-4}{-K} \) and \(\frac{x-1}{K}=\frac{y-4}{2}=\frac{z-5}{1} \) are coplanar if :

Corners points of the feasible region for an LPP are \((1, 1)(2, 0) (3, 1)(\frac32,4)\) and \((0,5)\).Let \(z = px + 4y\),  be the objective function. If maximum of z occurs at \((\frac32,4)\) and\((3,1)\),then the value of p is : 
 

The value of \(sin^{-1}\frac{12}{13} +cos^{-1}\frac45+tan^{-1}\frac{63}{16}\) is :

Anita and Bikram are two students. Their chances of solving a problem correctly are \(\frac13\) and \(\frac14\) respectively. If their probability of making a common error is  \(\frac{1}{20}\) and they both obtain same answer then the probability that their answer is correct, is :

Objective function \(z=30x-30y \) is subject to which combination of constraints, with feasible solution shown in the figure.

(A)\(x \geq 0, \quad y \geq 0, \quad x \leq 15\)
(B)\(y \leq 20, \quad x + y \leq 30\)
(C)\(x + y \leq 30, \quad x + y \leq 15, \quad 2x - y \leq 5\)
(D)\(2x + y \leq 30, \quad x + y \leq 15, \quad x > 15\)
(E)\(3x + y \leq 30, \quad x + 3y \leq 15, \quad y \geq 20\)
Choose the correct answer from the options given below:
 

The ratio of areas under the curves \(y=sinx \) and \(y=sin2x\) ,from \(x=0\) to  \( x=\frac{\pi}{3}\) is

Solution of a differential equation  \((1+ y2)dx=(\tan^{-1}y - x)dy\) is :

If \(\int e^x(tanx+1)secxdx=e^xf(x)+C,\) then \(f(x)\) is:
(A) \(e^X\)
(B) \(tanx\)
(C)\(secx\)
(D) \(secx \ tanx\)
choose the correct answer from the options given below

 

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

A vector \(\overrightarrow{r}\) is inclined at equal angles to the three axes. If the magnitude of \(\overrightarrow{r}\) is \(3\sqrt3\) units, then the value of \(\overrightarrow{r}\) is:

The number of solutions of the equation \(xydx— (x2-y2)dy=0\) with \( y(2)=3\) is :

which is the true of the following ?
(A)Any vector \(\overrightarrow{r}\) in space can be written as \((\overrightarrow{r}.\hat{i})\hat{i}+(\overrightarrow{r}.\hat{j})\hat{j}+(\overrightarrow{r}.\hat{k})\hat{k}\) 
(B)If  \(\overrightarrow{a}\)  is perpendicular to  \(\overrightarrow{b}\)\(|\overrightarrow{a}+\overrightarrow{b}|^2=|\overrightarrow{a}|^2+|\overrightarrow{b}|^2\) 
 
(C)If \(|\overrightarrow{a}|=2,|\overrightarrow{b}|=1 \) and \(\overrightarrow{a}.\overrightarrow{b}=1 \) ,the value of \((3\overrightarrow{a}-5\overrightarrow{b}).(2\overrightarrow{a}+7\overrightarrow{b})\) ia 1
(D) \(\overrightarrow{a}=5\hat{i}-\hat{j}-3\hat{k}\) and \(\overrightarrow{b}=\hat{i}+3\hat{j}-5\hat{k}\), is the angle between \(\overrightarrow{a}+\overrightarrow{b}\) and \(\overrightarrow{a}-\overrightarrow{b}\) is \(60\degree\)
Choose the correct answer from the options given below:
 

The value of C in Rolles's theorem for the function \(f(x)=e^xsinx,x\epsilon[0,\pi]\),is :

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:

The function \(f(x)=sinx+cosx,0\leq x\leq 2\pi \) is :

The tangent to the curve \(x=cost(3-2cos^2t),y=sint(3-2sin^2t)\) at  \(t=\frac{\pi}{4}\),makes with the \(x-axis\) an angle:

The value of det\((A^2-2A)\),If \(A=\begin{pmatrix}      1 & 3  \\[0.3em]    2  &1  \end{pmatrix}\),is