List of top Questions asked in CUET (UG)

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:

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

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

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

The ratio of areas under the curves \(y=sinx \) and \(y=sin2x\) ,from \(x=0\) to  \( x=\frac{\pi}{3}\) 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 value of C in Rolles's theorem for the function \(f(x)=e^xsinx,x\epsilon[0,\pi]\),is :

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

If cosy = xcos(a + y), then \(\frac{dy}{dx}\) =

The value of C which satisfies Rolle's Theorem for f(x) = sin⁴x + cos⁴x in \([0, \frac{π}{2}]\). Then C is:

Angle between tangents to the curve y=x²-5x+6 at the points (2, 0) and (3, 0) is:

The rate of change of the area of a circular disc with respect to its circumference when radius is 3 is:

The interval in which the \(f(x) = sinx-cosx, 0 ≤ x ≤ 2π\) is strictly decreasing is :

The value of \(\int_0^3 |2x-6|dx\) is:

The integral \(∫\frac{dx}{x^2(x^4+1)}^{\frac{3}{4}}\) equals_____.

The area of the shaded portion

is:

Area of the region bounded by \(y=-1, y=2, x=y^3 \space and \space x=0\) is:

The differential equation whose solution is Ax²+By²=1 where A and B are arbitrary constant is of:
(A) first order and first degree
(B) second order and first degree
(C) second order and second degree
(D) second order
Choose the correct answer from the options given below:

Integrating factor of the differential equation \((1-y²) \frac{dx}{dy} + xy = ay\) is:

Let \(\overrightarrow a = 4\hat i -\hat j + 3\hat k\) and \(\overrightarrow b = -2\hat i + \hat j-2\hat k\). Then
(A) \(\overrightarrow a\) is a unit vector
(B) \(\overrightarrow a\times \overrightarrow b=-\hat i + 2\hat j + 2\hat k\)
(C) \(\overrightarrow a\) and \(\overrightarrow b\) are parallel vectors
(D) \(\overrightarrow a\) and \(\overrightarrow b\)are neither parallel nor perpendicular vectors
Choose the correct answer from the options given below :

Let \(\overrightarrow a\) and \(\overrightarrow b\) be two unit vectors. If the vectors \(\overrightarrow c=5\overrightarrow a-4\overrightarrow b\) and \(\overrightarrow d = \overrightarrow a+2\overrightarrow b\) perpendicular to each other, then the angle between \(\overrightarrow a\) and \(\overrightarrow b\) is:

The equation of plane which cuts equal intercepts of unit length on the coordinate axes is:

If the straight lines \(x=1+s, y = -3-s, z=1+λs\) and \(x = \frac{t}{2},y=1+t, z=2-t\) with parameters s and t respectively, are coplanar, then \(λ\) is equal to:

Match List I with List II

Choose the correct answer from the options given below: