List of top Questions asked in CUET (PG)

If \(\vec{a},\vec{b},\vec{c}\) are non-coplanar unit vectors such that \(\vec{a}\times(\vec{b}\times \vec{c})=\frac{(\vec{b}+\vec{c})}{\sqrt2}\) then the angle between a and b is
The equation of the bisector of the acute angle between the lines 3x-4y+7=0 and 12x+5y-2=0
The tangent to the hyperbola x2-y2 = 3 are parallel to the straight line 2x + y +8=0 points are
Function f(x)=(x+1)cotx is continuous at x = 0, then the value of f(0) is
Given below are two statements: One is labelled as Assertion (A) and the other is labelled as Reason (R):
Assertion (A): Equation 5x-7y+z=11, 6x-8y-z=15 and 3x+2y-6z=7, then the system is consistent and has infinitely many solutions.
Reasons (R): If D=0 then the 3 linear equations is consistent and has infinitely many solutions if D1 = D2 = D3=0.
In the light of the above Statements, choose the correct answer from the options given below :
if \(\vec{a}\), \(\vec{b}\) and \(\vec{c}\) are three non-coplanar vectors, then \((\vec{a}+\vec{b}+\vec{c}) [(\vec{a}+\vec{b})\times(\vec{a}+\vec{c})]\) equal to
Find the sum of two consecutive numbers in which four times are first number is 12 more than the thrice of the second number
If α and β are the roots of a quadratic equation x2+αx + β=0 where β≠0, then what is the value of α + β?
The joint equation of the straight line x + y =1 and x-y = 4 is
A beam is supported at its ends by supporters which are 12 meters apart. Since the load is concentrated at its centre, there is a deflection of 3 cm at the centre and the deflected beam is in the shape of a parabola. How far from the centre is the deflection 1 cm?
The number of common tangents that can be drawn to the circle x2+y2-4x-6y-3=0 and x2+y2+2x+2y+1=0 is
The area of the region bounded by the curve x2=4y and the straight line x = 4y - 2 is
A single 6-sided dice is rolled, then the probability of getting an odd number is
In a class of 49 students, the ratio of girls to boys is 4:3. If 4 girls leave the class, the ratio of girls to boys would be
If income of A is 20% more than that of B, then income of B is how much percent less than that of A?
The average of 5 consecutive odd positive integers is 9. Then sum of smallest and greatest number is
If 2.5x=0.05 y, then find the value of \((\frac{y-x}{y+x}).\)
In the neighborhood of z = 1, the function f(z) has a power series expansion of the form f(z) = 1+(1-z)+(1-z)2 + .... then f(z) is
A rectangular box open at the top is to have volume of 32 cubic feets. The minimum outer surface area of the box is
The value of the dot product of the eigenvectors corresponding to any pair of different eigen values of a 4 × 4 symmetric positive definite matrix is
The matrix P is the inverse of a matrix Q. If I denotes the identity matrix, which one of the following options is correct?
If the matrices \(\left(\begin{matrix} 1 & 0 \\   0 & 0  \end{matrix}\right),\left(\begin{matrix}   -1 & 0 \\   0 & 0  \end{matrix}\right),\left(\begin{matrix}   i & 0 \\   0 & 0  \end{matrix}\right) and \left(\begin{matrix}   -i & 0 \\   0 & 0  \end{matrix}\right)\) form a group with respect to matrix multiplication, then which one of the following statements about the groups, thus formed is correct?
Which of the following are generators of the multiplicative group {(1,2,3,4,5,6), x7} where x7 denotes multiplication moduls 7?
The general solution of differential equation \(\frac{d^2y}{dx^2}+9y=sin^3x\) is
(given that c1 and c2 are arbitrary constants)
The solution of (x2 -√2y) dx + (y2 - √2x) dy = 0 is given by