List of top Questions asked in CUET (PG)

Let A(3, 0, - 1) , B(2, 10, 6) and C(1, 2, 1) be the vertices of a triangle and M be the mid-point of AC. If G divides BM in the ratio 2:1, then cos( ∠GOA ) (O being the origin) is equal to______.

If 2u=5x, is the relation between two variables u and x, and harmonic means of x is 0.8, find the harmonic mean of u.

The variance of a series of numbers 2, 3, 11 and x is 12.25. Find the value of x.

If A, G, H be respectively, the A.M., G.M., and H.M. of three positive numbers a, b, c; then the equation whose roots are these numbers is given by

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 region bounded by the curve y²=x, the y-axis and between y = 2 and y = 4 is

The area of the region bounded by the curve x²=4y and the straight line x = 4y - 2 is

If log₃2,log₃(2^x-5) and log₃(2^x-7/2) are in A.P., then x is equal to

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 \((\frac{y-x}{y+x}).\)

If P(x) is a polynomial of degree 10 with leading coefficient as 11 and having (x-1), (x-2), (x-3),...(x-10) as factor, then the coefficient of x⁹ in P(x) is

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