List of top Mathematics Questions asked in CUET (PG)

If the curve ay + x² = 7 and x³ = y, cut orthogonally at (1, 1), then the value of a is -

Given below are two statements :
Statement I: \(\int\limits_{-a}^af(x)dx=\int\limits_{0}^a[f(x)+f(-x)]dx\)
Statement II : \(\int\limits_{0}^1\sqrt{(1+x)(1+x^3)}dx\) is less than or equal to \(\frac{15}{8}\).
In the light of the above statements, choose the most appropriate answer from the options given below :

Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R.
3 Assertion A: \(\int\limits_{-x}^{3}(x^3+5)dx=30\)
Reason R: f(x) = x³ +5 is an odd function
In the light of the above statements, choose the correct answer from the options given below:

If A=\(\begin{bmatrix} 1&0 \\[0.3em] 2&-1 \end{bmatrix}\) B= \(\begin{bmatrix} 3&7 \\[0.3em] 4&8 \end{bmatrix}\) and C = \(\begin{bmatrix} -1&1 \\[0.3em] 0&0 \end{bmatrix}\). The value of A+ (B+C) is

The line integral per unit area along the boundary of small area around a point in vector field \(\overrightarrow A\) is called

If \(\overrightarrow r\) is the position vector of any point on a surface S that encloses the volume V, then find \(\iint\limits_S\overrightarrow r.d\overrightarrow S\)

The point(s) at which function f is given by \(f(x)={\begin{Bmatrix}\frac{x}{|x|};x\lt0  \\ -1; x\geq0\end{Bmatrix}}\) is continuous is/are

Given below are two statements :
Statement I: If the roots of the quadratic equation \(x^2-4x-log_3a=0\) are real, then the least value of a is 1/81.
Statement II: The harmonic mean of the roots of the equation \((5+ \sqrt2)x^2 - (4+\sqrt5)x + (8+2\sqrt5) = 0\) is 2.
In the light of the above statements, choose the correct answer from the options given below:

Which of the following functions is differentiable at x = 0?

If f and g are differentiable functions in (0, 1) satisfying f(0) = 2 = g(1), g(0) = 0 and f(1) = 6, then for some c ∈]0, 1[

If every pair from among the equation x² + px + qr = 0, x² + qx + rp = 0 and x² + rx + pq = 0 has a common root, then the product of three common roots is_______.

The H.P. of two numbers is 4 and the arithmatic mean A and geometric mean G satisfy the relation 2A + G² = 27, the numbers are

If x,y,z are all distinct and \(\begin{vmatrix} x & x^2 & 1+x^3\\ y & y^2 & 1+y^3 \\ z & z^2 & 1+z^3 \end{vmatrix}\)=0, then the value of xyz is

A. If A and B are two invertible matrices, then (AB)^-1 = A^-1 B^-1
B. Every skew-symmetric matrix of odd order is invertible
C. If A is non-singular matrix, then (A^T)^-1 = (A^-1)^T
D. If A is an involutory matrix, then (I+A) (I-A) = 0
E. A diagonal matrix is both an upper triangular and a lower triangular
Choose the correct answer from the options given below :

If A₁, A₂ be two AM's and G₁, G₂ be two GM's between a and b, then \(\frac{A1+A2}{G1G2}\) is equal to

Let \(a = cos\frac{2π}7 + isin\frac{2π}7\), a = a + a²+a⁴ and β = a³+ a⁵ +a⁶ then the equation whose root are α, β is

If f: R→R defined as of f(x) = x² + 1 then minimum value of f(x) is

If f: R→R is defined by f(x)=3x²-5 and g: R→R by g(x)=\(\frac{x}{x+1}\) then gof(x) is

The sides of three solid metallic cubes are 30cm, 40cm and 50cm respectively. Find the side of the new cube formed by melting the three cubes (in cm)

A triangle with vertices (4, 0), (-1,-1), (3, 5) is

Match List-I and List-II

LIST I		LIST II
A.	No. of triangles formed using 5 points in a line and 3 points on parallel line is	I.	20
B.	No. of diagonals drawn using the vertices of an octagon	II.	10
C.	The no. of diagonals in a regular polygon of 100 sides is	III.	45
D.	A polygon with 35 diagonals has sides	IV.	4850

Choose the correct answer from the options given below:

Which of the following is true:
A. If a cos A = b cos B, then the triangle is isosceles or right angled.
B. If in a triangle ABC, cos A cos B + sin A sin B sin C =1 then the triangle is isosceles right angled.
C. If the ex-radii r1, r2, r3 of ΔABC are in the HP, then it's sides are not in AP
Choose the correct answer from the options given below :

Given below are two statements: One is lebelled as Assertion A and the other is labelled as Reason R.
Assertion A: The number of parallelograms in a chess board is 1296.
Reason R: The number of parallelograms when a set of m parallel lines is intersected by another set of n parallel lines is ^mC₂.ⁿC₂
In the light of the above statements, choose the correct answer from the options given below:

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______.

Match List I with List II

Choose the correct answer from the options given below: