List of top Mathematics Questions asked in CUET (UG)

If f(x) is a function which is derivable in an interval 1 containing a point c, then match List I with List II.

List I		List II
A.	f(x) has second order derivate at x = c such that f'(c) = 0 and f'(c) < 0; then	I.	point of inflexion of f(x)
B.	Necessary condition for point x = c to be extreme point of f(x) is	II.	‘c’ is point of local minima of f(x)
C.	If f'(x) does not change its sign as x crosses the point x = c then it is called a	III.	c is a critical point of f(x)
D.	f(x) has second order derivate at x = c such that f'(c) and f'(c) > 0; then	IV.	‘c’ is point of local maxima of f(x)

Choose the correct answer from the options given below :

If the transpose of matrix A is matrix B, where \(A=\begin{bmatrix} 2a & 1 & 3b \\ 1 & 2 & 4c \\ 5 & 6 & 0 \end{bmatrix}\)and \(B=\begin{bmatrix} 4 & 1 & 5 \\ 1 & 2 & 6 \\ 9 & 3 & 0 \end{bmatrix}\)then the value of 3a + 2b + 4c is :

The solution set of inequalities :
x + 3 ≤ 0 and 2x + 5 ≤ 0; if x ∈ R is :

The ratio of speeds of a motor boat and that of current of water is 35:6. The boat goes against the current in 6 hours 50 minutes. The time taken by boat to come back is :

If A is a symmetric matrix and n ∈ N, then Aⁿ is :

If \(\vec{a}\) and \(\vec{b}\) are two non zero vectors such that \(|\vec{a}|\)=10, \(|\vec{b}|=2\) and \(\vec{a}.\vec{b}=12\), then value of \(|\vec{a}\times\vec{b}|\) is :

If xy = e^(x-y), then the value of \(\frac{dy}{dx}\) at (1, 1) is :

A retailer has 900 kg of wheat, a part of which he sells at 10% loss and the remaining at a profit of 8%. Overall, he makes a profit of 6%, the quantity sold at profit is :

The direction cosines of a line which makes equal angles with the co-ordinate axes is/are :

Value of 2⁴⁸ (mod 15) is :

A tank can be filled by two pipes A and B in 18 minutes and 24 respectively. Another tap C can empty the full tank in 36 mintues. If the tap C is opened 6 minutes after the pipes A and B are opened, the tank will become full in a total of :

Which of the following are not the probability distribution of a random variable ?
A.

X	0	1	2
P(X)	0.4	0.4	0.2

B.

X	0	1	2	3	4
P(X)	0.4	0.4	0.2	-0.1	0.3

C.

Y	-1	0	1
P(Y)	0.6	0.1	0.2

D.

Z	3	2	1	0	-1
P(Z)	0.3	0.2	0.4	0.1	0.05

E.

X	0	1	2
P(X)	\(\frac{25}{36}\)	\(\frac{10}{36}\)	\(\frac{1}{36}\)

Choose the correct answer from the options given below :

Which of the following statements is true ?
A. If the feasible region for a LPP is unbounded, maximum or minimum of the objective function Z = ax + by may or may not exist.
B. Maximum value of the objective function Z = ax + by in a LPP always occurs at only one corner point of the feasible region.
C. In a LPP, the minimum value of the objective function Z = ax + by (a, b > 0) is always 0 if origin is one of the corner points of feasible region.
D. In a LPP the max value of the objective function Z = ax + by is always finite.
Choose the correct answer from the options given below :

The angle at which the normal to the plane 4x - 8y + z = 7 is inclined to y-axis is :

Set A has elements and the set B has 6 elements, then the number of injective mappings that can be defined from A to B is :

The corner points of the feasible region determined by the system of linear inequalities are (0, 0), (0, 4), (4, 0), (2, 4) and (0, 5). If the maximum value of Z = ax + by where a, b > 0 occurs at both (2, 4) and (4, 0) then

If each side of a cube is x, then the angle between the diagonals of the cube is :

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

The general solution of the differential equation xdy - ydx - 0 represents :

ABCD is a rhombus, whose diagonals intersect at E. Then \(\overrightarrow{EA}+\overrightarrow{EB}+\overrightarrow{EC}+\overrightarrow{ED}\) equals to :

Match List I with List II

List I		List II
A.	\(\frac{d^2y}{dx^2}+(\frac{dy}{dx})^{\frac{1}{2}}+x^{\frac{1}{2}}\)	I.	order 2, degree 1
B.	\(\frac{dy}{dx}=\frac{x^{\frac{1}{2}}}{y^{\frac{1}{2}}(1+x)^{\frac{1}{2}}}\)	II.	order 2, degree not defined
C.	\(\frac{d^2y}{dx^2}=\cos3x+\sin3x\)	III.	order 2, degree 4
D.	\(\frac{d^2y}{dx^2}+2\frac{dy}{dx}+y=\log(\frac{dy}{dx})\)	IV.	order 1, degree 2

Choose the correct answer from the options given below :

The area of the region bounded by the curve \(y=\sqrt{3x+10}\), x-axis and between the lines x = -3 and x = 2 is equal to :

The area of the region bounded by |x| + |y| = 1, x ≥ 0 y ≥ 0 is :

The value of the integral \(\int\frac{1-\sin x}{\cos^2 x}dx\) is :

The slope of the normal to the curve y = 2x² + 3sinx at x = 0, is :