List of top Questions asked in CUET (UG)

For the function f(x) = 2e^5x + 10, which of the following is the most appropriate option.

The price per unit of a commodity produced by a company is given by P = 92 - 2x², where x is the quantity demanded. The marginal revenue of producing 3 units of such a commodity shall be :

If \(y=\sqrt{\log x+\sqrt{\log x+\sqrt{\log x+\sqrt{\log x+}}}}.....+\) then \(\frac{dy}{dx}\) is :

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 :

A matrix P of order 2 × 3 with each entry 0 or 1 and α is a scalar which is 3 or 4. If R = αA, the number of matrices R formed is :

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 :

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

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 :

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 :

Value of 2⁴⁸ (mod 15) is :

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

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 :

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 :

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 :

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

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 :

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

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

The vectors \(3\hat{i}-\hat{j}+2\hat{k},2\hat{i}+\hat{j}+3\hat{k}\) and \(\hat{i}+λ\hat{j}-\hat{k}\) are coplanar if λ is :

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