List of top Questions asked in CUET (UG)

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

The interval in which the function \(f(x) = 10-6x-2x²\) is decreasing is:

Area bounded by y=|x-5| and x-axis between x = 2; and x = 4 is:

The area of the region bounded by the line 2y = 5x +7, x-axis and the lines x - 1 and x -3 is :

The price relatives and weights of a set of commodities are given as:

Commodity	P	Q	R
Price Relative	100	130	180
Weight	x	2x	y

If the sum of weights is 54 and index for the set is 130, then the values of x and y are

Which one of the following is not an Arithmetic progression ?

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 :

The value of \(\int\limits_{-1}^1x^2 [x] dx\) is:

The value of \(\int\limits_{-3}^2x^2 |2x| dx\) is:

The integrating factor of differential equation \(\frac{dy}{dx}+y=\frac{1+y}{x}\) is:

The maximum value of Z= 2x + 3y subject to the constraints x≥0, y>0; x+y≤ 10, 3x+4y≤ 36 is:

If set A has 5 elements and set B has 7 elements than number of one-one and onto mapping from A to B is:

If f(x) - 27x³ and g(x) = \((x)^{\frac{1}{3}}\), then gof(x) is :

Match List I with List II

Choose the correct answer from the options given below:

A thief is spotted by a policeman from a distance of 100m. When the policeman starts the chase, the thief also starts running. If the speed of the thief be 8 km/hr and that of the policeman 10 km/hr, how far the thief will have run before he is overtaken ?

Sourav completes a journey in \(5\frac12\) hours. If he covers half of the distance at \( 5\ km/h\) and the remaining distance at \(6\  km/h\), then find the total distance covered by him.

If\(|\vec {a}+\vec {b}|=15, |\vec {a}-\vec{b}| =10,|\vec a|=\frac{11}{2}\) then the value of |\(\vec b\)| is/are:

A vector \(\overrightarrow{r}\) is inclined at equal angles to the three axes. If the magnitude of \(\overrightarrow{r}\) is \(3\sqrt3\) units, then the value of \(\overrightarrow{r}\) is:

A man spends 60% of his income and saves the remaining. His income increases by 28% and his expenditure also increases by 30%. Find the percentage increase in his savings.

In an examination the marks of six boys are 48, 59, 57, 37, 78, and 57 respectively. The average marks of all the six boys are :

A container is full of mango juice. One fifth of juice is taken out from this container and then an equal amount of water is poured into the bottle. This process is repeated 3 more times. The final ratio of juice and water in the container is:

Given expression:
\(\frac{(0.682)^2-(0.318)^2}{0.682-0.318}\)

Which of the following statements are true for rectangles?
A. All interior angles are right angles.
B. Diagonals are perpendicular to each other.
C. Diagonals are equal.
D. Opposite angles are supplementary
Choose the correct answer from the options given below:

The point on the curve y²=16x for which the y-coordinate is changing 2 times as fast as the x-coordinate is:

The straight line \( \frac{x+2}{3} = \frac{z-3}{ -2}, y-2 \) is