List of top Mathematics Questions asked in CUET (UG)

A man goes uphill with an average speed of 24 km/h and comes down with an average speed of 36 km/h. The distance travelled in both cases being the same. The average speed for the entire journey is:

The value of C in Rolles's theorem for the function \(f(x)=e^xsinx,x\epsilon[0,\pi]\),is :

The random variable X has a probability distribution P(X) of the following form, where k is some number.

Then P(x≤2) is:

Value of 2⁴⁸ (mod 15) is :

The value of k for which the matrix \(\begin{pmatrix} 0 & 2 & 4 \\ 2 & 0 & 5 \\ -3 & 5 & 0 \end{pmatrix}\) is a symmetric matrix is given by :

The difference between length and breadth of a rectangle is 15m. If the perimeter of rectangle is 162 m, then the area of the rectangle (in m²) is

The integral \(\int_0^1x(1-x)^n dx\) is equal to :

By investing ₹4650 in a \(7 \frac{1}{2} \%\)% stock, a person obtains an income of ₹300. The market price of the stock is:

The order and the degree of the differential equation
\(\frac{d^2y}{dx^2}=(1+\frac{dy}{dx})^{\frac{1}{2}}\)
respectively are :

The value of the sum of 10 term of the series
\(S_{10}=\frac{1}{2^2-1}+\frac{1}{4^2-1}+\frac{1}{6^2-1}+...\)

If \(\frac{d}{dx}(2\frac{d^2y}{dx^2})^3= 7\), then the sum of order and degree of the differential equation is:

If \(y=log[\frac{x^2}{e^2}]\) then value of \(\frac{d^2y}{dx^2}\) is:

The points of non differentiability of \(f(x) = |x-2| + |x - 3|\)
A. 1
B. 2
C. 3
D. 4
E. 5
Choose the correct answer from the options given below:

The number of phone calls (in thousands) are made by a telephone company for five weeks as given below:

Week	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)
No. of Telephone calls	\(110\)	\(130\)	\(93\)	\(104\)	\(211\)

Taking a period of moving averages as 3 weeks, the graph of moving averages can be depicted directly as :

The area of the shaded portion

is:

What is the maximum area of a rectangle which can be inscribed in a circle of radius 2 cm?

The maximum value of Z = 3x + 4y subject to constraint x + y ≤6, x, y ≥ 0 is:

The value of \(sin^{-1} [cos(sin^{-1}\frac {\sqrt{3}}{2})]\) is:

Let \(tan^{-1}y=tan^{-1}x+tan^{-1}(\frac{2x}{1-x^2})\). Then y is:

A 300 m long train is moving at a speed of 60 km/h. In what time will it cross a single pole?

If \(\begin{bmatrix}        x+4 & 2x & 2x           \\[0.3em]        2x & x+4           & 2x\\[0.3em]        2x   & 2x & x+4      \end{bmatrix}=\lambda(4-x)^2\),then value of \(\lambda \) is

If A and B are symmetric matrices, then which statements are correct?
(A) \((A-B)' = B' - A'\)
(B) \((AB+BA)\) is symmetric matrix
(C) \((AB)'= B'A'\)
(D)\( A'B' = B'A'\)
(E)\( (AB-BA) \)is skew symmetric matrix
Choose the correct answer from the options given below:

In an A.P., the product of the first term and the second term is 120 and the product of the second term and the third term is 168. Find the tenth term of the A.P. when common difference \(d>0\)

A metallic sphere of radius 8 cm is melted to form a cone with radius same as that of sphere. What is the height of the cone (in cm) ?