CUET UG Mathematics · Paper 4

If $\int_0^{a} 3x^2\,dx = 8$, then the value of $a$ is

The point of local maximum of $f(x) = x^3 - 6x^2 + 9x + 4$ is

If $A$ is a square matrix of order 4 and $|\text{adj}\,A| = 27$, then $A(\text{adj}\,A)$ is equal to

The area bounded by the curve $y = x|x|$, x-axis and the ordinates $x = -1$ and $x = 1$ is given by

The particular solution of the differential equation $\frac{dy}{dx} = y\tan x$, given that $y = 1$ when $x = 0$, is

Three numbers are chosen at random, without replacement, from the numbers 1 to 20. The probability that their product is even is

The value of $\cos^{-1}\left(-\frac{1}{2}\right) + \sin^{-1}\left(-\frac{1}{2}\right)$ is

If a line makes an angle of $30^\circ$ with the positive direction of x-axis, $120^\circ$ with the positive direction of y-axis, then the angle which it makes with the positive direction of z-axis is

The integrating factor of the differential equation $2x\frac{dy}{dx} - y = 3$ is

Which of the following properties is/are true for two matrices of suitable orders?

I. $(A + B)' = A' + B'$

II. $(A - B)' = B' - A'$

III. $(AB)' = A'B'$

IV. $(kAB)' = kB'A'$ ($k$ is a scalar)

The maximum value of $f(x) = \frac{\log x}{x}$, $x > 0$, is

Riya hits a target with probability $\frac{3}{4}$ and Sam hits it with probability $\frac{2}{3}$, independently of each other. Each fires one shot. Given that the target is hit, the probability that it was hit by exactly one of them is

If $2^{50} \equiv r \pmod{7}$, where $0 \le r < 7$, then $r$ equals

A random sample of 16 bulbs has a mean life of 1,040 hours and a standard deviation $s = 120$ hours (computed with divisor $n - 1$). To test the null hypothesis that the population mean life is 1,000 hours, the value of the t statistic is

A man rows to a place 48 km away and comes back in 14 hours. He finds that he can row 4 km with the stream in the same time as 3 km against the stream. The speed of the stream is

In a 1 km race, Anil beats Bunty by 100 m, and in another 1 km race Bunty beats Chirag by 100 m. Running at the same speeds, by how many metres will Anil beat Chirag in a 1 km race?

The demand and supply functions of a commodity are $p_d = 30 - 2x$ and $p_s = 10 + 3x$, where $p$ is the price in ₹ and $x$ is the quantity. The producer surplus at market equilibrium is

What sum of money should be deposited at the end of every 6 months to accumulate ₹50,000 in 8 years, if money is worth 6% p.a. compounded semi-annually? [Given: $(1.03)^{16} = 1.6047$]

If $13 \le k \le 21$, $9 \le p \le 19$, $2 < m < 6$ and $k$, $p$, $m$ are integers, then which of the following inequality is always valid?