List of top Mathematics Questions asked in CUET (PG)

If two stones are thrown vertically upwards with their velocities in the ratio 2:5, then the ratio of the maximum heights attained by the stones is

Let z, \(z_1, z_2\) be complex numbers. Then which of the following statements are True?
(A) \(e^z\) is never zero
(B) \(|e^{ix}|=1\) if x is real
(C) \(e^z = 1\) if z is an integral multiple of \(2\pi i\)
(D) \(e^{z_1} = e^{z_2}\) if and only if \(z_1 - z_2 = \frac{2\pi i n}{\sqrt{3}}\), where n is an integer
(E) \(|e^z|>e^z\) for \(z \neq 0\)
Choose the correct answer from the options given below:

The equation of cone with vertex at (0, 0, 0) and passing through the circle given by
\(x^2 + y^2 + z^2 + x - 2z + 3y - 4 = 0, x - y + z = 2\), is

The Laplace transform of \( \cos\sqrt{t} \) is:

If \(1, \alpha_1, \alpha_2, \alpha_3, \ldots, \alpha_{n-1}\) are n roots of the equation, \( x^n = 1 \) then the value of \( (1-\alpha_1)(1-\alpha_2)(1-\alpha_3)\ldots(1-\alpha_{n-1}) \) is

Match List-I with List-II

\[ \begin{array}{|l|l|} \hline \textbf{List-I} & \textbf{List-II} \\ \hline (A) \; \dfrac{y^2}{36} - \dfrac{x^2}{16} = 1 & (I) \; \text{Eccentricity is } 2\sqrt{2} \\ (B) \; 7x^2 + 12xy - 2y^2 - 2x + 4y - 7 = 0 & (II) \; \text{Eccentricity is } \tfrac{3}{2} \\ (C) \; 7x^2 - y^2 = 224 & (III) \; \text{Eccentricity is } \tfrac{\sqrt{13}}{3} \\ (D) \; \dfrac{x^2}{16} - \dfrac{y^2}{20} = \dfrac{1}{9} & (IV) \; \text{Asymptotes are } y = \pm \tfrac{3}{2}x \\ \hline \end{array} \]

If the radius of curvature (\(\rho\)) at (0, 1) of \(y = e^x\) is \(\alpha\sqrt{\beta}\), then \(\alpha^2+\beta\) is:

If three forces of magnitudes 8 newtons, 5 newtons and 4 newtons acting a point are in equilibrium, then the angle between the two smaller forces is

The complex number \(z_1, z_2\) and origin, form an equilateral triangle only if:

Let \(f\) be a continuous real valued function, defined by, \(f(x) = \sin x\), for all \(x \in [-\frac{\pi}{2}, \frac{\pi}{2}]\). Then which of the following does not hold.

The integral \( \int_{0}^{\pi/2} \sin^5 x \cos^7 x \,dx = \)

Every continuous real valued function on [a, b] is
(A). Constant.
(B). Bounded above.
(C). Bounded below.
(D). Unbounded.
Choose the correct answer from the options given below:

Let an unbiased die be thrown and the random variable X be the number appears on its top. Then the expectation of X is

If a subset B is a basis of a vector space V, then
(A). B generates V.
(B). B contains zero vector.
(C). B is linearly independent.
(D). B is the only basis of V.
Choose the correct answer from the options given below:

Let \(<G,*> \) be a group. Then for all a, b, c \(\in\) G
(A). (a*b)*c \(\in\) G
(B). a*b = b*a
(C). a*(b*c) = (a*b)*c
(D). a*b = a*c implies b = c.
Choose the correct answer from the options given below:

Which of the following subsets form subgroups of the group <ℤ, +>?

(A). H₁ = {0}
(B). H₂ = {n+1 : n ∈ ℤ}
(C). H₃ = {2n : n ∈ ℤ}
(D). H₄ = {2n+1 : n ∈ ℤ}

Choose the correct answer from the options given below:

The solution of \(y = xp + \frac{m}{p}\) where \(p = \frac{dy}{dx}\) is

The series \( \sum_{n=1}^{\infty} \frac{1}{n} \)

What is the fundamental assumption behind a Markov model?

What is the key principle behind Monte Carlo simulation?

The equation of a straight line passes through the point (4,-5) and is perpendicular to the straight line 3x + 4y + 5 = 0.

Which of the following are subspaces of vector space \(\mathbb{R}^3\):
A. \( \{(x,y,z) : x+y=0\ \)
B. \( \{(x,y,z) : x-y=0\} \)
C. \( \{(x,y,z) : x+y=1\} \)
D. \( \{(x,y,z) : x-y=1\} \)}

Let \(m, n \in \mathbb{N}\) such that \(m<n\) and \(P_{m \times n}(\mathbb{R})\) and \(Q_{n \times m}(\mathbb{R})\) are matrices over real numbers and let \(\rho(V)\) denotes the rank of the matrix V. Then, which of the following are NOT possible.
A. \( \rho(PQ) = n \)
B. \( \rho(QP) = m \)
C. \( \rho(PQ) = m \)
D. \( \rho(QP) = \lfloor(m+n)/2\rfloor \), where \(\lfloor \rfloor\) is the greatest integer function

If \( A = \begin{pmatrix} 2 & 4 & 1 \\ 0 & 2 & -1 \\ 0 & 0 & 1 \end{pmatrix} \) satisfies \( A^3 + \mu A^2 + \lambda A - 4I_3 = 0 \), then the respective values of \( \lambda \) and \( \mu \) are: