Let h=2π−x. Then cosx=sinh and π−2x=2h. So x→π/2limπ−2xkcosx=h→0lim2hksinh=2k. For continuity: 2k=3, so k=6.
CUET UG 2023 — Mathematics Algebra
Match List - I with List - II.
| List - I | List - II |
|---|---|
| (A) If A and B are mutually exclusive events, then P(A∪B)= | (I) P(B)P(A∩B),P(B)=0 |
| (B) If A and B are independent events, then P(A∩B)= | (II) P(A)P(A∩B),P(A)=0 |
| (C) If A and B are two events of a sample space of an experiment, then P(A/B)= | (III) P(A)⋅P(B) |
| (D) If A and B are two events of a sample space of an experiment, then P(B/A)= | (IV) P(A)+P(B) |
Choose the correct answer from the options given below :
Held on 30 May 2023 · Verified 13 Jul 2026.
(A)-(IV), (B)-(III), (C)-(I), (D)-(II)
(A)-(III), (B)-(IV), (C)-(I), (D)-(II)
(A)-(II), (B)-(III), (C)-(IV), (D)-(I)
(A)-(I), (B)-(II), (C)-(III), (D)-(IV)
Sign in to track your attempts and accuracy.
Sign in to keep a private note on this question. Nothing you write is ever public.
If f(x) = 2x + 3, then f⁻¹(x) is:
If the roots of the equation x² - 5x + k = 0 are in the ratio 2:3, then the value of k is:
If $A = [a_{ij}]$ be square matrix of order 3, such that $a_{ij} = i + j$, $\forall i, j$ then which of the following are correct? (A) A is a skew-symmetric matrix. (B) A is a non-singular matrix. (C) The inverse of A does not exist. (D) A is a symmetric matrix. Choose the correct answer from the options given below:
A function $f: \mathbb{R} \rightarrow \mathbb{R}$ defined by $f(x) = \frac{x}{x^2+1}$ is (where $\mathbb{R}$ is a set of real number)
Assume $P$, $Q$, $R$ and $W$ are matrices of order $3 \times 3$, $a \times 4$, $b \times c$ and $d \times a$ respectively. If $PQ + WR$ is well defined, then the value of $ab + cd$ is:
Work through every CUET UG Algebra PYQ, year by year.