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

Match List - I with List - II List - I | List - II A. R = {(x, y) : x and y are students of the same school} | I. Symmetric B. R = {(L1, L2) : L1 ⊥ L2, where L is a set of all lines} | II. One-one C. A function f : R → R defined by f(x) = 2 − 3x is | III. Bijective D. A function…

Match List - I with List - II List - I | List - II A. The range of \(\sin^{-1}x\) is | I. \(\left[-\frac{\pi}{2},0\right)\cup\left(0,\frac{\pi}{2}\right]\) B. The range of \(\tan^{-1}x\) is | II. \(\left(-\frac{\pi}{2},\frac{\pi}{2}\right)\) C. The range of \(\text{cosec}^{-1}x\)…

The maximum value of \(z = 4x+2y\) subject to the constraints \(2x+3y\le28\), \(x+y\le10\), \(x,y\ge0\) is:

If \(A = \begin{bmatrix}\cos\alpha&\sin\alpha\\-\sin\alpha&\cos\alpha\end{bmatrix}\), then:

The probability distribution of X is x | 0 | 1 | 2 | 3 | 4 P(X = x) | 0.1 | 2k | k | k | 2k Then \(\text{Var}(X) =\)

If \(A = \begin{bmatrix}2&1&0\\3&1&2\\0&4&-1\end{bmatrix}\), then \(|\text{adj}(A)|\) is equal to

For two events \(A, B\): \(P(A\cup B) = \frac{7}{12}\), \(P(A) = \frac{5}{12}\), \(P(B) = \frac{3}{12}\). Then \(P(A\cap B) =\)

If \(\theta\) is the angle between any two vectors \(\vec{a}\) and \(\vec{b}\), then \(|\vec{a}\cdot\vec{b}| = |\vec{a}\times\vec{b}|\) for \(\theta\) equal to