A coin is tossed and a die is thrown. The probability that the outcome will be a tail on the coin or a number greater than 3 on the die is

The projection of the vector \(5\hat i+\hat j-3\hat k\) on the vector \(\hat i+2\hat j-3\hat k\) is

Match List-I with List-II List-I | List-II (A) \(\tan^{-1}\frac{2}{11}+\tan^{-1}\frac{7}{24}\) | (I) \(\frac{3\pi}{4}\) (B) \(\tan^{-1}2+\tan^{-1}3\) | (II) \(\pi\) (C) \(\tan^{-1}1+\tan^{-1}2+\tan^{-1}3\) | (III) \(\tan^{-1}\frac{1}{2}\) (D)…

The corner points of the bounded feasible region determined by a set of constraints in an LPP are P(0, 5) Q(3, 5), R(5, 0) and S(4,1). If the objective function is \(z=ax+2by\), where, \(a,b>0\), then the condition on \(a\) and \(b\) such that the maximum value of \(z\) occurs at…

Match List-I with List-II List-I | List-II (A) The number of possible matrices of order \(3\times3\) with each entry 1 or 0 | (I) \(2^4\) (B) The number of possible matrices of order \(2\times3\) with each entry 1 or 0 | (II) \(2^9\) (C) The number of possible matrices of order \…

The area of the region bounded by the curves \(y=x\) and \(y=x^3\) is:

A balloon which always remains spherical, has a variable diameter \(\frac{3}{2}(5x+7)\). Then the rate of change of its volume with respect to \(x\) is

\(\int e^{-x}(\cot x+\operatorname{cosec}^2x)\,dx=\)

The domain of the function \(y=\sin^{-1}(x-1)+\cos^{-1}\sqrt{x-1}\) is: