Mean and variance of a binomial distribution are 6 and 2 respectively.
The probability of 2 successes will be

If \(y=\sqrt{\sin x+\sqrt{\sin x+\sqrt{\sin x+\cdots \infty}}}\) then \(\frac{d y}{d x}\) equals to

Which of the following functions f(x) are differentiable at \(x = 0\)?
(A) \(|x|\)
(B) \(| x - 1|\)
(C) [x],where [t] denotes the greatest integer ≤ t
(D) \(| x + 1|\)
(E) \(x^2\)
Choose the correct answert from the option given below :

The region represented by the system of inequalities \(x, y \geq 0 ;-2 x+y \leq 4 ; x+y \geq 3\) and \(x-2 y \leq 2\) is

The value of the determinant \(\left|\begin{array}{cc}a \cos \theta & a \sin \theta \\ -a \sin \theta & a \cos \theta\end{array}\right|\) is:

Which of the following statements are NOT correct about Standard Normal Distribution?
(A) The probability curve of the Standard Normal Distribution is a bell-shaped curve.
(B) The Standard Normal variate ( Z ) score describes the position of each data point in terms of its distance from the mean, when measured in standard deviation units.
(C) The Z -score is negative if the data point lies above the mean, and positive if it lies below the mean.
(D) There is a \(95.45 \%\) probability of randomly selecting a score between \(\mu-\sigma\) and \(\mu+\sigma\), when \(\sigma\) is standard deviation and \(\mu\) is mean.
Choose the correct answer from the options given below :

A person can sell a maximum of 20 units of shirts and pants on which a profit of ₹40 is made on each shirt and a of ₹30 on each pant. A minimum of 2 shirts are being sold, while pants are sold at least 4 times as many as shirts the maximum profit is:

A cell of emf 1.1 V and internal resistance 0.5 \(\Omega\) is connected to a 0.5 \(\Omega\) wire. Another cell of same emf is added in series, but current remains unchanged. The second cell's internal resistance is :

If \(y=2 x(x-1)(2-x)\); then \(\frac{d^2 y}{d x^2}\) is:

The unequivocal proof that DNA is the genetic material came from the experiments of -

Which of the following reaction occurs at anode during discharging of lead storage battery?

A man rows 15 km upstream in 5 hours and 25 km downstream in 5 hours each time, then the speed of the stream is

The plates of a parallel plate capacitor are separated by a distance d with air as medium between the plates. In order to increase its capacitance by 60%, a slab of dielectric constant 5 having the same area as that of plates is introduced between the plates. The thickness of the dielectric slab is :