\(\int_0^2 x(2-x)^n d x\) is equal to

If \(y = x + \tan x\), then value of \(\frac{d^2y}{dx^2}\) at \(x = \frac{\pi}{4}\) is:

Consider the equation of the line \(\vec{r}=-\hat{i}+2 \hat{k}+\mu(4 \hat{i}-\hat{j}+2 \hat{k})\).
Match List-I with List-II

List-I	List-II
(A) It passes through the point	(I) \(4,-1,2\)
(B) Its direction ratios are	(II) \(\frac{4}{\sqrt{21}}, \frac{-1}{\sqrt{21}}, \frac{2}{\sqrt{21}}\)
(C) Its Cartesian form is	(III) \((-1,0,2)\)
(D) Its direction cosines are	(IV) \(\frac{x+1}{4}=\frac{y}{-1}=\frac{z-2}{2}\)

Choose the correct answer from the options given below :

Solution of the differential equation \(\frac{d y}{d x}=\sqrt{1+x^2+y^2+x^2 y^2}\) is : (Here \(C\) is an arbitrary costant)

Two pipes A and B can fill a tank in 24 minutes and 32 minutes respectively. If both the pipes are opened simultaneously, after how much time B should be closed so that the tank is full in 18 minutes?

Let f : R → R be defined as f(x) = [x], where [x] denotes the greatest integer less than or equal to x. Then which of the following statements are correct?
(A) f is one-one but not onto
(B) f is not onto
(C) f is not one-one
(D) f is one-one and onto
Choose the correct answer from the options given below:

Answer the question on basis of passage given below :
P block elements are placed in groups 13 to 18 of the periodic table. Their valence shell electronic configuration is \(ns^2 np^{1-6}\). Group 16 of the p block elements are known as the group of chalcogens having \(ns^2 np^4\) as their general electronic configuration. They exhibit number of oxidation states but the stability of \(- 2\) oxidation state decreases down the group. They are sometimes also known as group of chalcogens as the name is derived from the Greek word for brass and points to the association of sulphur and its congeners with copper. Their ionisation enthalpy decreases down the group. Oxygen shows anomalous behaviour due to its small size and high electronegativity.
Given below are the Hydrides formed by group 15 elements. Choose the correct decreasing order of basicity of the following hydrides :
(A) \(AsH_3\)
(B) \(PH_3\)
(C) \(NH_3\)
(D) \(BiH_3\)
(E) \(SbH_3\)
Choose the correct answer from the options given below :

Hybridization and shape of \(Cs \left[ FeCl _4\right]\) is :

The slope of the cut off voltage versus frequency of incident light is found to be \(4.12 \times 10^{-15} Vs\).
The value of Planck's constant is :

The molality of a solution prepared by dissolving \(4 . 0 ~ g ~ N a O H\) in \(1 0 0 0 ~ m L\) distilled water is _________ (Assume that the density of water is \(1 g mL ^{-1}\) )

Match List I with List - II.,

List - I	List - II
(A) TV Transmission	(I) Short wave bands
(B) Long distance radio broadcasts	(II) Microwave
(C) RADAR	(III) Infrared rays
(D) TV Remote	(IV) Satellite

Choose the correct answer from the options given below :

In 5 trials of binomial distribution, the probability of 3 successes is 4 times the probability of 2 successes.
The probability of success in each trial is :