If three balls are drawn one by one without replacement from a bag containing 5 white and 4 red balls, then the probability distribution of the number of white balls drawn is

The point on the curve \(y^2=8 x\) for which the abscissa and ordinate change at the same rate is :

Given \(A=\left[\begin{array}{ll}2 & 3 \\ 1 & 4\end{array}\right]\) and \(B=\left[\begin{array}{ll}x & y \\ 1 & 4\end{array}\right]\), If \(A=B\), then \(x\) and \(y\) are :

Match List I with List II

(List I)	(List II)
A. \(\frac{d}{d x}\left(a^x\right)\)	\(I.\) \(0\)
B. \(\frac{d}{d x}\left(x^a\right)\)	\(II.\) \(x^x\left(1+\log _e x\right)\)
C. \(\frac{d}{d x}\left(a^a\right)\)	\(III.\) \(a x^{a-1}\)
D. \(\frac{d}{d x}\left(x^x\right)\)	\(IV.\) \(a^x \log _e a\)

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If \(5 x+y \leq 100, x+y \leq 60, x \geq 0, y \geq 0\). Then one of the corner points of the feasible region is:

If \(y=x^x, \frac{d y}{d x}\) will be:

Points at which normal to the curve \(y=x^3-3 x\) is parallel to \(y\)-axis are:

The general solution of the differential equation \(x d y+e^{-y} d x=x e^{x-y} d x\) is (given C is constant of integration)

Answer the question on the basis of passage given below:
Second period elements of p-Block differs from the rest of their group members due to their small atomic size, high electronegativity, high ionization enthalpy and absence of d-orbitals. The elements from the second period like C, N, O have unique property of forming \(p \pi-p \pi\) multiple bonds whereas other heavier elements of p-block form \(d \pi-p \pi\) multiple bonds. This changes the properties of second period elements to great extent. Also the single bond strength of the p-block elements with their own atoms gets affected by their atomic size and presence of lone pairs.
Inert pair effect also affects the properties of the p-Block elements especially for those elements which are present from 4th period onward and this happens due to poor screening effect of inner (n-1)d subshell electrons.
The decreasing order of melting point of the following elements will be:
A. Nitrogen (N)
B. Phosphorus (P)
C. Arsenic (As)
D. Antimony (Sb)
E. Bismuth (Bi)
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A current of 2 A flows through a 2 \( \Omega \) resistor when connected with a cell. When the resistance is replaced by 10 \( \Omega \), a current of 0.5 A flows. The internal resistance of the cell is

A pair of dice is thrown 7 times. If getting a total of 7 is considered a success, the probability of exactly 6 successe, is:

Electrostatics deals with the study of forces, fields and potential arising from static charges. Which of the following statements are correct ?
(A) Electrostatic force is a conservative force
(B) Charge is quantized because only integral number of electrons can be transferred from one body to the other
(C) In a uniform electric field E , an electric dipole experiences a torque \(\tau\) and a net force F .
(D) The electric field lines start from positive charges and end at negative charges. If there is a single charge, these may start or end at infinity.
(E) If the uniform surface charge density of an infinite plane sheet is positive, the electric field is directed away from the plate.
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Darwin's finches and Australian marsupials are an example of: