A manufacturing company noticed that \(1 \%\) of its products are defective. If a dealer orders for 300 items from this company, then the probability that the number of defective items is atmost one is

If $f\left(x\right)=\frac{{\log }_e\left(1+x^2\left(\tan x\right)\right)}{\sin x^3},x\ne 0$ is to be continuous at $x=0$, then $f\left(0\right)$ must be equal to

\(\int_{5 \pi}^{25 \pi}|\sin 2 x+\cos 2 x| d x=\)

\(\sum_{k=1}^{\infty} \frac{1}{k !}\left(\sum_{n=1}^k 2^{n-1}\right)\) is equal to

If a Polynomial \(x^4+x^2+1\) is divisible by \(x^2+m x+1\) and \(x^2+n x+1\). Then \(m+n\) is equal to
(1) 2
(2) 0
(3) 3
(4) 4

If one of the lines \(2 x^2-x y+b y^2=0\) passes through the point \((-4,-2)\), then \(b^2=\)

A student is allowed to choose atmost \(n\) books from a collection of \(2 n+1\) books. If the total number of ways in which he can select atleast one book is 255 , then the value of \(n\) is

Benzamide \(\xrightarrow{\mathrm{Br}_2 / \mathrm{NaOH}} \mathrm{X} \xrightarrow[\text { alc. } \mathrm{KOH}]{\mathrm{CHCl}_3} \mathrm{Y}\)
The conversion of X to Y is

The process that mainly place in stars to produce energy

Two balls of charge \(q_1\) and \(q_2\) initially have a velocity of the same magnitude and direction. After a uniform electric field has been applied during a certain time, the direction of the velocity of the first ball changes by \(60^{\circ}\), and the velocity magnitude is reduced by half. The direction of the velocity of the second ball changes thereby by \(90^{\circ}\).
In what proportion will the velocity of the second ball change? Determine the magnitude of the charge-to-mass ratio for the second ball if it is equal to \(k_1\) for the first ball. The electrostatic interaction between the balls should be neglected.

The total number of $\mathrm{\sigma }$ and $\mathrm{\pi }-$bonds present in the following compound are

Two cars \(A\) and \(B\) are going around concentric circular paths of radii \(R_A\) and \(R_B\). If the two cars complete the circular paths in the same time, then the ratio of angular speed of \(A\) and \(B\) is

Two charged particles of masses in the ratio \(1: 3\) have charges in reciprocal ratio as their masses. They are placed in a uniform electric field and allowed to move. The ratio of their kinetic energies is