List of practice Questions

Evaluate the definite integral as limit of sums: \(∫^3_2 x^2dx\)

Find the intervals in which the function f given by f(x) = 2x³ − 3x² − 36x + 7 is (a) strictly increasing (b) strictly decreasing

Sand is pouring from a pipe at the rate of \(12 cm^3 /s\). The falling sand forms a cone on the ground in such a way that the height of the cone is always one-sixth of the radius of the base. How fast is the height of the sand cone increasing when the height is \(4 cm\)?

If $y = \sec\, x^?$, then $\frac{dy}{dx}$ is equal to:

Among the following compounds the one that is most reactive towards electrophilic nitration is :

If I =$ \int sec ^4x \, cosec ^2x \,dx$ =K tan ^3x +L tan x+M cot x + const, then

The solution set of constraints $x + 2y \ge 11,\, 3x + 4y \le 30, 2x + 5y \le 30$ and $x \ge 0 , y \ge 0$ , includes the point

Butene-1 may be converted to butane by reaction with

Which one of the following ions forms most stable complex compound?

In which of the following, functional group isomerism is not possible?

Which of the following cannot work as oxidizing agent ?

Three numbers are chosen from $1$ to $20$. Find the probability that they are not consecutive.

Find \(|\vec{a}|\) and \(|\vec{b}|\) ,if \((\vec{a}+\vec{b}).(\vec{a}-\vec{b})=8\) and \(|\vec{a}|=8|\vec{b}|.\)

A G.P. consists of an even number of terms. If the sum of all the terms is 5 times the sum of terms occupying odd places, then the common ratio is

In a $G.P$. of even number of terms, the sum of all terms is $5$ times the sum of the odd terms. The common ratio of the $G.P$. is

If $f(x) = x^3 - \frac{1}{x^3}$, then $f(x) + f(\frac{1}{x})$ is equal

If the coordinates of the middle point of the portion of a line intercepted between the coordinate axes is (3, 2) then the equation of the line will be

The eccentricity of the hyperbola whose latus rectum is $8$ and conjugate axis is equal to half of the distance between the foci is

A circular disc of radius $0.2\, m$ is placed in a uniform magnetic field of induction $(\frac{1}{\pi})Wb\,m^{-2}$ in such a way that its axis makes an angle of $60^{\circ}$ with $\vec{B}$. The magnetic flux linked with the disc is

Which magnetic materials have negative susceptibility?

A circular coil of wire consisting of 100 turns, each of radius 8.0 cm carries a current of 0.40 A. What is the magnitude of the magnetic field B at the centre of the coil?

Streamline flow is more likely for liquids with

The correct order of reactivity of the halides, ethyl chloride $(I)$, isopropyl chloride $(II)$ and benzyl chloride $(III)$ in $S_N1$ reaction is

Among the following molecules: $SO_2,SF_4,ClF_3, BrF_5$ and $XeF_4$, which of the following shapes does not describe any of the molecules mentioned?