List of practice Questions

Equation of two straight lines are $\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}$ and $\frac{x-4}{5}=\frac{y-1}{2}=z$ .Then

A bag contains $2n$ coins out of which $n-1$ are unfair with heads on both sides and the remaining are fair. One coin is picked from the bag at random and tossed. If the probability that head falls in the toss is $\frac{41}{56}$, then the number of unfair coins in the bag is

The equation of the curve passing through the point $\left(a, -\frac{1}{a}\right)$ and satisfying the differential equation $y-x \frac{dy}{dx}=a\left(y^{2}+\frac{dy}{dx}\right)$ is

If $a_{1}, a_{2}, a_{3}, \ldots, a_{n}$ are in A.P. where $a_{i}>0$ for all $i$, then $\frac{1}{\sqrt{a_{1}}+\sqrt{a_{2}}}+\frac{1}{\sqrt{a_{2}}+\sqrt{a_{3}}}+\ldots .+$ $\frac{1}{\sqrt{a_{n-1}}+\sqrt{a_{n}}}$ is?

Consider $\frac{x}{2}+\frac{y}{4} \ge1,$ and $\frac{x}{3}+\frac{y}{4} \le1, x, y \ge0.$ Then number of possible solutions are :

The locus of the mid-point of a chord of the circle $x^2+ y^2 = 4$, which subtends a right angle at the origin is

Which one is classified as a condensation polymer?

Which of the following has zero net dipole moment?

Mole fraction of the solute in a $1.00$ molal aqueous solution is

The angular speed of the electron in the $n^{th}$ orbit of Bohr hydrogen atom is

The electronic configuration of $Eu$ (Atomic $No. 63$), $Gd$ (Atomic $No. 64$) and $Tb$ (Atomic $No. 65$) are :

Net cell reaction of $Pt \left| H _{2}(640\, mm )\right| HCl \left| H _{2}(510\, mm )\right| Pt$.

$aK _{2} Cr _{2} O _{7}+ bKCl + cH _{2} SO _{4} \longrightarrow xCrO _{2} Cl _{2}+ yKHSO _{4}+ zH _{2} O$ The above equation balances when

Glycine in alkaline solution exists as______and migrates to__________.

The time period of a satellite of earth is $5$ hours. If the separation between the earth and the satellite is increased to $4$ times the previous value, the new time period will become

The ratio of the specific heats $\frac{C_{P}}{C_{V}}=\gamma$ in terms of degrees of freedom (n) is given by

If $\vec{E}$ and $\vec{B}$ are the electric and magnetic field vectors of e.m. waves then the direction of propagation of e.m. wave is along the direction of

A force of $2\hat{i}+3\hat{j}+4\hat{k}$ $N$ acts on a body for $4$ second, produces a displacement of $\left(3\hat{i}+4\hat{j}+5\hat{k}\right)$$m$. The power used is

The young's modulus of a wire of length $L$ and radius $r$ is $Y$ $N/m^{2}$. If the length and radius are reduced to $L/2$ and $r/2$, then its young's modulus will be

A man drags a block through $10\, m$ on rough surface $(\mu = 0.5)$. A force of $\sqrt{3}$ kN acting at $30^{\circ}$ to the horizontal. The work done by applied force is

A brick of mass $2\, kg$ slides down an incline of height 5m and angle $30^{\circ}$. If the coefficient of friction of the incline is $\frac{1}{ 2 \sqrt{3}}$ , the velocity of the block at the bottom of the incline is (Assume the acceleration due to gravity is $10\, m/s^2$)

The amplitude of a damped oscillator becomes $\left(\frac{1}{3}\right)rd$ in $2$ seconds. If its amplitude after $6$ seconds is $\frac{1}{n}$ times the original amplitude, the value of $n$ is

With the increase in temperature, the angle of contact

$3.6$ gram of oxygen is adsorbed on $1.2\, g$ of metal powder. What volume of oxygen adsorbed per gram of the adsorbent at $1\,atm$ and $273 \,K$ ?

In the clathrates of xenon with water, the nature of bonding between xenon and water molecule is