List of practice Questions

The distillation technique most suited for separating glycerol from spent-lye in the soap industry is :

Chlorobenzene is more reactive than benzene towards the electrophilic substitution reaction. Resonance destabilises the carbocation.

In an oscillator, for sustained oscillations, Barkhausen criterion is $A\beta$ equal to ($A =$ voltage gain without feedback, $\beta =$ feedback factor)

A particle moves along a circle of radius ?$r$? with constant tangential acceleration. If the velocity of the particle is ?$?$? at the end of second revolution, after the revolution has started then the tangential acceleration is

A bottle has an opening of radius $a$ and length $b$. A cork of length $b$ and radius $(a+ \Delta a)$ where $(\Delta a < < a)$ is compressed to fit into the opening completely (See figure). If the bulk modulus of cork is $B$ and frictional coefficient between the bottle and cork is $\mu$ then the force needed to push the cork into the bottle is :

Which of the following compounds is metallic and ferromagnetic ?

A and B are two parallel sided transparent slabs of refractive indices n$_1 $and n$_2$ respectively. A ray is incident at an angle $\theta$ on the surface of separation of A and B, and after refraction from B into air grazes the surface of B. Then

If $ y=tan^{-1}\left(\frac{2x}{1+3x^{2}}\right)+tan^{-1}\left(\frac{5+x}{1-5x}\right) $ , then $ \frac{dy}{dx}= $

Let $ A(a, 0) $ , $ B(0, b) $ and $ C (1, 1) $ be three points. If $ \frac{1}{a}+\frac{1}{b}=1 $ , then the three points are

If $p :$ Every square is a rectangle $q :$ Every rhombus is a kite then truth values of $p ? q$ and $p ? q$ are __________ and ___________ respectively.

The value of $ \displaystyle\lim_{x\to\infty} \left(\frac{x+5}{x+2}\right)^{x} $ is equal to

The coefficient of $ x^{2} $ in the expansion of $ (1 + x + x^{2} + x^{3})^{10} $ is

The mean of $ 100 $ items was $ 60 $ . Later it was found that two items were misread as $ 69 $ and $ 96 $ instead of $ 66 $ and $ 99 $ respectively. The correct mean of the $ 100 $ items is

A normal to the curve $ 2x^{2 }- y^{2} = 14 $ at the point $ (x_{1}, y_{1}) $ is parallel to the straight line $ x + 3y = 4 $ . Then the point $ (x_{1}, y_{1}) $ is

Let the function $ f(x) $ be continuous in the interval $ [a, b] $ and differentiable in $ (a, b) $ . Then there is at least one point $ c $ in $ (a, b) $ at which the tangent to the curve $ y = f (x) $ is parallel to

The value of integral \(\int{e^x}(\frac{cosx+sinx}{cos^2x})dx\)

When $ y = vx $ , $ y $ and $ x $ are variables, the differential equation $ \frac{dy}{dx}=\frac{2xy}{x^{2}-y^{2}} $ reduces to

If tan $ y=\frac{sin\,x+cos\,x}{cos\,x-sin\,x} $ , then $ \frac{dy}{dx}= $

Let $ P\left(x\right)=^{10}C_{x} \left(\frac{1}{2}\right)^{10} , x=0, 1, 2, \ldots,10 $ be the probability mass function of a binomial distribution $ X $ . Then the mean of $ X $ is

The function $ f (x) = |x-10| $ , $ x $ is real number, is

Two cars are in a race. The white car passed the finishing point with a velocity $ v\, ms^{-1} $ more and took time $ t\, s $ less than the red car. If both the cars start from rest and travel with constant accelerations $ a_w $ , and $ a_r $ respectively, $ \frac{v}{t} $ is given

Electrophile that participates in nitration of benzene is

A particle moving with an initial velocity $ u\, ms^{-1} $ is retarded by a force at the rate of $ a = - k \sqrt v $ . where $ K $ is a positive constant and $ v $ is the instantaneous velocity. The particle comes to rest in a time given by