List of practice Questions

A pendulum of length 1 m is released from $\theta$ = 60$^{\circ}$. The rate of change of speed of the bob at $\theta$= 30$^{\circ}$ is $(g=10 \, ms^{-1})$

A solution of methanol in water is $20\%$ by volume. If the solution and pure methanol have densities of $0.964 \; kg \; L^{-1}$ and $0.793 \; kg \; L^{-1}$, respectively, find the percent of methanol by weight?

A die has four blank faces and two faces marked $3$. The chance of getting a total of $12$ in $5$ throws is

If $a_1, a_2 , a_3 , a_4$ are in A.P., then $\frac{1}{\sqrt{a_{1}}+\sqrt{a_{2}}}+\frac{1}{\sqrt{a_{2}}+\sqrt{a_{3}}}+\frac{1}{\sqrt{a_{3}}+\sqrt{a_{4}}}=$

If $ \alpha $ and $ \beta $ are the roots of the equation $ a{{x}^{2}}+ $ $ bx+c=0,\text{ }\alpha \beta =3 $ and $a, b, c$ are in $A.P.$, then $ \alpha +\beta $ is equal to

A weak monobasic acid is 1% ionized in 0.1 M solution at $ 25{}^\circ C $ . The percentage of ionisation in its 0.025 M solution is

In the complex with formula $MCl_3 \cdot 4H_2O,$ the coordination number of the metal M is six and there is no molecule of hydration in it. The volume, if 0.1 M $AgNO_3$ solution needed to precipitate the free chloride ions in 200 mL of 0.01 M solution of the complex, is

Plot of $ log\text{ }x/m $ against log $p$ is a straight line inclined at an angle of $ 45{}^\circ $ . When the pressure is $ 0.5 \,arm $ and Freundlich parameter. $ k $ is $ 10 $ , the amount of solute adsorbed per gram of adsorbent will be $ (log\text{ }5=0.6990) $

A metal M of equivalent mass E forms an oxide of molecular formula $M_x O_y$. The atomic mass of the metal is given by the correct equation

The value of $ \displaystyle\lim _{x \rightarrow 0} \frac{\cot 4 x}{\text{cosec} 3 x}$ is equal to

The period of the function $f\left(x\right)= cos 4x+$ tan $3x$ is

What mass of calcium chloride in grams would be enough to produce 14.35 g of AgCl ? (At. mass : Ca =40 ; Ag = 108)

Intermediate involved in Reimer-Tiemann reactionis

Most impure form of carbon is

A tank is filled with water of density $1\frac{g}{{cm}^3}$ and oil of density $0.9\frac{g}{{cm}^3}$. The height of water layer is $100cm$ and that of oil layer is 400 $cm$. If $g=980\frac{cm}{s^2}$, then the velocity of efflux from an opening in the bottom of the tank will be-

The solution set of inequality $\frac{2x}{x^2 - 9} \leq \frac{1}{x + 2 }$ is

When a ceiling fan is switched off, its angular velocity reduces to half its initial value after it completes 36 rotations. The number of rotations it will make further before coming to rest is (Assuming angular retardation to be uniform)

Two identical objects each of mass $50 \,kg$ are kept at a distance of separation of $50\, cm$ apart on a horizontal table. The net gravitational force at the mid-point of the line joining their centres is

The perpendicular distance (d) of a line Ax + By + C = 0 from a point $(x_1, y_1)$ is given by :

Crystals of Bt toxin produced by some bacteria do not kill the bacteria themselves because -

A random variable X has the following probability distribution:

If the mean of the random variable X is \(\frac{1}{3}\), then the variance is

Describe characteristics and uses of coke.

Which is not true about acetophenone ?

$\int\left(\frac{x-a}{x}-\frac{x}{x+a}\right) dx$ is equal to