List of practice Questions

David invested in three schemes A, B, C at $10\%$, $12\%$, $15\%$ p.a. respectively. The total interest in one year was ₹3200. Also, $C$ was $150\%$ of $A$ and $240\%$ of $B$. What was the amount invested in $B$?

Let A, B, C be finite sets. Suppose that $n(A)=10, n(B)=15, n$ $(C)=20, n(A \cap B)=8$ and $n(B \cap C)=9$. Then the possible value of $n ( A \cup B \cup C )$ is

The equation of one of the common tangents to the parabola $y^{2}=8 x$ and $x^{2}+y^{2}-$

If $f\left(x\right) = \cos^{-1} \left[\frac{1-\left(\log x\right)^{2}}{1+\left(\log x\right)^{2}}\right] $ then the value of $f'(e)$ is equal to

If $\displaystyle\sum^n_{R = 0} (-1)^r \; \frac{^{n}C_{r}}{^{r+3}C_{r}} = \frac{3}{a+3} $ , then a - n is equal to

For the reaction $CO ( g )+\frac{1}{2} O _{2}( g ) \rightarrow CO _{2}( g )$ Which one of the statement is correct at constant $T$ and $P$ ?

After two hours, one-sixteenth of the starting amount of a certain radioactive isotope remained undecayed. The half life of the isotope is

A charged particle moves through a magnetic field perpendicular to its direction, then

Two conducting shells of radius $a$ and $b$ are connected by conducting wire as shown in figure. The capacity of system is :

Two plano-concave lenses $(1$ and $2)$ of glass of refractive index $1.5$ have radii of curvature $25 \,cm$ and $20 \,cm$. They are placed in contact with their curved surface towards each other and the space between them is filled with liquid of refractive index $4/3$. Then the combination is

Correct formula of the complex formed in the brown ring test for nitrates is

For the reaction $H _{2}( g )+ Br _{2}( g ) \rightarrow 2 HBr ( g )$, the experiment data suggested that $r = k \left[ H _{2}\right]\left[ Br _{2}\right]^{1 / 2} .$ The molecularity and order of the reaction are respectively:

Two Polaroids P₁ and P₂ are placed with their axis perpendicular to each other. Unpolarised light l₀ is incident on P₁. A third polaroid P₃ is kept in between P₁ and P₂ such that its axis makes an angle 45º with that of P₁. The intensity of transmitted light through P₂ is

A beam of light from a source L is incident normally on a plane mirror fixed at a certain distance x from the source. The beam is reflected back as a spot on a scale placed just above the source L. When the mirror is rotated through a small angle θ, the spot of the light is found to move through a distance y on the scale. The angle θ is given by

Which of the following does not contain Plane of symmetry?

At $ t = 0 $, a particle of mass $ m $ having velocity $ v_0 $ starts moving through a liquid kept in a horizontal tube and experiences a drag force $ F_d = - k \frac{dv}{dt} $. It covers a distance $ L $ before coming to rest. If the times taken to cover the distances $ L/2 $ and $ L $ are $ t_2 $ and $ t_4 $, respectively, then the ratio $ t_2/t_4 $ (ignoring gravity) is:

An OPAMP is connected in a circuit with a Zener diode as shown in the figure. The value of resistance $ R $ in kΩ for obtaining a regulated output $ V_0 = 9 \, \text{V} $ is:

A sphere of radius $ R $ has a uniform charge density $ \rho $. A sphere of smaller radius $ \frac{R}{2} $ is cut out from the original sphere, as shown in the figure below. The center of the cut-out sphere lies at $ z = \frac{R}{2} $. After the smaller sphere has been cut out, the magnitude of the electric field at $ z = - \frac{R}{2} $ is $ \frac{\rho R}{2 \epsilon_0} $. The value of the integer $ n $ is:

In a coaxial cable, the radius of the inner conductor is 2 mm and that of the outer one is 5 mm. The inner conductor is at a potential of 10 V, while the outer conductor is grounded. The value of the potential at a distance of 3.5 mm from the axis is: