List of practice Questions

A double convex lens has focal length 25 cm. The radius of curvature of one of the surfaces is double of the other. Find the radii if the refractive index of the material of the lens is 1.5 :

Assuming that the gravitational potential energy of an object at infinity is zero, the change in potential energy (final - initial) of an object of mass m, when taken to a height h from the surface of earth (of radius R), is given by,

A plane is inclined at an angle $\alpha = 30^{\circ}$ with a respect to the horizontal. A particle is projected with a speed $u = 2 ms^{-1}$ from the base of the plane, making an angle $q = 15^{\circ}$ with respect to the plane as shown in the figure. The distance from the base, at which the particle hits the plane is close to : (Take $g = 10 \; ms^{-2}$)

A cylindrical plastic bottle of negligible mass is filled with $310\, ml$ of water and left floating in a pond with still water. If pressed downward slightly and released, it starts performing simple harmonic motion at angular frequency $\omega$. If the radius of the bottle is $2.5\, cm$ then $\omega$ close to : (density of water = $10^3 \; kg / m^3$)

A plano convex lens of refractive index $\mu_1$ and focal length $f_1$ is kept in contact with another plano concave lens of refractive index $\mu_2$ and focal length $f_2$. If the radius of curvature of their spherical faces is R each and $f_1 = 2f_2$, then $\mu_1$ and $\mu_2$ are related as :

A uniform metallic wire has a resistance of $18 \; \Omega$ and is bent into an equilateral triangle. Then, the resistance between any two vertices of the triangle is :

In a process, temperature and volume of one mole of an ideal monoatomic gas are varied according to the relation $VT = K$, where $K$ is a constant. In this process the temperature of the gas is incresed by $\Delta T$. The amount of heat absorbed by gas is (R is gas constant) :

The relations amongst the three elements earth's magnetic field, namely horizontal component H, vertical component V and dip d are, (B$_E$ = total magnetic field)

The outcome of each of $30$ items was observed; $10$ items gave an outcome $\frac{1}{2} - d$ each, $10$ items gave outcome $\frac{1}{2}$ each and the remaining 10 items gave outcome $\frac{1}{2} + d$ each. If the variance of this outcome data is $\frac{4}{3}$ then |d| equals :

Two numbers a and b are inversely proportional to each other. If a increases by 100%, then b decreases by:

Choose the sentence that is grammatically correct.

Choose the sentence that is grammatically correct.

Choose the sentence that is grammatically correct.

Directions: In each of the questions given below, each sentence is labelled with a letter. From the given choices, choose the most logical order of sentences that constructs a coherent paragraph.

1. The responsible citizen helped to foil the plan of a hijack.
2. The deep pockets of his leather jacket contained what had been feared!
3. A person called up the airport and gave a message.
4. All the passengers were carefully frisked, and one of them was asked to step aside.

Directions: Choose the correct meaning for each of the foreign language words and phrases given below.
malus

Directions: Choose the correctly spelled words to fill in the blanks.
It is our responsibility to leave a green and clean world for our _____ .

Directions: Choose the correctly spelled words to fill in the blanks.
The patient‘s death was the result of sheer —— on the part of the surgeon.

Fill in the blank with the correct options.
Son, —— ! Research the company before you apply for the job.

Find the value of log_y(x⁴) if log_x(y³) = 2

How many terms are in the Arithmetic Progression 20, 25, 30,..., 135, 140?

If log₁₀10=1, log₁₀100=2, what is the value of log₅125?

A and B together can do a piece of work in 30 days. A having worked for 16 days, B finishes the remaining work alone in 44 days. In how many days shall B finish the whole workalone?

If the side of a square increases by 30% its area increases by:

A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 27, then how old is B?

Sarthak bought 7 new trading cards to add to his collection. The next day his dog ate half of his collection. There are now only 31 cards left. How many cards did Sarthak start with ?