List of practice Questions

For the following question, enter the correct numerical value upto TWO decimal places. If the numerical value has more than two decimal places, round-off the value to TWO decimal places. (For example: Numeric value 5 will be written as 5.00 and 2.346 will be written as 2.35) On interchanging the resistances, the balance point of a meter bridge shifts to the left by 10 cm. The resistance of their series combination is 1 k\(\Omega\). How much was the resistance on the left slot before interchanging the resistances? ____ \(\Omega\).
For the following question, enter the correct numerical value upto TWO decimal places. If the numerical value has more than two decimal places, round-off the value to TWO decimal places. (For example: Numeric value 5 will be written as 5.00 and 2.346 will be written as 2.35) The image of an object placed in front of a concave mirror of focal length 12 cm is formed at a point which is 10 cm more distant from the mirror than the object. The magnification of the image is ____.
One mole of a monoatomic ideal gas undergoes the process $A \to B$ as shown in the given $P$–$V$ diagram. The specific heat capacity in the process is
A parallel plate capacitor is made of two square plates of side $a$, separated by a distance $d$ ($d \ll a$). The lower triangular portion is filled with a dielectric of dielectric constant $K$, as shown in the figure. The capacitance of this capacitor is
A magnetic dipole in a constant magnetic field has
A shell is fired from a fixed artillery gun with an initial speed $u$ such that it hits the target on the ground at a distance $R$ from it. If $t_1$ and $t_2$ are the values of the time taken by it to hit the target in two possible ways, the product $t_1t_2$ is
A particle executing SHM along a straight line has zero velocity at points $A$ and $B$ whose distances from $O$ on the same direction $OAB$ are $a$ and $b$ respectively. If the velocity at the midpoint between $A$ and $B$ is $v$, then its time period is
The frequency of a tuning fork P is $a%$ less than a standard fork A. The frequency of another fork Q is $b%$ greater than that of A. When P and Q are sounded together, $x$ beats are produced in one second. The frequency of the standard fork is (in Hz)
A tank full of water has a small hole at the bottom. If one-fourth of the tank is emptied in $t_1$ seconds and the remaining three-fourths of the tank is emptied in $t_2$ seconds, then the ratio $t_1/t_2$ is
A metallic wire of density $d$ floats horizontally in water. The maximum radius of the wire so that the wire may not sink will be (surface tension of water = $T$)
For the following question, enter the correct numerical value upto TWO decimal places. If the numerical value has more than two decimal places, round-off the value to TWO decimal places. (For example: Numeric value 5 will be written as 5.00 and 2.346 will be written as 2.35) The eccentricity of the ellipse \[ \frac{x^2}{25} + \frac{y^2}{16} = 1 \] is \( \dfrac{3}{__} \).
A block of mass $m$ is kept on a platform which starts from rest with constant acceleration $\dfrac{g}{2}$ upward, as shown in the figure. Work done by the normal reaction on the block in time $t$ is:
Expression for time in terms of $G$ (universal gravitational constant), $h$ (Planck constant) and $c$ (speed of light) is proportional to:
In a car race on a straight road, car A takes a time $t$ less than car B at the finish and passes the finishing point with a speed $v$ more than that of car B. Both the cars start from rest and travel with constant accelerations $a_1$ and $a_2$ respectively. Then $v$ is equal to
If the midpoints of the sides $BC$, $CA$ and $AB$ of a triangle $ABC$ are respectively $(2,1)$, $(-1,-2)$ and $(3,3)$, then the equation of the side $BC$ is
Two vertices of a triangle are $(5,-1)$ and $(-2,3)$. If the origin is the orthocentre of this triangle, then the coordinates of the third vertex of that triangle are
For the following question, enter the correct numerical value upto TWO decimal places. If the numerical value has more than two decimal places, round-off the value to TWO decimal places. (For example: Numeric value 5 will be written as 5.00 and 2.346 will be written as 2.35) If \( z \), \( iz \) and \( z+iz \) are the vertices of a triangle and if \( |z| = 4 \), then the area (in sq. units) of that triangle is ______.
For the following question, enter the correct numerical value upto TWO decimal places. If the numerical value has more than two decimal places, round-off the value to TWO decimal places. (For example: Numeric value 5 will be written as 5.00 and 2.346 will be written as 2.35) There are 10 points in a plane out of which 6 are collinear. The number of straight lines formed by joining all these points is ____.
For the following question, enter the correct numerical value upto TWO decimal places. If the numerical value has more than two decimal places, round-off the value to TWO decimal places. (For example: Numeric value 5 will be written as 5.00 and 2.346 will be written as 2.35) Minimum number of times a fair coin must be tossed so that the probability of getting at least one head is more than 99% is ____.
For the following question, enter the correct numerical value upto TWO decimal places. If the numerical value has more than two decimal places, round-off the value to TWO decimal places. (For example: Numeric value 5 will be written as 5.00 and 2.346 will be written as 2.35) An envelope is known to have come from either `LONDON` OR `CLIFTON`. On the postal card only two successive letters `ON` are visible. The probability that the envelope comes from LONDON is \( \dfrac{12}{__} \).
Let $f$ be a polynomial function such that $f'(x)=f(x)\,f''(x)$ for all $x\in\mathbb{R}$. Then:
The minimum distance of a point on the curve $y=x^2-4$ from the origin is
Evaluate: \[ \int \frac{dx}{\cos x+\sqrt{3}\sin x} \]
If \[ \int \frac{1}{(x+100)\sqrt{x+99}}\,dx = f(x)+c \] then $f(x)=$
Evaluate: \[ \int_{0}^{\pi} \frac{x\sin x}{1+\cos^2 x}\,dx \]