List of practice Questions

If the line px + qy = 0 coincides with one of the lines given by $ax^2 + 2hxy + by^2 = 0$, then
$AB$ and $CD$ are $2$ line segments ; where $A(2,3,0),B (6, 9, 0), C(-6, -9, 0). P $ and $Q$ are midpoint of $AB$ and $CD$, respectively and $L$ is the midpoint of $PQ$. Find the distance of $L$ from the plane $3x + 4z + 25 = 0$
On heating water, bubbles being formed at the bottom of the vessel detatch and rise. Take the bubbles to be spheres of radius $R$ and making a circular contact of radius r with the bottom of the vessel. If $r << R$, and the surface tension of water is T, value of r just before bubbles detatch is (density of water is $\rho_{w}$ )
Steel ruptures when a shear of $ 3.5 \times 10^8 \,Nm^{-2}$ is applied. The force needed to punch a $1\, cm$ diameter hole in a steel sheet $0.3\, cm$ thick is nearly :
The radius of an atom is $300\,pm$. If it crystallizes in a face-centered cubic lattice, length of the edge of the unit cell is
Sodium dissolves in liquid $NH_3$ to give a deep blue solution. This is due to
A 150 watt bulb emits light of wavelength 6600 $?$ and only 8% of the energy is emitted as light. How many photons are emitted by the bulb per second?
Schottky defect in crystals is observed when
In the following sets of ions, which one is not isoelectronic with the rest of the species? $ { O^{2-}, F^- , Na, Mg^{2+}, Al^{3+}, Ne} $
The reaction, $ { CH_3CH_2I + KOH_{(aq)} -> CH_3CH_2OH + KI}$ is classified as
The angle between the lines whose direction cosines satisfy the equations $l + m + n = 0 $ and $ l^2= m^2 + n^2 $is
The angular frequency of the damped oscillator is given by, $\omega = \sqrt{\left(\frac{k}{m} - \frac{r^{2}}{4m^{2}}\right)}$ where $k$ is the spring constant, $m$ is the mass of the oscillator and $r$ is the damping constant. If the ratio $\frac{r^{2}}{mk}$ is $8\%$, the change in time period compared to the undamped oscillator is approximately as follows :
The coefficient of $x^{1012}$ in the expansion of $(1 + x^n + x^{253})^{10}$, (where n $\le$ 22 is any positive integer), is :-
The coefficient of $x^{50}$ in the binomial expansion of $(1 + x)^{1000} + x (1 + x)^{999} + x^2(1 + x)^{998} + .... + x^{1000}$ is:
The magnetic properties of a magnet is lost at its
A concave mirror forms an enlarged, erect, virtual image of an object, only when the object is placed
The ratio of $ \frac{C_P}{C_V}$ for a diatomic gas is
A policeman on duty detects a drop of $15 \%$ in the pitch of the horn of a motor car as it crosses him. If the velocity of sound is $330 \, m \, s^{-1}$ , calculate the speed of the car.
What is the dimensional formula for universal gravitational constant $G$ ?
Two boys are standing at ends $A$ and $B$ of a ground where $AB = 200\, m$. The boy at B starts running in a direction perpendicular to $AB$ with a speed of $6\, m \,s^{-1}$? The boy at A starts simultaneously with a velocity of $10 \, m \, s^{-1}$ and catches the other at time t where the time $t$ is
The centre of mass of a system of two bodies of masses $M$ and $m, (M > m)1$ separated by a distance $d$ is
A proton and helium nucleus are shot into a magnetic field at right angles to the field with same kinetic energy. Then the ratio of their radii is
The increase in the height of the tower of height $200\,m$ to get its coverage range tripled is
In an inelastic collision, which of the following is true?
The universal gas law $\left( \frac{PV }{T} = { constant} \right)$ is applicable to