List of practice Questions

The radius of the circle $x^2+Y^2+4x+6y+13=0$ is
The center of the circle $x = 2 + 3 \cos \theta ,y=3\, \sin \theta -1$ is
The sum of the focal distances of any point on the conic $\frac{x^2}{25}+\frac{y^2}{16}=1$ is
In a $\triangle A B C$ if the sides are $a=3, b=5$ and $c=4$, then $\sin \frac{B}{2}+\cos \frac{B}{2}$ is equal to :
$\int\limits_{0}^{\pi /4} \log (1 + \tan \, x ) dx$ is equal to :
$(0, - 1)$ and $(0, 3)$ are two opposite vertices of a square. The other two vertices are :

If \(\omega\) is a complex cube root of unity, then $ \begin{vmatrix} 1 & \omega& \omega^2 \\[0.3em] \omega& \omega^2 & 1 \\[0.3em] \omega^2 & 1& \omega \end{vmatrix}$ is equal to

The solution of $\sin^{-1}\,x-\sin^{-1}\,2x=\pm\frac{\pi}{3}$ is
The area bounded by the parabola $y^2 = 4ax$ and the line $x = a$ and $x = 4a$ is
Which of the following species has a bond order other than $3$ ?
Nylon-$66$ is an example of:
Which one of the following product is formed when calcium salt of adipic acid is heated ?
A can is taken out from a refrigerator at $0^{\circ} C$. The atmospheric temperature is $25^{\circ}C$. If $t_1$ is the time taken to heat from $0^{\circ} C$ to $5^{\circ} C$ and $t_2$ is the time taken from $10^{\circ} C$ to $15^{\circ}C$, then :
Initially two gas samples $1$ and $2$ are at the same condition. The volume of the two are halved, one isothermally and the other adiabatically. What is the relation between the final pressure $P_1$ and $ P_2$ ?
A rocket of mass $1000\, kg$ is exhaust gases at a rate of $4\, kg/s$ with a velocity $3000\, m/s$. The thrust developed on the rocket is :
Energy gas between valence band and conduction band of a semiconductor is :
A body of mass $5\, kg$ is suspended by a spring balance on an inclined plane as shown in figure. The spring balance measure :
Angular momentum is conserved :
An object is placed at a distance $20\, cm$ from the pole of a convex mirror of focal length $20\, cm$. The image is produced at :
A proton moving vertically downward enters a magnetic field pointing towards north. In which direction proton will deflect?
In $2 HI \rightleftharpoons H _{2}+ I _{2}$ , the forward reaction is not affected by change in :
A train covers 180 km distance in 4 hours. Another train covers the same distance in 1 hour less.What is the difference in the distances covered by these trains in one hour?
A train covered a certain distance at a uniform speed. If the train had been 6 km/hr faster, then it would have taken 4 hours less than the scheduled time. And, if the train were slower by 6km/hr, then the train would have taken 6 hours more than the scheduled time. The length of the journey is
A ladder 15 m long reaches a window which is 9 m above the ground on one side of a street.Keeping its foot at the same point, the ladder is turned to the other side of the street to reach a window 12 m high. Find the width of the street.
The horizontal distance between two trees of different heights is 60 m. The angle of depression of the top of the first tree when seen from the top of the second tree is \(45^\circ\). If the height of the second tree is 80 m, then find the height of the first tree.