List of practice Questions

If $2A+3B =\begin{bmatrix} {2}&{-1} &{4}\\ {3}&{2}& {5} \\ \end{bmatrix} $ and $A+2B \begin{bmatrix} {5}&{0} &{3}\\ {1}&{6}& {2} \\ \end{bmatrix} $then $B =$
The equivalent resistance between the points P and Q in the network shown in the figure is given by:
Some physical constants are given in List 1 and their dimensional formulae are given in List 2.Match the correct pairs in the lists:
Which is not the unit of electric field?
Which of the following rays can be polarised?
Quantum nature can prove :
Huygens wave theory cant explain:
Vector which is perpendicular to $ a\,\cos \,\theta \,\hat{i}+b\,\sin \,\theta \,\,\hat{j} $ is
A radioactive isotope has a half life of $10$ days. If today $125$ mg is left over, what was its original weight $40$ days earlier ?
A circular coil of $20$ turns and radius $10 \,cm$ is placed in uniform magnetic field of $ 0.10\,T $ normal to the plane of the coil. If the current in coil is $5 \,A$, then the torque acting on the coil will be
The projection of the vector $2\hat{i}+\hat{j}-3\hat{k}$ on the vector $\hat{i}-2\hat{j}-\hat{k}$ is
An automobile travelling at 50 km/h, can be stopped at a distance of 40 m by applying brakes. If the same automobile is travelling at 90 km/h, all other conditions remaining same and assuming no skidding, the minimum stopping distance in metres is:
An ideal gas is taken from point $ A $ to the point $ B $ , as shown in the $ p-V $ diagram, keeping the temperature constant. The work done in the process is :
The prokaryotic cell does not contain :

A man buys a watch for Rs. 1950 in cash and sells it for Rs. 2200 at a credit of 1 year. If the rate of interest is \(10\%\) per annum, the man.

What is the distance in cm between two parallel chords of lengths 32 cm and 24 cm in a circle of radius 20 cm?
Four points A,B,C,D on a line: AB=BC=CD, length AB=1m. Ant at A to reach sugar at D, but repellents at B and C: ant cannot come within 1m of repellents.

Circle diameter = 3 cm. AB and MN are diameters, perpendicular. CG ⟂ AB, AE:EB = 1:2, DF ⟂ MN, NL:LM = 1:2. Find DH in cm.

Consider the triangle $ABC$ where $BC = 12$ cm, $DB = 9$ cm, $CD = 6$ cm, and $\angle BCD = \angle BAC$.

What is the ratio of the perimeter of $\triangle ADC$ to that of $\triangle BDC$? 

$P, Q, S, R$ are points on a circle of radius $r$, such that $PQR$ is an equilateral triangle and $PS$ is a diameter. What is the perimeter of quadrilateral $PQSR$?
Most firms consider expert individuals to be too elitist, temperamental, egocentric, and difficult to work with. Force such people to collaborate on a high-stakes project and they might just come to fisticuffs. Even the very notion of managing such a group seems unimaginable. So most organizations fall into default mode, setting up project teams of people who get along nicely.

Ram and Shyam run a race between points A and B, 5 km apart. Ram starts at 9:00 a.m. from A at a speed of 5 km/hr, reaches B, and returns to A at the same speed. Shyam starts at 9:45 a.m. from A at a speed of 10 km/hr, reaches B, and comes back to A at the same speed. 

If $R = \frac{30^{65} - 29^{65}}{30^{64} + 29^{64}}$, then:
If $a_1=1$ and $a_{n+1} - 3a_n + 2 = 4n$, find $a_{100}$.
Rightmost non-zero digits of $30^{270}$ is: