List of practice Questions

If $ 3\le 3t-18\le 18, $ then which one of the following is true?

If $A$ and $B$ are non-empty sets such that $A \supset B$, then

If $a , \,b$ and $c$ are three non-zero vectors such that each one of them being perpendicular to the sum of the other two vectors, then the value of $| a + b + c |^{2}$ is

If f(x)=$ \left(\frac{x}{2}\right)^{10}, then\, f \left(1\right)+\frac{f '\left(1\right)}{\lfloor1}+\frac{f \left(1\right)}{\lfloor2}+\frac{f '\left(1\right)}{\lfloor3}+\ldots+\frac{f ^{\left(10\right)}\left(1\right)}{\lfloor10}$ is equal to

If $ \theta $ is semi vertical angle of a cone of maximum volume and given slant height, then $ tan\theta $ is equal to

If the conjugate of a complex number $z$ is $\frac{1}{i - 1}$ , then $z$ is

If the semi-major axis of an ellipse is 3 and the latus rectum is $\frac{16}{9},$ then the standard equation of the ellipse is

The area bounded by the parabola $ {{y}^{2}}=8x $ and its latus rectum in sq unit is

The domain of the function $f \left(x\right)=\frac{\log_{2}\left(x+3\right)}{x^{2}+3x+2}$ is

The least integer satisfying $\frac{396}{10}-\frac{19-x}{10} < \frac{376}{10}-\frac{19-9x}{10}$ is

The value of the integral $\displaystyle \int_0^1$ $\frac{x^{3}}{1+x^{8}} dx$ is equal to

$\left(\frac{1+\cos\left(\frac{\pi}{12}\right) + i \sin\left(\frac{\pi}{12}\right)}{1+\cos \left(\frac{\pi}{12}\right) - i \sin\left(\frac{\pi}{12}\right)}\right)^{72}$ is equal to

If $6^{th}$ term of $G.P.$ is $2$, then the product of first $11$ terms of the $G.P.$ is equal to

If A\B = {a, b}, B\A = {c, d} and A\B = {e, f}, then the set B is equal to

If $^n$C$_2$ + $^n$C$_3$ = $^6$C$_3$ and $^n$C$_x$ = $^n$C$_3$, x ? 3, then the value of x is equal to

The area bounded by the curves $y = - x^2 + 3$ and $y = 0$ is

The number of diagonals in a hexagon is

Two numbers $x$ and $y$ have arithmetic mean $9$ and geometric mean $4$. Then $x$ and $y$ are the roots of

What do you think Dinamani is the name of? Give a reason for your answer.

Find three different irrational numbers between the rational numbers \(\frac{5}{7}\) and \(\frac{9}{11}\).

A battery of $6\,V$ and internal resistance $2 \Omega$ is connected to a silver voltameter. If the current of $1.5\, A$ flows through the circuit, the resistance of the voltameter is

A carbon resistor is marked with the ring coloured brown, black, green and gold. The resistance in ohm is

A Carnot engine is operating between a hot body and cold body maintained at temperature $T_1$ and $T_2$ respectively. Consider the following three cases : The temperature of the hot body is changed to $T_1 + \Delta T$ and cold body is at $T_2$ : The temperature of the hot body is at $T_1$ and cold body is changed to $T_2 + \Delta T$ : The temperature of the hot body is at $T_1$ and cold body is changed to $T_2 - \Delta T$

A ground receiver receives a signal at $5\, MHz$, transmitted by a ground transmitter at a height of $320\, m$, which is $110\, km$ away from it. Then it can communicate through (radius of earth $R \,= \,6400 \,km$)

A linear harmonic oscillator with force constant 3.210N m and amplitude 0.01 m has a