List of practice Questions

If a car accelerates from 20 m/s to 40 m/s in 10 s and its forward thrust is equal to 3 kN, what is the mass of car?
The moment of the force, \(\overrightarrow{F}=4\hat{i}+5\hat{j}-6\hat{k}\) at (2, 0, -3), about the point (2, -2, -2), is given by

A juggler keeps on moving four balls in the air throwing the balls after intervals. When one ball leaves his hand (speed = 20ms-1) the position of other balls (height in metre) will be (Take g = 10ms-2)

There is a plane of uniform positive charge density \( \sigma \) parallel to the yz-plane and located at \( x = 2d \). A point charge \( q^+ \) is placed at the origin. Solve for the position \( x \) along the x-axis, where a positive test charge will have a net force of zero. 

If the price of Sugar increases by 20%, and Salman intends to spend only an additional 5% on Sugar, then find out the percentage decrease in his sugar consumption.
Electric potential at any point is $V = - 5x + 3y + \sqrt {15 z}, $then the magnitude of the electric field is
Two cells of internal resistances $r_1 $ and $r_2 $ and of same emf are connected in series, across a resistor of resistance R. If the terminal potential difference across the cells of internal resistance $r_1$ is zero, then the value of R is
Which of the following animals does not undergo metamorphosis ?
Which one of these animals is not a homeotherm ?
Which of the following organisms are known as chief producers in the oceans ?
The number of ways in which first, second and third prizes can be given to $5$ competitors is
$\displaystyle\lim_{x\to0} \sqrt{\frac{x-\sin x}{x+\sin^{2}x}} $ is equal to
The coefficient of $x^3$ in the expansion of $\left(x -\frac{1}{x}\right)^{7}$ is :
The value of $\displaystyle\lim_{n \to\infty} \frac{1+2+3+...n}{n^{2}+100}$ is equal to :
If $ \hat{i} + \hat{j}, \hat{j} + \hat{k}, \hat{i} + \hat{k}$ are the position vectors of the vertices of a triangle $ABC$ taken in order, then $\angle A$ is equal to
The equation of the circle which passes through the point $(4, 5)$ and has its centre at $(2, 2)$ is
In how many ways can $12$ gentlemen sit around a round table so that three specified gentlemen are always together?
Eccentricity of ellipse $\frac{x^{2} }{a^{2}} + \frac{y^{2}}{b^{2}} = 1 $ if it passes through point $(9, 5)$ and $(12, 4)$ is
If $a, b, c$ are in G.P., then
If $A = \frac{1}{3} \begin{bmatrix}1&2&2\\ 2&1&-2\\ a&2&b\end{bmatrix} $ is an orthogonal matrix, then
Choose the answer figure which completes the problem figure matrix:
Problem Figure
figure matrix
Beryllium shows diagonal relationship with aluminium. Which of the following similarity is incorrect ?
Chloroform, $CHCl _{3}$, boils at $61.7^{\circ} C$. If the $K_{b}$ for chloroform is $3.63^{\circ} C / molal$, what is the boiling point of a solution of $15.0\, kg$ of $CHCl _{3}$ and $0.616\, kg$ of acenaphthalene, $C _{12} H _{10}$ ?
If $V$ is the volume of one molecule of gas under given conditions, the van der Waal?s constant $b$ is
For the reaction taking place at certain temperature ${NH_2 COONH_4 (s) <=> 2NH_3 (g) + CO_2 (g) }$, if equilibrium pressure is 3X bar then $ \Delta_G$ would be