List of practice Questions

The vernier scale of a travelling microscope has $50$ divisions which coincide with $49$ main scale divisions. If each main scale division is $0.5\, mm$, then the least count of the microscope is
The velocity of centre of mass of the system remains constant, if the total external force acting on the system is
The velocity of light in air is $3 \times 10^8 \,m s^{-1}$ and that in water is $2.2 \times 10^8\, m s^{-1}$. The polarising angle of incidence is
The variation of density of a solid with temperature is given by the formula
The vector of ??reakbone fever?
The velocity-displacement graph of a particle is as shown in the figure. Which of the following graphs correctly represents the variation of acceleration with displacement ?
The velocity head of a stream of water is 40 cm. Then, the velocity of flow of water is
The variance of first 25 natural numbers is
The variance of first n natural numbers is :
The variance of random variable $X$ i.e. $\sigma^{2}_{x}$ or var$(X)$ is equal to
The variance of the numbers $2, 3, 11 $ and $x$ is $\frac{49}{4}$. Find the value of $x$.
The van't Hoff factor for a very dilute solution of $Fe_2(SO_4)_3$ is
The van't Hoff factor for a dilute solution of glucose is
The values of the determinant $ \begin{vmatrix} x+1& x+2 &x+4 \\[0.3em] x+3 & x+5 & x+8 & \\[0.3em] x+7 & x+10 & x+14 \end{vmatrix}$
The values of x satisfying $| x - 4 | + | x - 9 | = 5$, is :
The values of colligative properties of colloidal solution are of small order in comparison to those shown by true solutions of same concentration because of colloidal particles
The values of coefficients to balance the following reaction are $Cr\left(OH\right)_{3} + ClO^{-}+OH^{-}\to CrO_{4}^{2-}+ Cl^{-} + H_{2}O$
The value of x, so that the matrix $=\begin{bmatrix} x+a &b& c \\[0.3em] a& x+b & c \\[0.3em] a & b & x+c \end{bmatrix}$ has rank 3 , is
The value of $|z|^2 + |z - 3|^2 + |z - i|^2$ is minimum when $z$ equals.
The value of x where $\begin{bmatrix}6&x-2\\ 3&x\end{bmatrix}$, has no inverse is :
The value of universal gravitational constant $G=6.67 \times 10^{-11}\,N\,m^{2}\,kg^{-2}$. The value of $G$ in units of $g^{-1}\, cm^3\, s^{-2}$ is
The value of the sum $(\,^nC_1)^2+(\,^nC_2)^2+(\,^nC_3)^2+...+(\,^nC_n)^2$ is
The value of the term independent of x in the expansion of $\left(1+\frac{x}{2}-\frac{2}{x}\right)^{4}, x \ne 0$ is equal to
The value of the magnetic field induction at the centre of the coil, if l = 2A, h= 10 cm. in the following figure is
The value of the expression $\frac{1}{2} ( \sqrt{3} \sin 75^{\circ} - \cos \, 75^{\circ} )$ is :