List of practice Questions

The sum of the infinite series $\sin^{-1}\frac{1}{\sqrt2}+\sin^{-1}\left(\frac{\sqrt2-1}{\sqrt6}\right)+\sin^{-1}\left(\frac{\sqrt3-\sqrt2}{\sqrt{12}}\right)+...+\sin^{-1}\left(\frac{\sqrt n-\sqrt{n-1}}{\sqrt{n(n+1)}}\right)$ is

The sum of the numbers $436.32$, $227.2$ and $0.301$ in appropriate significant figures is

The sum of two positive integers is at most 5. The difference between two times of second number and first number is at most 4. If the first number is x and second number y, then for maximizing the product of these two numbers, the mathematical formulation is

The sum of the infinite series $ 1 + (1 + a) x + (1 + a + a^2) x^2 + (1 + a + a^2 + a^3) x^3+ ............$ where $0 < a, x < 1$ is

The sum of the infinite series $\frac{1}{2}\left(\frac{1}{3}+\frac{1}{4}\right)-\frac{1}{4}\left(\frac{1}{3^{2}}+\frac{1}{4^{2}}\right)+\frac{1}{6}\left(\frac{1}{3^{3}}+\frac{1}{4^{3}}\right)-...$ is equal to

The sum of the divisors of $2^4\cdot 3^3 \cdot 5^3$ is

The sum of an infinite number of terms of a G.P. is 20, and the sum of their squares is 100, then the first term of the G.P. is

The sum of squares of deviations for 10 observations taken from mean 50 is 250. The co-efficient of variation is

The structure of $ICl^-_2$ is

The structure of $IF_7$ is

The structure and hybridization of $ {Si(CH_3)_4}$ is

The structure of diborane $(B_2H_6)$ contains

The structure of $H_{2}O_{2}$ is

The structure of $H_2O_2$ is

The state of hybridisation of S in $SO_2$ is similar to that of

The state of hybridization of xenon in $XeF_6$ is

The stem of Maize and Sugarcane have supporting roots coming out of the lower nodes of the stem. These are called

The stopping potential for the photoelectric emitted from a ;metal surface of work function 1.7 eV is 10.4V,Find the wavelength of the radiation used Also identify the energy levels in hydrogen atom, which will emit this Wavelength

The standard variance of 35, 40, 42, 36, 27 :

The standard $E^{\circ}$ values of few redox couples are $Zn^{2+}/ Zn = -0.76\, V$, $Ag^+/ Ag = + 0.80 \,V$, $Cu^{2+}/Cu = 0.34\, V$. Choose the correct option.

The standard scale of temperature is

The square root of $\left(-5-12i\right)$ is

The square root of the number $(5+12i)$ is

The stain used to visualise mitochondria is

The standard deviation for the following data is.