List of practice Questions

ABCD is a parallelogram. If $P$ and $Q$ are the respective midpoints of$\overrightarrow{\mathrm{BC}}$ and $\overrightarrow{\mathrm{AD}},$ then $,\overrightarrow{\mathrm{AB}}+\overrightarrow{\mathrm{DC}}$ is equal to

The minimum value of $f(x)={\sin }^{4}x+{\cos }^{4}x,0\le x\le \frac{\pi }{2}$

An integrating factor of the differential equation $x\frac{dy}{dx}+y\log x=x{e}^x{x}^{-\frac{1}{2}\log x},(x>0)$

If $\overrightarrow{A}=\hat{i}+2\overrightarrow{j}+3\hat{k},\overrightarrow{B}=-\hat{i}+2\hat{j}+\hat{k},\overrightarrow{C}=3\hat{i}+j$ and $\overrightarrow{A}+1\overrightarrow{B}$ is perpendicular to $\overrightarrow{\mathrm{C}},$ thent is equal to

The probability that in a family of 5 members, exactly 2 members have birthdays on Sunday, is

The value of $\sec [{\tan }^{-1}\left(\frac{b+a}{b-a}\right)-{\tan }^{-1}\left(\frac{a}{b}\right)]$

If A1, A2; G1, G2; and H1, H2 are two AMs, GMs and HMs between two quantities, then the value of $\frac{G_1{G}_2}{H_1{H}_2}$ is

An electron jumps from the fourth orbit to the second orbit of hydrogen atom. If Rydberg’s constant R is equal to 10⁷ m^–1, then the frequency of the emitted radiation in Hz will be

A galvanometer has 40 divisions and a sensitivity of 12 μA/div. it can be converted into a voltmeter to read 3 V by connecting-

products can be

Among the following complex compounds–${\mathrm{K}}_3[\mathrm{Fe}(\mathrm{CN}{)}_6]$$(i)$$\left[\mathrm{Co}{\left({\mathrm{NH}}_3\right)}_6\right]{\mathrm{Cl}}_3$(ii) ${\mathrm{K}}_2[\mathrm{Pt}(\mathrm{CN}{)}_4]$$(\mathrm{iii})$$\left[\mathrm{Zn}{\left({\mathrm{H}}_2\mathrm{O}\right)}_6\right]{\left({\mathrm{NO}}_3\right)}_2$$(iv)$diamagnetic complexes are –

The solubility product of silver chloride is 1.8 × 10^-10 at 298 k. The solubility of AgCl in 0.01 M KCl aqueous solution in mol dm^-3 is

The actinoids exhibit more number of oxidation states in general than the lanthanoids because

The curve represented by the equation 4x² + 16y² - 24x - 32y - 12 = 0 is

The derivative of${\tan }^{-1}\left(\frac{\sqrt{1+x^2}-1}{x}\right)$ with respect to ${\tan }^{-1}\left(\frac{2x\sqrt{1-x^2}}{1-2x^2}\right)$ at $x=0$

The voltage gain is the highest in

A symmetric double convex lens is cut in two equal parts by a plane perpendicular to the principal axis. If the power of the original lens is 4D, the power of a cut lens will be

Five balls numbered 1 to 5 are suspended using separate threads. The pairs of balls (1, 2), (2, 4) and (5, 1) show attraction while the pairs (2, 3) and (4, 5) show repulsion. The ball 1 is :

If momentum $(p)$, area $(A)$ and time $(t)$ are taken to be fundamental quantities, then energy has the dimensional formula

Consider the following reactions, ‘I’ and ‘II’:

Which of the above reactions effectively give(s) 4-methyl hex-2-yne?

In OF2, H2O and OCl2, there is sp³ hybridisation of central atom. The bond length and bond angle of OF2, H2O and OCl2 are given as:

Which of the following is the correct statement about the differences in the bond angles of the compounds given above?

A sample containing 1.0 mole of an ideal gas is expanded reversibly and isothermally to ten times its original volume in two separate experiments. The expansion is carried out at 300 K and 600 K, respectively. Choose the correct option.

Which of the following statements about natural rubber is true?

A compound 'X' on heating gives a colourless gas. The residue is dissolved in water to obtain 'Y'. Excess CO2 is passed through aqueous solution of 'Y', when 'Z' is formed. 'Z', on gentle heating, gives back 'X'. The compound 'X' is

Acylation of the benzene ring is brought about by reacting it with acid halides in the presence of a Lewis acid. The compound ‘X’ used to bring about the above conversion is