List of practice Questions

For x > 0, $ lim_{ x \to 0} \Bigg [ (sin \, x)^{1/x} + \bigg( \frac{1}{x}\bigg)^{sin \, x} \Bigg ] $ is

Let, $\overrightarrow{a}=\widehat{i}+2\widehat{j}+\widehat{k}, \overrightarrow{c}=\widehat{i}+\widehat{j}+\widehat{k}.$ A vector coplanar to $\overrightarrow{a}$ and $\overrightarrow{c}$ of magnitude $\frac{1}{\sqrt{3}},$ then the vector is

If a, b,c are the sides of a triangle ABC such that $x^2 - 2(a+b+c)x+3\lambda(ab+bc+ca)=0$ has real roots, then

If $r, s, t$ are prime numbers and p , q are the positive integers such th a t LCM of p , q is $r^2 s^4 t^2$ then the number of ordered pairs (p, q) is

Half-life of a radioactive substance A is 4 days. The probability that a nucleus will decay in two half-lives is

The smallest ketone and its next homologue are reacted with $NH_2OH$ to form oxime

(I) 1, 2-dihydroxy benzene (II) 1, 3-dihydroxy benzene (III) 1, 4-dihydroxy benzene (IV) Hydroxy benzene The increasing order of boiling points of above mentioned alcohols is

$CuSO_4$decolourises on addition of KCN, the product is

A solution when diluted with $H_2 0$ and boiled, it gives a white precipitate. On addition of excess $NH_4 CI / NH_4 0H$, the volume of precipitate decreases leaving behind a white gelatinous precipitate. Identify the precipitate which dissolves in $NH_4 OH / NH_4 CI.$

$\xrightarrow{Cl_2,hv\, \, }N(isomeric\, products) C_5 H_{11} Cl$ $\xrightarrow{\, \, Fractional\, distillation \, }M(isomeric\, products)$ What are N and M?

$ MgSO_4 $ on reaction with $ NH_4OH $ and $ Na_2HPO_4 $ forms a white crystalline precipitate. What is its formula?

$MgSO_4$ on reaction with $NH_4 OH $ and $ Na_2 HPO_4$ forms a white crystalline precipitate. What is its formula?

A solid sphere of radius R has moment of inertia I about its geometrical axis. It is melted into a disc of radius r and thickness t. If it's moment of inertia about the tangential axis (which is perpendicular to plane of the disc), is also equal to I, then the value of r is equal to

Which of the following statement is (are) correct in the given figure ?

A solid sphere is in pure rolling motion on an inclined surface having inclination $?$

A double star system consists of two stars A and B which have time periods $T_ A $ and $T_B $ . Radius $ R_A $ and $ R_B $ and mass $ M_A $ and $M_B $ . Choose the correct option

If $e_1$ is the eccentricity of the ellipse $\frac {x^2}{16}+\frac{y^2}{25}=1$ and $e_2$ is the eccentricity of the hyperbola passing through the foci of the ellipse and $e_1e_2=1$ then equation of the hyperbola is

Angle of banking for a vehicle speed of $ 10\,m/s $ for a radius of curvature $ 10\,m $ is (assume $ g=10\,m/s^{2} $ )

Equation of progressive wave is $\hspace25mm y = A \sin \big(10 \pi x + 11 \pi t + \frac{\pi}{3}$.

Which of the following have highest electron affinity?

Which of the following will show geometrical isomerism?

Which one of the following contain isopropyl group?

Which of the following electronic configuration represents noble gas?

Which of the following amino acid is optically inactive?

Which have not left any evidences of organic evolution?