The value of \( C \) in Mean value theorem for the function \( f(x)=x^{2} \) in \( [2,4] \) is

If \( \vec{a}=\hat{i}+\lambda \hat{j}+2 \hat{k} ; \vec{b}=\mu \hat{i}+\hat{j}-\hat{k} \) are orthogonal and \( |\vec{a}|=|\vec{b}| \) then
\( (\lambda, \mu)= \)

If \(A, B\) and \(C\) are three independent events such that \(P(A)=P(B)=P(C)=P\), then \(P\) (at least two of \(A, B\) and \(C\) occur) is equal to

If \(f(x)=\sin ^{-1}\left(\frac{2 x}{1+x^{2}}\right)\), then \(f^{\prime}(\sqrt{3})\) is

If \(f(x)=a x+b\), where \(a\) and \(b\) are integers, \(f(-1)=-5\) and \(f(\beta)=3\), then \(a\) and \(b\) are respectively

If \(a>b>0, \sec ^{-1} \frac{a+b}{a-b}=2 \sin ^{-1} x\), then \(x\) is

Acute angle between the line \( \frac{x-5}{2}=\frac{y+1}{-1}=\frac{z+4}{1} \) and the plane \( 3 x-4 y-z+5=0 \) is

If \(4^{\text {th }}, 10^{\text {th }}\) and \(16^{\text {th }}\) terms of a G.P. are \(\mathrm{x}, \mathrm{y}\) and z respectively, then

Match List-I with List-II
\begin{array}{|l|l|l|l|}\hline & \text{List-I (Types of redox reactions)} & & \text{List-II (Examples)} \\\hline \text{a}. & \text{Combination reaction} & \text{(i)} & \mathrm{Cl}_{2(\mathrm{~g})}+2 \mathrm{Br}_{(\mathrm{aq})}^{-} \rightarrow 2 \mathrm{Cl}_{(\mathrm{aq})}^{-}+\mathrm{Br}_{2(\mathrm{l})} \\\hline \text{b.} & \text{Decomposition reaction} & \text{(ii)} & 2 \mathrm{H}_2 \mathrm{O}_{2(\mathrm{aq})} \rightarrow 2 \mathrm{H}_2 \mathrm{O}_{(1)}+\mathrm{O}_{2(\mathrm{~g})} \\\hline \text{c.} & \text{Displacement reaction} & \text{(iii)} & \mathrm{CH}_{4(\mathrm{~g})}+2 \mathrm{O}_{2(\mathrm{~g})} \xrightarrow{\Delta} \mathrm{CO}_{2(\mathrm{~g})}+2 \mathrm{H}_2 \mathrm{O}_{(1)} \\\hline \text{d.} & \text{Disproportionation reaction} & \text{(iv)} & \mathrm{H}_2 \mathrm{O}_{(1)} \xrightarrow{\Delta} 2 \mathrm{H}_{2(\mathrm{~g})}+\mathrm{O}_{2(\mathrm{~g})} \\\hline\end{array}

Choose the correct answer from the options given below.

A cubical Gaussian surface has side of length \(a=10 \mathrm{~cm}\). Electric field lines are parallel to \(X\)-axis as shown in figure. The magnitudes of electric fields through surfaces \(A B C D\) and \(E F G H\) are \(6 \mathrm{kNC}^{-1}\) and \(9 \mathrm{kNC}^{-1}\) respectively. Then, the total charge enclosed by the cube is
[Take, \(\varepsilon_0=9 \times 10^{-12} \mathrm{Fm}^{-1}\) ]

In tRNA the region that binds with mRNA is

In Kjeldahl's method, ammonia from \(5 \mathrm{~g}\) of food neutralizes \(30 \mathrm{~cm}^{3}\) of \(0.1 \mathrm{~N}\) acid. The percentage of nitrogen in the food is

An inductor of inductance \( L \) and resistor \( R \) are joined together in series and connected by a source of frequency \( \omega \). The power dissipated in the circuit is