If \( \vec{a}\) is a unit vector and \((\vec{x}-\vec{a}) \cdot(\vec{x}+\vec{a})=15\), then the value of \(|\vec{x}|\) is :

If \(A=\left[\begin{array}{ccc}0 & 2 & c \\ a & b & -1 \\ -5 & 1 & 0\end{array}\right]\) is a skew-symmetric matrix, then \((a+b+c)^3=\)

Consider the following hypothesis \(H_0: \mu=315\) and \(H_a: \mu \neq 315\).
A sample of 60 provided a sample mean of 324.6 . The standard deviation ( \(\sigma\) ) is 14 and level of significance \(\alpha=0.05\). Then the confidence interval is :
[Given : \(Z_{\alpha / 2} \frac{14}{\sqrt{60}}=3.54\)]

If \(A\) is an invertible matrix of order 2 , then \(\operatorname{det}\left((\operatorname{adj} A)^{-1}\right)\) is equal to

Area (in sq. units) of the region bounded by the curves \(y = - 1, y = 2 x = y^3\) and \(x = 0\) is

Consider the LPP: Maximize \(Z=x+y\) subject to the constraints \(x+2 y \leq 70,2 x+y \leq 95, x, y \geq 0\). The optimal feasible solution is:

The value of \(2 y-3 x\), if \(2\left[\begin{array}{cc}x & 5 \\ 7 & y-3\end{array}\right]+\left[\begin{array}{cc}3 & -4 \\ 1 & 2\end{array}\right]=\left[\begin{array}{cc}7 & 6 \\ 15 & 14\end{array}\right]\) is :

In the circuit diagram shown in the figure, the resistance \( R_1 = 10 \, \Omega \), \( R_2 = 15 \, \Omega \) and E= 20 V. When the switch S is closed, the ratio of \( i_1 \) to \( i_3 \) will be:

Which of the following combination is stored in animals ?
(A) Amylose
(B) Cellulose
(C) Amylopectin
(D) Glycogen
(E) Lactose
Choose the correct answer from the options given below :

Read the passage carefully and answer the questions
The speed at which a chemical reaction takes place is called the rate of reaction. The rate of reaction depends on various factors like concentration of the reactants, temperature, etc. The relation between the rate of reaction and the concentration of reacting species is represented by the equation r = k[A]^x[B]^y, where x and y are the order of the reaction with respect to the reactants A and B, respectively. The overall order of the reaction is x + y. The rate of reaction can also be increased by the use of a catalyst which provides an alternate pathway of lower activation energy. It increases the rate of forward and backward reaction to an equal extent. It does not alter the Gibbs energy of the reaction.
The rate law of a reaction is given by r = k[CH₃OCH₃]^3/2. If the pressure is measured in bar and time in minutes, then the unit of rate constant will be

Based on CFT, in octahedral crystal field, d orbitals split into orbitals of \(t_{2g}\) and \(e_{g}\) sets. Which d orbitals forms the \(t_{2g}\) set?

If the random variable \(X\) follows the Poisson distribution such that \(P(X=k)=P(X=k+1)\), then the mean value of \(X\) is :

Area bounded by \(y=|x-5|\) and the \(x\)-axis between \(x=2\) and \(x=4\) is: