\(\int \frac{1}{x^2\left(x^4+1\right)^{3 / 4}} d x\) is equal to :

If \(x=a t^2, y=2 a t\); then \(\frac{d^2 y}{d x^2}\) is equal to

The system of linear equations \(k x+5 y=5,2 x+3 y=5\) will be consistent if

The point of local maxima of the function \(f(x)=(x-2)^5(x+2)^2\) is

\(\int \frac{d x}{x^3 \sqrt{\left(1+x^4\right)}}=\)

If \(\vec{a} \cdot \vec{b}=\vec{a} \cdot \vec{c}, \vec{a} \times \vec{b}=\vec{a} \times \vec{c}\) and \(\vec{a} \neq \overrightarrow{0}\), then the vector \(\vec{b}\) is equal to:

For \(A=\left[\begin{array}{lll}a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33}\end{array}\right]\) if \(M_{i j}\) and \(A_{i j}\) are the minor and the cofactor of \(a_{i j}\) respectively, then \(|A|\) equals to :
(A) \(a_{11} A_{11}+a_{12} A_{12}+a_{13} A_{13}\)
(B) \(a_{21} A_{12}+a_{22} A_{22}+a_{23} A_{32}\)
(C) \(a_{11} M_{11}-a_{12} M_{12}+a_{13} M_{13}\)
(D) \(a_{11} M_{11}+a_{12} M_{12}+a_{13} M_{13}\)
Choose the correct answer from the options given below :

The number of all possible matrices of order \(2 \times 2\) with each entry \(0,1,2\), and 3 is:

Read the passage carefully and answer the Questions
The concentration dependence of the rate of a reaction is called the differential rate equation. It is not always convenient to determine the instantaneous rate, as it is measured by calculating the slope of the tangent at point 't' in the concentration vs time plot. This makes it difficult to determine the rate and hence the order of the reaction. This difficulty is overcome by integrating the differential rate equation. This integrated rate equation gives a direct relation between concentrations at different times and the rate constant. The integrated rate equations are different for the reactions having different reaction orders.
Choose the correct statement regarding kinetics of a chemical reaction.

Which of the following reagents convert an alcohol into an alkyl chloride?
(A) Conc. Hydrogen Chloride
(B) Phosphorus trichloride
(C) Phosphorus pentachloride
(D) Thionyl Chloride
Choose the correct answer from the options given below:

Arrange the following in order of their appearance, if a sperm starts travelling from testicular lobules?
(A) Urethra
(B) Vas deferens
(C) Urethral meatus
(D) Vasa efferentia
Choose the correct answer from the options given below:

Identify the final product \((C)\) in the reaction given below:
\(CH _3 CH _2 I + NaCN \rightarrow A \rightarrow\) (Partial hydrolysis \(\left./ OH ^{-}\right) \rightarrow b + NaOH + Br _2 \rightarrow C ?\)

The point on the unit circle with center (0, 0); where tangents are equally inclined to the co-ordinate axes are: