If \(x = at^2, y = 2at\) then \(\frac{d^2y}{dx^2} =\)

Acute angle between the lines \(\frac{x}{3}=\frac{y}{4}=\frac{z}{5}\) and \(\frac{x-1}{4}=\frac{y+1}{-3}=\frac{z+10}{5}\) is :

If \(A\) and \(B\) are square matrices of the same order 3 , such that \(\operatorname{det}(A)=3\) and \(A B=3 I\), where \(I\) is an identity matrix of order 3. Then the value of \(\operatorname{det}(B)\) is :

If order of matrices \(A, B\) and \(C\) are \(4 \times 3,5 \times 4\) and \(3 \times 7\) respectively, then order of \(C^{\prime} \times\left(A^{\prime} \times B^{\prime}\right)\) is :

If \(\left|\begin{array}{ccc}-1 & 1 & 0 \\ a & b & 1 \\ 1 & 2 & 1\end{array}\right|\) is a singular matrix, then the relation between a and b is:

The area of the region bounded by the circle \(x^2+y^2=1\) is ___________ sq. units.

Value of \(\int\left(\frac{1}{\log x}-\frac{1}{(\log x)^2}\right) d x\) is

The number of electric lines of force originating from a charge of 1 C is:

"The correct statement regarding the basicity of arylamines is :
A. Arylamines are generally more basic than alkylamines because of aryl group.
B. Aryl amines are generally more basic than alkylamines because the nitrogen atom in arylamines is 𝑠⁢𝑝 hybridised.
C. Aryl amines are generally less basic than alkylamines because the lone pair of electrons of nitrogen are delocalised by interaction with the pi electrons of the aromatic ring.
D. Aryl amines are generally more basic than alkylamines because the lone pair of electron of nitrogen are not delocalised by interaction with the pi electrons of aromatic ring.
E. Aryl amines are generally weaker bases than alkylamines due to electron withdrawing nature shown by aryl group.
Choose the correct answer from the options given below:"

Which of the following statements are correct with reference to the following reaction?
\(\mathrm{Zn}(s)+\mathrm{Cu}^{2+}(a q) \rightarrow \mathrm{Zn}^{2+}(a q)+\mathrm{Cu}(s)\)
(A) The reduction reaction is
\(\mathrm{Cu}^{2+}(a q)+2 e^{-} \rightarrow \mathrm{Cu}(s)\)
(B) The oxidation reaction is
\(\mathrm{Zn}(s) \rightarrow \mathrm{Zn}^{2+}(a q)+2 e^{-}\)
(C) The two half (oxidation and reduction) reactions constitute redox couple.
(D) The given reaction is not a redox reaction.
Choose the correct answer from the options given below:

Two large plane parallel sheets with equal but opposite surface charge densities +\(\sigma\) and -\(\sigma\). A point charge q placed at points \(P_1, P_2,\) and \(P_3\) experiences forces \(F_1, F_2,\) and \(F_3\) respectively. Then :

The molality of a solution prepared by dissolving \(4 . 0 ~ g ~ N a O H\) in \(1 0 0 0 ~ m L\) distilled water is __________ .
(Assume that the density of water is \(1 ~ g ~ m L ~ m L ^{ 1 }\) )

GnRH is secreted by: