The matrix \(A=\left[\begin{array}{ccc}a & -1 & 4 \\ -3 & 0 & 1 \\ -1 & 1 & 2\end{array}\right]\) is not invertible only if a =

If \(y=\sqrt{\frac{1-\sin ^{-1} x}{1+\sin ^{-1} x}}\), then \(\left(\frac{\mathrm{dy}}{\mathrm{d} x}\right)\) at \(x=0\) is

If \(x=-2\) and \(x=4\) are the extreme points of \(y=x^3-\alpha x^2-\beta x+5\), then

The co-ordinates of foci of the ellipse \(16 x^{2}+9 y^{2}=144\) are

If the area of a parallelogram whose diagonals are represented by vectors \(3 \hat{i}+\lambda \hat{j}+2 \hat{k}\) and \(\hat{i}-2 \hat{j}+3 \hat{k}\) is \(\frac{\sqrt{117}}{2}\) sq. units, then \(\lambda=\)

\(\int_2^5 2[x] d
18x=\{\) where \([x]\) denotes the greatest integer function \(\leq x\}\)

The area (in sq. units) of the region bounded by curves \(y=3 x+1, y=4 x+1\) and \(x=3\) is

If for some positive \(x \hat{I} R\), the frequency distribution of the marks obtained by 20 students in a certain test, is as follows

Then the mean of the marks is

If the planes \(\bar{r} \cdot(2 \hat{i}-\lambda \hat{j}+\hat{k})=3\) and \(\bar{r} \cdot(4 \hat{i}-\hat{j}+\mu \hat{k})=5\) are paralle, then values of \(\lambda\) and \(\mu\) are respectively

Which of the following is not a homogeneous function?

Select the correct statement/s regarding blood groups in human.
i. Some genetically determined blood group systems are ABO, Rh, Duffy, Lewis, Bombay blood group etc.
ii. Three types of agglutinogens are present on surface of human RBCs such as A, B and D.
iii. Individuals with blood group "AB Rh +ve" have A, B and D antigens on the surface of their RBCs and both antibodies 'a' and 'b' in their plasma.
iv. Haemolytic disease of Newborn occurs when mother with Rh-ve blood group conceives Rh -ve foetus.
v. Individuals with 'AB' blood group are called universal donors while those with 'O' blood group are called universal acceptors, with reference to blood transfusion.

A zener diode, having breakdown voltage 15 V is used in a voltage regulator circuit as shown. The current through the zener diode is

Two coils \(P\) and \(Q\) each of radius \(R\) carry currents I and \(\sqrt{8} \mathrm{I}\) respectively in same direction. Those coils are lying in perpendicular planes such that they have a common centre. The magnitude of the magnetic field at the common centre of the two coils is ( \(\mu_0=\) permeability of free space)