For any vector \(\vec{a}\), the value of \(|\vec{a} \times \hat{i}|^2+|\vec{a} \times \hat{j}|^2+|\vec{a} \times \hat{k}|^2\) is equal to :

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 maximum value of the function \(f(x)=-x^2+2 x-1\) is:

The slope of the normal to the curve \(y=2 x^2-4\) at \(P(1,-2)\) is:

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

The differential equation representing the family of curves \(y=A x+\frac{B}{x}, x \neq 0\), where A and B are arbitrary constants, is given by

If \(A =\left(\begin{array}{cc}2 & 3 \\ 5 & -2\end{array}\right)\), be such that \(A ^{-1}=K A\), then the value of \(K\) is :

Two slits are made 1 mm apart and the screen is placed 1 m away. What is the fringe width when a light used of wavelength 500 nm?

Read the passage carefully and give the answers to the question :
India was amongst the first countries in the world to initiate action plans and programmes at a national level to attain total reproductive health as a social goal.
These programmes called 'family planning' were initiated in 1951 and were periodically assessed over the past decades. Improved programmes covering wider reproduction-related areas are currently in operation. Creating awareness among the people about various reproduction-related aspects and providing facilities and support for building up a reproductively healthy society are the major tasks under these programmes.
'Saheli' - an oral contraceptive pill, also known as the 'Once a week' pill, was developed by :

Low concentration of oxygen in the blood and tissues of people living at high altitude is due to :

The corner points of the bounded feasible region for a linear programming problem (LPP) are \(\left(0, \frac{3}{2}\right),(1,2)\) and \((4,0)\).
If the objective function is \(Z=a x+b y\), where \(a\) and \(b\) are positive,
then the condition on \(a\) and \(b\) so that the maximum of \(Z\) occurs at \((1,2)\) and \((4,0)\) is :

The value of \(\int_2^4 \frac{x}{x^2+1} d x\) is equal to :

Which disease is not the sexually transmitted infection?