If \(\vec{a}, \vec{b}\) and \(\vec{c}\) are three vectors such that \(\vec{a}+\vec{b}+\vec{c}=\overrightarrow{0},|\vec{a}|=7,|\vec{b}|=3\) and \(|\vec{c}|=5\), then angle between \(\vec{b}\) and \(\vec{c}\) is

\(\int \frac{1 - \sin x}{\cos^2 x} dx\) is equal to:

A linear programming problem is as follows:
Maximize/minimize objective function \(z=2 x-y+5\) subject to constraints:
\(3 x+4 y \leq 60, \quad x+3 y \leq 30, \quad x \geq 0, y \geq 0 .\)
If the corner points of feasible region are \(A(0,10), B(12,6), C(20,0), O(0,0)\), then which of the following is true:

A person can row a boat at \(5 km / hr\) in still water. If the speed of water current in a river is \(1 km / hr\), and it takes him \(1\) hour to row to a place and come back, how far off is the place?

Which of the following statements are true
A. \(\vec{a}\) and \(-\vec{a}\) are always collinear.
B. Two collinear vectors are always equal in magnitude.
C. Two vectors having the same magnitude are equal.
D. Two collinear vectors having the same magnitude are equal.
E. If \(\hat{p}\) is a unit vector along line \(l\) then the projection of vector \(\vec{a}\) on line \(l\) is given by \(\vec{a} \cdot \hat{p}\)
Choose the correct answer from the options given below:

A bond of face value ₹1000 has a coupon rate 10% per annum paid semi-annually and matures in 4 years. If present value of the bond is ₹1100, then yield to maturity is:

Area of the region bounded by \(y=x^2\) and the line \(y=16\) is

Energy gap between valence band and conduction band of a semiconductor is approximately :

The value of the integral \(I=\int_{-3}^3|x| d x\) is:

If \(A=\left[\begin{array}{ccc}2 & 3 & 1 \\ 2 & -1 & 0\end{array}\right]\) and \(B^T=\left[\begin{array}{cc}4 & 4 \\ 6 & -2 \\ 2 & 0\end{array}\right]\) then \(4 A+B\) is

Area of cross section of a wire \(A\) is twice of \(B\) (given the wires are of the same length and of same material) then whose resistance will be more?

The electric field and magnetic field of a plane electromagnetic wave propagating in vacuum are expressed as
\(E_x=E_0 \sin (k z-\omega t)\)
\(B_y=B_0 \sin (k z-\omega t)\)
Which of the following statements are correct?
(A). The wave is propagating along the z- direction.
(B). The electric field Ex and magnetic field By are perpendicular to each other and perpendicular to the z direction.
(C) The electric and magnetic fields Ex and By are perpendicular to each other, and parallel to the direction of propagation.
(D) k is related to the wave length À of the wave by the usual equation \(k = A / 2 Tt\)
Choose the correct answer from the options given below:

Identify the incorrect fact about genetic modification.