The value of \( k \) such that the line \( \frac{x-4}{1}=\frac{y-2}{1}=\frac{z-k}{2} \) lies on the plane \( 2 x-4 y+z=7 \) is

If \(A\) is a matrix of order \(3 \times 3\), then \(\left(A^2\right)^{-1}\) is equal to

If a line makes angles \(90^{\circ}, 60^{\circ}\) and \(\theta\) with \(\mathrm{x}, \mathrm{y}\) and z axes respectively, where \(\theta\) is acute, then the value of \(\theta\) is

Recent studies suggest that \(12\%\) of the world population is left handed. Depending on parents' hand usage, the chances of having left handed children are as follows:
A: Both parents are left handed, chances of having left handed children \(= 24\%\)
B: Both parents are right handed, chances of having left handed children \(= 9\%\)
C: Father left handed and mother right handed, chances of having left handed children \(= 17\%\)
D: Father right handed and mother left handed, chances of having left handed children \(= 22\%\)
Given \(P(A) = P(B) = P(C) = P(D) = 1/4\) and L denotes child is left handed. What is the probability that \(P(A \mid L)\)?

If the angle between \( \vec{a} \) and \( \vec{b} \) is \( \frac{2 \Pi}{3} \) and the projection of \( \vec{a} \) in the direction of \( \vec{b} \) is \( -2 \), then \( \mid \) a
\( 1= \)

If \( U \) is the universal set with \( 100 \) elements; \( A \) and \( B \) are two sets such that \( n(A)=50, n(B)=60 \),
\( n(A \cap B)=20 \) then \( n\left(A^{\prime} \cap B^{\prime}\right)= \)

Consider the following statements :
Statement (I) : If either \(|\vec{a}|=0\) or \(|\vec{b}|=0\), then \(\vec{a} \cdot \vec{b}=0\)
Statement (II) : If \(\vec{a} \times \vec{b}=\overrightarrow{0}\), then \(a\) is perpendicular to \(b\).
Which of the following is correct?

The value of \(\int \frac{x e^{x} d x}{(1+x)^{2}}\) is equal to

Cooking is fast in a pressure cooker, because

The amount of energy released when one microgram of matter is annihilated is

The remainder when \(3^{100} \times 2^{50}\) is divided by 5 is

Which of the following aquatic plant does not show pollination by water?

Which one of the following has no unpaired electrons?