Inverse of a diagonal non-singular matrix is

diagonal matrix

zero matrix

skew symmetric matrix

scalar matrix

Which of the following is false?

(N, +) is a semi-group

(N, .) is a group

Set of even integers is a group under usual addition

(Z, +) is a group

For any two real numbers, an operation ∗ defined by a ∗ b = 1 + ab is

neither commutative nor associative

commutative but not associative

both commutative and associative

associative but not commutative

If \(\large \alpha \) and \(\large \beta \) are the roots of x\(\large ^{2} \) - ax + b\(\large ^{2} \) = 0, then \(\large \alpha ^{2} \) +\(\large \beta ^{2} \) is equal to

a\(\large ^{2} \) -2b\(\large ^{2} \)

2a\(\large ^{2} \) - b\(\large ^{2} \)

a\(\large ^{2} \) -b\(\large ^{2} \)

If \(\large \vec{a}=i+2j+2k,\left | \vec{b} \right |=5\) and the angle between  \(\large \vec{a}\) and \(\large \vec{b}\) is \(\large \frac{\pi }{6}\) , then the area of the triangle formed by these two vectors as two sides is

\(\large \frac{15 }{2}\)

15

\(\large \frac{15 }{4}\)

\(\large \frac{15\sqrt{3}}{2}\)

Derivative of tan\(\large ^{-1}\) \(\large \left ( \frac{x}{\sqrt{1-x^{2}}} \right )\) with respect to sin\(\large ^{-1}\) (3x – 4x\(\large ^{3}\)) is _____________

\(\large \frac{1}{\sqrt{1-x^{2}}}\)

\(\large \frac{3}{\sqrt{1-x^{2}}}\)

3

\(\large \frac{1}{3}\)

Slope of Normal to the curve \(\Large y=x^{2}-\frac{1}{x^{2}}at\left ( -1,0 \right )\) is

\(\Large \frac{1}{4}\)

\(\large- \frac{1}{4}\)

4

-4

A value of \(\theta \) for which\(\frac{2+3i\, sin\theta }{1-2i \, sin\theta }\)
is purely imaginary, is :

\(\frac{\pi }{3}\)

\(\frac{\pi }{6}\)

\(sin^{-1\left ( \frac{\sqrt{3}}{4} \right )}\)

\(sin^{-1}\left ( \frac{1}{\sqrt{3}} \right )\)