Correct Answer: B. 90cm²

Explanation

V = L x B x H

V = \(2x \times x \times x = 2x^3\)

= 54cm3

i.e. 2x3 = 54

x3 = \(\frac{54}{2}\) = 27

x = 3\(\sqrt{27}\)

x = 3

L = 2x i.e. 2 x 3 = 6cm

B = x i.e. x = 3cm

H = x i.e. x = 3cm

but A = 2(LB + LH + BH) = 2(6 x 3) + (6 x 3) + (3 x 3) = 2(18 + 18 + 9) = 2(45)

= 90cm²

Correct Answer: B. 54°

Explanation

In \(\bigtriangleup\) NPO + PNO + PNO +< NOP = 180^o(sum of interior angles of a \(\bigtriangleup\) )

i.e. NPO + 129 + 37 = 180

< NOP = 180 - (129 + 37) = 14^o

< MNP =< NOP = 14^o (alt.< s)

In \(\bigtriangleup\) MPN

< PMN +< MNP + y = 180(sum of interior angles of a \(\bigtriangleup\))

i.e. 112 + 14 + y = 180^o

y = 180 - (112 + 14) = 180 - 126 = 54^o

Correct Answer: D. 96cm²

Correct Answer: D. \(\begin{pmatrix} 0 & 10 \\ 9 & -4 \end{pmatrix}\)

Explanation

\(P = \begin{pmatrix} 2 & 1 \\ 5 & -3 \end{pmatrix} ; Q = \begin{pmatrix} 4 & -8 \\ 1 & -2 \end{pmatrix}\)

\(2P = \begin{pmatrix} 4 & 2 \\ 10 & -6 \end{pmatrix}\)

\(2P - Q = \begin{pmatrix} 4 & 2 \\ 10 & -6 \end{pmatrix} - \begin{pmatrix} 4 & -8 \\ 1 & -2 \end{pmatrix}\)

= \(\begin{pmatrix} 0 & 10 \\ 9 & -4 \end{pmatrix}\)

Correct Answer: C. 25

Explanation

6 + 8 + 6 + 5 = 25

Correct Answer: A. 25m/s

Explanation

\(\frac{720 \times 1000}{8 \times 60 \times 60}\) = \(\frac{20 \times 10}{8}\)

= \(\frac{200}{8}\)

= 25 m/s

Correct Answer: A. 16x²y(2 - 3xy²)

Correct Answer: B. \(\frac{1}{(x + 1)^{2}}\)

Explanation

\(y = \frac{x}{x + 1}\)

Using quotient rule because the function is of the form \(\frac{u(x)}{v(x)}\)

\(\frac{\mathrm d y}{\mathrm d x} = \frac{v\frac{\mathrm d u}{\mathrm d x} - u\frac{\mathrm d v}{\mathrm d x}}{v^{2}}\)

\(\frac{\mathrm d y}{\mathrm d x} = \frac{(x + 1) . 1 - x . 1}{(x + 1)^{2}}\)

= \(\frac{1}{(x + 1)^{2}}\)

Correct Answer: C. \(3 ms^{-2}\)

Explanation

The two time differentiation of distance with respect to time will give the acceleration.

\(s = \frac{3}{2}t^{2} - 3t\)

\(\frac{\mathrm d s}{\mathrm d t} = v = 3t - 3\)

\(\frac{\mathrm d v}{\mathrm d t} = a = 3\)

Explanation

Simplify \(^{n + 1}C_{4} - ^{n - 1}C_{4}\)

= \(\frac{(n + 1)!}{4! (n - 3)!} - \frac{(n - 1)!}{4! (n - 5)!}\)

= \(\frac{(n + 1)(n)(n - 1)(n - 2)(n - 3)!}{4! (n - 3)!} - \frac{(n - 1)(n - 2)(n - 3)(n - 4)(n - 5)!}{4! (n - 5)!}\)

= \(\frac{(n + 1)(n)(n - 1)(n - 2)}{4!} - \frac{(n - 1)(n - 2)(n - 3)(n - 4)}{4!}\)

= \(\frac{(n - 1)(n - 2) [n(n + 1) - (n - 3)(n - 4)]}{4!}\)

= \(\frac{(n - 1)(n - 2) [n^{2} + n - n^{2} + 7n - 12]}{24}\)

= \(\frac{(n - 1)(n - 2)[8n - 12]}{24}\)

= \(\frac{(n - 1)(n - 2)(2n - 3)}{6}\)