Correct Answer: D. 1

Explanation

Lim(\(\frac{1 - x}{x^2 - 3x + 2}\))

= \(^{lim}_{x \to 1} \begin{pmatrix} \frac{1 - x}{x^2 - 3x + 2} \end {pmatrix}\)

= \(^{lim}_{x \to 1} \begin{pmatrix} \frac{x - 1}{(x - 2)(x + 1)} \end {pmatrix}\)

= \(\frac{-1}{1 - 2}\)

= \(\frac{-1}{-1}\)

= 1

Correct Answer: A. N2000

Correct Answer: B. 7.49

Explanation

D14.95 = N112.00

D1.00 = \(\frac{N112}{D14.95} \times\) D1.00

= 7.49

Correct Answer: A. 4y\(^\frac{1}{3}\)

Explanation

If 2ⁿ = y,

then, 2\(^{(2 + \frac{n}{3})}\) = 2² x 2\(^\frac{n}{3}\)

= 4 x (2ⁿ)\(^{\frac{1}{3}}\)

But y = 2ⁿ, hence

2\(^{(2 + \frac{n}{3})}\) = 4 x y\(^{\frac{1}{3}}\)

= 4y\(^\frac{1}{3}\)

Correct Answer: B. 3/8

Explanation

\(\frac{\log \sqrt{27}}{\log 81}\)

= \(\frac{\log \sqrt{3^3}}{\log 3^4}\)

= \(\frac{\log 3^{\frac{3}{2}}}{\log 3^4}\)

= \(\frac{\frac{3}{2} \log 3}{4 \log 3}\)

= \(\frac{\frac{3}{2}}{4}\)

= \(\frac{3}{8}\)

Correct Answer: D. \(a * b = a - b + ab\)

Explanation

All other options given are commutative i.e. \(a * b = b * a\), except option D.

\(a * b = a - b + ab\)

\(b * a = b - a + ba\)

\(a - b = -(b - a) \neq b - a\)

Correct Answer: D. 214.5cm²

Explanation

The surface area of an open-top cylinder = πr(r + 2h),

where 'r' is the radius and 'h' is the height of the cylinder.

= \(\frac{22}{7}\) * 3.5 (3.5 + 2 * 8)

= 11 (3.5 + 16) → 11 (19.5)

= 214.5cm\(^2\)

Correct Answer: C. \( \frac{k}{\sqrt{1 - k^2}} \)

Explanation

\(\sin \theta = \frac{k}{1}\)

\(\implies 1^2 = k^2 + adj^2\)

\(adj = \sqrt{1 - k^2}\)

\(\therefore \tan \theta = \frac{k}{\sqrt{1 - k^2}}\)

Correct Answer: D. 8.26N

Correct Answer: C. 6006

Explanation

No of boys in the class = 7; Girls = 20-7 = 13

No of selection = \(^{13}C_{3} \times ^{7}C_{2} = \frac{13!}{(13-3)!3!} \times \frac{7!}{(7-2)!2!}\)

= \(286\times21 = 6006\)