Correct Answer: B. x = -2 or 7

Explanation

(x + 2)(x - 7) = 0

x + 2 = 0 \(\implies\) x = -2

x - 7 = 0 \(\implies\) x = 7

x = -2 or 7

Correct Answer: A. 3

Explanation

Total surface area of cube = 6s²

6s² = x

s² = x = \(\frac{x}{6}\).....(1)

volume of a cube = s² = \(\frac{x}{2}\)

s² = \(\frac{x}{2}\)......(2)

put(1) into (2)

s(\(\frac{x}{6}\)) = \(\frac{x}{2}\)

s = \(\frac{x}{2} \times \frac{6}{x}\)

= 3cm

Correct Answer: A. 144°

Explanation

Reflex< POS = 2x (angle at centre is twice that at circumference)

reflex< POS +< POS = 350^o(angles at a point)

i.e. 2x + 8x = 360^o

10x = 360^o

x = \(\frac{360}{10}\)

= 36^o

< PRS = \(\frac{1}{2}\)

< POS(< at centre twice that circumference)

= \(\frac{1}{2}\) x 8x = 4x

4 x 36^o

< PRS = 144°

Correct Answer: D. 0°

Explanation

\(\sin \theta = \tan \theta \implies \frac{\sin \theta}{1} = \frac{\sin \theta}{\cos \theta}\)

Equating, we have

\(\cos \theta = 1 \implies \theta = \cos^{-1} 1\)

= \(0°\)

Correct Answer: A. 1 sec and 7 sec

Explanation

\(s = ut + \frac{1}{2}at^{2}\)

\(s = ut - \frac{1}{2}gt^{2}\) (Upward movement against gravity)

\(35 = 40t - \frac{1}{2}10t^{2}\)

\(35 = 40t - 5t^{2}\)

\(5t^{2} - 40t + 35 = 0\)

\(t^{2} - 8t + 7 = 0\)

\((t - 1)(t - 7) = 0 \implies t = \text{1 sec and 7 sec}\)

Correct Answer: D. 9.0 cm

Explanation

Length of arc (in radians) = \(r \theta\)

\(10.8 = 1.2r\)

\(r = \frac{10.8}{1.2} = 9.0 cm\)

Correct Answer: B. 7/10

Correct Answer: D. (3x + 5y)(2x - y)

Explanation

\(6x^2 + 7xy - 5y^2\)

= \(6x^2 + 10xy - 3xy - 5y^2\)

= \(2x(3x + 5y) - y(3x + 5y)\)

= \((2x - y)(3x + 5y)\)

Correct Answer: D. 115°

Explanation

In triangle RXY, < RXY = < RYX (base angles of an isosceles triangle)

\(\implies\) 180° - 62° = 2 < RYX

118° = 2 < RYX \(\implies\) < RYX = 59°

In triangle RYZ, < RZY = 62° (base angles of an isosceles triangle)

\(\therefore\) < RYZ = 180° - (62° + 62°)

= 180° - 124° = 56°

\(\therefore\) < XYZ = 56° + 59°

= 115°

Correct Answer: B. 4-√7