Correct Answer: C. \(\frac{5}{12}\)

Explanation

Let the girls pocket money be rep. by x. The amount spent on books = \(\frac{1}{4}of\hspace{1mm}x = \frac{x}{4}\)

The amount spent on dress \(=\frac{1}{3} of \hspace{1mm}x=\frac{x}{3}\)

?The fraction that remains = \(\frac{x}{1}-\left(\frac{x}{4}+\frac{x}{3}\right)\\

\frac{3x+4x}{12}; = \frac{12x-7x}{12} = \frac{5x}{12} = \frac{5}{12}\)

Correct Answer: D. 5

Correct Answer: D. 2p + 1

Explanation

2p\(^2\) - 2

2(p\(^2\) - 1)

= 2(p + 1)(p - 1)

Correct Answer: A. 5

Explanation

P = {1, 2, 3, 4, 5, 6}; Q = {3, 4, 5, 6, 7, 8, 9}

P \(\cap\) Q) = {2, 3, 4, 5, 6}

n(P \(\cap\) Q) = 5

Correct Answer: C. 1.1

Correct Answer: C. 60cm²

Explanation

|VU| = |UT| = |TS|

|VS| = (4.8) x 3 = 14.4cm

|PQ| = |QR| = 4.8

|PR| = (4.8) x 2 = 9.6cm

Since quad. PRSV is a trapezium of height 5cm

Area of quad. PRSV = \(\frac{1}{2}(a + b)h\)

= \(\frac{1}{2}(14.4 + 9.6) \times 5\)

= \(\frac{1}{2}(24) \times 5\)

12 x 5 = 60cm²

Correct Answer: A. 250

Correct Answer: C. 269.5cm³

Explanation

Volume of a solid cylinder = Base area x height

Base area \(=\pi r^2 =\frac{22}{7} \times \frac{7}{2}\times \frac{7}{2} = \frac{77}{2}\)

Volume of a solid cylinder = \(\frac{77}{2}\times \frac{7}{1} = \frac{539}{2}cm^3\\

=269.5cm^3\)

Explanation

\(xy^{2} + x^{2} y = 4xy\)

Differentiating with respect to x,

\(2xy \frac{\mathrm d y}{\mathrm d x} + y^{2} + x^{2} \frac{\mathrm d y}{\mathrm d x} + 2xy = 4x \frac{\mathrm d y}{\mathrm d x} + 4y\)

\((2xy + x^{2} - 4x) \frac{\mathrm d y}{\mathrm d x} = 4y - y^{2} - 2xy\)

\(\frac{\mathrm d y}{\mathrm d x} = \frac{4y^{2} - y^{2} - 2xy}{2xy + x^{2} - 4x}\)

At (1, 3), Gradient = \(\frac{4(3) - (3)^{2} - 2(1)(3)}{2(1)(3) + 1^{2} - 4(1)}\)

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

= -1

Correct Answer: (b) 7.5