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Q:

The area of a field in the shape of a trapezium measures 1440sq m. The perpendicular distance between its parallel sides is 24cm. If the ratio of the sides is 5:3, the length of the longer parallel side is:

A) 75	B) 85
C) 95	D) 105

Answer & Explanation Answer: A) 75

Explanation:

Area of field = $\frac{1}{2} * (5 x + 3 x) * 24$ = 96x sq.m

96x = 1440 => x = $\frac{1440}{96}$ = 15

Hence, the length of longer parallel side = 5x = 75m

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Filed Under: Area
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Q:

If the diagonals of a rhombus are 24cm and 10cm the area and the perimeter of the rhombus are respectively.

A) 10	B) 11
C) 12	D) 13

Answer & Explanation Answer: D) 13

Explanation:

Area = $\frac{1}{2} * d i a g o n a l 1 * \frac{1}{2} d i a g o n a l 2$ = $\frac{1}{2} * 24 * 10$ sq.cm

$\frac{1}{2} * d a i g o n a l 1 = \frac{1}{2} * 24 = 12 c m$

$\frac{1}{2} * d i a g o n a l 2 = \frac{1}{2} * 10 = 5 c m$

side of a rhombus = (12)² + (5)² = 169 => AB = 13cm

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Q:

A parallelogram has sides 30m and 14m and one of its diagonals is 40m long. Then its area is

A) 136	B) 236
C) 336	D) 436

Answer & Explanation Answer: C) 336

Explanation:

let ABCD be the given parallelogram

area of parallelogram ABCD = 2 x (area of triangle ABC)

now a = 30m, b = 14m and c = 40m

s=1/2 x (30+14+40) = 42

Area of triangle ABC = $\sqrt{[s (s - a) (s - b) (s - c)]}$

= $\sqrt{[42 (12) (28) (2)]}$ = 168sq m

area of parallelogram ABCD = 2 x 168 = 336 sq m

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Q:

Who was the first recipient of a scholarship offered by the Indian Society of Oriental Arts in 1907

Answer

Nandala Bose

Workspace

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Subject: Indian Culture

Q:

The perimeters of two squares are 40cm and 32 cm. Find the perimeter of a third square whose area is equal to the difference of the areas of the two squares.

A) 12	B) 24
C) 36	D) 48

Answer & Explanation Answer: B) 24

Explanation:

side of first square = 40/4 =10cm

side of second square = 32/4 = 8cm

area of third squre = 10² - 8² = 36 sq cm

side of third square = $\sqrt{36}$ = 6 cm

required perimeter = 6*4 = 24cm

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Q:

A rectangular grassy plot 110m by 65cm has a gravel path .5cm wide all round it on the inside. Find the cost of gravelling the path at 80 paise per sq.mt

A) 680rs	B) 480rs
C) 340rs	D) 320rs

Answer & Explanation Answer: A) 680rs

Explanation:

area of theplot = 110 * 65 = 7150 sq.m
area of the plot excluding the path = (110-5)* (65-5) = 6300 sq.m
area of the path = 7150 - 6300 =850 sq.m
cost of gravelling the path = 850 x (80/100) = 680 Rs

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Q:

If the radius of a circle is decreased by 50% , find the percentage decrease in its area.

A) 75%	B) 65%
C) 35%	D) 25%

Answer & Explanation Answer: A) 75%

Explanation:

let original radius = r and new radius = (50/100) r = r/2

original area = ${πr}^{2}$ and new area = $π {(r / 2)}^{2}$

decrease in area = $3 {πr}^{2} / 4$ * $\frac{1}{{πr}^{2}}$ *100 = 75%

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Q:

A tea expert claims that he can easily find out whether milk or tea leaves were added first to water just by tasting the cup of tea. In order to check this claims 10 cups of tea are prepared, 5 in one way and 5 in other. Find the different possible ways of presenting these 10 cups to the expert.

A) 340	B) 210
C) 290	D) 252

Answer & Explanation Answer: D) 252

Explanation:

Since there are 5 cups of each kind,prepared with milk or tea leaves added first,are identical hence,total number of different people ways of presenting the cups to the expert is 10!/(5! x 5!)= 252

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Filed Under: Permutations and Combinations

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