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Part-B Section–V

**(ii) Mathematics Solved Paper**
101.

**The value of**
102. In a mixture of 35 litres, the ratio of milk and water is 5 : 2. Another 5 litres of milk is added to the mixture. The ratio of milk and water in the new mixture is—

(A) 3 : 1

(B) 1 : 3

(C) 2 : 3

(D) 3 : 2

103. Walking at 4 km an hour, a peon reaches his office 5 minutes late. If he walks at 5 km an hour, he will be 4 minutes too early. The distance of his office from the residence is—

(A) 5 km (B) 4 km

(C) 3 km (D) 2 km

104. If 5

(A) 0 (B) 1

(C) 2 (D) 3

105. The simple interest on a certain amount at 4% p.a. for 4 years is Rs. 80 more than the interest on the same sum for 3 years at 5% p.a. The sum is—

(A) Rs. 6000 (B) Rs. 7200

(C) Rs. 7500 (D) Rs. 8000

106. A trader marks an article at 30% more than the cost price. He gives 10% discount to his customers and gains Rs. 25·50 per article. The cost price of the article is—

(A) Rs. 150 (B) Rs. 200

(C) Rs. 175 (D) Rs. 250

107. The price of sugar is increased by 25%. How much per cent should a man decrease his consumption so that there is no increase in his expenditure ?

(A) 10% (B) 20%

(C) 5% (D) 15%

108. Rs. 6500 were divided equally among a certain number of persons. Had there been 15 more persons each would have got Rs. 30 less. The original number of persons was—

(A) 65 (B) 60

(C) 50 (D) 40

109. 2 men and 6 boys can do in 4 days a piece of work which would be done again in 4 days by 4 men and 3 boys. One man will do it in—

(A) 36 days (B) 24 days

(C) 16 days (D) 12 days

110. If sin A = 24/25, the value of tan A + sec A, where 0° < A < 90° is—

(A) 49 (B) 25

(C) 24 (D) 7

111. If tan A = n sin B and sin A = m sin B, then the value of cos

(A) m

(C) m

112. The angle of elevation of the top of a hill at the foot of a tower is 60° and the angle of elevation of the top of the tower from the foot of the hill is 30°. If the tower is 50 m high, the height of the hill is—

(A) 100 m (B) 125 m

(C) 150 m (D) 200 m

113. A steel wire when bent in the form of a square encloses an area of 121 sq. cm. If the same wire is bent into the form of a circle, the area of the circle is—

(A) 88 sq. cm (B) 142 sq. cm

(C) 154 sq. cm (D) 212 sq. cm

114. The number of spherical bullets that can be made out of a solid cube of lead whose edge measures 44 cm, if the diameter of each bullet be 4 cm, is—

(A) 2541 (B) 847

(C) 1270 (D) 363

115. The ratio between the radius of the base and the height of a cylinder is 2 : 3. If its volume is 1617 cm

(A) 575 cm2 (B) 770 cm2

(C) 1205 cm2 (D) 1500 cm2

116. The median of the following data is—

25, 34, 31, 23, 22, 26, 35, 26, 20, 32

(A) 25·5 (B) 26

(C) 26·5 (D) 25

117. The average weight of 10 men is decreased by 3 kg when one of them whose weight is 80 kg is replaced by a new person. The weight of the new person is—

(A) 70 kg (B) 60 kg

(C) 50 kg (D) 73 kg

118. The value of k so that the points A(k, 1), B(2, 1) and C(5,–1) are collinear is—

(A) 4 (B) 3

(C) 2 (D) 1

119. The common difference of the A.P. a, a + d, a + 2d,… for which the 20th term is 10 more than the 18th term, is—

(A) 4 (B) – 4

(C) – 5 (D) 5

120. Two dice are thrown simultaneously. The probability of getting a total of at least 10

is—

(A) 5/12 (B) 1/6

(C) 5/6 (D) 1/12

(A) 3 : 1

(B) 1 : 3

(C) 2 : 3

(D) 3 : 2

103. Walking at 4 km an hour, a peon reaches his office 5 minutes late. If he walks at 5 km an hour, he will be 4 minutes too early. The distance of his office from the residence is—

(A) 5 km (B) 4 km

(C) 3 km (D) 2 km

104. If 5

^{x–2}·3^{2x–3}= 135, then the value of x is—(A) 0 (B) 1

(C) 2 (D) 3

105. The simple interest on a certain amount at 4% p.a. for 4 years is Rs. 80 more than the interest on the same sum for 3 years at 5% p.a. The sum is—

(A) Rs. 6000 (B) Rs. 7200

(C) Rs. 7500 (D) Rs. 8000

106. A trader marks an article at 30% more than the cost price. He gives 10% discount to his customers and gains Rs. 25·50 per article. The cost price of the article is—

(A) Rs. 150 (B) Rs. 200

(C) Rs. 175 (D) Rs. 250

107. The price of sugar is increased by 25%. How much per cent should a man decrease his consumption so that there is no increase in his expenditure ?

(A) 10% (B) 20%

(C) 5% (D) 15%

108. Rs. 6500 were divided equally among a certain number of persons. Had there been 15 more persons each would have got Rs. 30 less. The original number of persons was—

(A) 65 (B) 60

(C) 50 (D) 40

109. 2 men and 6 boys can do in 4 days a piece of work which would be done again in 4 days by 4 men and 3 boys. One man will do it in—

(A) 36 days (B) 24 days

(C) 16 days (D) 12 days

110. If sin A = 24/25, the value of tan A + sec A, where 0° < A < 90° is—

(A) 49 (B) 25

(C) 24 (D) 7

111. If tan A = n sin B and sin A = m sin B, then the value of cos

^{2}A is—(A) m

^{2}/n^{2 }(B) m^{2}× n^{2}(C) m

^{2}– n^{2 }(D) m^{2}+ n^{2}112. The angle of elevation of the top of a hill at the foot of a tower is 60° and the angle of elevation of the top of the tower from the foot of the hill is 30°. If the tower is 50 m high, the height of the hill is—

(A) 100 m (B) 125 m

(C) 150 m (D) 200 m

113. A steel wire when bent in the form of a square encloses an area of 121 sq. cm. If the same wire is bent into the form of a circle, the area of the circle is—

(A) 88 sq. cm (B) 142 sq. cm

(C) 154 sq. cm (D) 212 sq. cm

114. The number of spherical bullets that can be made out of a solid cube of lead whose edge measures 44 cm, if the diameter of each bullet be 4 cm, is—

(A) 2541 (B) 847

(C) 1270 (D) 363

115. The ratio between the radius of the base and the height of a cylinder is 2 : 3. If its volume is 1617 cm

^{3}, the total surface area of the cylinder is—(A) 575 cm2 (B) 770 cm2

(C) 1205 cm2 (D) 1500 cm2

116. The median of the following data is—

25, 34, 31, 23, 22, 26, 35, 26, 20, 32

(A) 25·5 (B) 26

(C) 26·5 (D) 25

117. The average weight of 10 men is decreased by 3 kg when one of them whose weight is 80 kg is replaced by a new person. The weight of the new person is—

(A) 70 kg (B) 60 kg

(C) 50 kg (D) 73 kg

118. The value of k so that the points A(k, 1), B(2, 1) and C(5,–1) are collinear is—

(A) 4 (B) 3

(C) 2 (D) 1

119. The common difference of the A.P. a, a + d, a + 2d,… for which the 20th term is 10 more than the 18th term, is—

(A) 4 (B) – 4

(C) – 5 (D) 5

120. Two dice are thrown simultaneously. The probability of getting a total of at least 10

is—

(A) 5/12 (B) 1/6

(C) 5/6 (D) 1/12

**Answers :**

101. (B) 102. (A) 103. (C) 104. (D) 105. (D) 106. (A) 107. (B) 108. (C) 109. (B) 110. (D)

111. (A) 112. (C) 113. (C) 114. (A) 115. (B) 116. (B) 117. (C) 118. (C) 119. (D) 120. (D)