1

Raju, Ravi, and Ramu have income ratios 3:5:7 and expenditure ratios 4:6:8 respectively. If Raju’s income is Rs. 60,000 and he saves Rs. 1,500, find each one’s amount saved and the ratio of savings.

A) Raju = 1500, Ravi = 12250, Ramu = 23000; Ratio = 6:49:92

B) Raju = 1400, Ravi =13270, Ramu = 38000; Ratio = 6:49:92

C) Raju = 1450, Ravi =13270, Ramu = 38000; Ratio = 6:49:92

D) Raju = 1450, Ravi =13240, Ramu = 38500; Ratio = 6:49:92

2

The ratio of two numbers, A and B, is A:B = 10:18. You add the same small number, x, to both A and B. The new, modified ratio \$(A+x)/(B+x)\$becomes \$(\sqrt2)/(\sqrt 3)\$​. What is the number x?

A) \$x = 6 + 8 \sqrt 7\$

B) \$x = 6 + 9 \sqrt 7\$

C) \$x = 6 - 9 \sqrt 7\$

D) \$x = 6 + 8 \sqrt 6\$

3

A man travels by train, bus, and rickshaw with trip lengths in ratio 5:7:6 and fares in ratio 3:5:2 respectively. If total trip cost is 1170 units, find the amount spent on each and verify the fare per unit distance.

A) Train=183, Bus=561, Rickshaw=227, 3 : 5 : 7

B) Train=283, Bus=661, Rickshaw=227, 3 : 5 : 2

C) Train=293, Bus=651, Rickshaw=327, 3 : 7 : 2

D) Train=213, Bus=641, Rickshaw=247, 7 : 5 : 2

4

Given ellipsoid axes a = 6 cm, b = 8 cm, c = 3 cm, calculate volume, then find the radius of the sphere with equal volume.

A) \$404.19 cm^3\$ and  5.14 cm

B) \$143.19 cm^2\$ and  4.24 cm

C) \$603.19 cm^3\$ and  5.24 cm

D) \$563.19 cm^3\$ and  5.74 cm

5

A cylinder radius is 9 cm with volume \$4071.5 cm^2\$. If the height is increased by 20%, find the new volume and lateral surface area.

A) \$4,885.8 cm^3 and 182.5 cm^2\$

B) \$1,875.8 cm^3 and 2,082.5 cm^2\$

C) \$9,885.8 cm^3 and 1,082.5 cm^3\$

D) \$4,885.8 cm^3 and 1,082.5 cm^2\$

6

Given central angle COD = 109π radians in circle O, find the length of the minor arc COD as a reduced fraction of circle circumference.

A) \$1/4\$

B) \$1/8\$

C) \$1/2\$

D) \$1/6\$

7

For \$y = 3x^2 − 24x + 81\$ and y = 4x + b, find b values for which there is exactly one intersection and find corresponding x.

A) \$14/3\$

B) \$15/2\$

C) \$16/4\$

D) \$24/3\$

8

Solve inequalities 2(4x + 7) > 5x − 6 and 5x − 6 < 4x + 3 simultaneously, and specify all solution intervals.

A) \$(20/5, 9)\$

B) \$(-20/3, 9)\$

C) \$(-20/5, 5)\$

D) \$(17/4, 4)\$

9

A company sells phones for $68 and $95 each. Total phones sold are 120, with revenue $10,320. If a 10% rebate applies only to $95 phones, find number of phones sold of each type.

A) 40 phones at $68, 80 phones at $75

B) 40 phones at $67, 20 phones at $95

C) 40 phones at $68, 80 phones at $95

D) 30 phones at $68, 80 phones at $75

10

The side lengths of a triangle are a = 5x − 3, b = 4x + 6, and c = 3x + 9. Find the complete range of values for x that makes this triangle valid. Find the possible value(s) of x for which this triangle is right-angled.

A) Valid triangle: x > 1 Right-angled triangle: x = 1.76

B) Valid triangle: x > 7 Right-angled triangle: x = 2.75

C) Valid triangle: x > 0 Right-angled triangle: x = 1.76

D) Valid triangle: x > -7 Right-angled triangle: x = -1.76