**1. In how many ways 10 mangoes can be divided among 4 children?**

1) 280

2) 286

3) 284

4) 278

5) 282

**Directions: 7 boys and 7 girls sit in a row randomly. Find the probability that –**

**2. The girls sit together.**

1) 1/429

2) 2/429

3)3/421

4) 1/421

5) 1/427

**3. The boys and girls sit alternatively.**

1) 1/1715

2) 2/1715

3) 8/1715

4) 5/1714

5) 1/1716

**4. What will be the length of the diagonal of a square park whose area is equal to the area of a rectangular park of length**

**160 m and breadth 80 m?**

1) 180 m

2) 185 m

3) 172 m

4) 175 m

5) 160 m

**5. A train left from station A for station B at 4 pm at an average speed of 80 km/h. At 8 pm, another train also had left from**

**station A for station B on a parallel track at an average speed of 120 km/h. How far from A, is the another train expected**

**to overtake the first train?**

1) 900 km

2) 940 km

3) 960 km

4) 980 km

5) 920 km

**6. 8 men can complete a piece of work in 12 days. 10 women can do the same piece of work in 15 days where as 18 children**

**can complete in 10 days. 8 men, 25 women and 30 children work together for 2 days. If only men were to complete the**

**remaining work in 1 day, how many men would be required totally?**

1) 25

2) 16

3) 18

4) 30

5) 20

**7. A man buys a T.V valued at Rs. 36000. He pays Rs. 12000 at once and rest 18 months later on which he is charged simple**

**interest at the rate of 6% p.a. Find the total amount he pays for t.v.**

1) Rs. 38180

2) Rs. 38460

3) Rs. 38860

4) Rs. 38160

5) Rs. 38260

**8. A shopkeeper sells note book at the rate of Rs. 65 each and earns a commission of 5%. He also sells pen stand at**

**Rs.**

**90 each**

**and earns a commission of 15%. How much commission will he earn in two weeks, if he sells 12 note books and 8**

**pen stands a day?**

1) Rs. 2058

2) Rs. 2158

3) Rs. 2258

4) Rs. 2048

5) Rs. 2068

**9. Two partners invest**

**Rs.**

**1,20,000 and**

**Rs.**

**80,000 respectively in a business and agree that 30% of the profit should be**

**divided between them and the remaining profit is to be treated as interest on capital. If one partner gets**

**Rs.**

**1860 more than**

**the other, find the total profit made in the business.**

1) Rs. 31000

2) Rs. 30000

3) Rs. 28000

4) Rs. 32000

5) Rs. 29000

**10. A trader has 130 kg of pulses, part of which he sells at 12% profit and the rest at 25% profit. He gains 18% on whole.**

**What is the quantity sold at 25% profit?**

1) 65 kg

2) 60 kg

3) 70 kg

4) 64 kg

5) 68 kg

1. 2; Required number of ways

= n + r – 1 Cr – 1

= 10 + 4 –1 C4–1

= 13C3

= 13! / 3! 10!

= (13 * 12 * 11)/ (3*2)

= 286

2. 1;

When 7 girls sit together, regarding them as one group

(7 boys + 1 group of girls) = 8 objects.

Required probability = 8! * 7!/14!

= 1/429

3. 5;

If we begin with boy, then 7 boys can sit in 7 odd places in 7! ways and 7 girls in 7 even places in 7! ways, Therefore total ways = 7! × 7!. Similarly, if we begin with girls then 7! × 7!

Required probability = 2 * 7! * 7!/ 14!

= 1/1716

4. 5

1/2 * Diagonal^2 = 160*80

D = sqroot(2*160*80) = 160m

5. 3

Distance travelled by first train in 4 h = 80 × 4 = 320 km

Relative speed = (120 – 80) = 40 km/hr

Let x be the time taken by the second train to overtake

the first train.

Then, 40 = 320/x

x = 8h

Distance from A = 120 * 8 = 960km

6. 2; (8 × 12) men = (10 × 15) women = (18 × 10) children

16 men = 25 women = 30 children

Now, 8M + 25W + 30C = 8M + 16M + 16M = 40 men

8 men’s 1 day work = 1/12

40 men's 1 day work = 1/12 * 40/8 = 5/12

40 men's 2 day work = 5/12 * 2 = 5/6

Remaining Work = 1 - 5/6 = 1/6

Remaining work will be completed by 40 men in 2/5 days.

To complete in one day man required = 40 * 2/5 = 16 men

7. 4

Interest charge on (36000 – 12000 = 24000)

= (24000 * 18 * 6)/(100 * 12) = 2160

The total amount paid for T.V

= 12000 + 24000 + 2160 = Rs. 38,160

8. 1;

12 notebooks in a day, then in two weeks (i.e. 14 days)

= 14 × 12 = 168 notebook

Commission earned = 65 × 168 × 5/100 = Rs. 1546

8 pen stands in a day, then in two weeks (i.e. 14 days)

= 8 × 14 = 112 pen stands

Commission earned = 112 × 90 × 15/100 = Rs. 1512

Total commission earned = 546 + 1512 = Rs. 2058

9. 1; The ratio of profit = 12 : 8 = 3 : 2

Total Profit = 1860 (100/30)(3+2/3-2)

= 1860 * 100/30 * 5 = Rs. 31000

10. 2

The quantity sold at 25% profit

Where, N = total quantity, P = % gain on whole

x = part sold at x% profit

y = part sold at y% profit

= (p-x/y-x)N

= (18-12)/(25-12) * 130

6/13 * 130 = 60kg

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