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Q1. Ram travelled from Delhi to Agra covering total distance of 250 km in 8 hours. Partly by car at 30 km/hr and rest by train at 35 km/hr. The distance travelled by car is ––– (in km)
1) 160 km 
2) 176 km 
3) 182 km 
4) 200 km 
5) None of these

Q2. Find the number of different words that can be formed from 15 consonants and 5 vowels by taking 2 consonants and 4 vowels in each word ?
1) 296 
2) 525 
3) 635 
4) 455 
5) None of these

Q3. Find the number of ways of distributing 7 identical balls into three boxes so that no box is empty and each box being large enough the accommodate all balls ?
1) 7C3 
2) 6C3 
3) 7C3 × 3C1 
4) 6C2 
5) None of these

Q4. The surface area of a cube is 1176 cm2. Find its volume ?
1) 2744 cm^3 
2) 1728 cm^3 
3) 2197 cm^3 
4) 2658 cm^3 
5) None of these

Q5. The average of first 100 natural number is –––
1) 52 
2) 52.50 
3) 50.50 
4) 51 
5) None of these

Q6. A starts some business with Rs. 40000. After 3 months B joins him with Rs. 50000. At the end of the year, in what ratio should they share the profits ?
1) 14 : 15 
2) 2 : 3 
3) 15 : 14 
4) 4 : 3 
5) None of these

Q7. In an examination, a candidate got 40 % marks and failed by 36 marks. If the passing marks are 60% of the total marks, then the maximum marks will be –––
1) 180 
2) 160 
3) 210 
4) 150 
5) None of these

Q8. A cistern has two taps which fill it in 12 min and 15 min respectively. There is also a waste pipe in the cistern. When all the pipes are opened, the empty cistern is full in 20 min. How long will the waste pipe take to empty a full cistern ?
1) 12 min 
2) 10 min 
3) 14 min 
4) 9 min 
5) None of these

Q9. A sum less than 6 in throw of two dice, find probability ?
1) 4/9
2) 5/18
3) 3/7
4) 7/18
5) None of these

Q10. A bag contains 4 green and 6 white balls. Two balls are drawn from the bag in succession without replacement. What is the probability that both are different color ?
1) 2/5
2) 4/15
3) 8/15
4) 2/3
5) None of these

Solutions:

Q1 – 5
Solution: x/30 + (250-x)/35 = 8 => x = 180km

Q2 – 5
Solution: Required number of words = (15C2 x 5C4) x 6! = 378000

Q3 – 4
Solution: Required Number of ways = (7-1)C(3-1) = 6C2

Q4 – 1
Solution: 6a² = 1176 => a² = 196 => a = 14 cm.
So, a^3 = (14)^3 = 2744 cm^3

Q5 – 3
Solution: 100×101/2/100 = 50.50

Q6 – 5
Solution: Req. Ratio = 40000 x 12 : 50000 x 9 = 48 : 45 = 16 : 15

Q7 – 1
Solution: 0.4x + 36 = 0.6x => 0.2x = 36 => x = 180

Q8 – 2
Solution: Work o=done by waste pipe in 1min = (1/12 + 1/15) – 1/20 = 1/10
So, Waste pipe can empty the cistern in 10 min.

Q9 – 2
Solution: A = Getting total less than 6= [(1, 1), (1, 2), (2, 1), (2, 2), (3, 1), (1, 3), (4, 1), (1, 4), (3, 2),(2, 3)] = n(A) = 10, n(S) = 36
So, P(A) = 10/36 = 5/18

Q10 – 3
Solution: Req. Probability = (4C1 x 6C1)/10C2 = 8/15