**Q1. There were two solid spherical balls. Ratio between radius of first ball to that of second ball is 4 : 3. Second ball was cut into two equal halves and the difference between total surface area of first ball and total surface area of a part of second ball is 1424.5 cm². Find value of radius of bigger ball?**

(a) 14 cm

(b) 16 cm

(c) 10.5 cm

(d) 20 cm

(e) 28 cm

**Q2. The ratio of time taken by boat A to cover a certain distance in upstream to time taken by boat B to cover same distance in downstream in same river is 7 : 4 respectively. The time taken by boat A to cover another distance in upstream is 75% more than the time taken by it to cover that distance in downstream in the same river. Find speed of boat B in still water is what percent of speed of boat A in still water?**

(a) 150%

(b) 120%

(c) 125%

(d) 80%

(e) 100%

**Q3. Surbhi starts from point A at 1 : 00 pm and move towards point B at a speed of 45 km/hr while Sandeep leaves point B at 3 : 00 pm and move towards point A at a speed of 55 km/hr speed. If distance between A and B is 540 km then at what time Surbhi and Sandeep meet each other? **

(a) 6: 30 p.m.

(b) 7 : 30 p.m.

(c) 7 : 00 p.m.

(d) 8 : 00 p.m.

(e) 7 : 45 p.m.

**Q4. If two dice and one coin are rolled & tossed simultaneously then find the probability that the coin shows head and the numbers on the top faces of the dice are not same? **

(a) 1/4

(b) 1/6

(c) 1/12

(d) 5/12

(e) 5/18

**Q5. A car is at a distance of 400 m from the P end of a bridge of length PQ. There is also a dog standing at the distance of 4/9 of PQ from P end. When dog and car move towards P end then they reach at P end at the same time and when dog moves towards Q end and car after reaching P moves back for Q then they reach Q at same time. Speed of car is what percent more than the speed of dog? **

(a) 500%

(b) 600%

(c) 900%

(d) 750%

(e) 800%

**Q6. Aman left City A for City D via City B & City C and Bhanu left City B for City D via City C at the same time, they both reach City C after 5 hours and Aman reaches City D 66 minutes earlier than Bhanu. City D is 180 km away from City C. If Aman is travelling at 72 km/hr, then find the distance between City B and City C is how much more than distance between City A and City B? **

(a) 90 km

(b) 165 km

(c) 190 km

(d) 110 km

(e) 140 km

**Q7. Ratio of volume of sphere to volume of solid cylindrical toy with hemispherical top is 14 : 3. If radius of sphere is twice of radius of toy, then find the ratio of total surface area of sphere to surface area of the toy.**

(a) 9 : 7

(b) 336 : 131

(c) 91 : 69

(d) 151 : 97

(e) 199 : 162

**Q8. A boat covers total distance of 360km downstream in three equal parts with the speed of boat be 4x km/hr, 5x km/hr and 7x km/hr respectively. If speed of stream is x km/hr and boat takes total 29.5 hours, then find in what time boat will cover total given distance upstream in three equal parts with three given speeds?**

(a) 36 hours

(b) 40 hours

(c) 45 hours

(d) 48 hours

(e) 54 hours

**Q9. The sides of triangle PQR are ‘p’ cm, ‘q’ cm and ‘r’ cm and the sides of triangle ABC are ‘a’ cm, ‘b’ cm and ‘c’ cm. If p² + q² + r² = 100, a² + b² + c² = 100 and pa + qb + rc = 100 then the triangles PQR and ABC will be **

(a) of equal perimeter

(b) of equal area

(c) similar

(d) congruent

(e) all of the above

**Q10. Inside a square plot a circular garden is developed which exactly fits in the square plot and the diameter of the garden is equal to the side of the square plot which is 28 meters. What is the area of the space left out in the square plot after developing the garden?**

(a) 98 m^{2}

(b) 146 m^{2}

(c) 84 m^{2}

(d) 168 m^{2}

(e) 68 m^{2}

**Q11. Time taken by a boat to cover ‘D’ km upstream is 5 hours while the boat covers ‘D+5’ km downstream in 3 hours. The boat takes 12 hours to cover ‘D+10’ km downstream & return ‘2D – 4’ km upstream. Find speed of boat in still water.**

(a) 4 kmph

(b) 3.5 kmph

(c) 5 kmph

(d) 3 kmph

(e) 2.5 kmph

**Q12. A cube is such that its face diagonal is height of cylinder while its body diagonal is diameter of a sphere in which the cylinder is enclosed. Radius of cylinder is 3.5 cm which is half of side of cube. If cylinder is extracted from sphere then what volume of sphere will remain? (use √2 = 1.41 √3 = 1.71) (approx.)**

(a) 525 cm^{3}

(b) 518 cm^{3}

(c) 533 cm^{3}

(d) 541 cm^{3}

(e) 512 cm^{3}

**Q13. A box contains 8 red, 4 green & 5 pink gems. A table top is to be decorated with 10 gems. What is the probability that the decoration contains at least 5 red & 3 pink gems and also all three colored gems are there?**

(a) 560/2431

(b) 280/2431

(c) 140/2431

(d) 700/2431

(e) 420/2431

**Q14. A train driver leaves Gorakhpur at 6: 30 am and expects to reach at a place 600 km from Gorakhpur at 2: 30 pm. At 12:30 pm he finds that he has covered only 40% of the distance. By how much he has to increase the speed of the train in order to reach at scheduled time? **

(a) 180 km/hr

(b) 120 km/hr

(c) 150 km/hr

(d) 100 km/hr

(e) 140 Km/hr

**Q15. ‘X’ meters long train cross a pole in ‘t’ sec and a platform which is ‘L’ meters long in 20 sec. If speed of train is 72 km/hr, then what will be value of ‘t’ and ‘L’**

(a) 16 & 140

(b) 12 & 200

(c) 8 & 240

(d) 8 & 200

(e) 16 & 120

**Solutions**