JEXPO 2014 Mathematics solved question

JEXPO 2014 Question And Solution

1. If x4+1=1297 and y4-1=2400, then y2-x2= ?   Ans.- C) 13

2. If x2-ax-6=0 and x2+ax-2=0 have one common root, then a can be – Ans.- A) -1

3.  The number of real roots of the quadratic equation 3x2+4=0 is – Ans.- A) 0

4.  The total cost of 10 erasers and 5 sharpeners is at least Rs. 65. The cost of eraser cannot exceed Rs. 4. find the minimum possible cost of each sharpener. – Ans.- C) Rs. 5

5. A sum was borrowed at simple interest at R% p.a. for 2 years. If it had been borrowed at (R+5)% p.a., total interest would have become Rs. 200 more. Find the sum (in Rs.). – Ans.- B) 2000

6. If one of the roots of an equation, x2-2x+c=0 is thrice the other, then C= ?  Ans.- D) 3/4

7. If A and B are complementary angles, then the value of (sin2A+sin2B)/(cosec2A-tan2B) is – Ans.- B) 1

8. If 100 cm is divided into two parts such that the sum of 2 times the smaller part and 1/3 of the larger parts, is less than 100 cm, then which of the following is correct ? – Ans.- C) larger portion is always greater than 60.

9. The length of an arc, which subtends an angle of 30 degree at the center of the circle of radius 42 cm is – Ans.- C) 11 cm

10. The simplified value of : cosec2a (1+ 1/seca) (1- 1/seca) is – A) 1

11. The number of diagonal of a regular polygon is 27. Then each of the interior angle of the polygon is –A) 500/3

12.  If sin A = 1/2  and 90<A<180, then the value of A in circular measure is – C) 5π/6

13. Ajay invests Rs. m for 7 months and Rs. n for the remaining part of year. Sohail invested Rs. n for 9 months and Rs. m for the remaining part of year. If at the end of the year, they share profits equally, then what is the relation between m and n ? – C) m=n

14. If sin2a+sina=1 then the value of cos4a+cos2a is – C) 1

15. The cost of a television is Rs. 15625. Its value depreciates at the rate of 8% p.a. Calculate the total depreciation at the end of 3 years- A) Rs. 3458

16.  A car covers a distance of 420 KM at a constant speed. If its speeds is 10 kmph less, it would have taken one hour more to travel the same distance. Find the speed of the car. – D) 70 kmph.

17. X and Y can do a piece of work in 4 and 6 days. If Y works on the first day and they work on alternate days, in how many days will twice the amount of work be completed ? – A) 9 2/3

18.  If the sum of the roots of an equation, x2+px+1=0 (p>0) is twice the difference between them then p= ?--  C) 4/v3

19. If A= (x-a)(x-b)(x-c)… (x-z), then the number of terms in the expression of (a+A)(b+A)(c+A)…(z+A) is – A) 1

20. 55% of 1000 / 60% of 2000 =? – A) 11/24

21. If 2a=4b=8c=64, then which of the following relations hold true ?-- D) a+b+c=11

22. If (2)^2x-2= (8)^y-1 = 16 ^ x-25 then find the sum of x and y.  – Wrong options.

23. If the diameter of a circle is equal to the diagonal of a square. Then the ratio of their areas is – C) 11:7

24. 9 years ago A’s age and B’s age were in the ratio 5:7. Which of the following cannot be the ratio of their ages 5 years from now? – D) 15:16

25.  The profit made in selling 5m of a cloth equals the cost price of 2m of that cloth. Find the profit percentage.--- Answer should be 40%

26. Find the number of soaps of size 2.1 cm x 3.7 cm x 2.5 cm that can be put in a cuboidal box of size 6.3 cm x 7.4 cm x 5 cm. – B) 12

27. If tan A = 1/2  and tan B = 1/3 then – A) A+B=π/4

28. Four times the sum of the areas of the two circular face of a cylinder is equal to the twice its curved surface area. Find the diameter of the cylinder if its height is 8 cm. – B) 8 cm

29.  If x^y=y^x where x and y are distinct natural numbers then find x+y.  D) None of the above

30. The average age of 27 boys of a class is 16 years and if their teacher is included the average is increased by 1/2  years. find the age of the teacher? – B) 30 years.

31.  An escalator has 50 steps. Ajoy starts walking up on it at 3 steps/sec. If the escalator moves up at 2 steps/sec, find the time (in seconds) he would reach its top. – B) 10 Sec.

32.  (0.010240)^1/5 = ?  -- C) 0.4 
33. If (18-2m)/5 + (4m+3)/7 >= m/5 + 8/7 then – C) m<-51
34. Solve for t, 3t-8<= -t in the set of whole numbers. – A) 0,1,2
35. In a triangle which is not equilateral, the sides (in cm) are integers. The longest side is 3 cm. The perimeter of the triangle is – B) 7 cm
36.  A sum of money invested at compound interest double itself in six years. in how many years will it become 64 times itself at the same rate of compound interest ?- B) 36
37. A dishonest shopkeeper sells the item at cost price but for every kg he gives 200 gm less. his profit percentage is – B) 25%
38. Two taps A and B can fill a tank in 10 minutes and 15 minutes respectively. In how many minutes will the tank be full if B was opened three minutes after A was opened? – C) 7.2
39.  The adjacent angles of a rhombus are 2x-35 and x+5, find x – A) 70
40. A sum of Rs. 1500 amounts to Rs. 1680 in 3 years at simple interest. If the interest rate is increased by 2%, it would amount to – C) Rs. 1590
41. If 3^5x+(81)^2 x 6561/3^2x = 3^7, then x=   ---  Don’t know…
42. Find the area of a right isosceles triangle whose hypotenuse is 16v2 cm – C) 128 cm2
43. If xyz=0, then find the value of (a^x)^yz +(a^y)^zx + (a^z)^xy. – A) 3
44. Ratan spends 70% of his income. His income increased by 25% and also his expenditure increases by 25%. Find the percentage increase in his savings-   A) 25%
45. The ratio of the tens digits and units digits of a two digits number is 2:3. How many possible numbers are there?- A) 3
46. A teacher wanted to distribute 2025 chocolates equally among x number of students. If each student gets x chocolates, find x- C) 45
47. If a regular hexagon is inscribed in a circle of radius 4 cm, then find the area of the polygon in cm2- B) 24v3
48. 2[(16-15)-1 + (13-8)-2]-1 + (1024)0]=? - B) 38/13
49. When a person travelled at 25% faster than his usual speed, he reached his destination 48 minutes early. By how many minutes would he be late if he travelled at 20% less than his usual speed? – C) 60
50. There are three amounts a,b and c such  that b is simple interest on c and c is simple interest on a. which of the following must be always be true?- C) c² = ab

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