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Engineering eLitmus Aptitude

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1. The set of all integers x such that |x “ 3| < 2 is equal to




2. The Range of the function f(x) = (x - 2) / (2 - x) is




3. The value of (i)i is




4. -------------- is equal to




5. The roots of the quadratic equation ax2 + bx + c = 0. will be reciprocal to each other if




6. If a, ß are the roots of ax2 - 2bx + c = 0 then a3 ß3 + a2ß3 + a3ß2 is




7. The sixth term of a HP is 1/61 and the 10th term is 1/105. The first term of the H.P. is




8. Let Sn denote the sum of first n terms of an A.P..If S2n = 3Sn, then the ratio S3n / 5n is equal to




9. Solution of |3 “ x| = x “ 3 is




10. If the product of n positive numbers in 1, then their sum is




11. A lady gives a dinner party to six quests. The number of ways in which they may be selected from among ten friends, if two of the friends will not attend the party together is




12. Two squares are chosen on a chessboard at random. What is the probability that they have a side in common?




13. 2.42n + 1 + 33n+1 is divisible by




14. A man can hit the target once in four shots. If he fires four shots in succession, what is the probability that he will hit the target?




15. If x is very large and n is a negative integer or a proper fraction, then an approximate value of ((1 + X) / x )n is




16. Find the values of n for which n+18 and n+90 is a perfect square ?




17. If | r- 6 | = 11 and |2q - 12| = 8, what is the minimum possible value of q / r ?




18. If a1 = 1 and an+1 = 2an + 5, n=1, 2....... then a100 is equal to




19. If a = tan60 tan 420 and B = cot660 cot 780




20. Let R1 and R2 respectively denote the maximum and minimum possible remainders when (276)n is divided by 91 for any natural number n,n>= 144. Find R1+R2.




21. If 2x+y = 10, 2y+z = 20 and 2x+z = 30. Where x, y,and z are real number. What is the value of 2x ?




22. If sin? + cos? = v2sin?, then




23. Two dices are thrown simultaneously. What is the probability that the sum of the two number is 10 or the product of two numbers is >= 25 or both?




24. Value of is




25. If sin? + cosec? = 2, then value of sin3? + cosec3? is




26. If cosec? + cot ? = 5 / 2 , then the value of tan? is




27. In how many ways can 10 engineers and 4 doctors be seated at a round table if all the 4 doctors do not sit together?




28. If length of the sides AB, BC and CA of a triangle are 8cm, 15 cm and 17 cm respectively, then length of the angle bisector of ?ABC is




29. A man from the top of a 100 metre high tower sees a car moving towards the tower at an angle of depression of 300. After sometimes, the angle of depression becomes 600. The distance (in metres) traveled by the car during this time is




30. The shadow of a tower of height (1 + v3) metre standing on the ground is found to be 2 metre longer when the sun's elevation is 300, then when the sun's elevation was




31. What is the approx. value of W, if W=(1.5)11, Given log2 = 0.301, log3 = 0.477.




32. Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour?




33. The distance between the lines 4x + 3y = 11 and 8x + 6y = 15 is




34. The straight lines x + y “ 4 = 0, 3x + y “ 4 = 0, x + 3y “ 4 = 0 form a traigle which is




35. Incentre of the triangle whose vertices are (6, 0) (0, 6) and (7, 7) is




36. The area bounded by the curves y = |x| - 1 and y = - |x| + 1 is




37. The coordinates of foot of the perpendicular drawn from the point (2, 4) on the line x + y = 1 are




38. Three lines 3x + 4y + 6 = 0, 2x 3y 2 2 0 + + = and 4x 7y 8 0 + + = are




39. Angle between the pair of straight lines x2 “ xy “ 6y2 “ 2x + 11y “ 3 = 0 is




40. If a circle passes through the point (a, b) and cuts the circle x2 + y2 = 4 orthogonally, then locus of its centre is




41. Centre of circle whose normals are x2 - 2xy - 3x + 6y = 0 is




42. Centre of a circle is (2, 3). If the line x + y = 1 touches, its equation is




43. The centre of a circle passing through the points (0, 0), (1, 0) and touching the circle x2 + y2 = 9 is




44. The line y = mx + 1 is a tangent to the parabola y2 = 4x if




45. The angle between the tangents drawn from the origin to the parabola y2 = 4a (x “ a) is




46. The area of the triangle formed by the tangent and the normal to the parabola y2 = 4ax, both drawn at the same end of the latus rectum and the axis of the parabola is




47. The eccentricity of the eclipse 16x2 + 7y2 = 112 is




48. A common tangent to the circle x2 + y2 = 16 and an ellipse x2 / 49 + y2 / 4 = 1 is




49. If the hyperbolas x2 - y2 = a2 and xy = c2 are of equal size, then




50. If a circle cuts rectangles hyperbola xy = 1 in the point (xi, yi), i = 1, 2, 3, 4 then




51. A boat M leaves shore A and at the same time boat B leaves shore B. They move across the river. They met at 500 yards away from A and after that they met 300 yards away from shore B without halting at shores. Find the distance between the shore A & B.




52. Harish and Peter working separately can paint a building in 18 days and 24 days respectively. If they work for a day alternately, Harish beginning, in how many days, the painting work will be completed ?




53. A tank has two compartments I and II. Two taps X and Y, whose filling rates are in ratio of 2:1, are used to fill the tank. The ration fo time taken by tap X to fill compartment I and tap Y to fill compartment II is 16:25. Find the ratio of the times taken by tap X to fill compartment II and tap Y to fill compartment I.




54. At the end of year 1998, Shepard bought nine dozen goats. Henceforth, every year he added p% of the goats at the beginning of the year and sold q% of the goats at the end of the year where p > 0 and q > 0. If Shepard had nine dozen goats at the end of year 2002, after making the sales for that year, which of the following is true?




55. A real number x satisfying 1- (1/n) ≤ 3 + (1/n), for every positive integer n, is best described by ≤




56. Given that -1 ≤ v ≤ 1, -2 ≤ u ≤ -0.5, and -2 ≤ z ≤ -0.5 and w = vz/u, then which of the following is necessarily true?




57. A can complete a piece of work in 4 days. B takes double the time taken by A, C takes double that of B, and D takes double that of C to complete the same task. They are paired in groups of two each. One pair takes two-thirds the time needed by the second pair to complete the work. Which is the first pair?




58. Two men X and Y started working for a certain company at similar jobs on January 1, 1950. X asked for an initial salary of Rs. 300 with an annual increment of Rs. 30. Y asked for an initial salary of Rs. 200 with a rise of Rs. 15 every 6 months. Assume that the arrangements remained unaltered till December 31, 1959. Salary is paid on the last day of the month. What is the total amount paid to them as salary during the period?




59. A rectangular sheet of paper, when halved by folding it at the midpoint of its longer side, results in a rectangle, whose longer and shorter sides are in the same proportion as the longer and shorter sides of the original rectangle. If the shorter side of the original rectangle is 2, what is the area of the smaller rectangle?




60. Let A be a natural number consisting only 1. B is another natural number which is equal to quotient when A is divided by 13. C is yet another natural number equal to the quotient when B is divided by 7. Find B-C.




61. Let A be a natural number consisting only 1. B is another natural number which is equal to quotient when A is divided by 13. C is yet another natural number equal to the quotient when B is divided by 7. Find B-C.




62. Let f : R ? R be a function defined by f(x) = max. {x, x3}. The set of all points where f(x) is not differentiable is




63. A biker notices a certain number(2 digits number) on the milestone before starting the journey. After riding for an hour he notices a milestone with reversed digits of the previous number. Now after riding for another hour he notices that the number on a new milestone had same digits as the first one (in the same order) but with a "0" between the 2 digits. If the rider maintains a constant speed throughout, Calculate his speed.




64. PT Usha and Shelly John decide to run a marathon between Ramnagar and Jamnagar. Both start from Ramnagar at 1 pm. On the way are two towns Ramgarh and Rampur, separated by a distance of 15 km. PT Usha reaches Ramgarh in 90 minutes running at a constant speed of 40 kmph. She takes additional 30 minutes to reach Rampur. Between Rampur and Jamnagar she maintains an average speed of V kmph (where V is a whole number),Shelly John being a professional marathon runner, maintains a constant speed of 18 kmph. They both reach Jamnagar together after 'n' hours, 'n' being a whole number. What could be total time taken by PT Usha?




65. If 1/a + 1/b + 1/c = 1 / (a + b + c); where a + b + c 1 0; abc 1 0, then what is the value of ( a + b ) ( b + c ) ( c + a )?




66. Find the number of ways you can fill a 3 x 3 grid (with 4 corners defined as a, b, c, d), if you have 3 white marbles and 6 black marbles.




67. If N = 82^3 - 62^3 - 203 then N is divisible by:




68. A hexagon of side a cm is folded along its edges to obtain another hexagon What is the % decrease in the area aof orignal hexagon ?




69. The area bounded by curve y = 4x “ x2 and x “ axis is




70. The area bounded by curve y = 4x “ x2 and x “ axis is




71. If v,w,x,y, and z are non negative integers, each less than 11, then how many distinct combinations of (v,w,x,y,z) satisfy v(11^4) + w(11^3) +x(11^2) + y(11) + z =151001 ?




72. The area bounded by the curves y = x4 - 2x3 + x2 - 3, the x-axis and the two ordinates corresponding to the points of minimum of this Function is