Central Industrial Security Force (CISF) Paper on 5 July 2013

Discussion in 'Latest Placement papers' started by krishna, Aug 21, 2013.

  1. krishna

    krishna Banned

    Directions—(Q. 1–5) The President of a club is appointing nine officials A, B, C, D, E, F, G, H and I to serve on three committees to study three different aspects of activities of the club. There will be a Games Committee, a Food Service Committee and an Entertainment Committee. The appointments must respect the following—
    >> Each committee must have exactly three members.
    >> No person can serve on more than one committee.
    >> H must serve on the Entertainment Committee.
    >> C and D must serve on the same committee.
    >> A and B cannot serve on the same committee.
    >> E cannot serve on the same committee as I.
    >> F must serve on the same committee as B or H or both B and H.
    1. If B and G serve on the Games Committee, which of the following must serve on the Food Service Committee ?
    (A) A
    (B) D
    (C) E
    (D) F
    Ans : (B)

    2. Which of the following groups could constitute the Games Committee ?
    (A) A, B, E
    (B) A, D, G
    (C) C, H, E
    (D) F, I, B
    Ans : (D)

    3. If A is assigned to the Food Service Committee and C is appointed to Entertainment Committee, then which of the following must be true ?
    1. G is appointed to the Food Service Committee.
    2. E is appointed to the Games Committee.
    3. I is appointed to the Entertainment Committee.
    (A) I only
    (B) III only
    (C) I and III only
    (D) II and III only
    Ans : (A)

    4. If F serves on the Food Service Committee and C serves on the same committee as H, then which of the following must serve on the Games Committee ?
    1. A
    2. G
    3. I
    (A) I only
    (B) III only
    (C) I and II only
    (D) II and III only
    Ans : (C)

    5. If I is on the Entertainment Committee and B is on the Food Service Committee, then which of the following must be true ?
    (A) F is on the Entertainment Committee
    (B) C is on the Games Committee
    (C) G is on the Food Service Committee
    (D) F is on the Games Committee
    Ans : (A)

    Directions—(Q. 6–10) Letters of certain words have been rearranged and the jumbled spellings have been given below. Out of the choices given below each question, choose the last letter of the correct word—
    6. AYDOT
    (A) A
    (B) D
    (C) T
    (D) Y
    Ans : (D)

    7. ILCEOP
    (A) C
    (B) E
    (C) L
    (D) O
    Ans : (B)

    8. CAPCET
    (A) A
    (B) C
    (C) P
    (D) T
    Ans : (D)

    9. VISERL
    (A) E
    (B) L
    (C) R
    (D) S
    Ans : (C)

    10. ERVSECI
    (A) E
    (B) I
    (C) R
    (D) S
    Ans : (A)

    Directions—(Q. 11–15) Find out the correct answer out of the four alternatives given below each question and then mark it in your answer sheet.
    11. Ice : Coolness : : Earth : ?
    (A) Forest
    (B) Weight
    (C) Gravitation
    (D) Ocean
    Ans : (C)

    12. Coconut : Shell : : Letter : ?
    (A) Mail
    (B) Letter-box
    (C) Stamp
    (D) Envelope
    Ans : (D)

    13. Income is related to profit in the same way as expenditure is related to—
    (A) Loss
    (B) Surplus
    (C) Balance
    (D) Sale
    Ans : (A)

    14. Much is related to many in the same way as measure is related to—
    (A) Calculate
    (B) Count
    (C) Weigh
    (D) Measurement
    Ans : (B)

    15. Clue is related to Mystery in the same way as warning is related to—
    (A) Precaution
    (B) Disaster
    (C) Risk
    (D) Danger
    Ans : (D)

    16. Find the oddman out—
    (A) MOndAy
    (B) tUESdAy
    (C) WEdNESdAy
    (D) thUrSdAy
    Ans : (B)

    17. Three of the following four are alike in a certain way and hence form a group. Which is the one that does not belong to the group ?
    (A) CUSTOMER : SGPSYYBK
    (B) INTEREST : UUHVJYUQ
    (C) OVERSEAS : TCHWWKCW
    (D) BANKING : HPLOSGI
    Ans : (B)

    18. Three of the following four have similar relationship and hence form a group. Which one does not belong to the group ?
    (A) PROFIT : RPQCKR
    (B) OTHERS : QRJCTQ
    (C) LEGUME : NCISOC
    (D) CANKER : EYPIGP
    Ans : (A)

    19. Three of the four groups of letters given below are alike in a certain way while one is different. Choose the odd one—
    (A) GWOURV
    (B) LZKMSU
    (C) JOEHNP
    (D) SFXPMG
    Ans : (D)

    20. Three of the four groups of letters given below are alike in a certain way while one is different. Choose the odd one—
    (A) IW
    (B) MS
    (C) FT
    (D) JU
    Ans : (D)

    Directions—(Q. 21–25) Find out the missing term in the following letternumber series—
    21. H 4 W, I 18 V, K 48 T, N 100 Q, ?, W 294 H
    (A) P 1485 S
    (B) R 180 M
    (C) S 198 I
    (D) T 206 K
    Ans : (B)

    22. 1 ED, 2 FD, 3 KH, ?, 15 KG, 48 KF
    (A) 12 PX
    (B) 6 RI
    (C) 9 LV
    (D) 8 TQ
    Ans : (B)

    23. M 4, T 7, P 7, Q 10, S 10, N 13, ?, K 16
    (A) V 4
    (B) K 7
    (C) T 13
    (D) G 15
    Ans : (C)

    24. R 5 P, T 6 M, V 9 J, X 15 G, ?
    (A) A 12 L
    (B) I 18 X
    (C) Z 25 D
    (D) U 20 Q
    Ans : (C)

    25. DGK 0, GKP 3, ?, PVC 15
    (A) GKV 5
    (B) KPV 8
    (C) PVZ 9
    (D) KPU 11
    Ans : (B)

    26. If the first 6 letters of the English Alphabet series are written in reversed order, then the next 6 letters are written in reversed order and so on, and at the end Y is interchanged by Z, then which letter is fourth letter to the right of 13th letter from the left ?
    (A) M
    (B) N
    (C) Q
    (D) P
    Ans : (B)

    27. If the English Alphabet series is written in the reverse order and every alternate letter starting from Y is dropped, which letter will be exactly in the middle of the remaining letters of the Alphabet series ?
    (A) L
    (B) O
    (C) M
    (D) N
    Ans : (D)

    28. If the letters in each of the following five groups of letters are first rearranged in the alphabetical order and then the groups of letters so formed are rearranged as in a dictionary, which letter group would have its group of letters in the MIDDLE among the five letter-groups ?
    MEET, DEAF, ROAD, CODE, LACK
    (A) LACK
    (B) MEET
    (C) ROAD
    (D) DEAF
    Ans : (C)

    29. The letters skipped in between the adjacent letters in the series are followed by equal space. Which of the following series observes this rule ?
    (A) HKNGSW
    (B) EIMQVZ
    (C) SUXADF
    (D) RVZDHL
    Ans : (D)

    30. Select the series in which the letters skipped in between adjacent letters do not decrease in order—
    (A) MGVFK
    (B) PJXHM
    (C) EQZFI
    (D) GWIQU
    Ans : (B)

    Directions—(Q. 31–35) These questions are based on code language which utilizes letters in the English Alphabet. In each question, there is a word written in capital letters, with one letter underlined. For each letter in that word there is a code written in small letters. That code is denoted by either (A), (B), (C), or (D), not in the same order. You have to find out the exact code for the underlined letter in the word. The letter of the that code is the answer. Please note that the same letter appearing in other word(s) may be coded differently.
    31. D U E L
    (A) g
    (B) i
    (C) p
    (D) j
    Ans : (C)

    32. P I T Y
    (A) g
    (B) b
    (C) r
    (D) k
    Ans : (B)

    33. R I N G
    (A) it
    (B) rk
    (C) mp
    (D) ti
    Ans : (A)

    34. G O A L
    (A) c
    (B) q
    (C) e
    (D) j
    Ans : (C)

    35. S L A P
    (A) dx
    (B) ms
    (C) vp
    (D) io
    Ans : (C)

    Directions—(Q. 36–40) Study the following arrangements carefully and answer the questions given below—
    Series I. MNLqd fuw2UFOKP6hs (14) SHV 7gc8RIE(13)xtk
    Series II. azj14GJBopir5v9TQY(10) emn(11) DACby(12)xWZ
    36. How many capital letters are in Series I and in Series II each of which is either followed by or preceded by the same positioned capital letter of English alphabet from the other end ?
    (A) 4, 3
    (B) 6, 2
    (C) 8, 1
    (D) 10, 0
    Ans : (A)

    37. If the positions of the first twelve elements of Series I are reversed, and similarly the positions of the last twelve elements of Series II are reversed, then the third element to the right of the seventh element from the left end of Series I will be ……, whereas the third element to the left of the seventh element from the right end of Series II will be ……
    (A) L, x
    (B) j, x
    (C) U, (11)
    (D) x, L
    Ans : (A)

    38. Which of the following pairs of elements shows the elements of Series I and Series II respectively, which are exactly in the middle of the seventh element from the left end and the sixth element from the right end in Series I and II ?
    (A) hy
    (B) Hy
    (C) sQ
    (D) Sq
    Ans : (C)

    39. Three of the following four are alike in a certain way based on their position in the above series. Which is the one that does not belong to that group ?
    (A) azj
    (B) emb
    (C) qdf
    (D) xtk
    Ans : (B)

    40. How many such vowels are there in the above arrangements, each of which is immediately preceded by a digit and immediately followed by a consonant ?
    (A) 1
    (B) 2
    (C) 3
    (D) 4
    Ans : (B)
  2. krishna

    krishna Banned

    Directions—(Q. 41– 44) In the following coded arithmetic equations certain symbols are used with the following meaning—
    I. P @ Q means add P to Q;
    II. P & Q means subtract Q from P;
    III. P # Q means multiply P with Q; and
    IV. P $ Q means divide P by Q.
    Now study the given information and answer the question following it—
    Three persons A, B and C complete a work in 20 days. B and C together are 4/3 times as efficient as A and B together. On the other hand A and C together are 5/4 times as efficient as B and C together.
    41. Which of the following equations represents the number of days in which A alone can finish the same work ?
    (A) 24 # 20 $ (24 & 20)
    (B) 30 # 20 & (30 @ 20)
    (C) 30 # 20 $ (30 & 20)
    (D) 40 # 20 $ (40 & 20)
    Ans : (C)

    42. Which of the following equations represents the number of days in which B and C together can finish the same work ?
    (A) 24 # (3 @ 3) $ 4
    (B) 20 # (12 & 6) $ 3
    (C) 20 # (12 & 6) $ 5
    (D) 30 # 20 $ (40 & 20)
    Ans : (D)

    43. Which of the following equations represents the number of days in which A and B working together can finish the same work ?
    (A) 20 # (3 @ 3) $ 4
    (B) 40 # 20 $ (40 & 20)
    (C) 20 # (12 & 6) $ 5
    (D) 20 # (12 & 6) $ 3
    Ans : (B)

    44. Which of the following equations represents the number of days in which A and C working together can finish the same work ?
    (A) 40 # 20 $ (40 & 20)
    (B) 20 # (12 & 6) $ 5
    (C) 20 # (3 @ 3) $ 4
    (D) 20 # (12 & 6) $ 3
    Ans : (B)


    45. A travel towards East. B travels towards North. C and D travel in opposite directions. D travels towards right of A. Which of the following is definitely true ?
    (A) B and C travel in opposite directions
    (B) C travels towards West
    (C) D travels towards North
    (D) B and C travel in the same direction
    Ans : (D)

    46. A cow runs 20 metres towards East and turns to right, runs 10 metres and turns to right, runs 9 metres and again turns to left, runs 5 metres and then turns to left, runs 12 metres and finally turns to left and runs 6 metres. Now which direction is the cow facing ?
    (A) North
    (B) East
    (C) South
    (D) West
    Ans : (A)

    47. A boy started walking positioning his back towards the sun. After sometimes, he turned left, then turned right and then towards the left again. In which direction is he going now ?
    (A) East or West
    (B) North or West
    (C) South or West
    (D) North or South
    Ans : (D)


    48. If Thursday was the day after the day before yesterday five days ago, what is the least number of days ago when Sunday was three days before the day after tomorrow ?
    (A) 1
    (B) 2
    (C) 3
    (D) 4
    Ans : (D)

    49. In a row of boys facing North, a boy is thirteen from the left. When shifted to his right by three places, he becomes seventeenth from right end of the row. How many boys are there in the row ?
    (A) 32
    (B) 31
    (C) 33
    (D) 30
    Ans : (A)

    50. 136 vehicles are parked in a parking lot in a single row. After the first car there is one scooter. After the second car, there are two scooters. After the third car, there are three scooters and so on. Work out the number of scooters in the second half of the row—
    (A) 61
    (B) 62
    (C) 63
    (D) 64
    Ans : (C)

    51. Three of the following four are alike in a certain way and hence form a group. Which one of the following does not belong to that group ?
    (A) 7
    (B) 9
    (C) 17
    (D) 33
    Ans : (B)

    52. Choose the odd numeral pair in the following—
    (A) 140 – 45
    (B) 120 – 35
    (C) 110 – 35
    (D) 80 – 25
    Ans : (B)

    53. Choose that set of numbers from the four alternative sets, that is similar to the given set—
    Given set — (246, 257, 358)
    (A) (145, 235, 325)
    (B) (143, 253, 246)
    (C) (273, 365, 367)
    (D) (233, 343, 345)
    Ans : (A)

    54. Choose the one which is different from the rest—
    (A) 248
    (B) 326
    (C) 392
    (D) 414
    Ans : (C)

    55. Three of the following four are alike in a certain way and so form a group. Which is the one that does not belong to that group ?
    (A) 156
    (B) 152
    (C) 72
    (D) 42
    Ans : (B)

    Directions—(Q. 56–60) In each question below, is given a statement followed by two assumptions numbered I and II. An assumption is something supposed or taken for granted. You have to consider the statement and the following assumptions and decide which of the assumptions is implicit in the statement. Give answer—
    (A) If only assumption I is implicit;
    (B) If only assumption II is implicit;
    (C) If neither I nor II is implicit; and
    (D) If both I and II are implicit.

    56. Statement—To achieve economic development, people should work hard.
    Assumptions :
    I. Achieving economic development is desirable.
    II. Working hard is not impossible.
    Ans : (D)

    57. Statement—He is too industrious to be poor.
    Assumptions :I. Very industrious people also can be poor.
    II. Very lazy people also can be rich.
    Ans : (C)

    58. Statement—Visitors may use lift at their own risk.
    Assumptions :I. Using lift is not always safe.
    II. Visitors do not want to use lift.
    Ans : (A)

    59. Statement—This book is so designed that even a layman can easily learn science in the absence of a teacher.
    Assumptions :I. Learning science by everybody is desirable.
    II. A layman generally finds it difficult to learn science on his own.
    Ans : (B)

    60. Statement—Although the rates of this hotel are comparable with other hotels, the amenities provided here are far superior.
    Assumptions :I. Rates are independent of amenities provided.
    II. Rates are dependent on amenities provided.
    Ans : (C)
  3. krishna

    krishna Banned

    CISF aptitude

    1. What is the number of ways of arranging, the letters of the word 'BANANA' so that no two N's appear together ?

    (a) 40 (Ans)

    (b) 60

    (c) 80

    (d) 100



    2. Consider the equation (x - p) (x + 6) + 1 = 0 having integral co efficient. If the equation has integral roots, then what values can P have ?

    (a) 4 or 8 (Ans)

    (b) 5 or 10

    (c) 6 or 12

    (d) 3 or 6



    3. What is the equivalent binary number of the decimal number 13.625 ?

    (a) 1101.111

    (b) 1111.101

    (c) 1101.101 (Ans)

    (d) 1111.111



    4. What is the value of (i + √3 / - i + √3)200 + (i - √3 / i + √3)200 + 1 ?

    (a) -1

    (b) 0 (Ans)

    (c) 1

    (d) 2



    5. The order of a set A is 3 and that of a set B is 2. What is the number of relations from A to B ?

    (a) 4

    (b) 6

    (c) 32

    (d) 64 (Ans)



    6. What is the value of log√aβ(H) / log√aβ g(H) ?

    (a) logaβ (a)

    (b) logaβg (aβ)

    (c) logaβ (aβ g) (Ans)

    (d) logaβ (β)



    7. The 59th term of an AP is 449 and the 449th term is 59. Which term is equal to 0 (zero) ?

    (a) 501st term

    (b) 502nd term

    (c) 508th term (Ans)

    (d) 509th term



    8. For a set A, consider the following statements :

    1. A È P (A) = P (A)

    2. {A} Ç P (A) = A

    3. P (A) - {A} = P (A)

    Where P denotes power set. Which of the statement given above is/are correct ?

    (a) 1 only (Ans)

    (b) 2 only

    (c) 3 only

    (d) 1, 2 and 3



    9. If the AM and HM of two numbers are 27 and 12 respectively, the what is their GM equal to ?

    (a) 12

    (b) 18 (Ans)

    (c) 24

    (d) 27



    10. If A = 1/2 and tan B = 1/3 then what is the value of (A + B) ?

    (a) 0

    (b) p/4 (Ans)

    (c) p/2

    (d) p



    11. What is ∫ x4 + 1 / x2 + 1 dx equal to ?

    (a) x3 / 3 - x + 4 tan-1 x + c

    (b) x3 / 3 + x + 4 tan-1 x + c

    (c) x3 / 3 - x + 2 tan-1 x + c (Ans)

    (d) x3 / 3 - x - 4 tan-1 x + c

    Where is a constant of integration.



    12. What is the value of lim (x + 6 / x + 1)x+4 ?
    1® ¥

    (a) e

    (b) e2

    (c) e4

    (d) e5 (Ans)



    13. What is the area of the triangle with vertices (0, 2, 2), (2, 0, -1) and (3, 4, 0) ?

    (a) 15/2 square units (Ans)

    (b) 15 square units

    (c) 7/2 square units

    (d) 7 square units



    14. If 1/2 - √-2 is one of the roots of ax2 + bx + c = 0 where, a, b, c are real, then what are the values of a, b, c respectively ?

    (a) 6, -4, 1 (Ans)

    (b) 4, 6, -1

    (c) 3, -2, 1

    (d) 6, 4, 1



    15. If w is a complex cube root of unity and x = w2 - w - 2 then what is the value of x2 + 4x + 7 ?

    (a) -2

    (b) -1

    (c) 0 (Ans)

    (d) 1



    16. If cos x ≠ -1, then what is sinx / 1 + cos x equal to ?

    (a) cot x/2

    (b) cot x/2

    (c) tan x/2 (Ans)

    (d) -tan x/2



    17. The angle of elevation of the tip of a flag post from a point 5 m away from its base is 750. What is the approximate height of the flag post ?

    (a) 15 m

    (b) 17 m

    (c) 19 m (Ans)

    (d) 21 m



    18. If A = P {1, 2} where P denotes the power set, then which one of the following is correct ?

    (a) {1, 2} Ì A

    (b) 1 Î A

    (c) φ Ï A

    (d) {1, 2} Î A (Ans)



    19. Let O (0, 0, 0), P(3, 4, 5), Q (m, n, r) and R (1, 1, 1) be the vertices of a parallelogram taken in order. What is the value of m + n + r?

    (a) 6

    (b) 12

    (c) 15 (Ans)

    (d) More than 15



    20. What is the solution of the differential equation 3ex tan y dx + (1 + ex) sec2 y dy = 0 ?

    (a) (1 + ex) tan y = c

    (b) (1 + ex)3 tan y = c

    (c) (1 + ex)2 tan y = c

    (d) (1 + ex) sec2 y = c (Ans)

    Where c is a constant of integration



    21. What is the locus of points, the difference of whose distance from two points being constant ?

    (a) Pair of straight lines

    (b) An ellipse

    (c) A hyperbola (Ans)

    (d) A parabola



    22. What is the differential equation for y2 = 4a (x - a) ?

    (a) yy' - 2xyy' + y2 = 0

    (b) yy' (yy' + 2x) + y2 = 0

    (c) yy' (yy' - 2x) + y2 = 0 (Ans)

    (d) yy' - 2xyy' + y = 0



    23. If (4, 0) and (-4, 0) are the foci of ellipse and the semi-minor axis is 3, then the ellipse passes through which one of the following points ?

    (a) (2, 0)

    (b) (0, 5)

    (c) (0, 0)

    (d) (5, 0) (Ans)



    24. Under what condition do the planes bx - ay = n, cy - bz = l, az - cx = m intersect in a linev ?

    (a) a + b + c = 0

    (b) a = b = c

    (c) al + bm + cn = 0 (Ans)

    (d) l + m + n =



    25. What is their maximum point on their curve x = exy ?

    (a) (1, e)

    (b) (1, e-1) (Ans)

    (c) (e, 1)

    (d) (e-1, 1)



    26. The function f (x) = ex, x Î R is

    (a) Onto but not one-one

    (b) One-one onto

    (c) One-one but not onto (Ans)

    (d) Neither one-one not onto



    27. If y sin-1 (4x / 1 + 4x2) , then what is dy/dx equal to ?

    (a) 1/1+ 4x2

    (b) 1/1+ 4x2

    (c) 4/1+ 4x2 (Ans)

    (d) 4x/1+ 4x2



    Directions : for the next 3 (three) questions to follow :

    The table below gives an incomplete frequency distribution with two missing frequencies f1 and f2.
    Value of X Frequency
    0 f1
    1 f2
    2 4
    3 4
    4 3

    The total frequency is 18 and the arithmetic mean of X is 2.



    28. What is the value of f2 ?

    (a) 4 (Ans)

    (b) 3

    (c) 2

    (d) 1



    29. What is the standard deviation ?

    (a) √5/2

    (b) √5/3

    (c) 4/3 (Ans)

    (d) 16/9



    30. What is the coefficient of variance ?

    (a) 200/3 (Ans)

    (b) 50√5/9

    (c) 600/√5

    (d) 150



    31. What is the sum of all natural numbers between 200 and 400 which are divisible by 7 ?

    (a) 6729

    (b) 8712

    (c) 8729 (Ans)

    (d) 9276



    32. The mean and variance of a binomial distribution are 8 and 4 respectively. What is P(X = 1) equal to ?

    (a) 1/212 (Ans)

    (b) 1/28

    (c) 1/26

    (d) 1/24



    33. What is ∫eIn x sin x dx equal to ?

    (a) eIn x (sin x - cos x) + c

    (b) (sin x - x cos x) + c (Ans)

    (c) (x sin x + cos x) + c

    (d) (sin x + x cos x) + c

    Where c is a constant of integration.



    34. An observed event B can occur after one of the three events A1, A2, A3. If P (A1) = P (A2) = 0.4, P(A3) = 0.2 and P(B|A1) = 0.25, P(B|A2) = 0.4, P(B|A3) = 0.125, What is the probability of A1 after observing B ?

    (a) 1/3

    (b) 6/19

    (c) 20/57 (Ans)

    (d) 2/5



    35. Let X be the set of all graduates in India. Elements x and y in X are said to be related if they are graduates of the same university. Which one of the following statement is correct ?

    (a) Relation is symmetric and transitive only

    (b) Relation is reflexive and transitive only

    (c) Relation is reflexive and symmetric only (Ans)

    (d) Relation is reflexive, symmetric and transitive.



    36. If x2 + y2 = 1, then what is 1 + x + iy equal to ?
    1 + x - iy

    (a) x - iy

    (b) x + iy

    (c) 2x

    (d) -2iy

    (Ans : )

    37. Consider the following statements :

    ® ® ®
    1. for any three vectors a, b, c ;

    ® ® ® ® ®
    a. {(b + a) * (a + b + c)} = 0


    2. For any three coplanar unit vectors

    ® ® ® ® ® ®
    d, e, f ; (d * e). f = 1

    Which of the statements given above is/are correct ?

    (a) 1 only

    (b) 2 only

    (c) Both 1 and 2

    (d) Neither 1 nor 2

    (Ans : )



    Direction : For the next 3 (three) questions to follow : Consider the following lists : Each item under List I is associated with one or more items under List II.

    List I List II

    (Function) (Prperty)

    (a) sin x 1. Periodic function

    (b) cos x 2. None-periodic function

    (c) tan x 3. Continuous at every point on (-¥, ¥)

    4. Discontinuous function

    5. Differentiable at every point on (-¥, ¥)

    6. Not differentiable at every point on (-¥, ¥)

    7. has period p

    8. has period 2p

    9. increase on (0, p/2)

    10. decrease on (0, p/2)

    11. increase on (p/2, p)

    12. decrease on (p/2, p)



    38. A is associated with

    (a) 1, 3, 5, 8, 9, 12 (Ans)

    (b) 2, 4, 6, 8, 10, 11

    (c) 1, 3, 5, 7, 10, 11

    (d) None of these



    39. B is associated with

    (a) 2, 3, 5, 8, 9, 12

    (b) 1, 3, 5, 8, 10, 12 (Ans)

    (c) 1, 3, 5, 8, 9, 12

    (d) None of these



    40. C is assciated with

    (a) 1, 4, 6, 7, 9, 11 (Ans)

    (b) 2, 4, 6, 8, 9

    (c) 1, 4, 6, 7, 9

    (d) None of these



    41. If p and q are positive integers, then which one of the following equations has p - √q as one of its roots ?

    (a) x2 - 2px - (p2 - q) = 0

    (b) x2 - 2px + (p2 - q) = 0 (Ans)

    (c) x2 + 2px - (p2 - q) = 0

    (d) x2 + 2px + (p2 - q) = 0



    42. Given two squares of sides x and y such that y = x + x2. What is the rate of change of area of the second square with respect to the area of the first square ?

    (a) 1 + 3x + 2x2 (Ans)

    (b) 1 + 2x + 3x2

    (c) 1 - 2x + 3x2

    (d) 1 - 2x - 3x2



    43. The planes px + 2y + 2z - 3 = 0 and 2x - y + z + 2 = 0 intersect at an angle p/4. What is the value of p2 ?

    (a) 24 (Ans)

    (b) 12

    (c) 6

    (d) 3



    ® ® ® ®
    44. If the angle between the vectors a and b is p/3, what is the angle between - 5 a and 6 b ?

    (a) p/6

    (b) 2p/3 (Ans)

    (c) 2p/5

    (d) 3p/7



    45. What is the degree of the differential equation d2y / dx2 - √1 + (dy/dx)3 = 0 ?

    (a) 1 (Ans)

    (b) 2

    (c) 3

    (d) 6

    Where c is a constant of integration.

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