QUINTESSENCE: - Infomathsinfomathsonline.com/Que_papers/Worksheet-3 Maths.doc · Web view80. The equation of the circle having the chord x – y = 1 of the circle as a diameter is

INFOMATHS

WORKSHEET-3 (OLD QUESTIONS )

WORK-SHEET-3 (OLD QUESTIONS) WORK-SHEET-3 (OLD QUESTIONS) PROBABILITY 1. All the coefficients of the equation ax2 + bx + c = 0

are determined by throwing a six-sided un-biased dice. The probability that the equation has real roots is

HCU-2012 (a) 57/216 (b) 27/216 (c) 53/216 (d) 43/216

2. Suppose 4 vertical lines are drawn on a rectangular sheet of paper. We name the lines

and respectively. Suppose two players A and B join two disjoint pairs of end points within A1 to A4 and B1 to B4 respectively without seeing how the other is marking.What is the probability that the figure thus formed has disconnected loops?

HCU-2012 (a) 1/3 (b) 2/3 (c) 3/6 (d) 1/6

3. In a village having 5000 people, 100 people suffer from the disease Hepatitis B. It is known that the accuracy of the medical test for Hepatitis B is 90%. Suppose the medical test result comes out to be positive for Anil who belongs to the village, then what is the probability that Anil is actually having the disease.

HCU-2012 (a) 0.02 (b) 0.16 (c) 0.18 (d) 0.3

4. Let A, B and C be the three events such thatP(A) = 0.3, P(B) = 0.4, P(C) = 0.8, P(A B) = 0.08, P(A C) = 0.28, P(A B C) = 0.09.If P(A B C) 0.75, then P(B C) satisfies :

PU CHD-2012(A) P(B C) ≤0.23 (B) P(B C) ≤0.48(C) 0.23 ≤P(B C) ≤0.48 (D) P(B C) ≤0.15

5. A number is chosen from each of the two sets {1, 2, 3, 4, 5, 6, 7, 8, 9} and {1, 2, 3, 4, 5, 6, 7, 8, 9}. If P denotes the probability that the sum of the two numbers be 10 and Q the probability that their sum be 8, then (P + Q) is

PU CHD-2012

(A) (B) (C) (D)

6. Let P(E) denote the probability of event E. Given P(A)

= 1, P(B) , the values of P(A|B) and P (B|A)

respectively are NIMCET-2012

(a) (b) (c) (d)

7. A determinant is chosen at random from the set of all determinants of matrices of order 2 with elements 0 and 1 only. The probability that the determinant chosen is non-zero is

NIMCET-2012(a) 3/16 (b) 3/8 (c) 1/4 (d) None of these

8. Coefficients of quadratic equation ax2 + bx + c = 0 are chosen by tossing three fair coins where ‘head’ means one and ‘tail’ means two. Then the probability that roots of the equation are imaginary is

NIMCET-2012(a) 7/8 (b) 5/8 (c) 3/8 (d) 1/8

9. A problem in Mathematics is given to three students

A, B and C whose chances of solving it are

respectively. If they all try to solve the problem, what is the probability that the problem will be solved? NIMCET-2012, MP-2008(a) 1/2 (b) 1/4 (c) 1/3 (d) 3/4

10. If a fair coin is tossed n times, then the probability that the head comes odd number of times is

NIMCET-2012

(a) (b) (c) (d) None of

these11. One hundred identical coins each with probability P

of showing up heads re tossed. If 0 < P < 1 and the probability of heads showing on 50 coins is equal to that of heads on 51 coins; then the value of P is

NIMCET-2012

(a) (b) (c) (d)

12. Let P be a probability function on S = (l1, l2, l3, l4)

such that . Then P(l1)

is BHU-2012

(a) 7/18 (b) 1/3 (c) 1/6 (d) 1/513. The probability that A, B, C can solve problem is

respectively they attempt independently,

then the probability that the problem will solved is : BHU-2012

(a) 1/9 (b) 2/9 (c) 4/9 (d) 2/3

14. In a single throw with two dice, the chances of throwing eight is :

BHU-2012(a) 7/36 (b) 1/18 (c) 1/9 (d) 5/36

15. A single letter is selected at random from the word “probability”. The probability that it is a vowel, is :

BHU-2012(a) 3/11 (b) 4/11 (c) 2/11 (d) 0

16. An unprepared student takes a five question true-false exam and guesses every answer. What is the probability that the student will pass the exam if at least four correct answers is the passing grade?

HCU-2011(a) 3/16 (b) 5/32 (c) 1/32 (d) 1/8Answer questions 17 and 18 using the following text: In a country club, 60% of the members play tennis, 40% play shuttle and 20% play both tennis and shuttle. When a member is chosen at random,

17. What is the probability that she plays neither tennis nor shuttle?

HCU-2011(a) 0.8 (b) 0.2 (c) 0.5 (d) 0.4

18. If she plays tennis, what is the probability ability that she also plays shuttle?

HCU-2011(a) 2/3 (b) 2/5 (c) 1/3 (d) 1/2

19. If E is the event that an applicant for a home loan in employed C is the event that she possesses a car and A is the event that the loan application is approved, what does P(A|E C) represent in words?

HCU-2011(a) Probability that the loan is approved, if she is employed and possesses a car (b) Probability that the loan is approved, if she is either employed or possesses a car (c) Probability that the loan is approved, if she is neither employed nor possesses a car.(d) Probability that the loan is approved and she is employed, given that she possesses a car

20. An anti-aircraft gun can take a maximum of four slots at an enemy plane moving away from it. The probability of hitting the plane at the first, second, third and fourth slots are 0.4, 0.3, 0.2 and 0.1 respectively. The probability that the gun hits the plane then is

1

INFOMATHS


NIMCET-2011(a) 0.5 (b) 0.7235 (c) 0.6976 (d) 1.0

21. A random variable X has the following probability distributionx 0 1 2 3 4 5 6 7 8 P(X = x) a 3a 5a 7a 9a 11a 13a 15a 17a Then the value of ‘a’ is

NIMCET-2011(a) 1/81 (b) 2/82 (c) 5/81 (d) 7/81

22. Three coins are thrown together. The probability of getting two or more heads is

BHU-2011(a) 1/4 (b) 1/2 (c) 2/3 (d) 3/8

23. If four positive integers are taken at random and are multiplied together, then the probability that the last digit is 1, 3, 7 or 9 is :

PU CHD-2010

(A) (B) (C) (D)

24. The numbers X and Y are selected at random (without replacement) from the set (1, 2, .....3N). The probability that x2 – y2 is divisible by 3 is :

PU CHD-2010

(A) (B) (C) (D)

25. Probability of happening of an event A is 0.4 Probability that in 3 independent trials, event A happens atleast once is:PU CHD-2009(a) 0.064 (b) 0.144 (c) 0.784 (d) 0.4

26. A die is thrown. Let A be the event that the number obtained is greater than 3. Let B be the event that the number obtained is less than 5. Then P(A B) is : PU CHD-2009(a) 3/5 (b) 0 (c) 1 (d) 1/6

27. India plays two matches each with West Indies and Australia. In any match the probabilities of India getting points 0, 1 and 2 are 0.45, 0.05 and 0.50 respectively. Assuming that the outcomes are independent, the probability f India getting at least 7 points is NIMCET-2010 (a) 0.8750 (b) 0.0875 (c) 0.0625 (d)

0.025028. A coin is tossed three times The probabilities of

getting head and tail alternatively is NIMCET-2010

(a) 1/11 (b) 2/3 (c) 3/4 (d) 1/429. One hundred identical coins, each with probability P

of showing up a head, are tossed. If 0 < p < 1 and if the probability of heads on exactly 50 coins is equal to that of heads on exactly 51 coins then the value of p, is NIMCET-2010

(a) (b) (c) (d)

30. A dice is tossed 5 times. Getting an odd number is considered a success. Then the variance of distribution of success is

KIITEE-2010(a) 8/3 (b) 3/8 (c) 4/5 (d) 5/4

31. If A and B are events such that

then is

KIITEE-2010(a) 5/12 (b) 3/8 (c) 5/8 (d) 1/4

32. If A and B are any two mutually exclusive events, then P(A|AB) is equal to

(PGCET– 2009)(a) P(AB) (b) P(A)/(P(A) + P(B)) (c) P(B)/P(AB) (d) None of these

33. A man has 5 coins, two of which are double – headed, one is double – tailed and two are normal.

He shuts his eyes, picks a coin at random, and tosses it. The probability that the lower face of the coin is a head is (NIMCET – 2009)(a) 1/5 (b) 2/5 (c) 3/5 (d) 4/5

34. A and B are independent witnesses in a case. The probability that A speaks the truth is ‘x’ and that B speaks the truth is ‘y’. If A and B agree on a certain statement, the probability that the statement is true is (NIMCET – 2009)

(a) (b)

(c) (d)

35. Let A and B be two events such that

and .

Then events A and B are (NIMCET – 2009)

(a) independent but not equally likely(b) mutually exclusive and independent (c) equally likely and mutually exclusive(d) equally likely but not independent.

36. The probability that a man who is 85 yrs. old will die before attaining the age of 90 is 1/3. A1, A2, A3 and A4 are four persons who are 85 yrs. old. The probability that A1 will die before attaining the age of 90 and will be the first to die is

(NIMCET – 2009)

(a) (b) (c) (d)

37. An anti aircraft gun can take a maximum of four shots at an enemy plane moving away from it. The probabilities of hitting the plane at first, second, third and fourth shot are 0.4, 0.3, 0.2 and 0.1 respectively. The probability that the gun hits the plane then is

(MCA : NIMCET – 2009)(a) 0.6972 (b) 0.6978 (c) 0.6976 (d) 0.6974

38. Let A = [2, 3, 4, …., 20, 21] number is chosen at random from the set A and it is found to be a prime number. The probability that it is more than 10 is

(MCA : KIITEE – 2009)(a) 9/10 (b) 1/5 (c) 1/10 (d) None of these

39. Find the probability that a leap year will contain either 53 Tuesday or 53 Wednesdays.

HYDERABAD CENTRAL UNIVERSITY - 2009(a) 1/5 (b) 2/5 (c) 2/3 (d) 3/7

40. Probability that atleast one of A and B occurs is 0.6. If A and B occur simultaneously with probability 0.3, then P(A') + P(B') is

HYDERABAD CENTRAL UNIVERSITY - 2009(a) 0.9 (b) 1.15 (c) 1.1 (d) 2

41. The sum of two positive real numbers is 2a. The probability that product of these two numbers is not less than 3/4 times the greatest possible product is

HYDERABAD CENTRAL UNIVERSITY - 2009(a) 1/2 (b) 1/3 (c) 1/4 (d) 9/16

42. If two events A and B such that P(A') = 0.3, P(B) = 0.5 and P(A B) = 0.3, then P(B/AB') is :

NIMCET - 2008(a) 1/4 (b) 3/8 (c) 1/8 (d) None

43. A pair of unbiased dice is rolled together till a sum of either 5 or 7 is obtained. The probability that 5 comes before 7 is.

NIMCET - 2008(a) 3/5 (b) 2/5 (c) 4/5 (d) None

44. A letter is taken at random from the letters of the word ‘STATISTICS’ and another letter is taken at random from the letters of the word ‘ASSISTANT’. The probability that they are the same letter is.

NIMCET - 2008

2

INFOMATHS


(a) (b) (c) (d)

45. A six faced die is a biased one. It is thrice more likely to show an odd number than to show an even number. It is thrown twice. The probability that the sum of the numbers in the two throws is even, is.

NIMCET - 2008(a) 4/8 (b) 5/8 (c) 6/8 (d) 7/8

46. A letter is known to have come from either TATANAGAR or CALCUTTA. On the envelope, just two consecutive letters, TA, are visible. The probability that the letter has come from CALCUTTA is

NIMCET - 2008(a) 4/11 (b) 1/3 (c) 5/12 (d) None

47. A card is drawn from a pack. The card is replaced and the pack is reshuffled. If this is done six times, the probability that 2 hearts, 2 diamonds and 2 club cards are drawn is. KIITEE – 2008

(a) (b)

(c) (d) None

48. Two balls are drawn at random from a bag containing 6 white, 4 red and 5 black balls. The probability that both these balls are black, is :

MP COMBINED – 2008(a) 1/21 (b) 2/15 (c) 2/21 (d) 2/35

49. 6 boys and 6 girls sit in a row randomly. The probability that all the girls sit together is :

MP COMBINED – 2008

(a) (b) (c) (d)

50. Probabilities of three students A, B and C to pass an

examination are respectively , and . The

probability that exactly one student will pass is: MP COMBINED – 2008

(a) (b) (c) (d)

51. Different words are written with the letters of PEACE. The probability that both E’s come together is :

MP COMBINED – 2008(a) 1/3 (b) 2/5 (c) 3/5 (d) 4/5

52. The probability of throwing 6 at least one in four throws of a die is: MP COMBINED – 2008

(a) (b) (c) (d)

53. An untrue coin is such that when it is tossed the chances of appearing head is twice the chances of appearance of tail. The chance of getting head in one toss of the coin is :

MP COMBINED – 2008(a) 1/3 (b) 1/2 (c) 2/3 (d) 1

54. The probability of randomly chosing 3 defectless bulbs from 15 electric bulbs of which 5 bulbs are defective, is :

MP COMBINED – 2008

(a) (b) (c) (d)

55. Probability of four digit numbers, which are divisible by three, formed out of digits 1, 2, 3, 4, 5 is : MP COMBINED – 2008(a) 1/5 (b) 1/4 (c) 1/3 (d) 1/2

56. Let A and B be two events with P(A) = 1/2, P(B) = 1/3 and P(A B) = 1/4 , What is P(A B)?

KARNATAKA - 2007(a) 3/7 (b) 4/7 (c) 7/12 (d) 9/122

57. If three unbiased coins are tossed simultaneously then the probability of getting exactly two heads is

ICET - 2007(a) 1/8 (b) 2/8 (c) 3/8 (d) 4/8

58. A person gets as many rupees as the number he gets when an unbiassed 6 – faced die is thrown. If two such dice are thrown the probability of getting Rs. 10 is. ICET - 2007(a) 1/12 (b) 5/12 (c) 13/10 (d) 19/10

59. Let E be the set of all integers with 1 in their units place. The probability that a number n chosen from [2, 3, 4, … 50] is an element of E is

ICET - 2007(a) 5/49 (b) 4/49 (c) 3/49 (d) 2/49

60. A and B independent events. The probability that

both A and B occur is and the probability that

neither of them occurs is 1/6. Then the probability of occurrence of A is. ICET – 2005(a) 5/6 (b) 1/2 (c) 1/12 (d) 1/18

61. 8 coins are tossed simultaneously. The probability of getting atleast six heads is

ICET – 2005

(a) (b) (c) (d)

62. If two dice are tossed the probability of getting the sum at least 5 is PUNE Paper – 2007

(a) (b) (c) (d)

63. A and B play a game of dice. A throws the die first. The person who first gets a 6 is the winner. What is the probability that A wins?

PUNE Paper – 2007(a) 6/11 (b) 1/2 (c) 5/6 (d) 1/6

64. A player is going to play a match either in the morning or in the afternoon or in the evening all possibilities being equally likely. The probability that he wins the match is 0.6, 0.1 and 0.8 according as if the match is played in the morning, afternoon or in the evening respectively. Given that he has won the match, the probability that the match was played in the afternoon is

IP Univ. Paper – 2006

(a) (b) (c) (d) (e)

65. The probabilities that a husband and wife will be alive 20 years from now are given by 0.8 and 0.9 respectively. What is the probability that in 20 years at least one, will be alive?

Karnataka PG-CET : Paper – 2006 (a) 0.98 (b) 0.02 (c) 0.72 (d) 0.28

66. A bag contains 4 white and 3 black balls and a second bag contains 3 white and 3 black balls. If a ball is drawn from each of the bags, then the probability that both are of same colour is :

MP Paper – 2004

(a) (b) (c) (d)

67. The probability of getting atleast 6 head in 8 trials is: MP– 2004

(a) (b) (c) (d)

68. Prob. of getting an odd number or a no. less than 4 in throwing a dice is :

MP– 2004(a) 1/3 (b) 2/3 (c) 1/2 (d) 3/5

69. Given A and B are mutually exclusive events. IFP (B) = 0. 15, P(A B) = 0.85, P(A) is equal to UPMCAT Paper – 2002(a) 0.65 (b) 0.3 (c) 0.70 (d) N.O.T.

3

INFOMATHS


70. In a pack of 52 cards, the probability of drawing at random such that it is diamond or card king is :

UPMCAT Paper – 2002(a) 1/26 (b) 4/13 (c) 3/13 (d) 1/4

71. Given A and B are mutually exclusive events. if:P (A B) = 0.8, P(B) = 0.2 then P(A) is equal to UPMCAT–2002(a) 0.5 (b) 0.6 (c) 0.4 (d) N.O.T.

72. Two dice are thrown once the probability of getting a sum 9 is given by : UPMCAT Paper – 2002(a) 1/12 (b) 1/18 (c) 1/6 (d) N.O.T.

73. In a pack of 52 cards. Two cards are drawn at random. The probability that it being club card is :

UPMCAT Paper – 2002

(a) (b) (c) (d) N.O.T.

74. If P(A' B') is equal to 19/60 then P(AB) is equal to

UPMCAT Paper – 2002

(a) (b) (c) (d) N.O.T.

75. If the events A and B are mutually exclusive then P (A B) is given by : UPMCAT Paper – 2002(a) P(A) + P(B) (b) P(A)P(B) (c) P(A) P(B/A) (d) N.O.T.

76. If A and B are two events, the prob. that exactly one of them, occurs in given by: UPMCAT Paper – 2002

(a) (b)

(c) (d) None of these77. A bag contains 6 red and 4 green balls. A fair dice is

rolled and a number of balls equal to that appearing on the dice is chosen from the urn at random. The probability that all the balls selected are red is.

NIMCET – 2008 (a) 1/3 (b) 3/10 (c) 1/8 (d) none

78. A number x is chosen at random from (1, 2, …. 10). The probability that x satisfies the equation (x – 3) (x – 6) (x – 10) = 0 is

ICET - 2007(a) 2/5 (b) 3/5 (c) 3/10 (d) 7/10

TWO DIMENSIONAL GEOMETRY 1. Find the equation of the graph xy = 1 after a

rotation of the axes by 45 degrees anti-clockwise in the new coordinate system (x', y').

HCU-2012(a) x'2 – y'2 = 1 (b) (x'2 /2) - (y'2/2) = 1(c) (x'2 /2) + (y'2/2) = 1(d)

2. The number of points (x, y) satisfying (i) 3x - 4y = 25 and (ii) x2 + y2 25 is

HCU-2012(a) 0 (b) 1 (c) 2 (d) infinite

3. A point P on the line 3x + 5y = 15 is equidistant from the coordinate axes. Then P can lie in

HCU-2012(a) Quadrant I only (b) Quadrant I or Quadrant III only (c) Quadrant I or Quadrant II only (d) any Quadrant

4. A circle and a square have the same perimeter. Then HCU-2012

(a) their areas are equal (b) the area of the circle is larger (c) the area of the square is larger

(d) the area of the circle is times the area of the square

5. The eccentricity of the ellipse x2 + 4y2 + 8y – 2x + 1 = 0 is :

PU CHD-2012

(A) (B) (C) (D)

6. The orthocenter of the triangle formed by the lines xy = 0 and x + y = 1 is :

PU CHD-2012(A) (1/2, 1/2) (B) (1/3, 1/3)(C) (1/4, 1/4) (D) (0, 0)

7. The distance between the parallel lines y = 2x + 4 and 6x = 3y + 5 is

PU CHD-2012, NIT-2010

(A) (B) 1 (C) (D)

8. The lines 2x – 3y = 5 and 3x – 4y = 7 are the diameters of a circle of area 154 square units. Then the equation of this circle is (= 22/7)

PU CHD-2012(A) x2 + y2 + 2x – 2y = 62 (B) x2 + y2 + 2x – 2y

= 47(C) x2 + y2 – 2x + 2y = 47 (D) x2 + y2 – 2x + 2y

= 629. The focus of the parabola y2 – x – 2y + 2 = 0 is :

PU CHD-2012(A) (1/4, 0) (B) (1, 2) (C) (3/4, 1) (D) (5/4,

1)10. The medians of a triangle meet at (0, –3). While its

two vertices are (–1, 4) and (5, 2), the third vertex is at

PU CHD-2012(A) (4, 5) (B) (–1, 2) (C) (7, 3) (D) (– 4, – 15)

11. The area of the triangle having the vertices (4, 6), (x, 4), (6, 2) is 10 sq units. The value of x is

PU CHD-2012(A) 0 (B) 1 (C) 2 (D) 3

12. The position of reflection of point (4, 1) w.r.to line y = x – 1 is

Pune-2012(a) (-4, -1) (b) (1, 2) (c) (2, 3) (d) (3, 4)

13. 6x2 + 12x + 8 – y = 0 has its standard form as? Pune-2012

(a) (b)

(c) (d) None of these

14. If a given point is P(10,10) and the Eq. of circle is(x – 1)2 + (y – 2)2 = 144. Where does the pt. lies

Pune-2012(a) inside (b) on (c) outside (d) None of these

15. The point on the curve y = 6x = x2, where the tangent is parallel to x – axis is

NIMCET-2012(a) (0, 0) (b) (2, 8) (c) (6, 0) (d) (3, 9)

16. If (4, - 3) and (-9, 7) are the two vertices of a triangle and (1, 4) is its centroid, then the area of triangle is

NIMCET-2012

(a) (b) (c) (d)

17. The equation of the ellipse with major axis along the x-axis and passing through the points (4, 3) and (-1, 4) is

NIMCET-2012(a) 15x2 + 7y2 = 247 (b) 7x2 + 15y2 = 247 (c) 16x2 + 9y2 = 247 (d) 9x2 + 16y2 = 247

18. If the circles x2 + y2 + 2x + 2ky + 6 = 0 and x2 + y2

+ 2ky + k = 0 intersect orthogonally, then k is NIMCET-2012

(a) 2 of (b) – 2 or

4

INFOMATHS


(c) 2 or (d) – 2 or

19. Focus of the parabola x2 + y2 – 2xy – 4(x + y – 1) = 0 is

NIMCET-2012(a) (1, 1) (b) (1, 2) (c) (2, 1) (d) (0, 2)

20. If e and er be the eccentricities of a hyperbola and

its conjugate, then

NIMCET-2012(a) 0 (b) 1 (c) 2 (d) None of these

21. The straight line passes through the point and makes an angle of 60 with the x-axis. The length of the intercept on it between the point P and the line is :

BHU-2012(a) 1.5 (b) 2.5 (c) 3.5 (d) 4.5

22. The equation of the straight line passing through the point of intersection of 4x + 3y – 8 = 0 and x + y – 1 = 0, and the point (-2, 5) is :

BHU-2012(a) 9x + 7y – 17 = 0 (b) 4x + 5y + 6 = 0 (c) 3x – 2y + 19 = 0 (d) 3x – 4y – 7 = 0

23. The angle between the two straight line represented by the equation 6x2 + 5xy – 4y2 + 7x + 13y – 3 = 0 is:

BHU-2012

(a) (b)

(c) (d)

24. The equation of circle passing through (-1, 2) and concentric with x2 + y2 – 2x – 4y – 4 = 0 is :

BHU-2012(a) x2 + y2 – 2x – 4y + 1 = 0 (b) x2 + y2 – 2x – 4y + 2 = 0(c) x2 + y2 – 2x – 4y + 4 = 0 (d) x2 + y2 – 2x – 4y + 8 = 0

25. The radius of the circle on which the four points of intersection of the lines (2x – y + 1) (x – 2y + 3) = 0 with the axes lie, is :

BHU-2012

(a) 5 (b) (c) (d)

26. The focal distance of a point on the parabola y2 = 8x is 4. Its ordinates are :

BHU-2012(a) 1 (b) 2 (c) 3 (d) 4

27. The straight line x cos + y sin = p touches the

ellipse if :

BHU-2012(a) p2 = a2 cos2 - b2 sin2 (b) p2 = a2 cos2 + b2 sin2(c) p2 = a2 sin2 - b2 cos2 (d) p2 = a2 sin2 + b2 cos2

28. If the line lx + my = n touches the hyperbola

if :

BHU-2012(a) a2l2 – b2m2 = n2 (b) al – bm = n (c) a2l2 + b2m2 = n2 (d) al + bm = n

29. For the conic , the sum of reciprocals

of the segments of any focal chord is equal to : BHU-2012

(a) l (b) 2l (c) (d)

30. The equation of tangent at (2, 2) of the curve xy2 = 4 (4 – x) is :

BHU-2012(a) x – y = 4 (b) x + y = 4 (c) x – y = 2 (d) x + y = 2

31. A curve given in polar form as r = a(cos() + sec ()) can be written in Cartesian form as

HCU-2011(a) x(x2 + y2) = a(2x2 + y2) (b)

(c) (d) y = atan + x

32. The relation that represents the shaded region in the figure given below is

HCU-2011(a) y x (b) |y| |x| (c) y |x| (d) |y| x

33. The area enclosed within the lines |x| + |y| = 1 isNIMCET-2011

(a) 1 (b) 2 (c) 3 (d) 434. If 2x + 3y – 6 = 0 and 9x+ 6y – 18 = 0 cuts the axes

in concyclic points, then the center of the circle is: NIMCET-2011

(a) (2, 3) (b) (3, 2) (c) (5, 5) (d) (5/2, 5/2)35. The number of distinct solutions (x, y) of the system

of equations x2 = y2 and (x – a)2 + y2 = 1 where ‘a’ is any real number, can only be

NIMCET-2011(a) 0, 1, 2, 3, 4 or 5 (b) 0, 1 or 3 (c) 0, 1, 2 or 4 (d) 0, 2, 3 or 4

36. The vertex of parabola y2 − 8y +19 = 0 isNIMCET-2011

(a) (3, 4) (b) (4, 3) (c) (1, 3) (d) (3, 1)37. The eccentricity of ellipse 9x2 + 5y2 − 30y = 0 is

NIMCET-2011

(a) (b) (c) (d) 38. Point A is a + 2b, P is a and P divides AB in the ratio

of 2 : 3. The position vector of B is BHU-2011

(a) 2a – b (b) b – 2a (c) a – 3b (d) b39. If the position vectors of A and B are a and b

respectively, then the position vector of a point P which divides AB in the ratio 1 : 2 is

BHU-2011

(a) (b)

(c) (d)

40. The straight line touches the curve

y = be-x/a at the point BHU-2011

(a) where it crosses the y-axis (b) where it crosses the x-axis (c) (0, 0) (d) (1, 1)

41. Every homogeneous equation of second degree in x and y represent a pair of lines

BHU-2011(a) parallel to x-axis (b) perpendicular to y-axis

5

INFOMATHS


(c) through the origin (d) parallel to y-axis 42. The difference of the focal distances of any point on

the hyperbola is

BHU-2011(a) a (b) 2a (c) b (d) 2b

43. If in ellipse the length of latusrectum is equal to half of major axis, then eccentricity of the ellipse is

BHU-2011

(a) (b) (c) (d)

44. An equilateral triangle is inscribed in the parabola y2 = 4ax whose vertex is at the vertex of the parabola. The length of its side is

BHU-2011(a) (b) (c) (d)

45. Two circles x2 + y2 = 5 and x2 + y2 – 6x + 8 = 0 are given. Then the equation of the circle through their point of intersection and the point (1, 1) is

BHU-2011(a) 7x2 + 7y2 – 18x + 4 = 0 (b) x2 + y2 – 3x + 1 = 0 (c) x2 + y2 – 4x + 2 = 0 (d) x2 + y2 – 5x + 3 = 0

46. The equation represents a

BHU-2011(a) straight line (b) circle (c) parabola (d) pair of lines

47. The coordinates of the orthocenter of the triangle formed by the lines 2x2 – 2y2 + 3xy + 3x + y + 1 = 0 and 3x + 2y + 1 = 0 are

BHU-2011

(a) (b)

(c) (d)

48. The angle between the asymptotes of the hyperbola 27x2 – 9y2 = 24 is NIMCET-2010(a) 60 (b) 120 (c) 30 (d) 150

49. If any tangent to the ellipse intercepts

equal length l on the axes, then l = NIMCET-2010(A) a2 + b2 (B) (C) (a2 +b2)2 (D) N.O.T

50. If a p, b q, c r and = 0, then the value

of + is NIMCET-

2010 (a) 0 (b) 1 (c) -1 (d) 2

51. The number of integral values of m for which the x coordinate of the point of intersection of the lines 3x + 4y = 9 and y = mx + 1 is also an integer is

KIITEE-2010(a) 2 (b) 0 (c) 4 (d) 1

52. The pair of straight lines joining the origin to the common point of x2 + y2 = 4 and y = 3x + c perpendicular if c2 is equal to

KIITEE-2010(a) 20 (b) 13 (c) 1/5 (d) 1

53. Intercept on the line y = x by the circle x2 + y2 – 2x = 0 is AB. Equation of the circle on AB as diameter is

KIITEE-2010(a) x2 + y2 + x – y = 0 (b) x2 + y2 – x + y = 0

(c) x2 + y2 + x + y = 0 (d) x2 + y2 – x – y = 0

54. The locus of a point which moves such that the tangents from it to the two circles x2 + y2 – 5x – 3 = 0 and 3x2 + 3y2 + 2x + 4y – 6 = 0 are equal is

KIITEE-2010(a) 2x2 + 2y2 + 7x + 4y – 3 = 0 (b) 17x + 4y + 3 = 0 (c) 4x2 + 4y2 – 3x + 4y – 9 = 0 (d) 13x – 4y + 15 = 0

55. If a 0 and the line 2bx + 3cy + 4d = 0 passes through the points of intersection of the parabolas y2

= 4ax and x2 = 4ay, then KIITEE-2010

(a) d2 + (3b – 2c)2 = 0 (b) d2 + (3b + 2c)2 = 0 (c) d2 + (2b – 3c)2 = 0 (d) d2 + (2b + 3c)2 = 0

56. The distances from the foci of P (a, b) on the ellipse

are KIITEE-

2010

(a) (b)


57. The locus of a point P(,) moving under the condition that the line y = x + is a tangent to the

hyperbola is

KIITEE-2010(a) an ellipse (b) a circle (c) a parabola (d) a hyperbola

58. It the foci of the ellipse and the

hyperbola coincide, then the value

of b2 is KIITEE-2010

(a) 3 (b) 16 (c) 9 (d) 1259. The medians of a triangle meet at (0, - 3) and two

vertices are at (-1, 4) and (5, 2). Then the third vertex is at

KIITEE-2010(a) (4, 15) (b) (-4, 15) (c) (-4, 15) (d) (4, -15)

60. The length of the perpendicular drawn from the point (3, - 2) on the line 5x – 12y – 9 = 0 is

PGCET-2010

(a) (b) (c) (d) None of these

61. If the lines x – 6y + a = 0, 2x + 3y + 4 = 0 and x + 4y + 1 = 0 are concurrent, then the value of ‘a’ is

PGCET-2010(a) 4 (b) 8 (c) 5 (d) 6

62. the angle between the lines represented by x2 + 3xy + 2y2 = 0 is

PGCET-2010(a) tan-1(2/3) (b) tan-1(1/3) (c) tan-1(3/2) (d) None of these

63. If the circle 9x2 + 9y2 = 16 cuts the x-axis at (a, 0) and (-a, 0), then a is

PGCET-2010(a) 2/3 (b) 3/4 (c) 1/4 (d) 4/3

64. The length of the perpendicular drawn from the point (1, 1) on the 15x + 8y + 45 = 0 is

(PGCET paper – 2009)(a) 3 (b) 4 (c) 5 (d) 2

65. The equation of the line passing through the point of intersection 2x – y + 5 = 0 and x + y + 1 = 0 and the point (5, - 2) is

(PGCET paper – 2009)(a) 3x + 7y – 1 = 0 (b) x + 2y + 1 = 0

6

INFOMATHS


(c) 5x + 6y + 3 = 0 (d) None of these66. The point of intersection of the lines represented by

2x2 – 9xy + 4y2 = 0 is (PGCET paper – 2009)

(a) (0, 0) (b) (0, 1) (c) (1, 0) (d) (1, 1) 67. If y = x + c is a tangent to the circle x 2 + y2 = 8,

then c is (PGCET paper – 2009)

(a) 3 (b) 2 (c) 4 (d) 168. The equation of the parabola whose vertex is (1, 1)

and focus is (4, 1) is (PGCET paper – 2009)

(a) (y – 1)2 = 12(x – 1) (b) (y – 2)2 = 13(x – 2) (c) (y – 1)2 = 10(x + 1) (d) None of these

69. If the distance of any point (x, y) from the origin is defined as d(x, y)= max (|x|, |y|), then the locus of the point (x, y) where d(x, y) = 1 is MCA : NIMCET – 2009, KIITEE-2010(a) a square of area 1 sq. unit (b) a circle of radius 1 (c) a triangle (d) a square of area 4 sq. units

70. Let ABC be an isosceles triangle with AB = BC. If base BC is parallel to x-axis and m1, m2 are slopes of medians drawn through the angular points B and C, then (MCA : NIMCET – 2009)(a) m1m2 = - 1 (b) m1 + m2 = 0 (c) m1m2 = 2 (d) (m1 – m2)2 + 2m1m2=0

71. The straight lines and

meet on

(MCA : NIMCET – 2009)(a) a parabola (b) an ellipse (c) a hyperbola (d) a circle

72. The equation of the line segment AB is y = x, if A and B lie on the same side of the line mirror 2x – y = 1 the image of AB has the equation

(MCA : KIITEE - 2009)(a) 7x – y = 6 (b) x + y = 2 (c) 8x + y = 9 (d) None of these

73. The point (-1, 1) and (1, -1) are symmetrical about the line

(MCA : KIITEE - 2009)(a) y + x = 0 (b) y = x (c) x + y = 1 (d) None of these

74. The product of perpendiculars drawn from the point (1, 2) to the pair of lines x2 + 4xy + y2 = 0 is

(MCA : KIITEE - 2009)(a) 9/4 (b) 9/16 (c) 3/4 (d) None of these

75. The centroid of the triangle whose three sides are given by the combined equation (x2 + 7xy + 2y2) (y – 1) = 0 is

(MCA : KIITEE - 2009)

(a) (b)


76. Two distinct chords drawn from the point (p, q) on the circle x2 + y2 = px + qy, where pq 0 are bisected by the x-axis then

(MCA : KIITEE - 2009)(a) |p| = |q| (b) p2 = 8q2 (c) p2 < 8q2 (d) p2 > 8q2

77. The length of the latus rectum of the parabola x = ay2 + by + c is

(MCA : KIITEE - 2009)(a) a/4 (b) 1/4a (c) 1/a (d) a/3

78. The equation of the tangent to the x2 – 2y2 = 18 which is perpendicular to the line x – y = 0

(MCA : KIITEE - 2009)(a) x + y = 3 (b) x + y =3/2

(c) x + y + 2 = 0 (d) 79. The sides of the rectangle of the greatest area that

can be inscribed in the ellipse x2 + 2y2 = 8, are given by

HYDERABAD CENTRAL UNIVERSITY - 2009(a) (b) (c) (d)

80. The equation of the circle having the chord x – y = 1

of the circle as a

diameter is HYDERABAD CENTRAL UNIVERSITY - 2009

(a)

(b)

(c)

(d)

81. Loci of a point equidistant to (2, 0) and x = - 2 is HYDERABAD CENTRAL UNIVERSITY - 2009

(a) y2 = 8x (b) y2 = 4x (c) x2 = 2y (d) x2 = 16y

82. Given two fixed points A(-3, 0) and B(3, 0) with AB = 6, the equation of the locus of point P which moves such that PA + PB = 8 is HYDERABAD CENTRAL UNIVERSITY - 2009

(a) (b)

(c) (d)

83. If y = mx bisects the angle between the lines x2

(tan2 + cos2) + 2xy tan - y2 sin2 = 0 when = /3, then the value of is

NIMCET - 2008

(a) 1 (b) (c) (d)

84. If a, b, c are the roots of the equation x3 – 3px2 + 3qx – 1 = 0, then the centroid of the triangle with

vertices and is at the point

NIMCET - 2008

(a) (p, q) (b)

(c) (p + q, p – q) (d) (3p, 3q) 85. Equation of the common tangent touching the circle

(x – 3)2 + y2 = 9 and the parabola y2 = 4x above the x – axis is NIMCET - 2008(a) (b) (c) (d)

86. The coordinates of a point on the line x + y = 3 such that the point is at equal distances from the lines |x| = |y| are KIITEE - 2008(a) (3, 0) (b) (-3, 0) (c) (0, - 3) (d) None

87. Lines are drawn through the point P (-2, -3) to meet the circle x2 + y2 – 2x – 10y + 1 = 0. The length of the line segment PA, A being the point on the circle where the line meets the circle is.

KIITEE - 2008(a) (b) 16 (c) 48 (d) None

7

INFOMATHS


88. If the common chord of the circles x2 + (y - )2 = 16 and x2 + y2 = 16 subtend a right angle at the origin then is equal to. MCA : KIITEE - 2008(a) (b) (c) 4 (d) 8

89. The equation of any tangent to the circle x2 + y2 – 2x + 4y – 4 = 0 is

KIITEE - 2008(a) (b) (c) (d) None

90. The equation of the circle whose two diameters are 2x – 3y + 12 = 0 and x + 4y – 5 = 0 and the area of

which is 154 sq. units, will be :

MP COMBINED - 2008(a) x2 + y2 + 6x – 4y + 36 = 0 (b) x2 + y2 + 3x – 2y + 18 = 0(c) x2 + y2 – 6x + 4y + 36 = 0 (d) x2 + y2 + 6x – 4y – 36 = 0

91. The circle x2 + y2 – 2x + 2y + 1 = 0 touches: MP COMBINED - 2008

(a) Only x-axis (b) Only y-axis (c) Both the axes (d) None of the axes

92. If the line hx + ky = 1 touches the circle

, then the locus of the point (h, k)

will be: MP COMBINED - 2008

(a) x2 + y2 = a2 (b) x2 + y2 = 2a2

(c) x2 + y2 = 1 (d)

93. Equation of the circle concentric to the circle x2 + y2 – x + 2y + 7 = 0 and passing through (-1, -2) will be:

MP COMBINED - 2008(a) x2 + y2 + x + 2y = 0 (b) x2 + y2 – x + 2y + 2 = 0 (c) 2(x2 + y2) – x + 2y = 0 (d) x2 + y2 – x + 2y – 2 = 0

94. For the circle x2 + y2 – 4x + 2y + 6 = 0, the equation of the diameter passing through the origin is:

MP COMBINED - 2008(a) x – 2y = 0 (b) x + 2y = 0 (c) 2x – y = 0 (d) 2x + y = 0

95. The circle x2 + y2 + 2ax – a2 = 0: (MP COMBINED – 2008)(a) touches x – axis (b) touches y – axis (c) touches both the axis (d) intersects both the axes

96. The circles x2 + y2 + 2g1x + f1y + c1 = 0 and x2 + y2 + g2x + 2f2y + c2 = 0 cut each other orthogonally, then :

(MP COMBINED – 2008)(a) 2g1g2 + 2f1f2 = c1 + c2 (b) g1g2 + f1f2 = c1 + c2 (c) g1g2 + f1f2 = 2(c1 + c2) (d) g1g2 + f1f2 + c1 + c2 = 0

97. If the straight line 3x + 4y = touches the parabola y2 = 12x then value of is

(MCA : MP COMBINED – 2008)(a) 16 (b) 9 (c) – 12 (d) – 16

98. For the parabola y2 = 14x, the tangent parallel to the line x + y + 7 = 0 is :

(MCA : MP COMBINED – 2008)(a) x + y + 14 = 0 (b) x + y + 1 = 0 (c) 2(x + y) + 7 = 0 (d) x + y = 0

99. Eccentricity of the ellipse 9x2 + 5y2 – 30y = 0 is :(MP COMBINED – 2008)

(a) 1/3 (b) 2/3 (c) 4/9 (d) 5/9

100. For the ellipse , S1 and S2 are two foci

then for any point P lying on the ellipse S1P + S2P equals:

(MCA : MP COMBINED – 2008)(a) 6 (b) 8 (c) 12 (d) 16

101. The coordinates of the foci of the hyperbola 9x2 – 16y2 = 144 are:

(MCA : MP COMBINED – 2008)(a) (0, 4) (b) ( 4, 0) (c) (0, 5) (d) ( 5, 0)

102. The lengths of transverse and conjugate axes of the hyperbola x2 - 2y2 – 2x + 8y – 1 = 0 will be respectively:

(MCA : MP COMBINED – 2008)(a) (b)

(c) (d)

103. For the given equation x2 + y2 – 4x + 6y – 12 = 0, the centre of the circle is

KARNATAKA - 2007(a) (-2, 3) (b) (-3, 2) (c) (3, - 2) (d) (2, - 3)

104. The circumference of the circle x2 + y2 + 2x + 6y – 12 = 0 the centre of the circle is

KARNATAKA - 2007(a) 2 (b) 8 (c) 3 (d) None

105. The locus of a point which moves in a plane such that its distance from a fixed point is equal to its distance from a fixed line is.

KARNATAKA - 2007(a) Parabola (b) Hyperbola (c) Ellipse (d) Circle

106. In parabola y2 = 4kx, if the length of Latus Rectum is 2 then k is

KARNATAKA - 2007(a) +1/2 (b) –1/2 (c) 0 (d) +1/2 or – 1/2

107. The point of intersection of lines (i) x + 2y + 3 = 0 and (ii) 3x + 4y + 7 = 0 is

KARNATAKA - 2007(a) (1, 1) (b) (1, - 1) (c) (-1, 1) (d) (-1, -1)

108. The acute angle between the lines (i) 2x – y + 13 = 0 and (ii) 2x – 6y + 7 = 0

KARNATAKA - 2007(a) 0 (b) 30 (c) 45 (d) 60

109. If the points (k, - 3), (2, - 5) and (-1, -8) are collinear then K = ICET - 2007(a) 0 (b) 4 (c) – 2 (d) – 3

110. The equation of the line with slope -3/4 and y – intercept 2 is ICET - 2007(a) 3x + 4y = 8 (b) 3x + 4y + 8 = 0 (c) 4x + 3y = 2 (d) 3x + 4y = 4

111. If the lines x + 2y + 1 = 0, x + 3y + 1 = 0 and x + 4y + 1 = 0 pass through a point then a + =

ICET - 2007(a) (b) 2 (c) 1/ (d) 1/2

112. Equation of the line passing through the point (2, 3) and perpendicular to the segment joining the points (1, 2) – (1, 5) is

ICET – 2005(a) 2x – 3y – 13 = 0 (b) 2x – 3y – 9 = 0 (c) 2x – 3y – 11 = 0 (d) 2x – 3y – 7 = 0

113. The two sides forming the right angle of the triangle whose area is 24 sq. cm. are in the ratio 3:4. Then the length of the hypotenuse (in cm) is

ICET – 2005(a) 12 (b) 10 (c) 8 (d) 5

114. The equation of the circle passing through the origin and making intercepts of 4 and 3 or OX and OY respectively is ICET – 2005(a) x2 + y2 – 3x – 4y = 0 (b) x2 + y2 + 4x + 3y = 0 (c) x2 + y2 + 3x + 4y = 0 (d) x2 + y2 – 4x – 3y = 0

115. The equation of the straight line which cuts off equal intercepts from the axis and passes through the point (1, - 2) is ICET – 2005(a) 2x + 2y + 1 = 0 (b) x + y + 1 = 0

8

INFOMATHS


(c) x + y – 1 = 0 (d) 2x + 2y – 1 = 0 116. If the lines 2x + 3y = 6, 8x – 9y + 4 = 0, ax + 6y =

13 are concurrent, then a = ICET – 2005(a) 3 (b) – 3 (c) – 5 (d) 5

117. The points of concurrence of medians of a triangle is ICET – 2005

(a) incentre (b) orthocenter (c) centroid (d) circumcentre

118. If (0, 0), (2, 2) and (0, a) form a right angled isosceles triangle, then a =

ICET – 2005(a) 4 (b) – 4 (c) 3 (d) – 3

119. The area of the largest rectangle, whose sides are parallel to the coordinate axes, that can be inscribed

in the ellipse IP Univ.

Paper – 2006(a) 10 (b) 20 (c) 30 (d)

(e) 120. The orthocenter of the triangle determined by the

lines 6x2 + 5xy – 6y2 – 29x + 2y + 28 = 0 and 11x – 2y – 7 = 0 is

IP Univ. Paper – 2006(a) (-4, 5) (b) (4, 4) (c) (6, 7} (d) (2, 1) (e) (-1, 3)

121. a, b, c R. if 2a + 36 + 4c = 0, then the line ax + by + c = 0

(a) (b)

(c) (d) (e)

122. The distance of the point (x, y) form y-axis is Karnataka PG-CET : Paper 2006

(a) x (b) y (c) |x| (d) |y|123. If the lines 4x + 3y = 1, y = x + 5 and 5y + bx = 3

are concurrent, then the value of b is Karnataka PG-CET : Paper 2006

(a) 1 (b) 3 (c) 6 (d) 0124. The system of equations x + y = 2 and 2x + 2y = 3

has Karnataka PG-CET : Paper 2006 (a) No solution (b) a unique solution (c) finitely many solutions (d) infinitely many solutions

125. The radius of the circle 16x2 + 16y2 = 8x + 32y – 257 = 0

Karnataka PG-CET : Paper 2006 (a) 8 (b) 6 (c) 15 (d) None of these

126. Axis of the parabola x2 – 3y – 6x + 6 = 0 is Karnataka PG-CET : Paper 2006

(a) x = - 3 (b) y = - 1 (c) x = 3 (d) y = 1 127. The locus of a point which moves such that the

difference of its distances from two fixed points is always a constant is Karnataka PG-CET : 2006 (a) a circle (b) a straight line (c) a hyperbola (d) an ellipse

128. The Eccentricity of a rectangular hyperbola is : MP : MCA Paper – 2003

(a) (b) (c) (d) 2129. From a point (x1, y1) two tangent can be drawn on

circle x2 + y2 = a2 if: MP : MCA Paper – 2003


130. The sum of the distance of a point on the ellipse

to its foci is equal to : MP : MCA– 2003

(a) semi major axis (b) major axis (c) semi minor axis (d) minor axis

131. The foci of hyperbola 9x2 – 25y2 + 54x + 50y – 169 = 0 is

MP – 2003

(a) (-3, 1) (b)

(c) (d) None of these132. If two circles x2 + y2 + 2g1x + 2f1y + c1 = 0, x2 + y2

+ 2g2n + 2f2y + c2 = 0 will cut each other and

satisfies MP : MCA

Paper – 2003 (a) π/3 (b) π/2 (c) 3π/2 (d) π/4

133. Two circles x2 + y2 + 2gx + c = 0 and x2 + y2 + 2fy + c = 0 touch each other, then :

MP :– 2003 (a) g2 + f2 = c3 (b) g2 + f2 = c (c) c(g2 + f2) = g2f2 (d) g2 + f2c = g2f2

134. S1 = x2 + y2 – 4x – 6y + 10 = 0 S2 = x2 + y2 – 2x – 2y – 4 Angle between S1 and S2 is

UPMCAT : paper – 2002 (a) 90 (b) 60 (c) 45 (d) None of these

135. The equation of line passing through the intersection of lines 5x – 6y – 1 = 0 and 3x + 2y + 5 = 0 and perpendicular to 3x – 5y + 27 = 0 is :

UPMCAT :– 2002 (a) 5x + 3y + 10 = 0 (b) 5x + 3y + 21 = 0 (c) 5x + 3y + 18 = 0 (d) 5x + 3y + 8 = 0

136. The area of triangle formed by y = m1x + c, y = m2x + c2 and y axis is : UPMCAT : paper – 2002

(a) (b)

(c) (d)

137. Reflection of the point P(1, 2) in x + 2y + 4 = 0 is UPMCAT : paper – 2002

(a) (b)


138. The area of the region bonded by the curve y = x2 and the line y = x is UPMCAT : paper – 2002

(a) Sq U (b) Sq U

(c) Sq U (d) N.O.T.

139. If 4x2 + 9y2 + 12xy + 6x ….. + 9y – 4 = 0 represents two parallel lines then the distance between. The lines is: UPMCAT:– 2002


140. If (± 3, 0) be focus of ellipse and semi major axis is 6. Then equ. of ellipse is:

UPMCAT :– 2002

(a) (b)


141. If 2x2 – 5xy + 2y2 – 3x + 1 = 0, represents pairs of lines, then the angle between the lines is :

UPMCAT : paper – 2002 (a) tan-1 (2/3) (b) tan-1 (4/3) (c) tan-1 (3/4) (d) None of these

142. The condition that eqa. ax2 + by2 + 2gx + 2fy + 2hxy + c = 0 represents a pair of the line is

9

INFOMATHS


(i)

(ii) abc + 2fgh – af2 – bg2 – ch2 = 0 (iii) af + bg + ch = 0 (iv) af2 = bg2 ; h2 = ab

UPMCAT:– 2002 (a) i, ii (b) ii, iv (c) i, iv (d) i, ii and iv

143. A ellipse has , directrix is x + 6 = 0, and has a

focus at (0, 0) then the eqn. of ellipse is: UPMCAT :– 2002

(a) 3x2 + 4y2 + 12x – 36 = 0 (b) 3x2 + 4y2 – 12x + 36 = 0 (c) 3x2 + 4y2 – 12x – 36 = 0 (d) None of these

144. The eqn. of the ellipse has its centre at (1, 2), a focus at (6, 2) and passing through the point (4, 6) : UPMCAT :– 2002

(a) (b)


145. The tangents of the circle x2 + y2 = 4 at the points A and B meet at P(-4, 0). The area of the quadrilateral PAOB where O is the origin is.

KIITEE - 2008(a) 4 (b) (c) (d) None

146. The x2 + y2 + 2x = 0, R touches the parabola y2

= 4x externally. Then KIITEE - 2008

(a) > 1 (b) < 0 (c) > 0 (d) None

147. A point P on the ellipse has the

eccentric angle . The sum of the distance of P

from the two foci is. KIITEE - 2008

(a) 10 (b) 6 (c) 5 (d) 3

148. For the hyperbola which of the

following remains constant when varies? MCA : KIITEE - 2008

(a) directrix (b) eccentricity (c) abscissae of foci (d) abscissae of vertices

149. The sum of the intercepts made on the axes of co-ordinates by any tangent to the curve is equal to KIITEE - 2008(a) 4 (b) 8 (c) 2 (d) None

150. If the focus and directrix of a parabola are (-sin , cos ) and x cos + y sin = p respectively, then length of the latus rectum will be:

(MP COMBINED – 2008)(a) 2p (b) 4p (c) p2 (d) p(cos – sin )

151. The distance between the two focii of a hyperbola H is 12. The distance between the two directories of hyperbola H is 3. The acute angle between the asymptotes of H in degrees is

IP Univ. Paper – 2006(a) 30 (b) 40 (c) 45 (d) 60 (e) 70

152. L1 || L2. Slope of L1 = 9. Also L3 || L4. Slope of L4

. All these lines touch the ellipse

. The area of the parallelogram

determine by these lines is IP University : Paper - 2006

(a) 21 (b) 28 (c) 40 (d) 56 (e) 60

153. If P, Q, R, S are four distinct collinear points such

that , then, the value of is

IP University : Paper - 2006

(a) (b)

(c) (d) (e) N.O.T.

154. P moves on the line y = 3x + 10. Q moves on the parabola y2 = 24x. The shortest value of the segment PQ is IP University - 2006

(a) (b) (c) (d) (e) 6

155. The line 2x + y – 1 = 0 cuts the curve 5x2 + xy – y2 – 3x – y + 1 = 0 at P and Q. O is the origin. The acute angle between the lines OP and OQ is

IP University - 2006

(a) (b) (c) (d) (e)

156. The limiting points of the system of coaxial circles of which two members are x2 + y2 + 2x + 4y + 7 = 0 and x2 + y2 + 5x + y + 4 = 0 is:

MP : MCA Paper – 2003 (a) (-2, 1) and (0, - 3) (b) (2, 1) and (0, 3) (c) (4, 1) and (0, 6) (d) None of these

157. The length of common chord of the circles (x – a)2 + y2 = a2 and x2 + (y – b)2 = b2 is :

MP : MCA Paper – 2003

(a) (b)


158. An arch way is in the shape of a semi ellipse. The road level being the major axis. If the breadth of the road is 30 metres and the height of the arch is 6m at a distance of 2 metre from the side, then find the greatest height of the arch.

MP : MCA Paper – 2003

(a) m (b) m

(c) m (d) m

159. The locus midpoint of a chord of the circle x2 + y2 = 4, which subtend angle 90 at the centre.

UPMCAT : paper – 2002 (a) x + y + 3 = 0 (b) x2 + y2 = 0 (c) x + y + 2 = 0 (d) x2 + y2 = 2

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QUINTESSENCE: - Infomathsinfomathsonline.com/Que_papers/Worksheet-3 Maths.doc · Web view80. The equation of the circle having the chord x – y = 1 of the circle as a diameter is