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INFOMATHS
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
A4 B4
3.
4.
5.
A1 B1 ,
lines
A2 B2 ,
A3 B3
and
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
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
Let A, B and C be the three events such that
P(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
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
(B)
137
729
(C)
16
81
(D)
BHU-2012
(a) 7/18
13.
14.
15.
16.
17.
18.
19.
137
81
Let P(E) denote the probability of event E. Given P(A) = 1, P(B)

1
, the values of P(A|B) and P (B|A) respectively are
2
NIMCET-2012
1 1
(a) ,
4 2
7.
8.
9.
1 1
(b) ,
2 4
1
(c) ,1
2
1
(d) 1,
2
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
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
A problem in Mathematics is given to three students A, B and C
20.
21.
10.
(a)
11.
1
2
(b)
1
2n
(c)
1
2n1
1
(a)
2
49
(b)
101
50
(c)
101
22.
23.
(d) None of these
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
51
(d)
101
WORKSHEET-3 (OLD QUESTIONS )
(b) 1/3
(d) 1/5
1 1 1
, ,
3 3 3
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
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
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
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) 1/8
Answer 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,
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
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
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
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
NIMCET-2011
(a) 0. 5
(b) 0.7235 (c) 0.6976 (d) 1.0
A random variable X has the following probability distribution
x
0 1
2
3
4
5
6
7
8
7a
9a
11a
13a
15a
17a
NIMCET-2011
(a) 1/81
(b) 2/82
(c) 5/81
(d) 7/81
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
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)
24.
(c) 1/6
The probability that A, B, C can solve problem is
P(X = x) a 3a
5a
Then the value of ‘a’ is
1 1 1
whose chances of solving it are , , respectively. If they all
2 3 4
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
If a fair coin is tossed n times, then the probability that the head
comes odd number of times is
NIMCET-2012
Let P be a probability function on S = (l1, l2, l3, l4) such that
1
1
1
P  l2   , P  l3   , P  l4   . Then P(l1) is
3
6
9
respectively. Suppose two players A and B join two
(A)
6.
the
12.
1
8
(B)
2
7
(C)
1
625
(D)
16
625
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)
3N  1
N 1
5N  3
4N  3
(B)
(C)
(D)
N
9N  3
3N
9N  3
1
INFOMATHS
25.
26.
27.
28.
29.
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
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
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) 0.0250
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) 1/4
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)
30.
31.
1
2
(b)
49
50
(c)
101
101
(d)
51
101
39.
40.
41.
42.
43.
44.
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
If
A and
B
are
events
such
3
P  A  B  ,
4
that

 
(a)
45.

2
1
P  A  B   , P A  , then P A  B is
3
4
32.
33.
34.
KIITEE-2010
(a) 5/12
(b) 3/8
(c) 5/8
(d) 1/4
If A and B are any two mutually exclusive events, then P(A|AB)
is equal to
(PGCET– 2009)
(a) P(AB)
(b) P(A)/(P(A) + P(B))
(c) P(B)/P(AB)
(d) None of these
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
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)
(c)
35.
xy
xy  (1  x)(1  y )
(b)
1  x 1  y 
xy  1  x 1  y 
(d)
38.
1  x 1  y 
(c)
49.
and P ( A )

1
.
4
65
81
(b)
13
81
(c)
65
324
(d)
13
108
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
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
WORKSHEET-3 (OLD QUESTIONS )
50.
(b)
13
90
(c)
19
90
45  3 
 
2 4
90
2
(b)
1
132
(b)
1
44
(c)
5
132
(a)
2
(d)
7
132
1 1
,
3 4
and
1
. The probability that exactly one
5
5
12
(b)
7
30
MP COMBINED – 2008
(c)
13
30
(d)
3
5
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
The probability of throwing 6 at least one in four throws of a die
is:
MP COMBINED – 2008
(a)
53.
1
90  
4
Probabilities of three students A, B and C to pass an examination
student will pass is:
52.
5
8
(d) None
210
are respectively
51.
(d)
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
6 boys and 6 girls sit in a row randomly. The probability that all
the girls sit together is :
MP COMBINED – 2008
(a)
Then
1
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
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
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)
xy
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.
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)
37.
47.
Let A and B be two events such that
1
1
P ( A  B )  , P ( A  B) 
6
4
36.
46.
48.
xy
1  x 1  y 
(MCA : KIITEE – 2009)
(a) 9/10
(b) 1/5
(c) 1/10
(d) None of these
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
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
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
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/AB') is :
NIMCET - 2008
(a) 1/4
(b) 3/8
(c) 1/8
(d) None
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
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
1
6
(b)
2
3
(c)
625
1296
(d)
671
1296
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
2
INFOMATHS
54.
The probability of randomly chosing 3 defectless bulbs from 15
electric bulbs of which 5 bulbs are defective, is :
MP COMBINED – 2008
(a)
55.
56.
57.
58.
59.
60.
3
10
64.
66.
39
256
7
12
1
12
69.
70.
71.
1
3
and the probability that neither of them occurs is 1/6.
(b)
29
256
(c)
31
256
(d)
(b)
11
12
(c)
1
2
(d)
(b)
1
15
(c)
2
27
(d)
1
(b)
2
3
(c)
13
74.
75.
76.
1
10
(e)
16
256
(b)
1
286
(c)
37
256
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
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.
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
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.
WORKSHEET-3 (OLD QUESTIONS )
(b)
 3
 9 
 16  (c)  10 
 
 
41
60
(b)
37
60
(c)
31
60
   
(c) P  A  B   P  A  B 
77.
78.
(d) N.O.T.
(d) N.O.T.
P A B  P A B
(b)

 
P A B  P A B

(d) None of these
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
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
2
2
(b) (x' /2) - (y' /2) = 1
(c) (x'2 /2) + (y'2/2) = 1
(d)
2.
3.
1
20
28
256
2
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.
If A and B are two events, the prob. that exactly one of them,
occurs in given by:
UPMCAT Paper – 2002
(a)
4.
5.
1
(d)
3
(d)
1
 13 
 
If P(A'  B') is equal to 19/60 then P(AB) is equal to
UPMCAT Paper – 2002
(a)
37
256
5
6
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.
In a pack of 52 cards. Two cards are drawn at random. The
probability that it being club card is :
UPMCAT Paper – 2002
(a)
6.
7.
x' / 2  y' / 2 1
2
3
2
(B)
5
2
(C)
1
2
(D)
1
4
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)
The distance between the parallel lines y = 2x + 4 and 6x = 3y + 5
is
PU CHD-2012, NIT-2010
(A)
17
3
8.
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
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
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
The eccentricity of the ellipse x2 + 4y2 + 8y – 2x + 1 = 0 is :
PU CHD-2012
(A)
The probability of getting atleast 6 head in 8 trials is: MP– 2004
(a)
68.
73.
67
91
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
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
3
(a)
14
67.
(d)
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
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)
65.
24
91
If two dice are tossed the probability of getting the sum at least 5
is
PUNE Paper – 2007
(a)
63.
(c)
Then the probability of occurrence of A is.
ICET – 2005
(a) 5/6
(b) 1/2
(c) 1/12
(d) 1/18
8 coins are tossed simultaneously. The probability of getting
atleast six heads is
ICET – 2005
(a)
62.
7
10
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
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
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
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
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
A and B independent events. The probability that both A and B
occur is
61.
(b)
72.
(B) 1
(C)
3
5
(D)
17 5
15
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
3
INFOMATHS
(A) x + y + 2x – 2y = 62
(B) x + y + 2x – 2y = 47
(C) x2 + y2 – 2x + 2y = 47
(D) x2 + y2 – 2x + 2y = 62
2
The focus of the parabola y – x – 2y + 2 = 0 is :
PU CHD-2012
(A) (1/4, 0) (B) (1, 2)
(C) (3/4, 1) (D) (5/4, 1)
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)
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
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)
6x2 + 12x + 8 – y = 0 has its standard form as?
Pune-2012
2
9.
10.
11.
12.
13.
14.
15.
16.
2
2
(a)
 x  1
(c)
 x  2
2
2
18.
19.
20.
 x  1
  y  2
2
24.
25.
319
(b)
2
183
(c)
2

(c) 2 or
3
2
3
2

(d) – 2 or
3
2
26.
27.
tan 1
11
2
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
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
(b)
5
5
(c)
5
(d)
2 2
4 2
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
The straight line x cos  + y sin  = p touches the ellipse
x2 y 2

 1 if :
a 2 b2
BHU-2012
(b) p2 = a2 cos2  + b2 sin2
(d) p2 = a2 sin2  + b2 cos2
28.
If the line lx + my = n touches the hyperbola
x2 y 2

 1 if :
a 2 b2
BHU-2012
(a) a2l2 – b2m2 = n2
(c) a2l2 + b2m2 = n2
29.
For the conic
(b) al – bm = n
(d) al + bm = n
l
 1  e cos  , the sum of reciprocals of the
r
segments of any focal chord is equal to :
BHU-2012
(a) l
30.
31.
3
2
(b) 2l
(c)
2
32.
1
(c)
l
2
(d)
l
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
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)
Focus of the parabola x + y – 2xy – 4(x + y – 1) = 0 is
NIMCET-2012
(a) (1, 1)
(b) (1, 2)
(c) (2, 1)
(d) (0, 2)
If e and er be the eccentricities of a hyperbola and its conjugate,
2
(d)
2
381
(d)
2
(b) – 2 or
2
11
(a) p2 = a2 cos2  - b2 sin2
(c) p2 = a2 sin2  - b2 cos2
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
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
tan 1
(a) 5
(d) None of these
Pune-2012
(a) inside
(b) on
(c) outside (d) None of these
2
The point on the curve y = 6x = x , where the tangent is parallel to
x – axis is
NIMCET-2012
(a) (0, 0)
(b) (2, 8)
(c) (6, 0)
(d) (3, 9)
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
then
1

y  a x  
x

(b)
1

y 2  a  x2  2 
x


(d) y = atan  + x
The relation that represents the shaded region in the figure given
below is
1
1
 r2
2
e e
(a) 0
21.
(b)
(c)
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
138
(a)
2
17.
1
 y  2
6
1
  y  1
6

2
(b) 1
NIMCET-2012
(d) None of these
(c) 2
The straight line passes through the point


P 2, 3 and makes
an angle of 60 with the x-axis. The length of the intercept on it
between the point P and the line
22.
23.
x  3 y  12
is :
BHU-2012
(a) 1.5
(b) 2.5
(c) 3.5
(d) 4.5
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
The angle between the two straight line represented by the
equation 6x2 + 5xy – 4y2 + 7x + 13y – 3 = 0 is:
BHU-2012
(a)
tan 1
3
5
(b)
tan 1
5
3
WORKSHEET-3 (OLD QUESTIONS )
33.
34.
35.
(a) y  x
(b) |y|  |x| (c) y  |x|
(d) |y|  x
The area enclosed within the lines |x| + |y| = 1 is
HCU-2011
NIMCET-2011
(a) 1
(b) 2
(c) 3
(d) 4
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)
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
4
INFOMATHS
36.
(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
2
The vertex of parabola y − 8y +19 = 0 is
37.
(a) (3, 4)
(b) (4, 3)
(c) (1, 3)
(d) (3, 1)
The eccentricity of ellipse 9x2 + 5y2 − 30y = 0 is
NIMCET-2011
l on the axes, then l =
38.
39.
1
3
(b)
2
3
(c)
4
(d)
1
4
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) b
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
3
a  2b
(c)
3
b  2a
3
b  2a
(d)
3
(a)
40.
3
51.
53.
y = be-x/a at the point
41.
42.
BHU-2011
(a) where it crosses the y-axis
(b) where it crosses the x-axis
(c) (0, 0)
(d) (1, 1)
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
(c) through the origin
(d) parallel to y-axis
The difference of the focal distances of any point on the hyperbola
x2 y 2

 1 is
a 2 b2
54.
55.
56.
(a) a
(b) 2a
(c) b
(d) 2b
If in ellipse the length of latusrectum is equal to half of major axis,
then eccentricity of the ellipse is
BHU-2011
(a)
44.
45.
46.
3
2
(b)
1
(c)
2
2
(d)
1
3
2
An equilateral triangle is inscribed in the parabola y = 4ax whose
vertex is at the vertex of the parabola. The length of its side is
BHU-2011
(a) a 3
(b) 2a 3 (c) 4a 3 (d) 8a 3
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
The equation
x
2
57.
(a)
(c)
 4 3
 , 
 5 5
1 5
 , 
5 4
(b)
(d)
 3 1 
 , 
 5 5 
 2 1
 , 
 5 5
48. The angle between the asymptotes of the hyperbola 27x2 – 9y2 = 24
is
NIMCET-2010
(a) 60
(b) 120
(c) 30
(d) 150
WORKSHEET-3 (OLD QUESTIONS )
NIMCET-2010
(a) 0
(b) 1
(c) -1
(d) 2
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
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
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
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
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
The distances from the foci of P (a, b) on the ellipse
KIITEE-2010
(b)
4
5 a
5
(d) None of these
The locus of a point P(,) moving under the condition that the
x2 y 2

 1 is
a 2 b2
KIITEE-2010
(a) an ellipse
(c) a parabola
58.
(b) a circle
(d) a hyperbola
It the foci of the ellipse
x2 y 2
1


144 81 25
represents a
47.
is
line y = x +  is a tangent to the hyperbola
 4 y 2  4 xy  4   x  2 y  1
BHU-2011
(a) straight line
(b) circle
(c) parabola
(d) pair of lines
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
2
 p b c
 a q c  = 0, then the value of


 a b r 
x2 y 2

 1 are
9 25
5
(a) 4  b
4
4
(c) 5  b
5
BHU-2011
43.
2
p
q
r

+
p a q b r c
52.
x y
  1 touches the curve
a b
(B) a  b
(D) N.O.T
50. If a p, b  q, c  r and
(b)
The straight line
NIMCET-2010
(A) a2 + b2
(C) (a2 +b2)2
NIMCET-2011
(a)
X2 Y2

 1 intercepts equal length
a 2 b2
49. If any tangent to the ellipse
59.
60.
62.
and the hyperbola
coincide, then the value of b2 is
KIITEE-2010
(a) 3
(b) 16
(c) 9
(d) 12
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)
The length of the perpendicular drawn from the point (3, - 2) on
the line 5x – 12y – 9 = 0 is
PGCET-2010
(a)
61.
x2 y 2

1
25 b 2
28
13
(b)
31
13
(c)
30
10
(d) None of these
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
2
the angle between the lines represented by x + 3xy + 2y2 = 0 is
PGCET-2010
(a) tan-1(2/3)
(b) tan-1(1/3)
5
INFOMATHS
63.
64.
65.
66.
67.
68.
69.
70.
71.
72.
73.
74.
75.
(c) tan-1(3/2)
(d) None of these
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
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
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
(c) 5x + 6y + 3 = 0
(d) None of these
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)
2
2
If y = x + c is a tangent to the circle x + y = 8, then c is
(PGCET paper – 2009)
(a)  3
(b)  2
(c)  4
(d)  1
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
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
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
The straight lines
(c)
76.
77.
78.
2 
 ,0 
3 
7 2
, 

 3 3
(b)
x 2  x 2  x  3y 
(d) None of these
(d)
x y3 2 0
25
0
2
as a diameter is
HYDERABAD CENTRAL UNIVERSITY - 2009
(a)
(b)
(c)
(d)
81.
82.
21
0
2
25
x 2  x 2  3x  y 
0
2
25
x 2  x 2  x  3y 
0
2
25
x 2  x 2  3x  y 
0
2
x  x  3x  y 
2
2
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
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
x y
 1
8 6
x y
(c)

1
7 16
(a)
83.
(b)
(d)
x2 y2

1
16
9
x2 y2

1
16
7
If y = mx bisects the angle between the lines x2 (tan2 + cos2) +
2xy tan  - y2 sin2 = 0 when  = /3, then the value of
3m 2  4m
(a) 1
is
(b)
NIMCET - 2008
1
(c)
3
(d)
7 3
3
If a, b, c are the roots of the equation x3 – 3px2 + 3qx – 1 = 0, then
the centroid of the triangle with vertices
 1
 c, 
 c
85.
86.
 1  1
 a, ,  b, 
 a  b
is at the point
(a) (p, q)
and
NIMCET - 2008
(b)
 p q
 , 
 3 3
(c) (p + q, p – q)
(d) (3p, 3q)
Equation of the common tangent touching the circle (x – 3)2 + y2 =
2
9 and the parabola y = 4x above the x – axis is NIMCET - 2008
(a)
3 y  3x  1
(b)
3 y  ( x  3)
(c)
3y  x  3
(d)
3 y  (3x  1)
87.
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
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
88.
(a) 4 3
(b) 16
(c) 48
(d) None
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
89.
(a)  4 2 (b) 4 2
(c) 4
(d) 8
The equation of any tangent to the circle x2 + y2 – 2x + 4y – 4 = 0
is
KIITEE - 2008
7 2
 , 
3 3
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
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
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
79.
80.
84.
x y
x y 1
  k and   , k  0 meet
a b
a b k
on
(MCA : NIMCET – 2009)
(a) a parabola
(b) an ellipse
(c) a hyperbola
(d) a circle
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
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
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
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)
HYDERABAD CENTRAL UNIVERSITY - 2009
(a) 2, 2 (b) 4,2 2 (c) 2 2 ,4 (d) 4 2 ,4
The equation of the circle having the chord x – y = 1 of the circle
(a)
y  mx  3 1  m 2
(b)
y  mx  2  3 1  m 2
(c)
y  mx  m  2  3 1  m 2
(d) None
The sides of the rectangle of the greatest area that can be inscribed
in the ellipse x2 + 2y2 = 8, are given by
WORKSHEET-3 (OLD QUESTIONS )
6
INFOMATHS
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
:
91.
92.
22 

  
7 

107.
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
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
If the line hx + ky = 1 touches the circle
(x  y ) 
2
2
1
a2
108.
109.
,
110.
then the locus of the point (h, k) will be:
93.
94.
95.
96.
97.
98.
99.
(a) x2 + y2 = a2
MP COMBINED - 2008
(b) x2 + y2 = 2a2
(c) x2 + y2 = 1
(d)
x2  y2 
a2
2
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
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
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
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
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
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
Eccentricity of the ellipse 9x2 + 5y2 – 30y = 0 is :
(MP COMBINED – 2008)
(a) 1/3
(b) 2/3
(c) 4/9
(d) 5/9
2
100. For the ellipse
2
x
y

 1 , S1 and S2 are two foci then for
64 36
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)
2 3 ,2 6
(b)
(c)
4 3 ,4 6
(d)
111.
112.
113.
114.
115.
116.
117.
118.
119.
KARNATAKA - 2007
(a) +1/2
(b) –1/2
(c) 0
(d) +1/2 or – 1/2
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)
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
If the points (k, - 3), (2, - 5) and (-1, -8) are collinear then K =
ICET - 2007
(a) 0
(b) 4
(c) – 2
(d) – 3
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
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
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
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
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
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
(c) x + y – 1 = 0
(d) 2x + 2y – 1 = 0
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
The points of concurrence of medians of a triangle is
ICET – 2005
(a) incentre
(b) orthocenter
(c) centroid
(d) circumcentre
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
The area of the largest rectangle, whose sides are parallel to the
coordinate axes, that can be inscribed in the ellipse
x2 y 2

1
25 9
(a) 10
(b) 20
(c) 30
(d) 20 5 (e) 20 6
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)
3 6
1
1
3,
6
2
2
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
WORKSHEET-3 (OLD QUESTIONS )
IP Univ. Paper – 2006
(c)
 1 3
 , 
 3 5
5 3
 , 
2 7
(b)
(d)
 2 3
 , 
 3 4
1 3 
 , 
 7 11 
(e)
1 3
 , 
2 4
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) 0
124. 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
7
INFOMATHS
(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) 3
(b) 2
(c) 3 / 2
(d) 2
129. From a point (x1, y1) two tangent can be drawn on circle x2 + y2 =
a2 if:
MP : MCA Paper – 2003
(a)
x12  y12  a 2  0
(b)
x12  y12  a 2  0
(c)
x12  y12  a 2  0
(d) None of these
130. The sum of the distance of a point on the ellipse
x2 y 2

 1 to
a 2 b2
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)
(c)
3 
(b)

34,1
2
 3 
34,1

(d) None of these
2
132. If two circles x + y + 2g1x + 2f1y + c1 = 0, x2 + y2 + 2g2n + 2f2y
+ c2 = 0 will cut each other and satisfies
g1 g 2  f1 f 2 
c1  c2
2
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
1  c1  c2 
2 m1  m2
2
1  c1  c2 
(c)
2 m1  m2
2
(a)
1  c1  c2 
2 m1  m2
2
1  c2  c1 
(d)
2 m1  m2
2
(b)
(a)
(c)
(b)
 13 26 
,


5 
 5
(d) None of these
138. The area of the region bonded by the curve y = x2 and the line y =
x is
UPMCAT : paper – 2002
1
Sq U
64
1
(c)
Sq U
6
(a)
(b)
1
Sq U
12
(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
WORKSHEET-3 (OLD QUESTIONS )
4
(b)
13
5
(c)
13
(d) None of these
13
140. If (± 3, 0) be focus of ellipse and semi major axis is 6. Then equ.
of ellipse is:
UPMCAT :– 2002
(a)
(c)
x2 y 2

1
36 45
x2 y 2

1
36 27
(b)
x2 y 2

1
27 36
(d) None of these
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)
-1
(c) tan (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
(i)
a
h
g
h
b
f
g
f 0
c
(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
e
1
, directrix is x + 6 = 0, and has a focus at (0,
2
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)
(c)
 x  1
2

45
 x  1
20
2

 y  2
2
 1 (b)
20
 y  2
 x  1
45
2

 y  2
20
2
1
2
 1 (d) None of these
45
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) 6 2
(c) 3
(d) None
146. The x2 + y2 + 2x = 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
137. Reflection of the point P(1, 2) in x + 2y + 4 = 0 is
UPMCAT : paper – 2002
 13 26 
, 

 5 5 
 13 26 
 ,

5 5 
3
(a)

8
x2 y2

1
25
9
has the eccentric angle
. The sum of the distance of P from the two foci is.
KIITEE - 2008
(a) 10
(b) 6
148. For the hyperbola
(c) 5
x2
cos 
(d) 3

y2
sin 2 
following remains constant when  varies?
2
 1 which of the
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
x
y  2 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
8
INFOMATHS
(a) 30
(b) 40
IP Univ. Paper – 2006
(d) 60
(e) 70
(c) 45
152. L1 || L2. Slope of L1 = 9. Also L3 || L4. Slope of L4
these lines touch the ellipse

1
. All
25
x2 y 2

 1 . The area of the
25 9
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
PR
PS
RP RQ
is

 k , then, the value of
.
RQ
SQ
PS QS
1 k 
(a)  

 1 l 
(c)
1 k 
(b)  

1 k 
 1 k 


1 k 
(d)
1 k 


1 k 
(a)
(c)
IP University : Paper - 2006
2
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
2
2
(e) N.O.T.
(a)
154. P moves on the line y = 3x + 10. Q moves on the parabola y =
24x. The shortest value of the segment PQ is IP University - 2006
7
12
8
(b)
(c)
10
7
2
6
(d)
(c)
(e) 6
15
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)

7
(b)

6
(c)

5
(d)

4
WORKSHEET-3 (OLD QUESTIONS )
(e)
(b)
2ab
ab
a  b2
2
(d) None of these
a2  b2
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
2
(a)
2 a 2  b2
25  14
14
25  14
7
m
(b)
m
(d)
45  14
14
45  14
7
m
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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