Q1. The triangle with vertices (1, 5); (–3, 1) and (3, –5) is

(a)

isosceles

(b)

equilateral

(c)

right angled

(d)

None of these

Q2. If the points (4, – 4), (– 4, 4) and (x, y) form an equilateral triangle then

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

Q3. If (–4, 6), (2, 3) and (2, –5) are vertices of a triangle, then its incentre is

(a)

(–1, 2)

(b)

(2, –1)

(c)

(1, 2)

(d)

(2, 1)

Q4.Circumcentre of a triangle whose vertex are (0, 0), (4, 0) and (0, 6) is

(a)

(b)

(0, 0)

(c)

(2, 3)

(d)

(4, 6)

Q5.Orthocentre of a triangle whose vertex are (8, –2), (2, –2) and (8, 6) is

(a)

(8, –2)

(b)

(8, 6)

(c)

(d)

(0, 0)

Q6.The area of a triangle with vertices (3, 8); (–4, 2) and (5, –1) is

(a)

40.5

(b)

36.5

(c)

3.75

(d)

37.5

Q7.If D, E, F are mid points of the sides AB, BC and CA of a triangle formed by the points A(5, -1) B(-7, 6) and C(1, 3), then area of DDEF is

(a)

2/5

(b)

5/2

(c)

5

(d)

10

Q8. The point (4, 1) undergoes two successive transformations
(i) Reflection about the line y = x
(ii) Translation through a distance 2 units along the positive direction of x – axis
The final position of the point is given by the coordinates

(a)

(4, 3)

(b)

(3, 4)

(c)

(7/2, 7/2)

(d)

(1, 4)

Q9.If A(c, 0) and B(– c, 0) are two points, then the locus of a point P which moves such that
PA²+ PB² = AB² is

(a)

x2 – y2 =c2

(b)

y2 = 4cx

(c)

x2 + y2 = c2

(d)

None of these

Q10. Let A(2, 3) and B(–4, 5) are two fixed points. A point P moves in such a way that DPAB = 12 sq. units, then its locus is

(a)	x2 + 6xy + 9y2 + 22 x + 66y – 23 = 0	(b)	x2 + 6xy + 9y2 + 22 x + 66y + 23 = 0
(c)	x2 + 6xy + 9y2 – 22 x – 66y – 23 = 0	(d)	None of these

Q11.If sum of square of distances of a point from axes is 4, then its locus is

(a)

x + y = 2

(b)

x2 + y2 = 16

(c)

x + y = 4

(d)

x2 + y2 = 4

Q12.The extremities of diagonal of a right-angled triangle are (2, 0) and (0, 2), then locus of its third vertex is

(a)	x2 + y2 – 2x – 2y = 0	(b)	x2 + y2 + 2x – 2y = 0
(c)	x2 + y2 – 2x + 2y = 0	(d)	x2 + y2 + 2x + 2y = 0

Q13.Keeping coordinate axes parallel, the origin is shifted to a point (1, –2), then transformed equation of
x² + y² = 2 is

(a)	x2 + y2 + 2x – 4y + 3 = 0	(b)	x2 + y2 – 2x + 4y + 3 = 0
(c)	x2 + y2 – 2x – 4y + 3 = 0	(d)	x2 + y2 – 2x + 4y + 3 = 0

Q14.To remove xy term from the second degree equation 5x² + 8xy + 5y² + 3x + 2y + 5 = 0, the coordinates axes are rotated through an angle q, then q equals

(a)

p/2

(b)

p/4

(c)

3p/8

(d)

p/8

Q15.The ratio in which the line y – x + 2 = 0 divides the line joining (3, – 1) and (8, 9) is

(a)

2 : 3

(b)

3 : 2

(c)

– 2 : 3

(d)

– 3 : 2

Q16.The area of the triangle, formed by the straight lines 7x – 2y + 10 = 0, 7x + 2y – 10 = 0 and 9x + y + 2 = 0, is

(a)

(b)

(c)

(d)

None of these

Q17.Two vertices of a triangle are (3, – 1) and (– 2, 3) and its orthocenter is origin, the coordinates of the third vertex are

(a)

(b)

(c)

(d)

Q18.The equation of the internal bisector of ÐBAC of DABC with vertices A(5, 2), B(2, 3) and C(6, 5) is

(a)

2x + y + 12 = 0

(b)

x + 2y – 12 = 0

(c)

2x + y – 12 = 0

(d)

None of these

Q19.The equation of the straight line upon which the length of perpendicular from origin is  units and this perpendicular makes an angle of 75° with the positive direction of x – axis, is

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

Q20.The image of the point (– 8, 12) with respect to the line mirror 4x + 7y + 13 = 0 is

(a)

(16, – 2)

(b)

(– 16, 2)

(c)

(16, 2)

(d)

(– 16, – 2)

Q21.The equation of the straight line passing through the point of intersection of lines 3x – 4y – 7 = 0 and 12x – 5y – 13 = 0 and perpendicular to the line 2x – 3y + 5 = 0 is

(a)

33x + 22y + 13 = 0

(b)

33x + 22y – 13 = 0

(c)

33x – 22y + 13 = 0

(d)

None of these

Q22.If the family of lines x(a + 2b) + y(a + 3b) = a + b passes through the point for all values of a and b, then the coordinates of the points are

(a)

(2, 1)

(b)

(2, – 1)

(c)

(– 2, 1)

(d)

None of these

Q23.The value of k so that the lines 2x – 3y + k = 0, 3x – 4y – 13 = 0 and 8x – 11y – 33 = 0 are concurrent, is

(a)

7

(b)

– 7

(c)

5

(d)

– 5

Q24.Let P be the image of the point (– 3, 2) with respect to x-axis. Keeping the origin as same, the coordinate axes are rotated through an angle 60° in the clockwise sense. The coordinates of point P with respect to the new axes are

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

Q25.If for a variable line , the condition a^–2 + b^–2 = c^–2 (c is a constant) is satisfied, then the locus of foot of the perpendicular drawn from origin to this is

(a)

x2 + y2 =

(b)

x2 + y2 = 2c2

(c)

x2 + y2 = c2

(d)

x2 – y2 = c2

Q26.If A and B are two sets, then A Ç (A È B)¢ equals

(a)

A

(b)

B

(c)

f

(d)

none of these

Q27.Which of the following is an empty set ?
(a)The set of prime numbers which are even
(b)The solution set of the equation  = 0 ; x Î R
(c)(A x B) Ç (B x A), where A and B are disjoint
(d)The set of real which satisfy x² + ix + i – 1 = 0
Q28.If sets A and B are defined as : A = {(x, y) : y =, x ¹ 0, x Î R} ,  B = {(x, y) : y =-x, x Î R}, then

(a)

A Ç B = A

(b)

A Ç B = B

(c)

A Ç B = f

(d)

none of these

Q29.Let R be reflexive relation on a finite set A having n elements, and let there be m ordered pairs in R. Then       

(a)

m ³ n

(b)

m £ n

(c)

m = n

(d)

none of these

Q30.f(x) = | sin x | has an inverse if its domain is :

(a)

[ 0, p ]

(b)

(c)

(d)

none of these

Q31.Consider the following equations
(1) A – B = A – (A Ç B)           
(2) A = (A Ç B) È (A – B)
(2) A – (B È C) = (A – B) È (A - C)

Which of these is / are correct

(a)

1 and 3

(b)

2 only

(c)

2 and 3

(d)

1 and 2

Q32.If a is the set of the divisors of the number 15, B is the set of prime numbers smaller than 10 and C is the set of even numbers smaller than 9, then (A È C) Ç B is the set 

(a)

{1, 3, 5}

(b)

{1, 2, 3}

(c)

{2, 3, 5}

(d)

{2, 5}

Q33.x, y and z are rational numbers. Consider the following statements in this regard

(1)

x + 3 = y + z Þ x = y

(2)

xz = yz Þ x = y

Which of the above statement(s) is / are correct ? 

(a)

1 alone

(b)

2 alone

(c)

Both 1 and 2

(d)

Neither 1 nor 2

Q34.If second term of an AP is 2 and 7^th term is 22, then sum of 9 terms is

(a)

126

(b)

– 126

(c)

90

(d)

252

Q35.If S_n denotes the sum of the first n terms of an AP and S_2n = 3S_n, then

(a)

7

(b)

6

(c)

8

(d)

10

Q36.The sum of r terms of an AP is denoted by Sr and , then the ratio of the 7^th term and 5^th term of the AP is

(a)

(b)

(c)

(d)

Q37.A square is drawn by joining the mid points of the given square a third square in the same way and this process continues indefinitely. If a side of the first square is 16 cm, then the sum of the areas of all the squares

(a)

128 sq cm

(b)

256 sq cm

(c)

512 sq cm

(d)

1024 sq cm

Q38.If the p^th term of an AP is  and qth term is  then the sum of the first pq terms is

(a)

0

(b)

(pq – 1)

(c)

(pq + 1)

(d)

Q39.If the AM between p^th and q^th terms of an AP be equal to AM between r^th and s^th terms of the AP, then

(a)

p + s = q + r

(b)

p + q = r + s

(c)

p + r = q + s

(d)

p + q + r + s = 0

Q40.The value of 5 + 55 + 555 + …… to n terms is

(a)

10n + 1 – 10

(b)

(c)

[10n + 1 – 1 + 9n]

(d)

(10n + 1 – 10)