1) The distance between the points A(2,-3) and B(-6,3) is
a) 4 units b) 6 units c) 8 units d) 10 units
2) The distance between the points P(√5+1, √3 -1) and Q(√5-2), √3]+2) is
a) 3√2 units b) 4√3 units c) 3√5 units d) 2√6 units
3) If the distance between the points A(-3,4) and B(x,7) is 5 units , then x=?
a) -1 or 7 b) 1 or - 7 c) 5 or -3 d) - 5 or 3
4) If the distance between the points A(x,3) and B (3,5) is 4 units, then x=?
a) 2± 3√3 b) 3± 2√3 c) 3± 3√2 d) 2± 2√2
5) The distance of the point A(6-6) from the origin is
a) 2√3 units b) 6 units c) 12 unit d) 6√2 units
6) If P(x,y) is equidistant from A(6,-1) and B(2,3), then
a) 3x - y= 3 b) x - 3y= 3 c) x - y= 3 d) x + y= 3
7) A point P on the x-axis which is equidistant from the point A(7,6) and B(-3,4) is
a) P(3,0) b) P(0,3) c) P(-3,0) d) P(0,-3)
8) A point P on the y-axis which is equidistant from the points (-4,3) and B(5,2) is
a) (-2,0) b) (0,-2) c) (2,0) d) (0,2)
9) A is a point on the x-axis with absicca -8 and B is a point on the y-axis with ordinate 15. Distance AB=?
a) 13 units b) 15 units c) 17 units d) 23 units
10) if the points A(-2,3), B(1,2) and C(k,0) are collinear, then k=?
a) 5 b) 6 c) 7 d) 8
11) The vertices of a ∆ ABC are A(3,8), B(-4,2) and C(5,-1). The area of ∆ ABC is
a) 57 sq units b) 75 sq c) 57/2 sq units d) 75/2 sq units
12) The area of quadrilateral ABCD with A(1,1), B(7,-3), C(12,2) and D(7,21) as the vertices is
a) 35 sq units b) 65 sq units c) 85 sq units d) 115 sq units
13) In ∆ ABC having vertices A(-1,3), B(1,-1) and C(5,1), the length of the median AD is
a) 3 units b) 4 Units c) 5 units d) 6 units
14) In ∆ ABC, its vertices are A(7,-3), B(3,-1) and C(5,3). If BE is one of its medians, then BE=?
a) 2√2 units b) 3units c) √10 units d) none
15) In ∆ ABC with vertices A(-1,0), B(5,-2) and C(8,2), the centroid is
a) (4,0) b) (0,4) c) (6,0) d) (0,6)
16) In ∆ ABC having vertices A(5,2) and B(-7,-4) the centroid is G(-2,3). Then, the third vertex C is
a) (-6,9) b) (8,11) c) (-4,11) d) (- 6,11)
17) The points A (1,1), B(-1,-1) and C(-√3, √3) are the vertices of
a) an equilateral triangle
b) an isosceles triangle
c) a right angle triangle d) none
18) The points A(2a, 4a), B( 2a,6a) and C[(2+ √3)a, 5a] are the vertices of
a) an isosceles triangle
b) an equilateral triangle
c) a right angle triangle d) none
19) The points A(7,10), B(-2,5) and C(3,-4) are the vertices of
a) an isosceles triangle
b) a scalene triangle
c) an equilateral triangle d) none
20) The points A(2,6), B(5,1), C( 0,-2) and D(-3,3) are the vertices of
a) a rhombus b) a square c) a trapezium d) none
21) The points A(-1,0), B(0, 3), C(1,3) and D(0,0) ate the vertices of
a) a parallelogram
b) a rectangle
c) a rhombus d) none
22) 3 consecutive vertices of a parallelogram ABCD are A(3,-2), B(4 ,0) C(6,-3). The 4th vertex D is
a) (5,-5) b) -5,5) c) (- 3,8) d( 3,-8)
23) The vertices of a ∆ ABC are A(8,6), B( 8,-2) and C(2,-2). The coordinates of its circumcentre are
a) (5,-2) b) (5,2) c) (-5,2) d) (-5,-2)
24) a point P divides the joint of A(5,-2) and B(9,6) in the ratio 3:1. The coordinates of P is
a) (4,-7) b) (- 4,7) c) ( 7/2,4) d) (8,4)
25) The ratio in which the point P(1,2) divides the join of A(-2,1) and B(7,4) is
a) 1:2 b) 2:1 c) 3:2 d) 2:3
26) The ratio in which the line segment joining the points A(-12,2) and B (8,3) is divided by the y-axis is
a) 2:1 b) 1:2 c) 2:3 d) 3:2
27) The ratio in which the line segment joining the points P(4,5) and Q(-10,-2) is divided by the x-axis is
a) 3:2 b) 2:3 c) 5:2 d) 2:5
28) The vertices of ∆ ABC are A (0,6), B(8,12) and C(8,0). The coordinates of its incentre are
a) (-4,3) b) (5,6) c) (8,11) d) (16/3 ,6)
29) A circle passes through the points A (2,-9), B(5,-8) and C(2,1). The centre of the circle is
a) (2,-4) b) (-3,4) c) (3,-16/3) d) none
30) One end of the diameter of a circle is A(4,1) and its Centre is (3,3). The coordinates of the other end of the diameter is
a) (5,2) b) (-4,1) c) ( 4,-1) d) (2,5)
31) The slope of the line AB passing through the points A(-2,3) and B (8,-5) is
a) 4/5 b) -4/5 c) 5/4 d) -5/4
32) The inclination of the line joining the points A(x, -3) and B(2,5) is 135°. Then , the value of x is
a) 8 b) - 8 c) 10 d) - 10
33) The angle between the x-axis and the line joining the point A(3,-1) and B(4,-2) is
a) 45° b) 90° c) 135° d) 150°
34) if the line AB with A(-2,6) and B (4,8) is perpendicular to the line CD with C(8,12) and D(x, 24) then x=?
a) -4 b) 4 c) -6 d) 6
35) if the points A(x, -1), B(2,1) and C(4,5) are collinear , then x=?
a) 1 b) -2 c) -4 d) -5
36) If A(-2,1), B(2,3) and C(-2,-4) be the vertices of a ∆ ABC, then tanB=?
a) 1/3 b) 3/4 c) 2/3 d) 4/5
37) If the angle between two lines is π/4 and the slope of the line is 1/2, then the slope of the other line is
a) 2 or -1/2 b) 3 or -1/3 c) 4 or -1/4 d) 1/2 or -1/3
38) if θ is the angle between AB and CD with A(0,0), B(2,3), C(2,-2) and D(3,5) then tanθ =?
a) 9/13 b) 11/23 c) 8/17 d) 10/19
39) The slope of two lines AB and CD are (2- √3) and (2+ √3) respectively. The angle between these lines is
a) 30° b) 45° c) 60° d) 120°
40) If the slope of the line joining the points A(x,2) and B(6,-8) is -5/4; then x=?
a) -2 b) 2 c) -3 d) 3
41) If A(3,x), B(2,7), C(-1,4) and D(0,6) are the points such that AB|| CD, then x=?
a) 6 b) 8 c) 9 d) 12
42) If A(-2,6), B(4,x), C(3,-3) and D(5,-9) are the points such that AB is perpendicular to CD, then x=?
a) 9 b) 8 c) 7 d) 6
43) The vertices of a parallelogram ABCD are A(0,2), B(-2,-1), C(4,0) and D(2,3) and θ is the angle between the diagonals AC and BD. Then , tanθ =?
a) 3/2 b) 2/3 c) 2 d) 3
44) If A(-1,8), B(4,-2) and C(-5,-3) are the vertices of a ∆ ABC, then equation AB is
a) 2x - y +6=0
b) 2x + y -6=0
c) 3x - y +9=0
d) 3x + y -9=0
45) The vertices of a ∆ ABC are A(2,5), B(- 4,9) and C(-2,-1). The equation of the median BE is
a) x - 5y + 23 =0
b) 8x - y + 15=0
c) 7x + 4y -8=0 d) none
46) A line passes through the point P(0,5) and its inclination with the x-axis is 30°. The equation of the line is
a) x + √3 y - 5 √3=0
b) x - √3 y - 5 √3=0
c) x - √3 y +5 √3=0 d) none
47) The equation of the perpendicular bisectors of the line joining the points A(2,3) and B(6,-5) is
a) x +2y -6 =0
b) x - 2y -6 =0
c) x + 2y + 6 =0
d) x - 2y + 6 =0
48) A line passes through the points A(1,√3) and B(√2,√6). The angle which AB makes with the x-axis is
a) 30° b) 45° c) 160° d) 90°
49) If A(2,1), B(-2,3) and C(4,5) are the vertices of ∆ ABC, then the equation of altitude B is
a) x - 2y + 4 =0
b) x +2y -4 =0
c) x - 2y -4 =0
d) x +2y + 4 =0
50) If A(1,4), B(2,-3) and C(-1,-2) are the vertices of a ∆ ABC , then the equation of the right bisector of BC is
a) 3x - y -4 =0
b) 3x + y -4 =0
c) 3x - y + 4 =0 d) none
51) The equation of a line which is equidistant from the line x= - 2 and x= 6 is
a) x= 4 x= 2 c) x=3 d) none
52) The equation of a line which is equidistant from the line y = 8 and is y= -2 is
a) y= 6 b) y= 4 c) y = 3 d) none
53) The equation of a line passing through the point (3,-4) and parallel to the x-axis is
a) x-4= 0 b) x +4=0 c) y-4=0 d) y+4=0
54) The equation of a line with slope 1/2 and y-intercept -5/4 is
a) 2x - 4y - 5 =0
b) 2x - 4y +5 =0
c) 2x + 4y - 5 =0
d) 2x + 4y + 5 =0
55) A line cuts the y-axis at a distance of 3 units from the origin and makes an angle of 30° with the positive direction of the x-axis. The equation of the line is
a) y - √3x + 3√3 =0
b) x - √3y +3√3 =0
c) x + √3y - 3√3 =0 d) none
56) A line cuts off an intercept of 4 units on negative direction of the y-axis and makes an angle of 120° with the positive direction of the x-axis. The equation of the line is
a) √3x - y - 4 =0
b) √3x +y - 4 =0
c) √3x + y +4 =0 d) none
57) The equation of a line for which tanθ= 1/33 and y-intercept= 5 is
a) x - 3y - 5 =0
b) x + 3y - 5 =0
c) 2x +3y +5 =0 d) none
58) A line cuts the x-axis at a distance of 3 units to the left of the origin and has slope - 2. The equation of the line the line is
a) 2x - y + 6=0
b) 2x +y - 6 =0
c) 2x + y +6 =0
d) 2x - y - 6 =0
59) The lines 2x + 3y +7 =0 and 27x - 18y +25 =0 are
A) parallel to each other
b) coincident
c) perpendicular to each other d) none
60) The lines x + 2 y - 9 =0 and 2x + 4y + 5 =0 are
a) parallel to each other
b) coincident
c) perpy to each other
d) none
61) The angle made by the line x + √3y - 6 =0 with the positive direction of the x-axis is
a) 45° b) 60° c) 120° d) 150°
62) A line passes through the point (2,-5) and is parallel to the line 2x - 3y - 7 =0. The equation of the line is
a) 2x +3y - 14=0
b) 2x - 3y - 21 =0
c) 2x - 3y - 19 =0 d) none
63) A line passes through the point (-2, -4) and is perpendicular to the line 3x - y + 5 =0. The equation of the line is
a) x +3y +15 =0
b) 3x +y +15 =0
c) x +3y - 14 =0
d) x +3y +14 =0
64) The y-intercept of a line is -3 and it is perpendicular to the line 3x - 2y + 5 =0. The equation of the line is
a) 2x +3y +9 =0
b) 2x -3y +9 =0
c) 2x - 3y - 9 =0 d) none
65) The equation of the line perpendicular to the line x - 7y +5 =0 and having x-intercept 3 is
a) 7x + y -21 =0
b) x + 7y -21 =0
c) 7x + y - 15 =0 d) none
66) The equation of the line making intercept 2 and - 3 on the x-axis and y-axis respectively is
a) 3x + 2y - 6 =0
b) 3x - 2y + 6 =0
c) 3x - 2y - 6 =0 d) none
67) The equation of the line so that the line segment intercepted between the axes is bisected at the point (2,3) is
a) 3x + 2y - 12 =0
b) 2x + 3y - 12 =0
c) 3x + 2y +12 =0 d) none
68) If the straight line x/a + y/b =1 passes through the points A(8,-9) and B(12,-15), then
a) a= 3, b=2 b) a= 2, b=3 c) a= 4, b=9 c) a= 9, b=4
69) The equation of the line passing through the point P( 2,2) and cutting off intercept on the axis having sum 9 is
a) x + 2y - 6 =0 or 2x + y - 6 =0
b) x - 2y +6 =0 or 2x + y +6=0
c) x - 2y -6 =0 or 2x - y + =0 d) none
70) The equation of a line for which p=5 and α= 135° is
a) x + y + 3√2 =0
b) x - y + 5√2 =0
c) x + y + 5√2 =0 d) none
71) The equation of a line which p= 8 and α= 150° is
a) √3x - y +18=0
b) √3x + y - 16 =0
c) √3x - y + 16 =0 d) none
72) The slope of the line √3x + y + 2 =0 is
a) 1/√3 b) -1/√3 c) √3 d) -√3
73) The perpendicular distance of a line the origin is 5 units and the angle between the positive direction of the x-axis and the perpendicular is 30°. The equation of the line is
a) √3x + y - 10 =0
b) √3x - y + 10 =0
c) √3x - y - 10 =0 d) none
74) The equation 3x - 2y +4 =0 when reduced to intercept from takes the form x/a + y/b =1, where
a) a= 4/3, b= 2
b) a= -4/3, b= -2
c) a= -4/3, b= 2 d) none
75) The distance of the point P(4,1) from the line 3x - 4y +12 =0 is
a) 4 units b) 5 units c) 3 units d) 6 units
76) The distance of the point P(-1,1) from the line 12x - 5y + 82=0 is
a) 8units b) 6 units c) 5 units d) 7 units
77) The length of perpendicular from the origin to the line 4x + 3y -2 =0 is
a) 2/3 units b) 2/5 units c) 4/3 units d) 4/5 units
78) The distance between the Parallel lines 3x - 4y +9 =0 and 6x - 8y -17 =0 is
a) 5/2 unit b) 3 units c) 7/2 units d) 4 units
79) what are the point on the x-axis whose perpendicular distance from the line x/3 + y/4 =1 is 4 units ?
a) (8,0) and (2,0) b) (- 8,0) and (2,0) c) (8,0) and (-2,0) d) (-8,0) and (-2,0)
80) The perpendicular distance of a line from the origin 5 units and its slope is -1. The equation of the line
a) x - y +5√2 =0 or x - y - 5√2=0
b) x + y +5√2 =0 or x + y - 5√2=0
c) x - y + 2√5 =0 or x - y - 2√5=0 d) none
81) The distance between the parallel lines p(x + y)+ q = 0 and p(x + y) - r=0 is
a) |q+ r|/2p b) |q+ r|/√2p c) |q- r|/2p d) |q- r|/√2p
82) The point of intersection of the lines 5x +7y -3 =0 and 2x - 3y - 7=0 is
a) (2,-1) b) (-2,1) c) (-2,-1) d) (2,1)
83) The equation of the parallel to the y-axis and drawn through the point of intersection of the lines x -7y +15 =0 and 2x +y =0 is
a) x -1= 0 b) x +1=0 c) x -2=0 d) x +2=0
84) The equation of the line passing through the point of intersection of the lines x +2y +3 =0 and 3x +4y + 7=0 and parallel to the line y - x = 6 is
a) x - y=0 b) x + y=0 c) x + 2y -3 =0 d) 2x + y - 3=0
85) The image of the point P(3,8) in the line x +3y -7 =0 is
a) (1,4) b) (- 1,4) c) (1,-4) d) (-1,-4)
86) The point of intersection of the lines x - y -6 =0 and 4x - 3y - 20=0 and 6x +5y +8 =0 is
a) (2,4) b) (2,-4) c) (-2,4) d) (- 2,-4)
87) The area of the triangle formed by the lines - x +y =0, x + y =0 and x - c=0 is
a) c²/2 sq units b) 2c² sq units c) c² sq units d) 3c² sq units
88) if the lines 3x +y -2 =0 , kx + 2y - 3=0 and 2x - y -3 =0 are concurrent, then k=?
a) - 5 b) 5 c) -3 d) 3
89) The centre of the circle x²+ y²- 6x +4y -12 =0 is
a) (-3,2) b) (3,2) c) (3,-2) d) (-3,-2)
90) Radius of the circle x²+ y²- 4x +2y -45 =0 is
a) 5√2 b) 4√2 c) 3√5 d) 4√5
91) The end points of the diameter of a circle are A(2,-3) and B(-3,5). The equation of the circle is
a) x²+ y²+2x -y -21 =0
b) x²+ y² + x - 2y - 21 =0
c) x²+ y² + x -2y +21 =0 d) none
TEST PAPER -1
1) Which of the following
function is injective map?
a) f(x)= x²+ 2, x ∈(-∞, ∞)
b) f(x)= |x+ 2|, x ∈[-2,∞)
c) f(x)= (x-4)(x-5), x ∈(-∞, ∞)
d) f(x)= (4x²+ 3x-5)/(4+ 3x - 5x²), x ∈(-∞, ∞).
2) Let f(x)= 1/√{|x-1| - [x]} where [.] Denote the greatest integer function, then domain of f(x) is
a) (-1,1) b) (-∞,1) c) (-∞,-1) d) none
3) If x₁, x₂, x₃,...,xₙ are the roots of the equation, xⁿ+ ax + b =0, then the value of (x₁ - x₂)(x₁ - x₃)(x₁ - x₄)...(x₁ - xₙ) is equal to
a) nx₁ⁿ⁻¹ + a b) n(x₁)ⁿ⁻¹ c) nx₁+ b d) nx₁ⁿ⁻¹ + b
4) Matrix A is such that A²= 2A - I, where I is unit matrix, then for N≥ 2, Aⁿ is equal to
a) nA - (n - I)I
b) nA - I
c) 2ⁿ⁻¹A - (n -1)I
d) 2ⁿ⁻¹ A - I
5) Foot of perpendicular drawn from origin to the plane passing through (1,0,0),(0,1,0) and (0,0,1) is
a) (3,3,3) b) (1/2,1/2,1/2) c) 1/3,1/3,1/3) d) 2,2,2)
6) a, b, c are three vectors so that each one is perpendicular to the sum of the other two and also|a|= 5, |b|= 6, |c|= 7. Then |a+ b+ c| is
a) 2√55 b) √110 c) √55 d) none
7) The condition to the imposed on β so that (0,β) lies on or inside the triangle having sides y- 3x+ 2= 0, 3y- 2x-5= 0 and 4y + x -14= 0 is
a) 0<β< 5/3
b) 0<β< 7/2
c) 5/3≤β≤ 7/2
d) 5/2≤ β≤ 7/2
8) If a, b, c, d> 0; x ∈R and (a²+ b²+ c²)x² -2 (ab+ bc + cd)x + b²+ c²+ d²≤ 0, then
33 14 loga
65 27 logb
97. 40 logc is equal to
a) 1 -1 c) 0 d) 2
9) ₐᵇ∫ f(x) dx is equal to
a) ₐ₊ₜᵇ⁺ᵗ∫ f(x) dx
b) ₐ₊ₜᵇ⁻ᵗ ∫ f(x -t) dx
c) ₐ₋ₜᵇ⁻ᵗ∫ f(x+ t) dx
d) none
10) The mean deviation of an ungrouped data is 10. If each observation is increased by 4%, then the revised mean deviation is
a) 10.4 b) 10.04 c) 9.6 d) 10.0
11) If A and B are square matrix of the same order, then which of the following is always true?
a) adj(AB)= (adjB)(adj A)
b) A and B are non zero and |AB|= 0 <=> |A|= 0 and|B|= 0
c) (AB)⁻¹= A⁻¹B⁻¹
d) (A+B)⁻¹= A⁻¹ + B⁻¹
12) Two variable chords AB and BC of a circle x²+ y²= r² are such that AB= BC= r. Then the locus of point of intersection of tangents at A and C is
a) x²+ y²= 2r²
b) x²+ y²= 3r²
c) x²+ y²= 4r²
d) x²+ y²= 5r²
13) Consider the equation x⁴+ x²+1= 0. If x₁, x₂, x₃, x₄ are roots of this equation, then value of x₁⁶+ x₂⁶+ x₃⁶+ x₄⁶ equal to
a) 1 b) 2 c) 3 d) 4
14) If u lies on the circle|z-1|= 1, then (z-2)/z equal to
a) 0 b) 2 c) -1 d) none
15) One hundred identical coins, each with probability p of showing heads are tossed once. If 0 < p <1 and the probability of heads showing on 50 coins is equal to that of heads showing on 51 coins, the value of p is
a) 1/2 b) 51/101 c) 49/101 d) none
16) On the portion of the straight line x+ y= 12 which is intercepted between the axis, a square is constructed, away from the origin, with this portion as one of its side. If p denotes the perpendicular distance of a side of this square from the origin, then the maximum value of p is
a) 2√3 b) 3√2 c) 2/√3 d) 3/√2
17) If P is a point on the rectangular hyperbola x²- y²= a², C is its centre and S, S' are the two foci, then SP. S'P is equal to
a) 2 b) (CP)² c) (CS)² d) (SS')²
18) The angle between the lines whose direction cosines are given by the equations l²+ m²+ n²= 0, l+ m+ n= 0 is
a) π/6 b) π/4 c) π/3 d) π/2
19) Let f(x)= |x|/x if x≠ 0 and f(0)=0 and a, b belongs to R be such that a< b, then value of I= ᵇₐ∫ f(x) dx is
a) |b| - |a| b) (1/2) (b²- a²) c) max{|a|, |b|} d) min.{|a|, |b|}
20) If ω is complex cube root of unity, and the Matrix A as
A= ω 0
0 ω then A¹⁰⁰ is equal to
a) A b)!- A c) O d) none
21) The value of the determinant
ka k²+a² 1
kb k²+ b² 1
kc k²+c². 1 is
a) k(a+b)(b+c)(c+a)
b) kabc(a²+b²+c²)
c) k(a-b)(b-c)(c-a)
d) k(a+b-c)(b+c-a)(c+a-b)
22) If in the expansion of (x³- 1/x²)ⁿ, n ∈N, sum of the coefficient of x⁵ and x¹⁰ is 0, then the value of n is
a) 5 b) 10 c) 15 d) none
23) If A, B and C are three events such that P(B)= 3/4, P(A∩B∩C')=1/3 and P(A∩B∩C')=1/3, then P(B∩C) is = ?
a) 1/12 b) 1/6 c) 1/15 d) 1/9
24) The value of sin(2tan⁻¹(1/3))+ cos(tan⁻¹2√2) is
a) 12/13 b) 13/14 c) 14/15 d) none
25) If the lines x+ 3y = 4 and 3x+ y= 4 cuts the coordinate axes at four concyclic points, then the radius of that circle is equal to
a) 4√5/3 b) 3√5/4 c) 4/3 d) √5/3
26) If the coordinates axes are rotated by an angle 45° in clockwise direction (keeping origin fixed), then equation of hyperbola x²- y²= 2 becomes
a) xy -1=0 b) xy +1=0 c) xy +2 =0 d) none
27) Orthogonal trajectories of the system of curves (dy/dx)²= a/x are
a) 9a(y+ c)²= 4x³
b) (y+ c)= -2x³⁾²/3√a
c) (y+ c)= 2x³⁾²/3√a
d) 9a(y - c)²= 5x³
28) If ⁿC₁/ⁿC₀ + 2 ⁿC₂/ⁿC₁ + 3 ⁿC₃/ⁿC₂ + .....n ⁿCₙ/ⁿCₙ₋₁ = S, Then S will be
a) an integer b) n(n-1)/2 c) n(n+1)/2 d) 55, if n= 10.
29) If a,b,c,d,e are positive real numbers such that a+ b+ c+ d+ e = 8 and a²+ b²+ c²+ d²+ e² = 15, then
a) 1≤e<2 b) 0<e≤16/5 c) 2<e<3 d) 0<e <4
30) sinθ +√3 cosθ= 6x - x²-11, 0≤θ ≤4π, x ∈ R holds for
a) no value of x and θ
b) one value of x and two values of θ
c) two values of x and two values of θ
d) two pairs of values of (x,θ)
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