EDUCATION AIM CLASS X MATH CBSE QUESTIONS
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1
Write the coordinates of a point P on the x-axis which is equidistant from point A(-2, 0) and B(6,0)
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2
Find a relation between x and y if the points A(x, y), B(-4, 6) and C(-2, 3) are collinear.
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3
Find the area of a triangle whose vertices are given as (1, -1) (-4, 6) and (-3, -5).
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4
Find the ratio in which the line x – 3y = 0 divides the line segment joining the points (-2, -5) and
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5
Point A lies on the line segment XY joining X(6, -6) and Y (-4, -1) in such a way that XA:XY = 2:5.
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6
Find the coordinates of a point A, where AB is diameter of a circle whose centre is (2, -3) and B is
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7
Find the ratio in which the segment joining the points (1, -3) and (4, 5) is divided by x-axis? Also
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8
Find the point on y-axis which is equidistant from the points (5, -2) and (-3, 2).
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9
The distance between the points (a cosθ + b sinθ, 0) and (0, a sinθ – b cosθ), is
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10
If the point P(k,0) divides the line segment joining the points A(2, –2) and B(–7, 4) in the ratio
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11
The value of p, for which the points A(3, 1), B(5, p) and C(7, –5) are collinear, is
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12
If the point C (–1, 2) divides internally the line segment joining A(2, 5) and B(x,y) in the ratio
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13
Find the area of triangle PQR formed by the points P(– 5, 7), Q(– 4, – 5) and R(4, 5).
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14
A solid metallic sphere of radius 10·5 cm is melted and recast into a number of smaller cones, each
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15
Find the value of m for which the quadratic equation(m 1) x2 + 2 (m - 1) x + 1 = 0 has two real and
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16
Find the ratio in which P(4, m) divides the line segment joining the points A(2, 3) and B(6, -3).
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17
If A(-5, 7), B(-4, -5), C(-1, -6) and D(4, 5) are the vertices of a quadrilateral, find the area of
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18
If A(-2, 1) and B(a, 0), C(4, b) and D( 1, 2) are the vertices of a parallelogram ABCD, find the val
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19
Find the distance of a point P(x, y) from the origin.
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20
A line intersects the y-axis and x-axis at the points P and Q respectively. If (2, -5) is the mid-po
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21
If the distances of P(x, y), from A(5, 1) and B(-1, 5) are equal, then prove that 3x = 2y.
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22
In what ratio does the point (24/11, y) the line segment joining the points P(2, -2) and Q(3, 7) ?
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23
Find the sum of first 30 terms of AP : 30, 24, 18, In an AP if Sn = n (4n + 1), then find the AP.
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24
A solid piece of metal in the form of a cuboid of dimensions 11 cm x 7 cm x 7 cm is melted to form n
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25
which term of AP -11/2, -3, -1/2 ..... is 49/2? Find a and b so that the numbers a, 7, b, 23 are in
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26
Solve the following quadratic equations.x2+2√2x−6=0
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27
A cone of height 28 cm and radius of base 7 cm is made up of modelling clay. A child reshapes it in
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28
Solve the equation x2−2bx+(b2−a2)=0 for x
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29
Find the sum of first 20 terms of an ap whose nth term is 5-2n
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30
Let P and Q be the points of trisection of the line segment joining the point A(2,-2) and B (-7,4) s
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31
Prove that the points (3,0) (6,4) and (-1,3) are the vertices of a right-angled isosceles triangle.
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32
If the point P(x, y) is equidistant from the points A(a + b, b – a) and B(a – b, a + b). Prove that
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33
The sum of first three terms of an AP is '33. If the product of the first and the third exceeds the
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34
Find the value of 'p' for which the quadratic equation p(x−4)(x−2)+(x−1)2=0has real and equal roots.
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35
Had Aarush scored 8 more marks in a Mathematics test, out of 35 marks, 7 times these marks would hav
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36
The value of sin^(2)theta+(1)/(1+tan^(2)theta) is equal to
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37
Prove that: cos 80°/sin 10° + cos 59° cosec 31°
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38
The points A(4,7) ,B(p,3) and C(7,3) are the vertices of a right angled triangle, right-angled at B.
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39
Find the relation between x and y if the point a(x y) b(-5 7) c(-4 5) are collinear.
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40
The value of (1 + tan² θ)(1 –sin θ)( 1 + sin θ) = ………..
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41
On a straight line passing through the foot of a tower, two points C and D are at distances of 4 m a
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42
If a tower 30 m high, casts a shadow 10√3 m long on the ground, then what is the angle of elevation
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43
A vertical tower stands on a horizontal plane and is surmounted by a vertical flag-staff 6m. At a po
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44
If sinθ + cosθ = √3, then prove that tanθ + cotθ = 1.
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45
The rod AC of a TV disc antenna is fixed at right angles to the wall AB and a rod CD is supporting t
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46
The ratio of the length of a vertical rod and the length of its shadow is 1 : √3. Find the angle of
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47
tan^2(30)⋅sin30+cos60⋅sin^2(90)⋅tan^2(60)−2tan45⋅cos^2(0)⋅sin90
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48
Prove that (sinA-cosA+1)/(sinA+cosA-1) = 1/(secA-tanA)
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49
Prove that tan^2A/(tan^2A-1)+cosec^2A/(sec^2A-cosec^2A)=1/(1-2cos^2A)
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50
If secθ+tanθ=p, then find the value of cosecθ.
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51
If secθ+tanθ=p, show that secθ−tanθ=1/p. Hence, find the value of cosθ and sinθ
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52
Prove that b2x2 - a2y2 = a2b2, if : (i) x = a sec θ, y = b tan θ, or (ii) x = cosec θ, y = b cot θ.
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53
If sin(A+2B)=sqrt(3)/2 and cos(A+4B)=0,A B, and A+4B 90∘, then find A and B.
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54
If in a triangle ABC right angled at B, AB = 6 units and BC = 8 units, then find the value of sin A.
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55
If sinθ+cosθ= sqrt(3), then prove that tanθ+cotθ=1
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56
prove that cot(theta) -tan(theta) = (2cos^2(theta)-1)/(sin(theta)cos(theta))
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57
A card is drawn at random from a well shuffled pack of 52 playing cards. Find the probability that
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58
If 1 + sin2θ = 3 sinθ . cosθ, then prove that tan θ = 1 or 1/2.
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59
(sinθ+cosecθ)^2+(cosθ+secθ)^2=7+tan^2θ+cot^2θ
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60
If secθ=x+1/(4x), prove that tanθ+secθ = 2x or 1/2x
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61
Prove that: sinθ(1+tanθ)+cosθ(1+cotθ)=secθ+cosecθ.
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62
If bcos θ = a, then prove that cosec θ + cot θ = √(b+a)/(b-a)
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63
The area of a quadrant of a circle where the circumference of circle is 176 m is
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64
For an event E, P(E) + P(Ē)= x, then the value of x³– 3 is
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65
Prove that : (cosecθ−cotθ)^2= (1-cosθ)/(1+cosθ )
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66
The value of (sin20° cos70° + sin70° cos20°) is ---------
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67
Prove that :sqrt[(1-sinθ)/(1+sinθ)]=secθ−tanθ
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68
Prove that tan^2θ/(1+tan^2θ)+cot^2θ/(1+cot^2θ)=1
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69
Prove that (1+tanA-secA)x(1+tanA+secA)=2tanA
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70
From a point on the ground, the angles of elevation of the bottom and top of a transmission tower fi
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71
If x=3 sin θ+4cosθ, and y= 3cosθ−4sinθ then prove that x^2+y^2 =25
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72
If sinθ+sin^2θ=1, then prove that cos^2θ+cos^4θ=1
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73
The probability that the drawn card from a pack of 52 cards is neither an ace nor a spade is .
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74
which of the following cannot be the probability of an event
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75
An observer, 1.5 m tall, is 28.5 m away from a tower 30 m high. Determine the angle of elevation of
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76
The tops of two poles of height 16 m and 10 m are connected by a wire of length l metres. If the wir
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77
A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground
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78
The tops of two towers of height x and y, standing on level ground, subtend angles of 30∘ and 60∘ re
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79
The diameter of a car wheel is 42 cm. The number of complete revolutions it will make in moving 132
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80
From the top of a 7m high building, the angle of elevation of the top of a cable tower is 60 degree
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81
Two poles of equal heights are standing opposite to each other, on either side of the road, which is
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82
If cosecθ+cotθ = p, then prove that cosθ=(p^2+1)/(p^2−1)
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83
sin^230∘cos2^45∘+4tan^230∘+(1/2)sin^290∘−2cos^290∘+1/24
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84
If the perimeter of a circle is half to that of a square , then the ratio of the area of the circle
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85
A dice is rolled twice. Find the probability that 5 will not come up either time.
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86
If HCF of 144 and 180 is expressed in the form 13m – 16. Find the value of m.
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87
prove that 2-√3 is irrational given that √3 is irrational
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88
the zeros of the polynomial x^2-3x-m(m-3) are
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89
Find the greatest six digit number that is exactly divisible by 18, 24 and 36.
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90
If xy=180 and HCF(x,y)=3 then find the LCM(x,y)
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91
Find the sum of the exponents of the prime factors in the prime factorization of 196.
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92
The LCM of smallest two digits composite number and the smallest composite number is
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93
Express 429 as the product of its prime factors.
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94
Two positive integers a and b can be written as a = x3y2 and b = xy3, where x, y are prime numbers.
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95
If HCF (336,54)=6, find LCM (336,54)
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96
Find the HCF of the smallest prime number and the smallest composite number.
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97
Write a rational number between √2 and √3.
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98
Write whether (2√45 +3√20)/2√5 on simplification gives as rational or an irrational
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99
3 bells ring at an interval of 4, 7 and 14 minutes. All three bell rang at 6am, when the three balls
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100
Write the Smallest Number Divisible by Both 306and 657?
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101
The HCF and LCM of two numbers are 9 and 360 respectively. If one number is 45, find the other numbe
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102
find the probability that the randomly taken leap year has 52 sundays
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103
a die is thrown once find the probability of getting a prime number
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104
If two positive integers pand qare written as p=a^2b^3and q=a^3b; a,b are prime numbers, then verify
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105
Find HCF and LCM of 90 and 144 by the prime factorization method.
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106
The length, breadth and height of a room are 8m 50cm, 6m 25cm and 4m 75cm respectively. Find the len
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107
Explain whether (3×12×101)+4 is a prime number or a composite number.
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108
Find the smallest natural number by which 1200 should be multiplied so that the square root of the p
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109
Show that 7-√5 is irrational, given that √5 is irrational.
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110
Prove that √5 is irrational number.
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111
The volume of a right circular cylinder with its height equal to the radius is Find the height of
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112
A fruit vendor has 990 apples and 945 oranges. He packs them into basket.each basket contains only o
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113
A child has a die whose six faces show the letters as given below : The die is thrown once.
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114
prove that (2+root3)/5 is an irrational number given that root 3 is irrational number?? please fully
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115
Write one rational and one irrational number lying between 0.25 and 0.32.
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116
Prove that √3 is an irrational number.
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117
The exponent of 5 in the prime factorisation of 3750 is(a) 3(b 4(c) 5(d) 6
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118
Show that the sum of an AP whose first term is a, the second term b and the last term c, is equal to
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119
solve the equation 1+4+7+10+...+x = 287
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120
The area of a circular playground is 22176 m 2 . The cost of fencing this ground at the rate of Rs 5
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121
Find the area of the shaded region in figure ,if PQ=24 cm , PR= 7 cm and O is the center of the circ
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122
Find the curved surface area of the frustum of a cone, the diameters of whose circular ends are 20 m
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123
Find k for which the system x + 2y = 3 and 5x + ky + 7 = 0 is inconsistent.
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124
For what value of k, the system of equations x+y-4=0 and 2x+ky-3=0 has no solution.
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125
If the sum of first 7 terms of an AP is 49 and that of 17 terms is 289, find the sum of first n term
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126
Solve that following for x: 1/(2a+b+2x)=1/2a+1/b+1/2x
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127
If ratio of corresponding sides of two similar triangles is 5:6, then find the ratio of their areas.
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128
A bucket opens at the top, and made up of a metal sheet is in the form of a frustum of a cone.
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129
A group consists of 12 persons, of which 3 are extremely patient, other 6 are extremely honest and
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