Bihar Board Class 10 · Maths · Matric exam 2027
Bihar Board Class 10 Maths Question Paper 2024
The board’s 2024 question paper, set E — all 129 questions as printed; 98 objective answers from the board’s own key. Each question names its chapter, where that chapter’s most-asked questions are.
Full marks 100 · Time 3 h 15 min
Section A · Objective questions (100)
The mean of first seven multiples of 5 is
- (A) 25
- (B) 20 ✓
- (C) 30
- (D) 35
Answer (the board’s key): (B)
The median of 20, 13, 18, 25, 6, 15, 21, 9, 16, 8, 22 is
- (A) 18
- (B) 16 ✓
- (C) 6
- (D) 15
Answer (the board’s key): (B)
The mode of 23, 15, 25, 40, 27, 25, 22, 25, 20 is
- (A) 23
- (B) 25 ✓
- (C) 22
- (D) 15
Answer (the board’s key): (B)
The median of a frequency distribution is 40 and mean is 38.2. Then its mode is
- (A) 43
- (B) 43.6 ✓
- (C) 42
- (D) none of these
Answer (the board’s key): (B)
If the mean of x, x + 3, x + 5, x + 7 and x + 10 is 9 then the value of x is
- (A) 4 ✓
- (B) 6
- (C) 5
- (D) 7
Answer (the board’s key): (A)
The minimum value of a probability is
- (A) 0 ✓
- (B) 1
- (C) 2
- (D) none of these
Answer (the board’s key): (A)
If the probability of occurrence of an event A is 0.35 then the probability of non-occurrence of A is
- (A) 0.53
- (B) 6.5
- (C) 0.65 ✓
- (D) 3.5
Answer (the board’s key): (C)
In tossing of three coins the number of possible outcomes is
- (A) 3
- (B) 4
- (C) 8 ✓
- (D) 6
Answer (the board’s key): (C)
Which of the following number cannot be the probability of an event?
- (A) 0.5
- (B) 1.9 ✓
- (C) 80%
- (D) 3/4
Answer (the board’s key): (B)
In a throw of one die the probability of occurrence of a number 5 or less than 5 is .
- (A) 1/6
- (B) 1/5
- (C) 5/6 ✓
- (D) 1/2
Answer (the board’s key): (C)
What is the 35th term of the A.P. 20, 17, 14, 11, ... ?
- (A) 82
- (B) - 82 ✓
- (C) 72
- (D) - 72
Answer (the board’s key): (B)
How many terms are in A.P. 3, 8, 13, 18, ..., 93 ?
- (A) 19 ✓
- (B) 18
- (C) 20
- (D) 16
Answer (the board’s key): (A)
The sum of first 30 terms of the A.P. 1, 3, 5, 7, ... is
- (A) 900 ✓
- (B) 990
- (C) 890
- (D) 800
Answer (the board’s key): (A)
The point (-2sqrt(2), -2) lies in which quadrant ?
- (A) First
- (B) Second
- (C) Third ✓
- (D) Fourth
Answer (the board’s key): (C)
The distance between the points ( 5 cos 0, 0 ) and ( 0, 5 sin 0 ) is
- (A) 10
- (B) 5 ✓
- (C) 30
- (D) 25
Answer (the board’s key): (B)
If from a point B the length of perpendicular drawn to x-axis is 10 and the length of perpendicular drawn to y-axis is 5 then the co-ordinates of the point B are
- (A) (5, 10) ✓
- (B) (10, 5)
- (C) (10, 10)
- (D) (5, 5)
Answer (the board’s key): (A)
The distance between the points ( 1, - 3 ) and ( 4, - 6 ) is
- (A) 2sqrt(3)
- (B) 3sqrt(2) ✓
- (C) 9
- (D) 6
Answer (the board’s key): (B)
The point on y-axis which is equidistant from the points ( 5, - 2 ) and ( - 3, 2 ) is
- (A) ( 0, 3 )
- (B) ( - 2, 0 )
- (C) ( 0, - 2 ) ✓
- (D) ( 2, 2 )
Answer (the board’s key): (C)
ABCD is a rectangle whose vertices are A ( 0, 0 ), B ( 8, 0 ), C ( 8, 6 ) and D ( 0, 6 ). Then one of the diagonals of rectangle is
- (A) 12
- (B) 10 ✓
- (C) 14
- (D) 16
Answer (the board’s key): (B)
If ( 0, 4 ), ( 0, 0 ) and ( 3, 0 ) are the vertices of a triangle then perimeter of the triangle is
- (A) 8
- (B) 10
- (C) 12 ✓
- (D) 15
Answer (the board’s key): (C)
If 3x + 4y = 10 and 2x - 2y = 2 then
- (A) x = 2, y = 1 ✓
- (B) x = 1, y = 2
- (C) x = - 1, y = - 2
- (D) x = 3, y = 1
Answer (the board’s key): (A)
The pair of linear equations 3/2x + 5/3y = 7 and 9x - 10y = 14 is
- (A) consistent ✓
- (B) inconsistent
- (C) dependent
- (D) none of these
Answer (the board’s key): (A)
The graphs of the equations 2x + 3y + 15 = 0 and 3x - 2y - 12 = 0 are which type of straight lines ?
- (A) Coincident straight lines
- (B) Parallel straight lines
- (C) Intersecting straight lines ✓
- (D) None of these
Answer (the board’s key): (C)
The system of linear equations 2x - 3y = 5 and 4x - 6y = 7 has
- (A) one and only one solution
- (B) no solution ✓
- (C) infinitely many solutions
- (D) none of these
Answer (the board’s key): (B)
If straight lines 4x + py = 16 and 2x + 9y = 15 are parallel then what is the value of p ?
- (A) 1/3
- (B) 3
- (C) 18 ✓
- (D) - 3
Answer (the board’s key): (C)
Which of the following is not an A.P. ?
- (A) 5, 4 1/2, 4, 3 1/2, ...
- (B) - 1, -5/6, -2/3, -1/2, ...
- (C) 8, 14, 20, 26, ...
- (D) 4, 10, 15, 20, ... ✓
Answer (the board’s key): (D)
If (2x - 1), 7, 3x are in A.P., then what is the value of x ?
- (A) 3 ✓
- (B) 4
- (C) 1
- (D) 5
Answer (the board’s key): (A)
If a_n is n-th term of the A.P. 5, 12, 19, ... then what is the value of a_40 - a_35 ?
- (A) 20
- (B) 35 ✓
- (C) 30
- (D) 55
Answer (the board’s key): (B)
If the 7th term of an A.P. is 4 and its common difference is - 4, then what is its first term ?
- (A) 16
- (B) 20
- (C) 24
- (D) 28 ✓
Answer (the board’s key): (D)
If the sum of first n terms of an A.P. is (4n^2 + 2n) then the common difference of A.P. is
- (A) 6
- (B) 14
- (C) 8 ✓
- (D) 4
Answer (the board’s key): (C)
What is the reciprocal of sin theta * cot theta ?
- (A) tan theta
- (B) cos theta
- (C) sec theta ✓
- (D) cosec theta
Answer (the board’s key): (C)
cot 12 degree . cot 38 degree . cot 52 degree . cot 60 degree . cot 78 degree =
- (A) 1
- (B) sqrt(3)
- (C) 1/sqrt(3) ✓
- (D) 3
Answer (the board’s key): (C)
cosec (90 degree - theta) . cos (90 degree - theta) =
- (A) sec theta
- (B) tan theta
- (C) sin theta
- (D) cot theta
If sin theta = sqrt(2) cos theta then the value of sec theta is
- (A) 1/sqrt(3)
- (B) sqrt(3) ✓
- (C) sqrt(3)/2
- (D) 2/sqrt(3)
Answer (the board’s key): (B)
3 tan^2 60° =
- (A) 3
- (B) 1
- (C) 9 ✓
- (D) 1/3
Answer (the board’s key): (C)
If A, B, C are angles of a triangle ABC, then the value of cosec ((A+B)/2) is
- (A) tan C/2
- (B) sec C/2 ✓
- (C) cot C/2
- (D) sin C/2
Answer (the board’s key): (B)
If the radius of a circle becomes k times then the ratio of the areas of previous and new circles is
- (A) 1 : k
- (B) 2 : k^3
- (C) 1 : k^2 ✓
- (D) k^2 : 1
Answer (the board’s key): (C)
What is the total perimeter of a semicircle whose radius is k ?
- (A) pi k
- (B) (pi + 1) k
- (C) pi + 2k
- (D) (pi + 2) k ✓
Answer (the board’s key): (D)
The distance covered by a wheel of diameter 42 cm in 2 revolution is
- (A) 264 cm ✓
- (B) 132 cm
- (C) 84 cm
- (D) none of these
Answer (the board’s key): (A)
A, B, C and D are four points on the circumference of a circle of radius 8 cm such that ABCD is a square. Then the area of square ABCD is
- (A) 64 cm^2
- (B) 100 cm^2
- (C) 125 cm^2
- (D) 128 cm^2 ✓
Answer (the board’s key): (D)
If p(y) = (y+1)(y^3+2)(y^4+6) and g(y) = y^2 - 3y + 1 then the degree of p(y)/g(y) is
- (A) 6 ✓
- (B) 3
- (C) 5
- (D) 4
Answer (the board’s key): (A)
Which of the following is a quadratic equation ?
- (A) (x+1)(x-1) = x^2 - 4x^3
- (B) (x+4)^2 = 3x+4 ✓
- (C) 4x + 1/2x = 8x^2
- (D) (2x^2 + 4) = (5+x)(2x-3)
Answer (the board’s key): (B)
If product of the roots of the quadratic equation x^2-5x+p=10 is -4, then the value of p is
- (A) 4
- (B) 5
- (C) 6 ✓
- (D) 8
Answer (the board’s key): (C)
If (x-2) is a factor of px^2-x-6 then the value of p is
- (A) 2 ✓
- (B) 3
- (C) 1
- (D) 4
Answer (the board’s key): (A)
For what value of k, roots of the quadratic equation x^2+6x+k=0 are real and equal ?
- (A) 12
- (B) 9 ✓
- (C) 10
- (D) 6
Answer (the board’s key): (B)
What is the nature of the roots of the quadratic equation 4/3x^2-2x+3/4=0 ?
- (A) Real and unequal
- (B) Real and equal ✓
- (C) Not real
- (D) None of these
Answer (the board’s key): (B)
If one root of the quadratic equation y^2+3y-18=0 is -6 then its another root is
- (A) 3 ✓
- (B) -3
- (C) 6
- (D) 5
Answer (the board’s key): (A)
If alpha and beta are the roots of the quadratic equation x^2 - 8x + 5 = 0 then the value of alpha^2 + beta^2 is
- (A) 44
- (B) 54 ✓
- (C) 74
- (D) 64
Answer (the board’s key): (B)
The roots of the quadratic equation ax^2 - bx - c = 0, a != 0 are
- (A) (-b + sqrt(b^2 - 4ac)) / 2a
- (B) (b + sqrt(b^2 + 4ac)) / 2a ✓
- (C) (-b + sqrt(b^2 + 4ac)) / 2a
- (D) (b + sqrt(b^2 - 4ac)) / 2a
Answer (the board’s key): (B)
If x = 2 is a common root of both the equations 2x^2 + 2x + p = 0 and qx^2 + qx + 18 = 0 then the value of (q - p) is
- (A) -4
- (B) -3
- (C) 9 ✓
- (D) 4
Answer (the board’s key): (C)
2.13113111311113 ... is
- (A) a rational number
- (B) an irrational number ✓
- (C) an integer
- (D) none of these
Answer (the board’s key): (B)
The product of a rational number and an irrational number is which type of number?
- (A) A rational number
- (B) An irrational number ✓
- (C) A natural number
- (D) None of these
Answer (the board’s key): (B)
The simplest form of 0.57 (bar over 57) is
- (A) 19/33 ✓
- (B) 57/50
- (C) 57/100
- (D) 19/32
Answer (the board’s key): (A)
If 140 = 2^x * 5^y * 7^z then x + y - z =
- (A) 2 ✓
- (B) 4
- (C) 3
- (D) 1
Answer (the board’s key): (A)
(6 + sqrt(125)) - (3 + sqrt(5)) + (1 - 4sqrt(5)) is
- (A) a rational number ✓
- (B) an irrational number
- (C) not real
- (D) none of these
Answer (the board’s key): (A)
In p/q form of 0.375, the form of q is
- (A) 2^3 * 5^0 ✓
- (B) 2^3 * 5^2
- (C) 2^3 * 5^3
- (D) 2^2 * 5^3
Answer (the board’s key): (A)
The H.C.F. of two numbers is 15 and L.C.M. is 105. If one of the numbers is 5 then the other number is
- (A) 75
- (B) 15
- (C) 315 ✓
- (D) 525
Answer (the board’s key): (C)
If in division algorithm a = bq + r, b = 43, q = 31 and r = 32, the value of a will be
- (A) 1365 ✓
- (B) 1356
- (C) 1360
- (D) 1350
Answer (the board’s key): (A)
If q is a positive integer, which of the following is an even positive integer?
- (A) 2q + 1
- (B) 2q ✓
- (C) 2q + 3
- (D) 2q + 5
Answer (the board’s key): (B)
Which of the following has terminating decimal expansion?
- (A) 11/700
- (B) 91/2100
- (C) 343 / (2^3 * 5^3 * 7^3) ✓
- (D) 15 / (2^5 * 3^2)
Answer (the board’s key): (C)
The mid-point of the line segment joining the points A(-2, 8) and B(-6, -4) is
- (A) (-6, -4)
- (B) (-4, 2) ✓
- (C) (2, 6)
- (D) (-4, -6)
Answer (the board’s key): (B)
If the points (1, 2), (0, 0) and (a, b) are collinear then
- (A) a = b
- (B) a = 2b
- (C) 2a = b ✓
- (D) a + b = 0
Answer (the board’s key): (C)
Two vertices of a triangle ABC are A(2, 3) and B(1, -3) and centroid is (3, 0) then the co-ordinates of third vertex C are
- (A) (5, 2)
- (B) (1, 3)
- (C) (6, 0) ✓
- (D) (2, -3)
Answer (the board’s key): (C)
In triangle ABC, AD is bisector of angle BAC. If AB = 4 cm, AC = 6 cm, BD = 2 cm then the value of DC is
- (A) 3 cm ✓
- (B) 6 cm
- (C) 7 cm
- (D) 4 cm
Answer (the board’s key): (A)
In triangle ABC, DE || BC such that AD/DB = 4/(x-4) and AE/EC = 8/(3x-19) then the value of x is
- (A) 9
- (B) 10
- (C) 11 ✓
- (D) 12
Answer (the board’s key): (C)
If in triangle ABC, AB = 13 cm, BC = 12 cm and AC = 5 cm then the value of angle C is
- (A) 90° ✓
- (B) 30°
- (C) 60°
- (D) 45°
Answer (the board’s key): (A)
If the ratio of areas of two equilateral triangles is 9 : 4 then the ratio of their perimeters is
- (A) 27 : 8
- (B) 3 : 2 ✓
- (C) 9 : 4
- (D) 4 : 9
Answer (the board’s key): (B)
If in triangle ABC and triangle DEF, AB/DE = BC/EF = AC/DF = 5/7, then the ratio of the areas of triangle ABC and triangle DEF is
- (A) 5 : 7
- (B) 25 : 49 ✓
- (C) 49 : 25
- (D) 125 : 343
Answer (the board’s key): (B)
triangle ABC and triangle PQR are similar triangles. If AD and PS are bisectors of angle A and angle P respectively and AD = 6.5 cm, PS = 5.2 cm then area(triangle ABC) / area(triangle PQR) =
- (A) 49 : 16
- (B) 25 : 16 ✓
- (C) 36 : 49
- (D) 81 : 64
Answer (the board’s key): (B)
If one side of an equilateral triangle is a then its height is
- (A) a*sqrt(3)
- (B) (a/2)*sqrt(3) ✓
- (C) 2a*sqrt(3)
- (D) a/sqrt(3)
Answer (the board’s key): (B)
The perpendicular distance from the centre of a circle to a chord of length 8 cm is 3 cm. Then the radius of the circle is
- (A) 4 cm
- (B) 5 cm ✓
- (C) 10 cm
- (D) 8 cm
Answer (the board’s key): (B)
If two circles touch each other internally then the number of common tangents is
- (A) 1 ✓
- (B) 2
- (C) 3
- (D) 4
Answer (the board’s key): (A)
If the length of any chord of a circle is equal to the radius of the circle then the angle subtended by the chord at the centre is
- (A) 90°
- (B) 60° ✓
- (C) 30°
- (D) 120°
Answer (the board’s key): (B)
TP and TQ are two tangents drawn from an external point T to a circle whose centre is O such that ∠POQ = 120°. Then the value of ∠OTP is
- (A) 40°
- (B) 30° ✓
- (C) 50°
- (D) 60°
Answer (the board’s key): (B)
If tan 2A = cot (A - 18°) where 2A is an acute angle, then the value of A is
- (A) 72°
- (B) 36° ✓
- (C) 60°
- (D) 45°
Answer (the board’s key): (B)
If sin θ = sqrt(3)/2, 0 < 90° then tan^2 θ - 1 =
- (A) 1
- (B) 0
- (C) 2 ✓
- (D) - 1
Answer (the board’s key): (C)
9 cosec^2 22° - 9 cot^2 22° + 1 =
- (A) 9
- (B) 10 ✓
- (C) 1/9
- (D) 0
Answer (the board’s key): (B)
If sin θ = a/b then the value of cos θ is
- (A) b / sqrt(b^2 - a^2)
- (B) sqrt(b^2 - a^2) / b ✓
- (C) a / sqrt(b^2 - a^2)
- (D) b / a
Answer (the board’s key): (B)
If sec theta = 13/12 then cot theta =
- (A) 5/12
- (B) 5/13
- (C) 12/5
- (D) 13/5
(sec theta + tan theta) (1 - sin theta) =
- (A) sin theta
- (B) cos theta ✓
- (C) sec theta
- (D) cosec theta
Answer (the board’s key): (B)
Which of the following is not a polynomial ?
- (A) sqrt(3) x^2 - 5sqrt(2) x + 3
- (B) 3x^2 - 4x + sqrt(5)
- (C) x + 2sqrt(x) ✓
- (D) 1/5 x^3 - 3x^2 + 2
Answer (the board’s key): (C)
The degree of the polynomial (3x^2 - 7x + 2)(2x^4 + 3x^3 - 5x + 2) is
- (A) 2
- (B) 6 ✓
- (C) 4
- (D) 3
Answer (the board’s key): (B)
The zeroes of the polynomial x^2 - 13 are
- (A) 13, -13
- (B) 13, -sqrt(13)
- (C) sqrt(13), -sqrt(13) ✓
- (D) sqrt(13), -13
Answer (the board’s key): (C)
For what value of m, - 4 is one of the zeroes of the polynomial x^2 - x - (2m + 2) ?
- (A) 7
- (B) 8
- (C) 9 ✓
- (D) 5
Answer (the board’s key): (C)
If 1 is one zero of the polynomial p(x) = ax^2 - 3(a - 1)x - 1 then value of a is
- (A) 3
- (B) 1 ✓
- (C) 0
- (D) 2
Answer (the board’s key): (B)
Which of the following quadratic polynomials has zeroes 3/5 and -1/2 ?
- (A) 10x^2 + x + 3
- (B) 10x^2 + x - 3
- (C) 10x^2 - x + 3
- (D) 10x^2 - x - 3 ✓
Answer (the board’s key): (D)
If alpha and beta are the zeroes of the polynomial p(x) = x^2 - 3x - 4 then the value of 4/3(alpha + beta) is
- (A) 4 ✓
- (B) 3
- (C) -3
- (D) 1
Answer (the board’s key): (A)
If one zero of the polynomial p(x) is 5 then one factor of p(x) is
- (A) x - 5 ✓
- (B) x + 5
- (C) 1/(x - 5)
- (D) 1/(x + 5)
Answer (the board’s key): (A)
If p(x) = x^4 + 2x^3 - 17x^2 - 4x + 30 is divided by q(x) = x^2 + 2x - 15, then the degree of the quotient is
- (A) 4
- (B) 2 ✓
- (C) 3
- (D) 1
Answer (the board’s key): (B)
If alpha and beta are the zeroes of the polynomial x^2 + 5x + 8 then the value of alpha^2 + beta^2 + 2alpha beta is
- (A) 25 ✓
- (B) 5
- (C) 8
- (D) 64
Answer (the board’s key): (A)
If the areas of three adjacent faces of a cuboid are a, b, c respectively, then the volume of the cuboid is
- (A) abc
- (B) 2 abc
- (C) sqrt(abc) ✓
- (D) 3sqrt(abc)
Answer (the board’s key): (C)
The total surface area of a cube is 216 cm^2 then its volume is
- (A) 144 cm^3
- (B) 196 cm^3
- (C) 212 cm^3
- (D) 216 cm^3 ✓
Answer (the board’s key): (D)
The ratio of volumes of two cubes is 1 : 64. The ratio of their total surface area is
- (A) 1 : 4
- (B) 1 : 16 ✓
- (C) 1 : 18
- (D) 1 : 8
Answer (the board’s key): (B)
Two circular cylinders of equal volume have their heights in the ratio 1 : 2. The ratio of their radii is
- (A) 1 : sqrt(2)
- (B) sqrt(2) : 1 ✓
- (C) 1 : 2
- (D) 1 : 4
Answer (the board’s key): (B)
If the curved surface area of a cylinder is 1760 cm^2 and its base diameter is 28 cm then its height is
- (A) 10 cm
- (B) 15 cm
- (C) 20 cm ✓
- (D) 40 cm
Answer (the board’s key): (C)
If O is the centre and R is the radius of a circle and angle AOB = theta then the length of arc AB is
- (A) 2*pi*R*theta/180
- (B) 2*pi*R*theta/360 ✓
- (C) pi*R^2*theta/180
- (D) pi*R^2*theta/360
Answer (the board’s key): (B)
If l is slant height of a cone and r is the radius of its base then total surface area of cone is
- (A) pi*r*l + r
- (B) pi*r*l + pi*r^2 ✓
- (C) pi*r*l + r^2
- (D) pi*r*l + 2r^2
Answer (the board’s key): (B)
The ratio of volumes of two spheres is 125 : 27 then the ratio of their surface areas is
- (A) 9 : 25
- (B) 25 : 9 ✓
- (C) 5 : 3
- (D) 3 : 5
Answer (the board’s key): (B)
A sphere of radius 8 cm is melted to form a cone of height 32 cm. The radius of base of the cone is
- (A) 8 cm ✓
- (B) 9 cm
- (C) 10 cm
- (D) 12 cm
Answer (the board’s key): (A)
If the surface area of a sphere is 616 cm^2 then the diameter of sphere is
- (A) 7 cm
- (B) 14 cm ✓
- (C) 28 cm
- (D) 56 cm
Answer (the board’s key): (B)
Section B · Written questions (29)
Using Euclid division algorithm find the HCF of 148 and 185.
Find the mean of the following data : Variable: 2, 4, 6, 10, 12; Frequency: 3, 2, 3, 1, 2
If the angle between two tangents drawn from an external point P to a circle of radius 3 cm and centre O is 60 degree, find the length of OP.
For what value of k equations kx + y = 1 and (k - 1) x + 2y = 3 have no solution ?
Write the solution of the equation 3x + y = 11 in natural numbers.
Find the roots of the equation 1/x - 1/(x - 2) = 3, x not equal to 0, 2.
In triangle ABC, angle C = 90 degree and P, Q are mid-points of sides CA and CB respectively. Then prove that 4AQ^2 = 4AC^2 + BC^2.
If point A (x, 2) is equidistant from the points B (8, -2) and C (2, -2) then find the value of x.
In what ratio does the point (-4, 6) divide the line segment joining the points A (-6, 10) and B (3, -8)?
Find the area of the triangle ABC whose vertices are A (2, 1), B (4, 5) and C (0, 3) respectively.
Evaluate: (sec(90 degree - theta) cosec theta - tan(90 degree - theta) cot theta + cos^2 25 degree + cos^2 65 degree) / (3 tan 27 degree tan 63 degree)
Prove that (sec theta + tan theta) / (sec theta - tan theta) = ((1 + sin theta) / cos theta)^2.
Find the discriminant of the quadratic equation sqrt(2)x^2 - x - sqrt(2) = 0 and hence find the nature of the roots.
For what value of k will the equation kx(x - 2) + 6 = 0 have equal roots ?
Check whether 301 is a term of the list of numbers 5, 11, 17, 23, ...
Prove that (2 + sqrt(3))^2 is not a rational number.
Find the zeroes of the quadratic polynomial 3x^2 - x - 4 and verify the relationship between the zeroes and the co-efficients.
Divide polynomial 2x^4 + 3x^3 - 2x^2 - 9x - 12 by polynomial x^2 - 3.
Find the sum of 10 terms of A.P. 9, 17, 25, ...
Find the sum of first 15 multiples of 8.
In triangle PQR, two points S and T are on sides PQ and PR such that PS/SQ = PT/TR and angle PST = angle PRQ then prove that triangle PQR is an isosceles triangle.
If one zero of the polynomial (a^2 + 9)x^2 + 13x + 6a is reciprocal of the others, then find the value of a.
On adding 1 to the numerator of a fraction it becomes 1/2 and on adding 1 to the denominator it becomes 1/3. Write the equation for this statement.
Solve the pair of equations 8x + 5y = 9 and 3x + 2y = 4 by substitution method.
Prove that (sin A / (1 + cos A) + (1 + cos A) / sin A) * (sin A / (1 - cos A) - (1 - cos A) / sin A) = 4 cosec A cot A.
Metallic spheres of radii 6 cm, 8 cm and 10 cm respectively, are melted to form a single solid sphere. Find the radius of the resulting sphere.
The angles of elevation of the top of a tower from two points at distances of 4 m and 9 m from the base of the tower which are in the same straight line, are complementary. Prove that the height of the tower is 6 m.
Draw a circle of radius 6 cm. From a point 10 cm away from its centre, construct the pair of tangents to the circle and measure their lengths.
Find the median of the following data : Class-interval 40-45, 45-50, 50-55, 55-60, 60-65, 65-70, 70-75. Frequency 2, 3, 8, 6, 6, 3, 2.
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