Bihar Board Class 10 · Maths · Matric exam 2027
Bihar Board Class 10 Maths Model Paper 2022
The board’s 2022 model paper — all 138 questions as printed. Each question names its chapter, where that chapter’s most-asked questions are.
Time 3 h 15 min
Section A · Objective questions (100)
Which of the following is the smallest composite number ?
- (A) 1
- (B) 2
- (C) 3
- (D) 4
pi is -
- (A) an irrational number
- (B) a rational number
- (C) an integer
- (D) none of these
Which of the following is an irrational number ?
- (A) sqrt(3/12)
- (B) sqrt(2/10)
- (C) sqrt(7/7)
- (D) sqrt(2) x sqrt(2)
The L.C.M and H.C.F of two numbers are equal. Then the numbers are -
- (A) prime
- (B) equal
- (C) co-prime
- (D) composite
0.29(bar) =
- (A) 29/90
- (B) 29/100
- (C) 27/99
- (D) 29/99
1 - sin^2 60^0 =
- (A) 1
- (B) 1/2
- (C) 1/4
- (D) 0
Which of the following has terminating decimal expansion ?
- (A) 7/40
- (B) 5/21
- (C) 23/196
- (D) 31/121
Which of the following has non-terminating decimal expansion ?
- (A) 5/8
- (B) 6/15
- (C) 19/512
- (D) 31/343
The exponent of 5 in the prime factorization of 400 is -
- (A) 2
- (B) 3
- (C) 4
- (D) 1
If 130 = 15 x 8 + 10 and H.C.F(130, 15) = H.C.F(x, y) then (x, y) =
- (A) (15, 10)
- (B) (8, 10)
- (C) (15, 8)
- (D) (130, 8)
The rationalizing factor of sqrt(125) is -
- (A) sqrt(2)
- (B) sqrt(3)
- (C) sqrt(5)
- (D) 5sqrt(5)
Which of the following pair is co-prime ?
- (A) (9, 16)
- (B) (15, 20)
- (C) (21, 84)
- (D) (13, 65)
The number of zeros in a linear polynomial is -
- (A) 3
- (B) 2
- (C) 1
- (D) 0
Zero of the polynomial x-1 is -
- (A) 1
- (B) 0
- (C) 2
- (D) undefined
If zeros of any quadratic polynomial are -4 and 7 then the quadratic polynomial will be -
- (A) x^2 + 4x + 7
- (B) x^2 + 3x - 28
- (C) x^2 - 3x - 28
- (D) x^2 + 3x + 28
The sum and product of the zeros of a quadratic polynomial are 5 and 6 respectively then the quadratic polynomial will be -
- (A) x^2 - 5x - 6
- (B) x^2 - 5x + 6
- (C) x^2 + 5x - 6
- (D) x^2 + 5x + 6
If alpha and beta are the zeros of the polynomial y^2 - 6y + 8 then the value of alpha.beta is -
- (A) 8
- (B) -8
- (C) 6
- (D) -6
The polynomial f(x) = 3x^2 - 7x + 2 then the value of f(-1) is -
- (A) -8
- (B) 12
- (C) -12
- (D) 0
The zeros of the polynomial x^2 - 3 are -
- (A) 3, -3
- (B) sqrt(3), -sqrt(3)
- (C) sqrt(3), sqrt(3)
- (D) 3, 3
Which of the following is the solution of 6x - 2y = 0 and 10x + 2y = 32 ?
- (A) x = 6, y = 6
- (B) x = 2, y = 6
- (C) x = 6, y = 2
- (D) x = 2, y = 2
If the lines 4x + py = 6 and 12x + 9y = 15 are parallel then the value of p will be -
- (A) 1/3
- (B) 3
- (C) 6
- (D) -3
The value of K for which the system of equations x + 2y = 3, 5x + Ky = 15 has infinitely many solutions is -
- (A) 5
- (B) 20
- (C) 6
- (D) 10
Which of the following is a quadratic equation ?
- (A) (x + 2) (x - 2) = x^2 - 4x^3
- (B) (X + 2)^2 = 3(x + 4)
- (C) (2x^2 + 3) = (5 + x) (2x - 3)
- (D) 2x + 1/(2x) = 4x^2
The roots of quadratic equation px^2+qx+r = 0, p!=0 are
- (A) (q +/- sqrt(q^2-4pr)) / 2p
- (B) (-q +/- sqrt(q^2-4pr)) / 2p
- (C) (-q +/- sqrt(q^2-4pr)) / 2
- (D) (-q +/- sqrt(q^2+4pr)) / 2p
The nature of roots of the quadratic equation 6x^2+6x+1 = 0 is -
- (A) real and equal
- (B) not real
- (C) real and unequal
- (D) none of these
The sum of the roots of the equation 3x^2-18x+6=0 is -
- (A) 3
- (B) -3
- (C) -6
- (D) 6
The roots of the quadratic equation ax^2+bx+c = 0 (a!=0) will be reciprocal of each other, if
- (A) b = c
- (B) c = a
- (C) a = b
- (D) none of these
The 15th term of the A.P. : 1/2, 1, 3/2, 2, ... is -
- (A) 13/2
- (B) 15/2
- (C) 7
- (D) 17/2
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, ...
If in an A.P., first term is 9 and common difference is -3 then sum of its first 12 terms is -
- (A) 78
- (B) 90
- (C) -90
- (D) -78
Which term of the A.P. : 17, 34, 51, ... is 170 ?
- (A) 9th
- (B) 10th
- (C) 11th
- (D) 12th
The number of terms in an A.P. 51, 48, 45, ..., 6 is -
- (A) 14
- (B) 16
- (C) 17
- (D) 18
The number of odd numbers between 0 and 50 is -
- (A) 25
- (B) 26
- (C) 24
- (D) 27
In right triangle ABC, angle B=90 degree, AB = sqrt(15)cm, BC=1cm and AC = 4cm then tanA will be equal to -
- (A) sqrt(15)/4
- (B) sqrt(15)/1
- (C) 1/sqrt(15)
- (D) 4/sqrt(15)
If cosec(phi) = K then the value of cos(phi) is -
- (A) sqrt(K^2+1)/K
- (B) sqrt(K^2-1)/K
- (C) K/sqrt(K^2-1)
- (D) K/sqrt(K^2+1)
1/sec(phi) =
- (A) tan(phi)
- (B) cos(phi)
- (C) sec(phi)
- (D) cosec(phi)
cot(x) . tan(x) =
- (A) 1
- (B) -1
- (C) 0
- (D) 2
If cos(phi) = 1/2 then the value of cosec(phi) is -
- (A) 2
- (B) 2/sqrt(3)
- (C) sqrt(3)/2
- (D) 1/sqrt(3)
If Ø = 45^0 then secØ + cosecØ =
- (A) 1
- (B) sqrt(2)
- (C) 2
- (D) 2sqrt(2)
If sqrt(3)tanA - 3 = 0 then A =
- (A) 90^0
- (B) 60^0
- (C) 45^0
- (D) 30^0
(sec35^0 / cosec55^0)^2 =
- (A) -1
- (B) 0
- (C) 1
- (D) 2
Which of the following has the maximum value ?
- (A) cos45^0
- (B) sin0^0
- (C) cot45^0
- (D) cos60^0
Sin30^0 =
- (A) 1
- (B) 1/2
- (C) sqrt(3)/2
- (D) 1/sqrt(2)
cos^2Ø - 1 =
- (A) -sin^2Ø
- (B) sin^2Ø
- (C) 0
- (D) cot^2Ø
(1-sec^2Ø) x cot^2Ø =
- (A) 0
- (B) 1
- (C) -1
- (D) 2
Sinα x cotα =
- (A) 1
- (B) cosα
- (C) cos^2α
- (D) sin^2α
If theta/5 = 12^0 then 3x cosec^2theta =
- (A) 2/sqrt(3)
- (B) 4/3
- (C) 4
- (D) 4sqrt(3)
If sinx + sin^2x = 1 then cos^2x + cos^4x =
- (A) 1/4
- (B) 1/2
- (C) 1
- (D) 3/4
Which of the following is equal to cosec60^0 ?
- (A) sec30^0
- (B) sin60^0
- (C) cot30^0
- (D) tan60^0
If cosectheta - cottheta = x then cosectheta =
- (A) (x^2-1)/2x
- (B) (x^2-1)/2
- (C) (x^2+1)/2x
- (D) (x^2+1)/2
sec^260^0 - tan^260^0 + 1 =
- (A) 1
- (B) 2
- (C) -2
- (D) 0
cot(90^0 - A) =
- (A) cotA
- (B) secA
- (C) cosecA
- (D) tanA
(2tan30^0)/(1+tan^230^0) =
- (A) sin30^0
- (B) cos60^0
- (C) tan60^0
- (D) sin60^0
If a pole 6 meter high casts a shadow 2sqrt(3) meter long on ground, then the angle of elevation of sun is -
- (A) 15^0
- (B) 30^0
- (C) 45^0
- (D) 60^0
The height of a tower is 15 meter. When the angle of elevation of the sun is 60^0, what will be the length of the tower's shadow on the ground ?
- (A) 15 m
- (B) 15sqrt(3) m
- (C) 5sqrt(3) m
- (D) 45sqrt(3) m
The point of intersection of the coordinate axes is called -
- (A) abscissa
- (B) ordinate
- (C) origin
- (D) quadrant
In which quadrant does the point (-6, -8) lie ?
- (A) first quadrant
- (B) second quadrant
- (C) third quadrant
- (D) fourth quadrant
The distance of the point P(sin theta, cos theta) from the origin is -
- (A) 0 unit
- (B) 1 unit
- (C) 4 units
- (D) 2 units
The distance between the points R(1, 1) and S(-1, 5) is -
- (A) 4sqrt(5) units
- (B) 3sqrt(5) units
- (C) 2sqrt(5) units
- (D) 5 units
The graph of the line y=8 does not passes through which of the following points ?
- (A) (1, 8)
- (B) (4, 8)
- (C) (0, 8)
- (D) (8, 1)
Which of the following points lie in the first quadrant ?
- (A) (10, 4)
- (B) (-4, 3)
- (C) (-4, -3)
- (D) (4, -3)
The perpendicular distance of the point A(5, 6) from the y-axis is -
- (A) 5 units
- (B) 6 units
- (C) 11 units
- (D) sqrt(61) units
The coordinates of the midpoint of the line segment joining the points M(-2, 10) and N(-8, 14) are -
- (A) (-10, 24)
- (B) (6, 1)
- (C) (-5, 12)
- (D) (8, 6)
If (6, -8) and (-6, 8) are the coordinates of the ends points of the diameter of a circle, then the coordinates of the centre of the circle are -
- (A) (6, -6)
- (B) (-8, 8)
- (C) (0, 0)
- (D) (12, 16)
Points A(3, 4) and B(p, 1) are equidistant from the origin then the value of p is -
- (A) 2
- (B) +-sqrt(6)
- (C) +-6
- (D) +-2sqrt(6)
The area of the triangle formed by points A(0, 8), B(6, 12) and C(-16, -4) is -
- (A) 48 sq. units
- (B) 8 sq. units
- (C) 6 sq. units
- (D) 4 sq. units
The y-coordinates of a point which divides the line segment joining A(4, -3) and B(9, 7) in the ratio 3:2 internally is -
- (A) (3X9+2X4)/(3+2)
- (B) [3X7+2X(-3)]/(3+2)
- (C) [3X9+2X(-3)]/(3+2)
- (D) [3X7-2X(-3)]/(3+2)
Delta ABC in if angle A + angle C = 120^0 if then angle B =
- (A) 50^0
- (B) 60^0
- (C) 70^0
- (D) 90^0
If in ΔABC and ΔDEF, AB/DE = BC/FD then they will be similar when -
- (A) ∠A = ∠D
- (B) ∠B = ∠E
- (C) ∠A = ∠F
- (D) ∠B = ∠D
If ΔABC~ΔPQR and BC/QR = 1/5 then ar(ΔPQR)/ar(ΔABC) =
- (A) 25
- (B) 5
- (C) 1/5
- (D) 1/25
tan(90^0 - A) =
- (A) tanA
- (B) cotA
- (C) - cotA
- (D) - tanA
In the given figure DE||BC. If AD = 5 cm, DB = 6 cm and AE = 8 cm then EC =
- (A) 5.6 cm
- (B) 7.6 cm
- (C) 9.6 cm
- (D) 11.6 cm
Who said, 'the ratio of any two corresponding sides in two equiangular triangle is always the same' ?
- (A) Thales
- (B) Newton
- (C) Aryabhatta
- (D) Pythagoras
How many tangents can be drawn to a circle from an external point ?
- (A) 1
- (B) 2
- (C) 3
- (D) infinite
In the given figure PA and PB are two tangents to the circle with centre O such that angle APO = 40^0 then angle OAB =
- (A) 40^0
- (B) 30^0
- (C) 20^0
- (D) 90^0
In the given figure QOR is a diameter of a circle and PQ=PR, then angle PQR =
- (A) 90^0
- (B) 60^0
- (C) 45^0
- (D) 30^0
If AB and AC are two tangents to a circle with centre O such that angle BOC=110^0 then angle CAO=
- (A) 60^0
- (B) 45^0
- (C) 35^0
- (D) 150^0
From a point T the length of the tangent to a circle is 12cm and the distance of T from the centre is 13cm. The radius of circle is -
- (A) 6 cm
- (B) 12.5 cm
- (C) 25 cm
- (D) 5 cm
In the given figure, O is the centre of the circle and angle QPR=60^0 then angle OQR =
- (A) 60^0
- (B) 30^0
- (C) 120^0
- (D) 40^0
The range of the data 15, 20, 84, 29, 41, 45, 60, 65 is -
- (A) 69
- (B) 65
- (C) 84
- (D) 15
The arithemetic mean of 1, 2, 3, ..., n is -
- (A) n/2 + 1
- (B) n/2
- (C) (n+1)/2
- (D) (n-1)/2
If 3 Median = Mode + x Mean then the value of x is
- (A) 1/3
- (B) 3/2
- (C) 2
- (D) 2/3
The mode of the observation 12, 13, 11 ,14, 12, 13, 15, 11, 13, is-
- (A) 11
- (B) 12
- (C) 13
- (D) 15
If 10 is mean of 7, 9, 13, 15, x, then the value of x will be -
- (A) 6
- (B) 9
- (C) 11
- (D) 13
The maximum value of probability of any event is -
- (A) 1
- (B) 0
- (C) 2
- (D) 1/2
Which of the following cannot be probability of an event ?
- (A) 50%
- (B) 0.12
- (C) 3/4
- (D) 13/12
An unbiased die is thrown then the probability of getting a multiple of 2 is -
- (A) 1/2
- (B) 1/3
- (C) 2/3
- (D) 1/6
A card is drawn at random from a well shuffled deck of playing cards, then the probability of getting a red card is -
- (A) 1/2
- (B) 2/13
- (C) 3/13
- (D) None of these
Two unbiased coins are tossed then the probability of getting at least one head is -
- (A) 1/2
- (B) 1/4
- (C) 1/3
- (D) 3/4
The number of possible outcomes by tossing three coins is -
- (A) 3
- (B) 10
- (C) 6
- (D) 8
The area of a square inscribed in a circle of radius 8 cm is -
- (A) 64 cm^2
- (B) 84 cm^2
- (C) 100 cm^2
- (D) 128 cm^2
The ratio of circumferences of two circles is 4:5 then the ratio of their areas is -
- (A) 4:5
- (B) 5:4
- (C) 16:25
- (D) 25:16
If the area of an equilateral triangle is 9sqrt(3) cm^2 then its side is -
- (A) 6 cm
- (B) 3sqrt(3) cm
- (C) 3 cm
- (D) sqrt(3) cm
If the sum of the circumferences of two circles with radii R1 and R2 is equal to the circumference of a circle of radius R then
- (A) R1 + R2 > R
- (B) R1 + R2 = R
- (C) R1 + R2 < R
- (D) R1 + R2 = R/2
If the height and radius of the cone are thriced then volume of the cone will be -
- (A) 8 times
- (B) 16 times
- (C) 6 times
- (D) 27 times
The total surface area of a hemisphere with radius r is -
- (A) 4pi r^2
- (B) 3pi r^2
- (C) 2pi r^2
- (D) pi r^2
The volume of a frustum of a cone is -
- (A) 1/3 pi h(R^2 + r^2 + Rr)
- (B) 1/3 pi h(R^2 + r^2)
- (C) 1/3 pi (R^2 + r^2)
- (D) 1/3 pi R^2 r^2 h
What is the common difference of an A.P in which a18 - a14 = 32?
- (A) 4
- (B) -4
- (C) 8
- (D) -8
The diameter of sphere is 42cm then its surface area is -
- (A) 1386 cm^2
- (B) 4158 cm^2
- (C) 5544 cm^2
- (D) 2772 cm^2
The height of a cylinder is 14cm and its curved surface area is 264cm^2. The volume of the cylinder is -
- (A) 369 cm^3
- (B) 503 cm^3
- (C) 296 cm^3
- (D) 396 cm^3
Section B · Written questions (38)
If n is an odd integer then show that n^2 - 1 is divisible by 8.
Using Euclid's division algorithm, find the HCF of 960 and 432.
Find the largest number which divides 438 and 606, leaving remainder 6 in each case.
Find the zeros of the polynomial 5y^2 - 13y - 6.
Verify the relation between the zeroes and the coefficient of the quadratic polynomial x^2 + 9x + 20.
Find the value of K for which (y - 1), is a factor of polynomial (2y^3 + 9y^2 + y + K)
Solve : x - y = 3, x/3 + y/2 = 6
Find the nature of roots of the quadratic equation 16x^2 - 8x + 1 = 0.
Find the values of t for which the quadratic equation 2y^2 + ty = -3 has both equal roots.
Find the sum of first 51 terms of an A.P. whose second and third terms are 14 and 18 respectively.
If 4/5, K, 2 are three consecutive terms of an A.P. then find the value of K.
If cosecA = 4/3 then find the values of cosA and tanA
Find the value : 4(sin^2 60^0 + cos^2 60^0) / (tan^2 45^0 - cos^2 90^0 + sin 90^0)
Prove that (sec^2A - 1) (1 - cosec^2A) = -1
Prove that : tan1^0.tan2^0.tan3^0 ... tan89^0 = 1
If A and B are acute angles and sinA = cosB then prove that A+B=90^0.
If 3cotA = 4, then find the value of (2cosA+sinA)/(4cosA-sinA)
Find the ratio in which the line segment joining the points A(-3, 5) and B(4, -9) is divided by P(2, -5).
If points P(a, 0), Q(0, b) and R(2, 2) are collinear then prove that 1/a + 1/b = 1/2.
In the given figure AP/PB = AQ/QC and angle APQ = angle ACB then prove that ABC is an isosceles triangle.
In triangle ABC, AD is perpendicular to BC then prove that AB^2 - BD^2 = AC^2 - CD^2.
If TA and TB are two tangents drawn from the external point T to a circle with centre at O then prove that TA = TB.
Find the area of a sector of circle of radius 28 cm and central angle 45^0.
The radius of a wheel is 50cm. How many complete revolutions does the wheel make in 20 minutes when the wheel is travelling at a speed of 66 km per hour ?
The total surface area of a cube is 726 cm^2. Find its volume.
एक बेलनाकार खंभे का वक्रपृष्ठ का क्षेत्रफल 264 मी0^2 तथा इसका आयतन 924 मी0^3 है, तो खंभे की ऊँचाई ज्ञात करें।
अच्छी प्रकार से फेंटी गई 52 पत्तो की एक गड़डी में से एक पत्ता निकाला जाता है। लाल रंग का रानी प्राप्त करने की प्रायिकता ज्ञात करें।
अंग्रेजी वर्णमाला का एक अक्षर यादृच्छया चुना जाता है, तो इसके व्यंजन अक्षर होने की प्रायिकता ज्ञात करें
निम्न वितरण से माध्यिका की गणना करें -
निम्न बंटन का माध्य ज्ञात करें -
आलेखीय विधि से हल करें : x - y = 1, 2x + 3y = 12.
The angle of elevation of the top of a building from the foot of the tower is 30^0 and the angle of elevation of the top of the tower from the foot of the building is 60^0. If the tower is 60m high, find height of the building.
Prove that if a line is drawn parallel to one side of a triangle, the other two sides are divided in the same ratio.
Show that the points (-1, -2), (1, 0), (-1, 2) and (-3, 0) are the vertices of a square.
The coach of a cricket team buys 7 bats and 6 balls for Rs. 3800. Later he buys 3 bats and 5 balls for Rs. 1750. Find the cost of each bat and each ball.
If secθ + tanθ = m then prove that sinθ = (m^2 - 1)/(m^2 + 1)
Draw a pair of tangents to a circle of radius 4 cm which are inclined to each other at an angle of 60^0.
A solid consisting of a right circular cone of height 120 cm and radius 60 cm standing on a hemisphere of radius 60 cm is placed upright in a right circular cylinder full of water such that it touches the bottom. Find the volume of water left in the cylinder, if the radius of the cylinder is 60 cm and its height is 180 cm.
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