Bihar Board Class 10 · Maths · Matric exam 2027
Bihar Board Class 10 Maths Model Paper 2021
The board’s 2021 model paper — all 138 questions as printed. Each question names its chapter, where that chapter’s most-asked questions are.
Section A · Objective questions (100)
The simplest form of 92/115 is
- (A) 46/23
- (B) 4/5
- (C) 3/5
- (D) 3/4
How many maximum rational numbers can be possible between two rational numbers ?
- (A) 1
- (B) 2
- (C) 3
- (D) infinite
Which of the following has terminating decimal expansion ?
- (A) 7/88
- (B) 13/210
- (C) 15/1600
- (D) 17/110
The product of the zeroes of the polynomial dy^2 + by + a will be
- (A) -a/d
- (B) d/a
- (C) -d/a
- (D) a/d
The rationalising factor of sqrt(18) is -
- (A) sqrt(3)
- (B) sqrt(2)
- (C) sqrt(6)
- (D) sqrt(18)
The smallest prime number is -
- (A) 3
- (B) 2
- (C) 1
- (D) 0
If a = bq + r, where a and b are positive integers, then
- (A) r > b
- (B) r < 0
- (C) r < b
- (D) None of these
Which of the following is a rational number ?
- (A) 4 + sqrt(3)
- (B) sqrt(7)
- (C) sqrt(8)
- (D) (6*sqrt(5))/sqrt(5)
The zeroes of the quadratic polynomial x^2 + 12x + 35 are -
- (A) both positive
- (B) both negative
- (C) both equal
- (D) one positive and one negative
Which of the following is an irrational number ?
- (A) sqrt(121)
- (B) sqrt(196)
- (C) sqrt(27)
- (D) sqrt(289)
The zeroes of the polynomial (5y^2 - 25) are -
- (A) 5, -5
- (B) sqrt(5), -5
- (C) sqrt(5), -sqrt(5)
- (D) sqrt(5), sqrt(5)
The sum and product of the zeroes of a quadratic polynomial are 3 and -40 respectively then the quadratic polynomial is -
- (A) x^2 - 3x - 40
- (B) x^2 - 3x + 40
- (C) x^2 + 3x - 40
- (D) x^2 + 3x + 40
The pair of the equations x + 2y = 4 and 2x + 4y = 8 has
- (A) one solution
- (B) two solutions
- (C) no solution
- (D) infinitely many solutions
If zeroes of the polynomial x^2 + ax - b are reciprocal to each other, then the value of b will be -
- (A) 1
- (B) -1
- (C) 0
- (D) a^2
The angle of the semicircle is
- (A) 60^0
- (B) 45^0
- (C) 90^0
- (D) 30^0
The quadratic equation ax^2 + bx + c = 0 where a!=0, has no real roots, if
- (A) b^2 - 4ac > 0
- (B) b^2 != 4ac
- (C) b^2 - 4ac = 0
- (D) b^2 - 4ac < 0
If alpha and beta are the roots of the equation 2x^2 - x - 6 = 0, then (1/alpha + 1/beta) =
- (A) 6
- (B) -6
- (C) 1/6
- (D) -1/6
The 21st term of the A. P. : -3, 4, 11, 18 ......... is
- (A) 143
- (B) -143
- (C) 127
- (D) 137
Which of the following is a quadratic equation ?
- (A) x^3 - x^2 = (x-1)^3
- (B) x^2 - 4sqrt(x) + 14 = 0
- (C) x + 1/x = x^2
- (D) x^2 + 1/x^2 = 5
Which term of the A. P. 80, 76, 72, 68, ........ is 0 ?
- (A) 20th
- (B) 21st
- (C) 22nd
- (D) 23rd
If general term of an A. P. is 6 - 4n, then its common difference will be
- (A) 6
- (B) 4
- (C) -4
- (D) 2
Which of the following is an A. P. ?
- (A) -2, 4, -6, 8 .......
- (B) a, a^2, a^3, a^4, .......
- (C) 3/2, 1/2, -1/2, -3/2, .......
- (D) 1, 3, 9, 27, .......
The co-ordinates of the origin are -
- (A) (-1, -1)
- (B) (1, 1)
- (C) (-1, 0)
- (D) (0, 0)
If triangle ABC ~ triangle PQR and QR/BC = 2/3 then area(triangle PQR) / area(triangle ABC) =
- (A) 4/9
- (B) 2/3
- (C) 9/4
- (D) 3/2
In the given figure, the value fo x is -
- (A) 110^0
- (B) 60^0
- (C) 70^0
- (D) 35^0
The co-ordinates of the mid-point of the line segment joining the points R(0, 6) and S(8, 0) are -
- (A) (0, 0)
- (B) (0, 8)
- (C) (8, 16)
- (D) (4, 3)
The distance between the points (4, 6) and (8, 2) is -
- (A) 4sqrt(2) units
- (B) 6sqrt(2) units
- (C) 8sqrt(2) units
- (D) sqrt(2) units
Sin^2 60^0 + cos^2 60^0 =
- (A) 2
- (B) 3
- (C) 1
- (D) 0
If a pair of linear equations is consistent, then the lines will be -
- (A) always coincident
- (B) parallel
- (C) always intersecting
- (D) intersecting or coincident
In which quadrant does the point (-6, -5/2 ) lie ?
- (A) first
- (B) second
- (C) third
- (D) fourth
In ΔPQR, side QR is extended to a point S such that ∠PRS = 120^0 and ∠QPR = 63^0 then ∠PQR =
- (A) 63^0
- (B) 57^0
- (C) 60^0
- (D) 67^0
If the bisector of an angle of a triangle bisects the opposite side, then the triangle will be -
- (A) isosceles
- (B) equilateral
- (C) scalene
- (D) right-angled
In ΔABC, DE || BC and AD/DB = 2/3 then the value of AE/EC will be -
- (A) 3/5
- (B) 2/3
- (C) 3/2
- (D) 2/5
If in triangle ABC and DEF, AB/DE = BC/FD then they will be similar, when
- (A) ∠A = ∠F
- (B) ∠B = ∠E
- (C) ∠B = ∠D
- (D) ∠A = ∠D
In the given figure PQ is a tangent to a circle with centre at O. If OQ = 3 cm, PQ = 4 cm then OP =
- (A) 4 cm
- (B) 6 cm
- (C) 5 cm
- (D) 7 cm
The distance of the point P(8, 12) from the x-axis is -
- (A) 8 units
- (B) 12 units
- (C) 20 units
- (D) sqrt(208) units
The angle between tangent at a point on a circle and the radius through the point is -
- (A) 45^0
- (B) 60^0
- (C) 90^0
- (D) 120^0
In the given figure TP and TQ are the two tangents to the circle with centre O if angle PTQ = 50^0 then angle POQ =
- (A) 130^0
- (B) 25^0
- (C) 45^0
- (D) 50^0
In the given right triangle PQR, angle PRQ = theta, PQ = 3 cm, and PR = 6 cm then theta =
- (A) 30^0
- (B) 60^0
- (C) 45^0
- (D) 75^0
If tanA = 3/4, then the value of cosA is -
- (A) 3/5
- (B) 4/5
- (C) 5/4
- (D) 5/3
(cot 44^0)/(tan 46^0) =
- (A) 1/2
- (B) 0
- (C) -1
- (D) 1
Which of the following has the maximum value ?
- (A) tan45^0
- (B) sin45^0
- (C) sin30^0
- (D) cos90^0
If the circumference of a circle is 88 cm. then its radius is -
- (A) 7 cm
- (B) 14 cm
- (C) 21 cm
- (D) 28 cm
If triangle PQR is right angled at R, then the value of sin (P + Q) is -
- (A) 0
- (B) 1
- (C) -1
- (D) 1/3
If alpha/4 = 15^0 then sqrt(3)cosec alpha =
- (A) sqrt(3)/2
- (B) 2
- (C) 3
- (D) 1/3
If the sum of the areas of two circles with radii r_1 and r_2 is equal to the area of a circle of radius r, then
- (A) r = r_1 + r_2
- (B) r_1^2 + r_2^2 < r^2
- (C) r_1^2 + r_2^2 = r^2
- (D) r_1 + r_2 < r
sin (90^0 - A) =
- (A) sinA
- (B) tanA
- (C) secA
- (D) cosA
A ladder 15 m long just reaches the top of a vertical wall. If the ladder makes an angle of 60^0 with the wall, then height of the wall is -
- (A) 15 m
- (B) 7.5 m
- (C) 5 m
- (D) 30 m
The value of Cot 1^0 . Cot 89^0 is -
- (A) 1
- (B) 0
- (C) 2
- (D) 1/2
The total surface area of a sphere with radius r is -
- (A) pi r^2 sq. units
- (B) 2pi r^2 sq. units
- (C) 3pi r^2 sq. units
- (D) 4pi r^2 sq. units
If the mean of 6, 8, 9, x and 13 is 10, then the value of x will be -
- (A) 13
- (B) 12
- (C) 15
- (D) 14
If the height and radius of the cone are doubled, the volume of the cone will be -
- (A) 2 times
- (B) 4 times
- (C) 6 times
- (D) 8 times
For the following distribution - The lower limit of the modal class is
- (A) 15
- (B) 22
- (C) 20
- (D) 35
Which of the following can not be determined graphically ?
- (A) mean
- (B) median
- (C) mode
- (D) none of these
The volumes of two cubes are in the ratio 1 : 27, then the ratio of their edges is -
- (A) 1 : 9
- (B) 9 : 1
- (C) 1 : 3
- (D) 3 : 1
If tan theta = 1 then the value of theta will be -
- (A) 30^0
- (B) 45^0
- (C) 90^0
- (D) 60^0
The area of an equilateral triangle with side x is -
- (A) x^2 sq. units
- (B) sqrt(3)/4 x^2 sq. units
- (C) sqrt(3)/2 x^2 sq. units
- (D) sqrt(3)/4 x sq. units
A card is drawn at random from a well-shuffled deck of 52 playing cards. The probability of getting a queen is -
- (A) 1/26
- (B) 2/39
- (C) 5/39
- (D) 1/13
If P(E) = 0.08 then P(E') is equal to
- (A) 0.92
- (B) 0.02
- (C) 0.08
- (D) 0.52
(1 + tan^2θ) / (1 + cot^2θ) =
- (A) tan^2θ
- (B) sec^2θ
- (C) cot^2θ
- (D) -1
0.5(bar) =
- (A) 5/9
- (B) 1/2
- (C) 5/90
- (D) 5/3
The degree of the polynomial 2x^2 + 5x - 12 is -
- (A) 1
- (B) 2
- (C) 0
- (D) 3
sqrt(7) is -
- (A) a rational number
- (B) an irrational number
- (C) a natural number
- (D) none of these
x(x^2 + 2x) =
- (A) x^3 + 2x^2
- (B) x^2 + 2x
- (C) x^3
- (D) 1 + 2x^2
The HCF of 28 and 72 is -
- (A) 28
- (B) 1
- (C) 4
- (D) 2
The sum of the zeroes of the polynomial x^2 - x + 1 will be -
- (A) 1
- (B) -1
- (C) 0
- (D) 2
(sqrt(2))^2 - 2 =
- (A) sqrt(2)
- (B) 0
- (C) 2
- (D) 2sqrt(2)
Solutions of x + y = 3 and 3x - 2y = 4 are -
- (A) x = 2, y = 1
- (B) x = 1, y = 2
- (C) x = -1, y = 4
- (D) x = -1, y = -2
If alpha and beta are zeroes of the polynomial y^2 - y - 6 then alpha.beta =
- (A) 6
- (B) -6
- (C) 1
- (D) -1
The discriminant of the quadratic equation x^2 - 5x - 300 = 0 will be -
- (A) 1225
- (B) 1500
- (C) -1225
- (D) 1325
The common difference of the A.P. sqrt(18), sqrt(50), sqrt(98), sqrt(162) ....... is -
- (A) 2
- (B) 2sqrt(2)
- (C) 3
- (D) 2sqrt(3)
If y^2 + 1/y^2 = 14 then y + 1/y =
- (A) 16
- (B) 12
- (C) 8
- (D) +-4
If the nth term of an A.P. is 6n - 2 then the first term will be -
- (A) 2
- (B) 4
- (C) -2
- (D) 10
The ordinate of the point (-6, 10) is -
- (A) -6
- (B) 10
- (C) 4
- (D) -16
sec^2A - tan^2A =
- (A) 0
- (B) 1
- (C) -1
- (D) 2
If x, y, z are in A.P. then y =
- (A) (z - x) / 2
- (B) (z + x) / 2
- (C) x + z
- (D) (x + z) / 3
sinA x cosec A =
- (A) 1
- (B) 0
- (C) -1
- (D) 2
The area of the triangle formed by points A(6, 0), B(14, 0) and C(16, 8) is -
- (A) 32 sq. units
- (B) 16 sq. units
- (C) 44 sq. units
- (D) 64 sq. units
cot(90^0 - theta) =
- (A) cot(theta)
- (B) tan(theta)
- (C) cosec(theta)
- (D) sec(theta)
If the coordinates of the vertices of the triangle are (x1, y1), (x2, y2) and (x3, y3) then the coordinates of the centroid will be -
- (A) ((x1+x2+x3)/2, (y1+y2+y3)/2)
- (B) ((x1+x2+x3)/3, (y1+y2+y3)/3)
- (C) ((x1-x2-x3)/3, (y1-y2-y3)/3)
- (D) (x1 + x2 + x3, y1 + y2 + y3)
sin20° - cos70° =
- (A) 1
- (B) 0
- (C) 2sin20°
- (D) 2cos70°
(1 - cos^4A) =
- (A) sin^2A(1+sin^2A)
- (B) sin^2A(1-sin^2A)
- (C) cos^2A(1 - cos^2A)
- (D) sin^2A(1 + cos^2A)
If sqrt(2)cosθ = 1 then the value of θ is -
- (A) 30°
- (B) 45°
- (C) 60°
- (D) 90°
If tanθ = p/q then (cosθ + sinθ) / (cosθ - sinθ) =
- (A) (p + q) / (p - q)
- (B) (q + p) / (q - p)
- (C) (q - p) / (q + p)
- (D) (p - q) / (p + q)
If secA = 25/7 then sinA =
- (A) 24/25
- (B) 7/24
- (C) 7/25
- (D) 25/24
tan^2 45° - 1 =
- (A) 1
- (B) 0
- (C) -1
- (D) 1/2
(1 + tan^2A) / sec^2A =
- (A) sin^2A
- (B) 0
- (C) 1
- (D) -1
In Δ ABC, D and E are points on the sides AB and AC respectively such that DE || BC. If AD/DB = 4/5 and AC = 18 cm. then AE =
- (A) 6 cm
- (B) 8 cm
- (C) 10 cm
- (D) 12 cm
An unbiased die is thrown then the probability of getting a prime number is -
- (A) 1
- (B) 1/2
- (C) 1/3
- (D) 1/4
If the ratio of the areas of two circles is 4 : 25 then the ratio of their radii will be -
- (A) 3 : 5
- (B) 5 : 2
- (C) 1 : 5
- (D) 2 : 5
A card is drawn at random from a well shuffled deck of playing cards, then the probability of getting a red face card is -
- (A) 1/26
- (B) 2/13
- (C) 3/13
- (D) 3/26
If the mean and median of a distribution are respectively 4.6 and 4.8 then mode =
- (A) 5
- (B) 5.1
- (C) 5.2
- (D) 5.3
The median of the observations 8, 12, 7, 14, 6, 13, 15 will be -
- (A) 9
- (B) 10
- (C) 11
- (D) 12
The difference of three times of median and two times of mean is equal to -
- (A) mean
- (B) median
- (C) mode
- (D) none of these
Angle subtended by minute hand of a watch in 1 minute is -
- (A) 30^0
- (B) 15^0
- (C) 12^0
- (D) 6^0
The volume of a right circular cylinder whose radius of the base is r and height be h is
- (A) 1/3 pi r^2h cubic units
- (B) 2/3 pi r^2h cubic units
- (C) 1/3 pi r^2h^2 cubic units
- (D) pi r^2h cubic units
In an equilateral triangle ABC, if AD perpendicular BC then AD^2 =
- (A) 3CD^2
- (B) 4CD^2
- (C) 3/2 DC^2
- (D) CD^2
The curved surface area of a hemisphere with radius r is
- (A) pi r^2 sq. units
- (B) pi r^2/2 sq. units
- (C) 2 pi r^2
- (D) 3 pi r^2 sq. units
In the given figure, O is the centre of a circle and angle AOC = 130^0. Then angle OAC =
- (A) 65^0
- (B) 50^0
- (C) 130^0
- (D) none of these
Tally mark of 14 is -
- (A) XIV
- (B) |||| |||| |||
- (C) |||| |||| |||
- (D) |||| |||| ||||
Section B · Written questions (38)
Find the L.C.M. of the numbers 72 and 120 by prime factorisation method.
Prove that 3 root 2 is an irrational number.
Divide 2y^2 + 3y + 1 by y + 2.
If alpha and beta are the zeroes of the polynomial g(x) = x^2 - 7x + 6, then find the value of alpha + beta.
Find the zeroes of the polynomial x^2 - 7 and verify the relation between the zeroes and the co-efficients.
Find the value of K for which the equation x^2 - 8x + k = 0 has real and equal roots.
Solve the quadratic equation 9x^2 - 12x + 4 = 0.
Find the sum of the first 20 terms of the A. P. 2, 5, 8, 11, ...........
Find the common difference of an A.P. whose 11th term is 38 and 16th term is 73.
Find the value of p, if the point A(0, 2) is equidistant from point (3, p) and (p, 5).
Find the coordinates of the point dividing the line segment PQ joining P(1, -2) and Q(-3, 4) internally in the ratio 1 : 2.
The diagonals AC and BD of a trapezium ABCD intersect each other at O where AB || DC. show that triangle DOC and triangle AOB are similar.
सिद्ध करें कि त्रिज्या के बराबर जीवा वृत्त के केन्द्र पर 60^0 का कोण बनाती है।
यदि tanA = 1, तो सिद्ध करें कि 2sinAcosA = 1.
2(sin^2 45^0 + cos^2 45^0) / (tan^2 30^0 + cos^2 90^0) का मान ज्ञात करें।
सिद्ध करें कि sec^4A - sec^2A = tan^2A + tan^4A
दो वृत्तों की त्रिज्याएँ क्रमश: 19 सेमी0 और 9 सेमी0 हैं। उस वृत्त की त्रिज्या ज्ञात करें जिसकी परिधि इन दोनों वृत्तों की परिधियों के योग के बराबर है।
यदि sinθ = 4/5 तो (4 + 4sinθ) / (1 + cosθ) का मान ज्ञात करें।
यदि cosec4θ = sec(θ - 20^0), जहाँ 4θ एक न्यून कोण है, तो θ का मान ज्ञात करें।
एक बेलन की त्रिज्या तथा ऊँचाई क्रमश: 4 मी0 तथा 14 मी0 है, तो बेलन का आयतन ज्ञात करें।
एक समबाहु त्रिभुज की भुजा 12 सेमी0 है तो इसका क्षेत्रफल ज्ञात करे।
निम्न वितरण से माध्य की गणना करें -
घनाभ का पार्श्व पृष्ठीय क्षेत्रफल ज्ञात करें, जो 6 मी0 लंबा, 4 मी0 चौड़ा और 2 मी0 ऊँचा है।
अंग्रेजी वर्णमाला का एक अक्षर यादृच्छया चुना जाता है, तो इसके स्वर अक्षर होने की प्रायिकता ज्ञात करें।
दो संख्याओं 16 तथा 28 का ल0 स0 112 है। तो इनका म0 स0 ज्ञात करें।
30 बल्बों के एक समूह में 5 बल्ब खराब है। इस समूह में से एक बल्ब यादृच्छया निकाला जाता है। निकाले गए बल्ब के खराब होने की प्रायिकता ज्ञात करें।
समकोण त्रिभुज ABC में <C = 90^0 तथा CD perpendicular AB है, तो सिद्ध करें कि AB x CD = BC x CA
हल करें :- 2x + 3y = 11 और 2x - 4y = -24
सिद्ध करें कि sqrt((1 + cosA) / (1 - cosA)) = cosecA + cotA
52 पत्तों की अच्छी प्रकार से फेंटी गई एक गड्डी में से एक पत्ता निकाला जाता है। लाल रंग का बादशाह प्राप्त करने की प्रायिकता ज्ञात करें।
ग्राफीय विधि से हल करें - 5x - 3y - 7 = 0, x + 4y - 6 = 0
सिद्ध करें कि दो समरूप त्रिभुजों के क्षेत्रफलों का अनुपात उनकी संगत भुजाओं के वर्गों के अनुपात के बराबर होता है।
सिद्ध करें कि (sin theta + cos theta)/(sin theta - cos theta) + (sin theta - cos theta)/(sin theta + cos theta) = 2/(1 - 2cos^2 theta)
24 सेमी0 व्यास वाले एक लंबवृत्तीय बेलनाकार बर्तन में कुछ पानी है। इसमें 60 शंक्वाकार ठोस लोहे के कुछ टुकड़े इस प्रकार डाले गए कि यह पानी में पूरी तरह डूब गए जबकि प्रत्येक के आधार की त्रिज्या 3 सेमी0 तथा ऊँचाई 0.04 मी0 है। पानी के स्तर में हुई वृद्धि ज्ञात कीजिए।
भूमि के एक बिन्दु से एक 20 मी0 ऊँचे भवन के शिखर पर लगी एक संचार मीनार के तल एवं शिखर के उन्नयन कोण क्रमशः 45^0 और 60^0 हैं। संचार मीनार की ऊँचाई ज्ञात करें।
दो संख्याओं के वर्गों का अन्तर 45 है। छोटी संख्या का वर्ग बड़ी संख्या की 4 गुनी है। दोनों संख्याओं को ज्ञात करें।
7.6 सेमी0 लंबाई का एक रेखाखण्ड खींचें। इस रेखाखण्ड पर एक ऐसा बिन्दु A ज्ञात करें जो इस रेखाखण्ड को 5 : 8 के अनुपात में बाँटे।
अकबर और रोहन की मासिक आय का अनुपात 9 : 7 है और इनके खर्चों का अनुपात 4 : 3 है। यदि प्रत्येक व्यक्ति प्रति महीने में ₹5000 बचा लेते हैं, तो उनकी मासिक आय ज्ञात करें।
The same preparation, with Medha Ma’am — on your phone
Every question of every chapter with its model answer, practice questions in the board’s own shapes, 60 minutes of class a day, written answers marked, a test every Sunday and a WhatsApp report to parents.
Medha Ma’am is an AI teacher, not a live tutor. Every answer is checked twice; a person takes responsibility.