On this page we have uploaded MBOSE SSLC Class 10 Question Paper for Maths released by www.mbose.in. The question paper provided here from Meghalaya State Board. Download the 2021 question paper pdf as well.
Meghalaya State Board has published subject wise question paper for this year Class 10 students in its official portal www.mbose.in. Here we have published Class 10 MBOSE question paper 2021-22 for Maths subject. For more information regarding Meghalaya SSLC Class 10 2021 Exam Date, Exam Pattern, Time, Date, How to prepare follow our website.
Meghalaya Board (MBOSE) SSLC Class 10 Question Papers – Maths Subject
(Mathematics)
Section – A
(1) Find the prime factorization of 96.
(2) Find the 5th term of the sequence an = 2n + 5.
(3) Write the discriminant of the quadratic equation
3x2 – 2x + 8 = 0.
(4) What is the area of an equilateral triangle of side ‘a’ ?
(5) In how many points does a line intersect the circle at most?
(6) Fond the area of a circle whose radius is 10.5 m. (Use π = 22/7)
(7) Evaluate:
Sin 60° cos 30° + cos 60° Sin 30°
(8) Find the class mark of class 10 – 25.
Section – B
(9) Solve the quadratic equation 3x2 – x – 2 = 0 by factorization.
(10) If A = 30°, verify that
Sin 2A = 2 Sin A Cos A
(11) Find the value of x (0° ∠x ∠90°) in tan 3x = Sin 45° Cos 45° + Sin 30°
Or
In △ ABC, right angled at B, if AB = 5, BC = 12 and AC = 13, find Sin A and tan A.
(12) Find the distance between the pair of points (–6, 7) and (–1, –5).
(13) Find the coordinates of the midpoint of the line segment joining the points P (12, -8) and Q (8, -4).
Or
Find the coordinates of the centroid of the triangle whose vertices are (8, 0), (0, 6) and (8, 12).
(14) In the figure below, AB is a common tangent to the given circles, which touch externally at P. If AP = 3·2 cm, find the length of AB:
(15) In the above figure, ABC is a triangle. D and E are the points on the sides AB and AC respectively, such that DE ∥ BC. If AD = x cm, DB = (x – 2) cm, AE = (X + 2) cm and EC = (x – 1) cm, find the value of x.
Section – C
(16) (a) When are two triangles said to be similar?
(b) Define an equilateral triangle.
(17) The two tangents drawn from an external point P to a circle with centre O are PA and PB. If ∠APB = 70°, what is the value of ∠AOB?
Or
In the figure below, AD is the bisector of ∠A in △ABC, intersecting the side BC at D. If AB = 5cm, AC = 4.2cm and DC = 2.1 cm, find BD:
(18) Find the angle subtended at the centre of a circle of radius 5 cm by an arc of length 5π/3 cm.
Or
The difference between the circumference and the radius of a circle is 37 cm. Find the area of the circle. (Use π = 22/7)
(19) A bag contains 6 red balls, 8 white balls, 5 green balls and 3 black balls. One ball is drawn at random from the bag. Find the probability that the ball drawn is-
(a) white;
(b) red or black.
(20) Find the HCF and LCM of 84, 90, 120 by applying prime factorization method.
Or
Given that HCF (306, 657) = 9, find the LCM of 306 and 657.
(21) Which term in the A.P. 68, 64, 60, ….. is –8 ?
Or
Find the sum of 100 terms of the A.P. 2, 4, 6, ….. .
(22) Find a quadratic polynomial whose zeroes are –5 and –7.
(23) Evaluate:
4/Cot230 ° + 1/Sin230° – 2Cos245°-sin20°
Or
If tan (A – B) = 1/√3 and tan (A + B) = √3, 0° ∠(A + B) ∠90° and A > B, find A and B.
Section – D
(24) The sum of two numbers is 16. The sum of their reciprocals is 1/3. Find the numbers.
Or
The sum of the numerator and denominator of a fraction is 12. If the denominator is increased by 3, the fraction becomes 1/2. Find the fraction.
(25) (a) The value of cot90° = _____.
(b) If Cos θ = 1, then θ = 0°
(c) Write down the relation between sin θ, cos θ and tan θ.
(26) Find the coordinates of the point, which divides the join of A (–1, 7) and B (4, – 3) in the ratio 2 : 3.
Or
If the points (2, 1) and (1, – 2) are equidistant from the point (x, y), Prove that x + 3y = 0.
(27) (a) Define a right triangle.
(b) The length of the diagonal of a square of side ‘a’ is _____.
Section – E
(28) Solve the following system of linear equations:
2x + y = 7
4x – 3y + 1 = 0
(29) If the total surface area of a solid hemisphere is 462 cm2, find its volume. (Use π = 22/7)
Or
A cone of height 20 cm and radius of base 5 cm is made up of modelling clay. A child reshapes it in the form of a sphere. Find the diameter of the sphere.
(30) Find the mean of the following data:
Marks |
0 – 10 | 10 – 20 | 20 – 30 | 30 – 40 | 40 – 50 | 50 – 60 |
Number of Students | 12 | 18 | 27 | 20 | 17 |
6 |
Or
Find the mode of the following frequency distribution:
Class Interval |
10 – 15 | 15 – 20 | 20 – 25 | 25 – 30 | 30 – 35 | 35 – 40 |
Frequency | 30 | 45 | 75 | 35 | 25 |
15 |
Section – F
(31) Answer the following as directed (any eight) :
(a) The common difference of the A.P. 4, 1, –2, –5, ….. is
(A) 3
(B) –3
(C) 4
(D) 2
(b) Every composite number can be expressed as a product of
(A) primes
(B) coprimes
(C) twin primes
(D) None of the above
(c) In which quadrant does the point (–2, 6) lie?
(A) 1st quadrant
(B) 2nd quadrant
(C) 3rd quadrant
(D) 4th quadrant
(d) The area of a circle with radius ‘r’ is
(A) πr2 square units
(B) 2 πr2 square units
(C) 1/2 πr2 square units
(D) 3 πr2 square units
(e) Define constant polynomial.
(f) If the polynomial ax2 + bx + c is a perfect square, then b2 = 4ac. (State whether True or False)
(g) What is the degree of a cubic polynomial?
(h) Find the circumference of a circle whose radius is 10.5 m. (Use π = 22/7)
(i) How many tangents can be drawn to a circle from a point outside the circle?
(j) Each quadratic equation has at most two roots. (State whether True or False)
(k) Write the value of sec 60 °.
(l) The total surface area of a right circular cylinder of radius ‘r’ and height ‘h’ is _____. (Fill in the blank)
(m) A polynomial having _____ terms is called binomial. ( Fill in the blank )
(n) π is an irrational number. (State whether True or False)
(32) Answer any six from the following:
(a) Express 0·125 as a rational number.
(b) Find the zeroes of the polynomial x2 – 2x – 3.
(c) Find the distance between the pair of points ( , 0) a and (0, ) b .
(d) A chord of a circle of radius 14 cm subtends a right angle at the centre. What is the area of the minor sector? (Use π = 22/7)
(e) A die is thrown once. What is the probability of getting a number other than 4?
(f) The difference between two numbers is 26 and one number is three times the other. Find the numbers.
(g) Find the coordinates of the midpoint of the line segment joining the points P(7, 0) and Q(–5, 4).
(h) Find the sum of the first 100 natural numbers.
(i) Find the value of x (0° ∠ x ∠90°) in 2Cos 3x = 1.
(j) If α, β are zeroes of the polynomial P(x) = 3x2 – 2x – 6, then find 1/α + 1/β.
(k) 1 is a=Determine the value of ‘k’ for which x = 1 is a solution of the equation x2 + kx + 3 = 0.