On this page we have uploaded MBOSE HSSLC Class 11 Question Paper for Maths released by www.mbose.in. The question paper provided here from Meghalaya State Board. Download the 2022 question paper pdf as well.
Meghalaya State Board has published subject wise question paper for this year Class 11 students in its official portal www.mbose.in. Here we have published Class 11 MBOSE question paper 2022-23 for Maths subject. For more information regarding Meghalaya HSSLC Class 11 2022 Exam Date, Exam Pattern, Time, Date, How to prepare follow our website.
Meghalaya Board (MBOSE) HSSLC Class 11 Question Papers – Maths Subject
Class XI (Mathematics)
Question Paper 2022
Section – A
(1) Write the set in the set-builder form {1, 4, 9, ……, 100}.
(2) Write the set {x : x ∈ R, – 4 < x ≤ 6} as interval.
(3) If A = {3, 6, 9, 12, 15, 18, 21}
B = {4, 8 12, 16, 20}
Find (i) A ∩ B and (ii) A – B
(4) Find the modulus of the complex number – 2 + √5i
(5) Solve 3x + 8 > 2 when x is an integer
(6) If nC8 = nC2, Find nC2
7.) Find the slope of the straight line parallel to the straight line passing through the points (–2, 3) and (8, –5).
8.) Find the equation of a circle with centre (–2, 3) and radius 4.
9.) If the set of natural numbers is the universal set, then find the complement of the set
{ x : x is a prime number }
10.) Find the radian measure of 240 °
11.) Write the contrapositive and converse of the statement.
“If x is a prime number, then x is odd.”
12.) Write the following statement in the form “if–then”
“A quadrilateral is a parallelogram if its diagonals bisect each other.”
(13) Find the median of the data 6, 7, 10, 12, 13, 4, 8 12
(14) Write the general term in the expansion of (x2 – y)6
(15) If the set A has 3 elements and the set B = {3, 4, 5}, then find the number of elements in A × B.
(16) Find the domain and range of the relation R defined by
R = {(x, x + 5) : x ∈ {0, 1, 2, 3, 4, 5}}
(17) Find the nth term of the series
3 × 12 + 5 × 22 + 7 × 32 ……..
(19) How many 3 digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming the repetition of the digits is allowed?
(20) If E an F are events such that P (E) = 1/4, P (F) = 1/2 and P (E∩F) = 1/8 find P (E or F).
Section – B
(21) Prove that
cos (π/4 – x) cos (π/4 – y) – sin (π/4 – x) sin (π/4 – y) = sin (x + y)
(22) Express the complex number
(1/3 + 3i)3 in the form a + ib
(23) Show that the points P (-2, 3, 5), Q (1, 2, 3) and R (7, 0, -1) are collinear.
(24) Find the sum of odd integers from 1 to 2001.
(25) Find the co-ordinates of the focus, the vertex, the axis the length of the latus rectum of the parabola y2 = 12x
(26) One card is drawn from a well shuffled deck of 52 cards. If each outcome is equally likely, calculate the probability that the card will be
(i) not an ace
(ii) not a black card.
Section – C
(27) Prove that
2cos π/13 cos 9π/13 + cos 3π/13 + cos 5π/13 = 0
Or
Prove that
cos4x + cos3x + cos2x/sin4x + sin3x + sin2x = cot2x
(28) The sum of first three terms of a G.P. is 16 and the sum of next three terms is 128. Determine the first term and the sum of n terms of the G.P.
Or
Find the sum to n term of the series whose nth term is given by n2 + 2n.
(29) Convert the complex number –1–i into polar form.
Or
In how many ways one can select a cricket team of eleven players from 17 players in which only 5 bowlers can bowl if each cricket team of 11 must include exactly 4 bowlers.
(30) Find the equation of the hyperbola whose foci are (±5, 0) and the transverse axis is of length 8 units.
Or
Find the equation of the ellipse with foci (±5, 0) and the length of major axis is 26 units.
(31) Find the general solution of the equation cos4x = cos2x
(32) Find the derivative of sinx + cosx/sinx – cosx
Section – D
(33) Using the principle of mathematical induction prove that 1/2 + 1/4 + 1/8 + ……. + 1/2n = 1 – 1/2n.
(34) Solve the system of inequations graphically
3x + 4y ≤ 60, x + 3y ≤ 30, x ≥ 0, y ≥ 0
Or
Find (x + 1)6 + (x – 1)6. Hence or otherwise evaluate (√2 + 1)6 + (√2 – 1)6
(35) In a survey it was found that 21 people liked product A, 26 liked product B and 29 liked product C. If 14 people liked products A and B, 12 people liked products C and A, 14 people liked products B and C and 8 liked all the three products. Find how many liked products C only.
(36) Calculate the mean, variance and standard deviation for the following distribution.
Class | 30 – 40 | 40 – 50 | 50 – 60 | 60 – 70 | 70 – 80 | 80 – 90 | 90 – 100 |
Frequency | 3 | 7 | 12 | 15 | 8 | 3 | 2 |
The diameters of circles (in mm) drawn in a design are given below.
Diameters | 33 – 36 | 37 – 40 | 41 – 44 | 45 – 48 | 49 – 52 |
No. of circles | 15 | 17 | 21 | 22 | 25 |
Calculate the standard deviation and the mean diameter of the circle.