On this page we have uploaded MBOSE HSSLC Class 12 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 12 students in its official portal www.mbose.in. Here we have published Class 12 MBOSE question paper 2022-23 for Maths subject. For more information regarding Meghalaya HSSLC Class 12, 2022 Exam Date, Exam Pattern, Time, Date, How to prepare follow our website.
Meghalaya Board (MBOSE) HSSLC Class 12 Question Papers – Maths Subject
Section – A
(1) If A = {1, 2, 3, …., 13, 14} and R is a relation on A given by R = {(x, y) : 3x – y = }. Find the range of R.
Or
Find the principal value of tan-1 (-1).
(2) Find g ° ∫, if ∫: R → R and g: R → R are given by ∫ (x) = 8x3 and g (x) = x1/3.
(3) Construct a 2×2 matrix whose elements are given by
Or
Find AB, if A = Photo and B = Photo
(4) Find the unit vector in the direction of the vector Photo
Or
Find the scalar and vector components of the vector with initial point A(2, 1) and terminal point B (-5, 7).
(5) Prove that y = ex + 1 is a solution of the differential equation y″ – y′ = 0.
(6) If y = Sin (ax + b), then find dy/dx.
Or
Prove that logarithmic function, i.e., ∫ (x) = log x is strictly increasing on (0, ∝).
(7) Evaluate:
(8) Find the slope of the tangent of the curve y = x3 – 3x + 2 at x = 2.
(9) Evaluate:
∫ Sec x(Sec x + tan x) dx
Or
Evaluate:
(10) Find the Cartesian equations of the plane Photo
(11) Given that E and are events such that P (E) = 0.6, P (F) = 0.3 and P (E ∩ F) = 0.2 Find P(E / F).
(12) Given two independent events A and B such that P (A) = 0.3 P (B) = 0.6, find P (neither A nor B).
(13) Find dy/dx if (x – y) = π.
Or
Find dx/dθ if x = α (θ – Sin θ).
(14) Find the projection of the vector on the vector
Or
Show that
(15) Find the rate of change of the area of a circle with respect to its radius r at r = 6.
(16) Write the degree and order of the following differential equation:
Choose the correct answer:
(17) The maximum value of z = 3x + 4y
Subject to the constraints
X + y ≤ 4
x ≥ 0, y ≥ 0 is
(a) 12
(b) 16
(c) 28
(d) 18
(18) Cos-1 (Cos 7π/6) is equal to
(a) 7π/6
(b) 5π/6
(c) π/3
(d) π/6
Or
If ∫ : R → R be given by ∫ (x) = (3 – x3)1/3, then f ° f (x) is
(a) x1/3
(b) x3
(c) x
(d) None of the above
(19) The derivative of cos (√x) is
(a) Sin (√x)
(b) Sin √x/2√x
(c) – cos (√x)/2√x
(d) – Sin (√x)/2√x
(20) is equal to
(a) tan x + cot x + c
(b) tan x – cot x +c
(c) tan x. cot x + c
(d) None of the above
Or
dx is equal to
(a)
(b)
(c)
(d)
Section – B
(21) Let f : N → N defined by
State whether the function f is bijective. Justify your answer.
Or
Write the following function in simplest form:
(22) If A =
then verify that A′ A = I, I is identity matrix.
Or
Find the value of x if
(23) Find the second-order derivative of x3 log x.
(24) Show that
is continuous at x = 2.
Or
Prove that the function f is given by f (x) =1| x – 1|, x ∈ R is not differentiable at x = 1.
(25) Evaluate:
Or
Evaluate:
(26) Relation R in the set Z of all integers defined as R = {(x, y): x – y is an integer}. Prove that R is reflexive as well as symmetric.
Or
Prove that the function f : R → R given by f (x) = 2x is both one – one and onto.
Section – C
(27) Find A2 – 5A + 6I, if
Or
Using properties of determinant, prove that
(28) Solve the following graphically:
Minimize z = 3x + 5y
Subject to the constraints
X + 3y ≥ 3
X + y ≥ 2
X, y ≥ 0
(29) A particle moves along the curve 6y = x3 + 2. Find the points on the curve at which the y – coordinate is changing 8 times as fast as the x – coordinate.
Or
Using differentials, find the approximate value of (26)1/3.
(30) Solve the following homogeneous differential equation:
Or
Find the general solution of the following linear differential equation:
(1 + x2) dy + 2xy dx = cot x dx (x ≠ 0)
(31)
Or
Find the vector and Cartesian equations of the line that passes through the points (3, – 2, – 5) and (3, – 2, 6).
(32) Using properties of integral calculus, prove that
Or
Evaluate ∫32 x2 dx as a limit of sum.
Section – D
(33) Solve the following system of linear equations using matrix method:
2x + 3y + 3z = 5
X – 2y + z = -4
3x – y – 2z = 3
Or
Using elementary transformation, find the inverse of the following matrix:
(34) Find the equation of the plane through the line of intersection of the planes x+ y + z = 1 and 2x + 3y + 4z = 5 which is perpendicular to x – y + z = 0.
(35) A square piece of tin of side 18 cm is to be made into a box without top by cutting a square from each corner and folding up the flaps to form the box. What should be the side of the square to be cut off so that the volume of the box is the maximum possible?
Or
Using integration, find the area of region bounded by the triangle whose vertices are (–1, 0), (1, 3) and (3, 2).
(36) There are three coins. One is a two-headed coin (having head on both faces), another is a biased coin that comes up heads 75% of the time and third is an unbiased coin. One of the three coins is chosen at random and tossed, it shows heads, what is the probability that it was the two-headed coin?
Or
A die is thrown 6 times. If ‘getting an odd number’ is a success, then what is the probability of-
(i) 5 successes;
(ii) at least 5 successes;
(iii) at most 5 successes?