On this page we have uploaded UBSE Intermediate Class 12 Question Paper for Maths released by ubse.uk.gov.in. The question paper provided here from Uttarakhand State Board. Download the 2023 question paper pdf as well.
Uttarakhand State Board has published subject wise question paper for this year Class 12 students in its official portal ubse.uk.gov.in. Here we have published Class 12 UBSE question paper 2023 for Maths subject. For more information regarding Uttarakhand Intermediate Class 12, 2023 Exam Date, Exam Pattern, Time, Date, How to prepare follow our website.
Uttarakhand Board (UBSE) Intermediate Class 12 Question Papers – Maths Subject
(1) (a) Principal value of Cos-1 (1/√2) is-
(i) 3π/4
(ii) π/4
(iii) -π/4
(iv) π/3
(b) Matrices A and B will, be inverse of each other only if-
(i) AB = BA
(ii) AB = BA = 0
(iii) AB = 0, BA = I
(iv) AB = BA = I
(c) Differentiation of Sin (x2) with respect to ‘x’ is-
(i) Cos (x2)
(ii) 2x Sin (x2)
(iii) 2x Cos (x2)
(iv) Cos (2x)
(d) If f (a + b – x) = f (x), then ∫ba × f(x) dx is equal to-
(i) 0
(ii) a + b/2 ∫ba f (b + x) dx
(iii) b – a/2 ∫ba f (x) dx
(iv) a + b/2 ∫ba f (x) dx
(e) The order of the differential equation Photo is:
(i) 2
(ii) 1
(iii) 0
(iv) 3
(f) Direction cosines of the vector a = î + ĵ – 2k̂ are-
(i) (1/6, 1/6, -2/6)
(ii) (1, 1, -2)
(iii) (√6, √6, -2√6)
(iv) (1/√6, 1/√6, -2/√6)
(g) The Cartesian equation of the plane r. (î + ĵ – k̂) = 2 is
(i) x + y – z = 0
(ii) x + y – z = 2
(iii) x + y – z = 1
(iv) x + y + z + 2 = 0
(h) If A and B are independent events, where probabilities P (A) = 0.3 and P (B) = 0.6, then value of P (A ∩ B) will be-
(i) 1
(ii) 0.18
(iii) 0.9
(iv) 0.01
(2) Find the value of Cos (Sec-1 x + Cosec-1 x), |x|≥1.
(3) If a matrix has 14 elements, what are the possible orders it can have?
(4) Find dy/dx, if y + Siny = Cosx.
(5) The total revenue in Rupees received from the sale of x units of a product is given by R (x) = 3×2 + 36x + 5. Find the marginal revenue when x = 15.
(6) Integrate the function tan-1 x/1 + x2 with respect to ‘X’.
(7) Find the integral:
∫ (4e3x + 2) dx.
(8) If a = 2î -3ĵ + k̂ and b = 3î -3ĵ + 3k̂, then calculate a. B.
(9) Find the equation of a line parallel to X – axis and passing through the origin.
(10) In a set rational numbers Q, a binary operation ‘×’ is defined as follows:
a × b = a + ab; a, b ∈ Q
Show that ‘×’ is neither commutative nor associative.
Or
Show that the relation R in set of real numbers R defined as R = {(a, b): a ≤b}, is reflexive and transitive.
(11) Find the intervals in which the function f given by f (x) = 2x3 – 3x2 – 36x is increasing.
(12) Evaluate
(13) Find the angle between the two planes 3x – 6y + 2z = 10 and 2x + 2y – 2z = 15.
(14) In a box containing 100 bulbs, 10 are defective. What is the probability that out of a sample of 5 bulbs, none is defective?
(15) Consider the function f: R → R given by f (x) = 4x + 3. Show that f is invertible. Find the inverse function of f.
Or
Prove that-
tan-1 (√1 + x – √1 – x/√1 + x + √1 – x) = π/4 – 1/2 Cos-1x; -1/√2 ≤x ≤1.
(16) For what value of x , [1 2 1] = 0?
(17) If x = a (Cos t + t sin t) and y = a (Sin t – t Cos t), find d2y/dx2.
(18) Evaluate
Or
(19) If a = î + ĵ + k̂ and b = 2î + ĵ + 3k̂ then find the value of 2 a – b and |a × b|.
(20) Find the shortest distance the lines r = (î + ĵ) + λ (2î – ĵ + k̂) and r = (2î + ĵ – k̂) + µ (3î – 5ĵ + 2k̂).
Or
Find the coordinates of the point where the line through and A(3, 4, r) and B(5, 1, 6) crosses the XY – Plane.
(21) Solve the following system of liner equations, using matrix method-
X + y + z = 6
X + 3z = 11
X – 2y + z = 0
(22) Show that the altitude of the right circular cone of maximum volume that can be inscribed in a sphere of radius r is 4r/3.
Or
Find the equations of the tangent and normal to the parabola Y2 = 4ax at the point (at2, 2at).
(23) Find the area of the smaller region bounded by the ellipse x2/9 + y2/4 = 1 and the line 2x + 3y = 6.
(24) Find the Particular solution of the differential equation (x + y) dy + (x – y) dx = 0, given that Y = 1 when x = 1.
Or
Find a particular solution of the differential equation dy/dx + Y Cot x = 4x Cosec x (x ≠ 0), given that Y = 0 when x = π/2.
(25) By graphical method, minimize and maximize Z = 60x + 40y under the following Constraints:
X + 2y ≤ 12
2x + y ≤ 12
4x + 5y ≥ 20
X, Y ≥ 0
(26) A manufacturer has three machine operators A, B and C. The first operator A produces 4% defective items, where as the other two operators B and C produces 5% and 7% defective items respectively. A is on the job for 50% of the time, B is on the job for 30% of the time and C is on the job for 20% of the time. A defective item is produced, what is the probability that it was produced by B?
Or
Find the probability distribution of number of doublets in three throws of a pair of dice.