KSEEB Model Questions Class 12 Mathematics | II PUC Math Model Paper 2023 – 24

KSEEB Model Question Papers For Class 12 Mathematics

2nd PUC is the final school level exam conducted by KSEEB in which lakhs of students appear every year. It is one of the competitive public exam where students are expected to perform well and make records with high percentage of marks. It is students’ responsibility to be in the form of preparation through regular learning and classroom education. Mathematics is the most important subject of science stream in which students learn some difficult parts of advanced mathematics. For that more practice is required and students get model question papers on mathematics from the official website of KSEEB i.e. kseeb.kar.nic.in to practice regularly. Though detailed syllabus have been provided to students and textbooks are designed according to it still students have to give extra efforts for the preparation of final exam. Smart preparation strategy is required to fulfil the exam requirements and fill minds with self-confidence before attempting the final exam.

Mathematics in the 2nd PUC syllabus covers all detail starting from basic concepts to advanced portion with full explanation and exercises in textbooks. Acquiring the depth knowledge of each topics needs time and students should learn chapters constantly for being in the form of preparation. After completing their textbooks with teachers’ guidance students should make their own strategy to continue their preparation till the final exam. In the prolonged process students get enough time to practice model question papers multiple times which flows positive energy among them. Maths is such a subject where calculation and analytical part takes time more than other subjects. So, students should make plan of time management in exam for attempting all questions within time according to their convenience. Model question papers of maths are prepared by experts after following the exam pattern and previous year question papers. Student will have an idea about repetitive questions and they can understand the important chapters from exam perspective easily. It is students’ duty to download and follow class 12 maths model question papers from the below link:

KSEEB Model Question Papers For Class 12th Math 2023 – 24

Second PUC Model Question Paper

Subject: Maths (2023-24)

Part – A

(1) The relation R in the set {1, 2, 3} given by {(1,2), (2,1)} is

(a) reflexive

(b) symmetric

(c) transitive

(d) equivalence relation

(2) If f: R be defined as f(x) = x4, then the function f is

(a) one-one and onto

(b) many-oneandonto

(c) one-one but not onto

(d) neither one-one nor onto

(3) The principal value branch of cot−1 is

(a) [-π/3, π/2]

(b) (-π/2, π/2)

(c) (0, π]

(d) (0, π)

(4) The number of all possible matrices of order 3 × 3 with each entry 0 or 1 is

(a) 27

(b) 18

(c) 81

(d) 512

(5) Let A be a nonsigular matrix of order 3×3 and | adj A|= 25, then a possible value of |A| is

(a) 625

(b) 25

(c) 5

(d) 125

(6) Which of the following x belongs to domain of the greatest integer function f(x) = x, 0 < x < 3 is not differentiable

(a) 2 and 3

(b) 1 and 2

(c) 0 and 2

(d) 1 and 3

(7) If y = log7 2x, then dy/dx is

(a) 1/xlog7

(b) 1/7log

(c) logx/7

(d) 7/logx

(8) The point of inflection of the function y = x3 is

(a) (2, 8)

(b) (1, 1)

(c) (0, 0)

(d) (–3, -27)

(9) ∫ sin2x dx is

(a) – sin2x/2 + c

(b) – cos2x/2 + c

(c) cos2x/2 + c

(d) sin2x/2 + c

(10) ∫ ex (1/x – 1/x2) dx is

(a) e-x (1/x) + c

(b) e-x (1/x2) + c

(c) ex (1/x) + c

(d) ex (1/x2) + c

(11) If θ is the angle between any two vectors a and b, then a.b = |a x b|, when tan θ is equal to,

(a) 1

(b) 1/ √3

(c) c √3

(d) 0

(12) Unit vector in the direction of = 2 î + 3 ĵ + k̂ is

(a) 2î + 3ĵ + k̂/14

(b) 2î – 3ĵ + k̂/√14

(c) 2î + 3ĵ + k̂/√1

(d) 2î + 3ĵ – k̂/14

(13) If the direction cosines l, m, n of a line are 0, 1/2, √3/2 2 then the angle made by the line with the positive direction of y – axis is

(a) 60°

(b) 30°

(c) 90°

(d) 45°

(14) In a Linear programming problem, the objective function is always

(a) a cubic function

(b) a quadratic function

(c) a linear function

(d) a constant function

(15) If A and B are two non empty events such that P A/B = P B/A and P( A∩B ) ≠ ∅ then

(a) A ⊂ B but A ≠ B

(b) A = B

(c) B ⊂ A but A ≠ B

(d) P (A) = P (B)

(II) Fill in the blanks by choosing the appropriate answer from those given in the bracket

(0, 1, 4, 1/36, 7, 1/6)

(16) The value of sin [π/3 – sin-1 (-1/3)] is —————.

(17) A square matrix A is a singular matrix if |A| is ————————-.

(18) The order of the differential equation d4y/dx4 + sin (yIII) = 0 is —————–.

(19) The lines x-5/k = y+2/-5 = z/1 and x/1 = y/2 = z/3 are perpendicular, then k is ———————-.

(20) The probability of obtaining an even prime number on each die, when a pair of dice is rolled is ————————————–.

PART – B

Answer any six questions

(21) Prove that 2 sin-1 3/5 = tan-1 24/7

(22) Find the equation of line joining (1, 2 ) , ( 3, 6 ) using determinant method

(23) Find dy/dx, if y + siny = cosx

(24) Find the rate of change of the area of a circle with respect to its radius r when r = 3 cm

(25) Find the local minimum value of the function f given by f(x) = 3 + |x|, x ∈ R

(26) Find ∫ dx/(x+1)(x+2)

(27) Evaluate ∫π/20 (sin2x/2 – cos2x/2 – cos2x/2) dx

(28) Find the projection of the vector a = 2î + 3ĵ + 2k̂ on the vector b = î + 2ĵ + k̂

(29) Find the angle between the pair of lines given by r = 3î + 2 ĵ – 4 k̂ + (î + 2 ĵ + 2 k̂) and r = 5 î – 2 ĵ + μ (3 î + 2 ĵ + 6 k̂)

(30) A fair die is rolled. Consider events E = {1, 3, 5}, F = {2, 3} , find P (E/F)

(31) If A and B two events such that P (A) = 1/4, P (B) = 1/2 and P (A ∩ B) = 1/8, find P (not A and not B)

PART – C

(32) Show that the relation R in the set A = {1, 2, 3, 4, 5} given by R = {(a, b): |a − b| is even} is an equivalence relation

(33) Write in the simplest form tan-1 (√1+x2-1/x), x ≠ 0

(34) Express A = [PHOTO] as the sum of a symmetric anda skew symmetric matrix.

(35) Differentiate n2 with respect to

(36) Differentiate , x > 0 with respect to x

(37) Find the interval in which the function f(x) = 10 – 6x – 2x2 is strictly increasing

(38) Find ∫x sin-1x dx

(39) Find the equation of curve passing through the point (–2, 3) , given that the slope of the tangent to the curve at any point (x, y) is 2x/y2

(40) Show that the position vector of the point P, which divides the line joining the points A and B having position vectors and internally in the ratio m:n is mb+na/m+n

(41) Find a unit vector perpendicular to each of the vectors ( + ) and ( –  ), where = 3 î + 2 ĵ + 2 k̂ and b = î + 2 ĵ – 2 k̂

(42) A bag contains 4 red and 4 black balls, another bag contains 2 red and 6 black balls. One of the two bags is selected at random and a ball is drawn at random from the bag and it is found to be red .Find the probability that the ball is drawn from first bag?

PART – D

(43) Let f : N → Y be a function defined as f(x) = 4x + 3, where Y = {y ∈ N ∶ y = 4x + 3 for some x ∈ N}. Show that f is invertible. Find the inverse of f.

(44) PHOTO then calculate AC, BC and (A + B ) C. Also verify (A + B) C = AC + B C

(45) Solve the system of linear equations by matrix method 2x – 3y + 5z = 11, 3x +2y – 4z = –5, x + y – 2z = – 3

(46) If y = 3 cos (logx) + 4 sin (logx), show that x2y2 + xy1 + y = 0

(47) Find the integral of 1/x2-a2 with respect to x and hence evaluate ∫ dx/x2-16

(48) Find the area of the region bounded by the ellipse x2/16 + y2/+9 = 1 using integration.

(49) Find the general solution of the differential equation x dy/dx + 2y = x2 logx, (x ≠ 0 )

(50) Derive the equation of a line in space through a given point and parallel to a vector both in the vector and Cartesian form

PART – E

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35. MATHEMATICS MQP II PUC 2023-24

 

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Updated: September 16, 2023 — 7:18 pm

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