ISC Maths Specimen Paper 2023 Section B Solved for ISC Class-12

ISC Maths Specimen Paper 2023 Section B Solved for ISC Class-12. Step by step solutions as council prescribe guideline of model sample question paper.

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ISC Maths Specimen Paper 2023 Section B Solved for ISC Class-12

Board	ISC
Class	12th (xii)
Subject	Maths
Topic	Specimen Paper Solved
Syllabus	Revised Syllabus
Session	2022-23
Question Type	Sec-B Subjective questions
Section	B (15 Marks)
Max mark	80

ISC Maths Specimen Paper 2023 Solved Class-12

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ISC SPECIMEN QUESTION PAPER 2023

MATHEMATICS

Maximum Marks: 80

Time Allowed: Three hours

(Candidates are allowed additional 15 minutes for only reading the paper. They must NOT start writing during this time).

This Question Paper consists of three sections A, B and C.
Candidates are required to attempt all questions from Section A and all questions EITHER from Section B OR Section C.
Section A: Internal choice has been provided in two questions of two marks each, two questions of four marks each and two questions of six marks each.
Section B: Internal choice has been provided in one question of two marks and one question of four marks.
Section C: Internal choice has been provided in one question of two marks and one question of four marks.
All working, including rough work, should be done on the same sheet as, and adjacent to the rest of the answer.
The intended marks for questions or parts of questions are given in brackets [ ].
Mathematical tables and graph papers are provided.

SECTION B – 15 MARKS

ISC Maths Specimen Paper 2023 Solved Class-12

Question 15: In subparts (i) and (ii) choose the correct options and in subparts (iii) to (v), answer the
questions as instructed.
(i) If 𝑎⃗ = 𝑖̂+ 2𝑗̂+ 3𝑘̂ and 𝑏⃗⃗ = -𝑖̂+ 2𝑗̂+ 𝑘̂ and 𝑐⃗ = 3𝑖̂+ 𝑗̂, find 𝑡 such that 𝑎⃗ + 𝑡𝑏⃗⃗ is perpendicular to 𝑐⃗ is

(a) 0
(b) 5
(c) 4
(d) 2

(ii) The planes 2x – y + 4z = 5 and 5x – 2·5y + 10z = 6 are

(a) parallel
(b) intersect on y axis
(c) perpendicular
(d) pass through (0, 0, 5/4)

(iii) Find a vector of magnitude of 10 units and parallel to the vector 2𝑖̂+ 3𝑗̂− 𝑘̂.

(iv) Find the position vector of a point R which divides the line joining the two-points 𝑃 and 𝑄 with position vectors 2𝑖̂+𝑗̂and 𝑖̂− 2𝑗̂respectively in the ratio of 2:1 externally.

(v) Find the equation of the plane with intercept 3 on the 𝑦 − axis and parallel to 𝑥𝑧 −plane.

Question 16: (i) Find the area of the triangle whose adjacent sides are 𝑖̂+ 4𝑗̂– 𝑘̂ and 𝑖̂+ 𝑗̂+ 2𝑘̂.

(ii) For any two non-zero vectors 𝑎⃗ and 𝑏⃗⃗, if | 𝑎⃗.𝑏⃗⃗ |=|𝑎⃗ ×𝑏⃗⃗|, then find the angle between them.

Question 17: (i) Show that …………… point of intersection.

(ii) Find the equation of the plane passing through the points (0,4, −3) and (6, −4,3) if the sum of their intercepts on three axes is 0.

Question 18: If the area is bounded by the parabola 𝑦² = 16𝑥 and the line 𝑦 = 4𝑚𝑥 is 1/12 sq units, then using integration, find the value of 𝑚. (𝑚 > 0).