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

**Warning :-** before viewing solution view Question Paper

### 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.

OR

(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.

OR

(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).

**SECTION B Maths ISC Specimen Paper Solved 2023 Class-12 PDF Solution**

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