ISC Mathematics Semester-1 Solved Specimen Paper 2022 Class-12

ISC Mathematics Semester-1 Solved Specimen Paper 2022 Class-12 for practice.  Step by step solutions of ISC Class-12 specimen model sample paper .  During solutions of semester-1 Mathematics specimen paper we explain with figure , graph, table whenever necessary so that student can achieve their goal in next upcoming exam of council .

ISC Mathematics Semester-1 Solved Specimen Paper 2022 Class-12

Board	ISC
Class	12th (XII)
Subject	Mathematics
Topic	Semester-1 ISC Specimen Paper Solved
Syllabus	on bifurcated syllabus (after reduction)
session	2021-22
Question Type	MCQ/ Objective (as prescribe by council)
Total question	Total- 33 with all parts
Max mark	80

Solved Class-12 for practice Set of Mathematics Semester-1 ISC Specimen Model Sample Paper 

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Question-1

The function f: R → R defined by 𝑓(𝑥) = 𝑠𝑖𝑛 (3𝑥 + 2), ∀ 𝑥 ∈ 𝑅 is:

(a) One-One
(b) Onto
(c) Neither one-one nor onto
(d) one-one but not onto.

Question 2 

What will be the Principal value of 𝐶𝑜𝑠𝑒𝑐−1 (−√2) ?

Question 3

If set A contains 5 elements and set B contains 6 elements, then the number of one-one onto  mappings from A to B is:

(a) 720
(b) 120
(c) 0
(d) none of the above.

Question 4

If 𝛼 ≤ 2𝑆𝑖𝑛−1𝑥 + 𝐶𝑜𝑠−1𝑥 ≤ 𝛽, then (𝛼, 𝛽) is:

Question 5

Let A be the set of all students of a boy’s school. Then the relation R in A is defined by: R = {(a,b) : a is sister of b} is

(a) an equivalence relation
(b) symmetric relation
(c) an empty relation
(d) a universal relation

Question 6

∀ 𝑥 ∈ 𝑅, 𝐶𝑜𝑡−1

Question 7

The value of ………….

Question 8

From the matrix equation 𝐴𝐵 = 𝐴𝐶, it can be concluded that 𝐵 = 𝐶 provided:

(a) 𝐴 is singular matrix
(b) 𝐴 is non-singular matrix
(c) 𝐴 is a symmetric matrix
(d) 𝐴 is a skew symmetric matrix

Question 9

What is the transpose of a column matrix?

(a) Zero matrix
(b) Diagonal matrix
(c) Column matrix
(d) Row matrix

Question 10

What is the multiplicative inverse of matrix 𝐴 is?

Question 11

If 𝐴 and 𝐵 are two non singular matrices, and 𝐴𝐵 exists, then (𝐴𝐵)

Question 12

If ∆= …………..

(a) ∆
(b) 𝑘∆
(c) 3𝑘∆
(d) 𝑘3∆

Question 13

If 𝑦 = 𝑡 2 and t = x + 3 then 𝑑𝑦/𝑑𝑥 is equal to:

Question 14

The set of points, where the function 𝑓(𝑥) = 𝑥 |𝑥| is differentiable in:

(a) (−∞, ∞)
(b) (−∞, 0) ∪ (0, ∞)
(c) (0, ∞)
(d) [0, ∞ )

Question 15

If sin−1 𝑥 + sin…………

Question 16

The value of lim ………….

Question 17

What will be the value of x for the determinant equation………..

Question 18

Any tangent to the curve 𝑦 = 3𝑥 7 + 5𝑥 + 3 :

(a) is parallel to x – axis
(b) is parallel to y – axis
(c) makes an acute angle with x – axis
(d) makes on obtuse angle with y – axis

Question 19

he second derivative of 𝑦 = ………..

Question 20

What will be the derivative of sin …………

Question 21

Ramu purchased 5 pens, 3 bags and 1 instrument box and paid ` 16. From the same shop Venkat purchased 2 pens , 1 bag and 3 instrument boxes and paid ` 19 while Gopi purchased 1 pen, 2 bags and 4 instrument boxes and paid ` 25

Question 22

A Norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular  window as shown in the figure given below. The total perimeter of the window is 10 m.

Question 23

Consider the mapping 𝑓: 𝐴 → 𝐵 is defined by 𝑓(𝑥) …………..

Question 24

What will be the value of m if the vector 2𝑖̂+ 𝑚𝑗̂+ 𝑘̂ is perpendicular to 2𝑖̂− 𝑗̂+ 3𝑘̂?

(a) 7
(b) 0
(c) 1
(d) −1

Question 25

What will be the angle between the two lines ……………

Question 26

What are the direction ratios of the line passing through two points (-2, 4, 5) and (1, 2, 3)?

(a) < 1, 2, 3 >
(b) < −3, 2, 2 >
(c) < 2, 4, 5 >
(d) < 0, −1, 4 >

Question 27

The equation of the line passing (1, −1, 0) and parallel to the line 𝑥−1…………..

Question 28

The given figure shows an air plant holder which is in the shape of a tetrahedron. Let A(1, 1, 1), B(2, 1, 3), C(3, 2, 2) & D(3, 3, 4) are the vertices of air plant holder. Based on the above information answer the following questions.

………………

Question 29

A company sells its product for ₹ 20 per unit. Fixed costs for the company is ₹ 45,000 and variable costs is estimated to run 25% of total revenue. If 𝑥 denotes number of units produced, then what will be the total cost function?
(a) 45000 + 5𝑥
(b) 15000 + 4𝑥
(c) 45000 + 2𝑥
(d) 4500 + 20 x

Question 30

The demand function for a certain commodity is given by 𝑝 = 4000 − 100𝑥 . What will be the total revenue from the sale of 3 units?

(a) 11,100
(b) 1000
(c) 4500
(d) 2000

Question 31

A company sells 𝑥 packets of biscuits each day at ₹ 10 a packet. The cost of manufacturing these packets is ₹ 5 per packet plus a fixed daily overhead cost of ₹ 700. What will be the profit function?

(a) 6𝑥 – 400
(b) 5𝑥 – 700
(c) 10𝑥 – 500
(d) 5𝑥 – 10

Question 32

The cost function of a firm is given by (𝑥) = 3𝑥² − 2𝑥 + 6. The average cost of the firm at 𝑥 = 3 is:

(a) 11
(b) 17
(c) 9
(d) 27

Question 33

The demand function for a certain product is represented by the equation: 𝑝 = 𝑎𝑥² + 𝑏𝑥 + 𝑐 where 𝑥 is the number of units demanded and 𝑝 is the price per unit…..

Other Subject Solved Specimen Paper for ISC  Class-12 Semester-1

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