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Organisation : Council For The Indian School Certificate Examinations
Class : Class XII
Document Type : Specimen Question Paper
Subject : Mathematics
Semester : 1 And 2
Year : 2022
Website : https://cisce.org/publications.aspx

ICSE Class XII Mathematics Question Paper

Council For The Indian School Certificate Examinations (ICSE) Class XII Mathematics Specimen Question Papers Semester 1 and 2 for the year 2022.

Related / Similar Question Paper : ICSE Class XII Geography Question Paper 2022

Class XII Mathematics Questions

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)?
(a) 3𝜋4
(b) − 𝜋6
(c) 𝜋4
(d) − 𝜋4

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
(a) (0, 𝜋)
(b) (− 𝜋2 , 𝜋2)
(c) (− 3𝜋 2 , 𝜋2)
(d) None of the above.

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(−𝑥) =
(a) 𝜋 − 𝑐𝑜𝑡−1𝑥
(b) −𝑡𝑎𝑛−1 𝑥
(c) −𝑐𝑜𝑡−1𝑥
(d) 𝜋 + 𝑐𝑜𝑡−1𝑥

Question 7
The value of | 1 log𝑎 𝑏 log𝑏 𝑎 1 | is:
(a) 1 − log 𝑎𝑏
(b) 1 − log 𝑏 log 𝑎
(c) 0
(d) log 𝑎𝑏 − 1

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?
(a) 𝐴
(b) 𝐴2
(c) |𝐴|
(d) 𝑎𝑑𝑗𝐴|𝐴|

Question 11
If 𝐴 and 𝐵 are two non singular matrices, and 𝐴𝐵 exists, then (𝐴𝐵)−1 is
(a) 𝐴−1𝐵−1
(b) 𝐵−1𝐴−1
(c) 𝐴𝐵
(d) None of the above

Question 12
If ∆= |𝑎 𝑏 𝑐 𝑥 𝑦 𝑧 𝑝 𝑞 𝑟|, then |𝑘𝑎 𝑘𝑏 𝑘𝑐 𝑘𝑥 𝑘𝑦 𝑘𝑧 𝑘𝑝 𝑘𝑞 𝑘𝑟| is
(a) ∆
(b) 𝑘∆
(c) 3𝑘∆
(d) 𝑘3∆

Question 13
If 𝑦 = 𝑡2 and t = x + 3 then 𝑑𝑦𝑑𝑥 is equal to:
(a) (𝑥 + 3)2
(b) 2(𝑥 + 3)
(c) 2𝑡
(d) 2(𝑥 + 3)2

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−1 𝑦 = 𝜋2 , then 𝑑𝑦𝑑𝑥 is equal to
(a) 𝑥𝑦
(b) − 𝑥𝑦
(c) 𝑦𝑥
(d) − 𝑦𝑥

Question 16
The value of lim𝑥→0log(1+𝑥)𝑥 is equal to
(a) e
(b) 0
(c) 1
(d) −1

Question 17
What will be the value of x for the determinant equation |3 − 𝑥 6 3−6 3 − 𝑥 33 3 3 − 𝑥| = 0?
(a) 6
(b) 3
(c) 0
(d) -6

Question 18
Any tangent to the curve 𝑦 = 3𝑥7 + 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
The second derivative of 𝑦 = 𝑥3 − 5𝑥2 + 𝑥 is
(a) 10𝑥 − 5
(b) 6x − 10
(c) 3×2 − 10x
(d) 3𝑥2 − 10𝑥 + 1

Question 20
What will be the derivative of sin−1 ( 2𝑥1+𝑥2) with respect to cos−1 (1−𝑥21+𝑥2) ?
(a) -1
(b) 1
(c) 2
(d) 4