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Mathematics: CUET Mock Test - 1 - CUET MCQ


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40 Questions MCQ Test CUET Mock Test Series - Mathematics: CUET Mock Test - 1

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Mathematics: CUET Mock Test - 1 - Question 1

Which of these is not a type of relation?

Detailed Solution for Mathematics: CUET Mock Test - 1 - Question 1

Surjective is not a type of relation. It is a type of function. Reflexive, Symmetric and Transitive are type of relations.

Mathematics: CUET Mock Test - 1 - Question 2

Let a binary operation ‘*’ be defined on a set A. The operation will be commutative if ________

Detailed Solution for Mathematics: CUET Mock Test - 1 - Question 2

A binary operation ‘*’ defined on a set A is said to be commutative only if a * b = b *a, ∀ a, b ∈ A.
If (a * b) * c = a * (b * c), then the operation is said to associative ∀ a, b∈ A.
If (b ο c) * a = (b * a) ο (c * a), then the operation is said to be distributive ∀ a, b, c ∈ A.

Mathematics: CUET Mock Test - 1 - Question 3

tan−1√3+sec−12–cos−11 is equal to ________

Detailed Solution for Mathematics: CUET Mock Test - 1 - Question 3

tan−1 √3 = π/3, sec−12 = π/3, cos−11 = 0
 tan−1√3 + sec−12 – cos−11 = π/3 + π/3
= 2π/3

Mathematics: CUET Mock Test - 1 - Question 4

sin-1⁡x in terms of cos-1⁡ is _________

Detailed Solution for Mathematics: CUET Mock Test - 1 - Question 4

Let sin-1⁡x = y
⇒ x = sin⁡y
⇒ x = √1 - cos2y
⇒ x2 = 1 - cos2y
⇒ cos2y = 1 - x2
∴ y = cos-1⁡ √1 - x2 = sin-1⁡x

Mathematics: CUET Mock Test - 1 - Question 5

 Which of the following relations is symmetric but neither reflexive nor transitive for a set A = {1, 2, 3}.

Detailed Solution for Mathematics: CUET Mock Test - 1 - Question 5

A relation in a set A is said to be symmetric if (a1, a2)∈R implies that (a1, a2)∈R,for every a1, a2∈R.
Hence, for the given set A={1, 2, 3}, R={(1, 2), (2, 1)} is symmetric. It is not reflexive since every element is not related to itself and neither transitive as it does not satisfy the condition that for a given relation R in a set A if (a1, a2)∈R and (a2, a3)∈R implies that (a1, a3)∈ R for every a1, a2, a3∈R.

Mathematics: CUET Mock Test - 1 - Question 6

If f : R→R, g(x) = 3 x 2 + 7 and f(x) = √x, then gοf(x) is equal to _______

Detailed Solution for Mathematics: CUET Mock Test - 1 - Question 6

Given that, g(x) = 3 x 2 + 7 and f(x) = √x
∴ gοf(x) = g(f(x)) = g(√x) = 3(√x)2 + 7 = 3x + 7.
Hence, gοf(x) = 3x + 7.

Mathematics: CUET Mock Test - 1 - Question 7

Let I be a set of all lines in a XY plane and R be a relation in I defined as R = {(I1, I2):I1 is parallel to I2}. What is the type of given relation?

Detailed Solution for Mathematics: CUET Mock Test - 1 - Question 7

This is an equivalence relation. A relation R is said to be an equivalence relation when it is reflexive, transitive and symmetric.
Reflexive: We know that a line is always parallel to itself. This implies that I1 is parallel to I1 i.e. (I1, I2)∈R. Hence, it is a reflexive relation.
Symmetric: Now if a line I1 || I2 then the line I2 || I1. Therefore, (I1, I2)∈R implies that (I2, I1)∈R. Hence, it is a symmetric relation.
Transitive: If two lines (I1, I3) are parallel to a third line (I2) then they will be parallel to each other i.e. if (I1, I2) ∈R and (I2, I3) ∈R implies that (I1, I3) ∈R.

Mathematics: CUET Mock Test - 1 - Question 8

What is the principle value of  .

Detailed Solution for Mathematics: CUET Mock Test - 1 - Question 8

Let  = y
sec y = 2/√3
sec⁡ y = secπ/6
⇒ y = π/6

Mathematics: CUET Mock Test - 1 - Question 9

What is sec-1⁡x in terms of tan-1⁡?

Detailed Solution for Mathematics: CUET Mock Test - 1 - Question 9

Let sec-1⁡x = y
⇒ x = sec⁡y
⇒ x = √ 1 + tan2y
⇒ x2 - 1 = tan2y
∴ y = tan-1√x2 - 1 = sec-1⁡x

Mathematics: CUET Mock Test - 1 - Question 10

If A =  and B = , then find A + B.

Detailed Solution for Mathematics: CUET Mock Test - 1 - Question 10

Given that, A =   and B =
Then A + B = 

Mathematics: CUET Mock Test - 1 - Question 11

If f : R → R is given by f(x) = (5 + x4)1/4, then fοf(x) is _______

Detailed Solution for Mathematics: CUET Mock Test - 1 - Question 11

Given that f(x) = (5 + x4)1/4
∴ fοf(x) = f(f(x)) = (5 + {(5 + x4)1/4}4)1/4
= (5 + (5 + x4))1/4 = (10+x4)1/4

Mathematics: CUET Mock Test - 1 - Question 12

Let ‘*’ be a binary operation on N defined by a * b =a - b + ab2, then find 4 * 5.

Detailed Solution for Mathematics: CUET Mock Test - 1 - Question 12

The binary operation is defined by a * b = a - b + ab2.
∴ 4 * 5 = 4 - 5 + 4(52) = -1 + 100 = 99.

Mathematics: CUET Mock Test - 1 - Question 13

[-1, 1] is the domain for which of the following inverse trigonometric functions?

Detailed Solution for Mathematics: CUET Mock Test - 1 - Question 13

[-1, 1] is the domain for sin-1⁡x.
The domain for cot-1⁡x is (-∞,∞).
The domain for tan-1⁡⁡x is (-∞,∞).
The domain for sec-1⁡⁡x is (-∞,-1] ∪ [1,∞).

Mathematics: CUET Mock Test - 1 - Question 14

 If A + B =  and A = . Find the matrix B.

Detailed Solution for Mathematics: CUET Mock Test - 1 - Question 14

Given that,
A + B =  and A = 
⇒ B = (A + B) - A = 
B = 

Mathematics: CUET Mock Test - 1 - Question 15

 A function is invertible if it is ____________

Detailed Solution for Mathematics: CUET Mock Test - 1 - Question 15

A function is invertible if and only if it is bijective i.e. the function is both injective and surjective. If a function f: A → B is bijective, then there exists a function g: B → A such that f(x) = y ⇔ g(y) = x, then g is called the inverse of the function.

Mathematics: CUET Mock Test - 1 - Question 16

Let M={7,8,9}. Determine which of the following functions is invertible for f:M→M.

Detailed Solution for Mathematics: CUET Mock Test - 1 - Question 16

The function f = {(7,7),(8,8),(9,9)} is invertible as it is both one – one and onto. The function is one – one as every element in the domain has a distinct image in the co – domain. The function is onto because every element in the codomain M = {7,8,9} has a pre – image in the domain.

Mathematics: CUET Mock Test - 1 - Question 17

Let R be a relation in the set N given by R={(a,b): a+b=5, b>1}. Which of the following will satisfy the given relation?

Detailed Solution for Mathematics: CUET Mock Test - 1 - Question 17

(2,3) ∈ R as 2+3 = 5, 3>1, thus satisfying the given condition.
(4,2) doesn’t belong to R as 4+2 ≠ 5.
(2,1) doesn’t belong to R as 2+1 ≠ 5.
(5,0) doesn’tbelong to R as 0⊁1

Mathematics: CUET Mock Test - 1 - Question 18

If f: N→N, g: N→N and h: N→R is defined f(x) = 3x - 5, g(y) = 6y2 and h(z) = tan⁡z, find ho(gof).

Detailed Solution for Mathematics: CUET Mock Test - 1 - Question 18

Given that, f(x) = 3x - 5, g(y) = 6y2 and h(z) = tan⁡z,
Then, ho(gof) = hο(g(f(x)) = h(6(3x-5)2) = tan⁡(6(3x - 5)2)
∴ ho(gof) = tan⁡(6(3x - 5)2)

Mathematics: CUET Mock Test - 1 - Question 19

Let ‘*’ be defined on the set N. Which of the following are both commutative and associative?

Detailed Solution for Mathematics: CUET Mock Test - 1 - Question 19

The binary operation ‘*’ is both commutative and associative for a * b = a + b.
The operation is commutative on a * b = a + b because a + b = b + a.
The operation is associative on a * b = a + b because (a + b) + c = a + (b + c).

Mathematics: CUET Mock Test - 1 - Question 20

Let ‘*’ be a binary operation defined by a * b = 4ab. Find (a * b) * a.

Detailed Solution for Mathematics: CUET Mock Test - 1 - Question 20

Given that, a * b = 4ab.
Then, (a * b) * a = (4ab) * a
= 4(4ab)(a) = 16a2 b.

Mathematics: CUET Mock Test - 1 - Question 21

(a,a) ∈ R, for every a ∈ A. This condition is for which of the following relations?

Detailed Solution for Mathematics: CUET Mock Test - 1 - Question 21

The above is the condition for a reflexive relation. A relation is said to be reflexive if every element in the set is related to itself.

Mathematics: CUET Mock Test - 1 - Question 22

Let ‘*’ be a binary operation defined by a * b = 3ab + 5. Find 8 * 3.

Detailed Solution for Mathematics: CUET Mock Test - 1 - Question 22

It is given that a * b=3ab + 5.
Then, 8 * 3 = 3(83) + 5 = 3(512) + 5 = 1536 + 5 = 1541.

Mathematics: CUET Mock Test - 1 - Question 23

Which of the following is not a type of binary operation?

Detailed Solution for Mathematics: CUET Mock Test - 1 - Question 23

Transitive is not a type of binary operation. It is a type of relation. Distributive, associative, commutative are different types of binary operations.

Mathematics: CUET Mock Test - 1 - Question 24

Which of the following relations is reflexive but not transitive for the set T = {7, 8, 9}?

Detailed Solution for Mathematics: CUET Mock Test - 1 - Question 24

The relation R= {(7, 7), (8, 8), (9, 9)} is reflexive as every element is related to itself i.e. (a,a) ∈ R, for every a∈A. and it is not transitive as it does not satisfy the condition that for a relation R in a set A if (a1, a2)∈R and (a2, a3)∈R implies that (a1, a3) ∈ R for every a1, a2, a3 ∈ R.

Mathematics: CUET Mock Test - 1 - Question 25

Which of the following condition is incorrect for matrix multiplication?

Detailed Solution for Mathematics: CUET Mock Test - 1 - Question 25

Matrix multiplication is never commutative i.e. AB ≠ BA. Therefore, the condition AB = BA is incorrect.

Mathematics: CUET Mock Test - 1 - Question 26

 Which of the following is not the property of transpose of a matrix?

Detailed Solution for Mathematics: CUET Mock Test - 1 - Question 26

 (AB)’ = (BA)’is incorrect. We know that matrix multiplication is not commutative i.e. AB ≠ BA. Hence, its transpose will also not be commutative.
(AB)’=B’A’

Mathematics: CUET Mock Test - 1 - Question 27

Find the transpose of the matrix A = 

Detailed Solution for Mathematics: CUET Mock Test - 1 - Question 27

To find the transpose of the matrix of the given matrix, interchange the rows with columns and columns with rows.
Hence, we get A’ = 

Mathematics: CUET Mock Test - 1 - Question 28

Which of the following is the reversal law of transposes?

Detailed Solution for Mathematics: CUET Mock Test - 1 - Question 28

According to the reverse law of transposes the transpose of the product is the product of the transposes taken in the reverse order i.e. (AB)’ = B’ A’.

Mathematics: CUET Mock Test - 1 - Question 29

The matrix A =  is a ____________

Detailed Solution for Mathematics: CUET Mock Test - 1 - Question 29

Given that, A = 
⇒ A’ = 
i.e.A=A’. Hence, it is a symmetric matrix.

Mathematics: CUET Mock Test - 1 - Question 30

Which of the following conditions holds true for a skew-symmetric matrix?

Detailed Solution for Mathematics: CUET Mock Test - 1 - Question 30

A matrix is said to be skew-symmetric if it is equal to the negative of its transpose i.e. A = -A’.

Mathematics: CUET Mock Test - 1 - Question 31

The matrix A =  is __________

Detailed Solution for Mathematics: CUET Mock Test - 1 - Question 31

The given matrix A =  is skew symmetric.
⇒ A’ =  = A
∴ A = -A’. Hence, it is a skew-symmetric matrix.

Mathematics: CUET Mock Test - 1 - Question 32

If A = , then which of the following statement is incorrect?

Detailed Solution for Mathematics: CUET Mock Test - 1 - Question 32

Given that, A = 
∴ A’ = 
⇒ -A ’=  ≠ A. Hence, it is not a skew symmetric matrix.

Mathematics: CUET Mock Test - 1 - Question 33

Which of the following conditions holds true for a symmetric matrix?

Detailed Solution for Mathematics: CUET Mock Test - 1 - Question 33

A matrix is A said to be a symmetric matrix if it is equal to its transpose i.e. A = A’.

Mathematics: CUET Mock Test - 1 - Question 34

How many elementary operations are possible on Matrices?

Detailed Solution for Mathematics: CUET Mock Test - 1 - Question 34

There are a total of 6 elementary operations that are possible on matrices, three on rows and three on columns.

Mathematics: CUET Mock Test - 1 - Question 35

Which of the following matrices will remain same if the elementary operation R1 → 2R1 + 3R2 is applied on the matrix?

Detailed Solution for Mathematics: CUET Mock Test - 1 - Question 35

Consider matrix A =  , applying the elementary operation R1 → 2R1 + 3R2.

herefore, the matrix A =  , remains same after applying the elementary operation.

Mathematics: CUET Mock Test - 1 - Question 36

 Which of the following is not a valid elementary operation?

Detailed Solution for Mathematics: CUET Mock Test - 1 - Question 36

The elementary operation Ri →1 + kRi is incorrect, the valid elementary operations on matrices are as follows.

  • Interchanging any two rows and columns
  • The multiplication of the elements of any row or column by a non-zero number.
  • The addition to the elements of any row or column, the corresponding elements of any other row and column multiplied by any non-zero number.
Mathematics: CUET Mock Test - 1 - Question 37

Which of the following column operation is incorrect for the matrix A = ?

Detailed Solution for Mathematics: CUET Mock Test - 1 - Question 37

The column operation C2→2+2C2 is incorrect. A non-zero number cannot be directly added to any column or row in a matrix.

Mathematics: CUET Mock Test - 1 - Question 38

Which of the following relations is transitive but not reflexive for the set S = {3, 4, 6}?

Detailed Solution for Mathematics: CUET Mock Test - 1 - Question 38

For the above given set S = {3, 4, 6}, R = {(3, 4), (4, 6), (3, 6)} is transitive as (3,4)∈R and (4,6) ∈R and (3,6) also belongs to R . It is not a reflexive relation as it does not satisfy the condition (a,a)∈R, for every a∈A for a relation R in the set A.

Mathematics: CUET Mock Test - 1 - Question 39

Which of the following relations is symmetric and transitive but not reflexive for the set I = {4, 5}?

Detailed Solution for Mathematics: CUET Mock Test - 1 - Question 39

R= {(4, 5), (5, 4), (4, 4)} is symmetric since (4, 5) and (5, 4) are converse of each other thus satisfying the condition for a symmetric relation and it is transitive as (4, 5)∈R and (5, 4)∈R implies that (4, 4) ∈R. It is not reflexive as every element in the set I is not related to itself.

Mathematics: CUET Mock Test - 1 - Question 40

Which of the following is not a property of invertible matrices if A and B are matrices of the same order?

Detailed Solution for Mathematics: CUET Mock Test - 1 - Question 40

 (AB)-1 = A-1 B-1 is incorrect. The correct formula is (AB)-1 = B-1 A-1. B-1 A-1 ≠  A-1 B-1 as matrix multiplication is not commutative.

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