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Mathematics: CUET Mock Test - 7 - CUET MCQ


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40 Questions MCQ Test CUET Mock Test Series - Mathematics: CUET Mock Test - 7

Mathematics: CUET Mock Test - 7 for CUET 2024 is part of CUET Mock Test Series preparation. The Mathematics: CUET Mock Test - 7 questions and answers have been prepared according to the CUET exam syllabus.The Mathematics: CUET Mock Test - 7 MCQs are made for CUET 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Mathematics: CUET Mock Test - 7 below.
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Mathematics: CUET Mock Test - 7 - Question 1

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

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

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 - 7 - Question 2

The given graph is for which equation?

Detailed Solution for Mathematics: CUET Mock Test - 7 - Question 2

There are 2 curves.

The black curve is the graph of y = cotx
The red curve is the graph for y = cot-1x
This curve does not pass through the origin but approaches to infinity in the direction of x axis only.
The part of the curve that lies in the (x, y) coordinate gradually meets to the x-axis.
This graph lies above +x axis and –x axis.

Mathematics: CUET Mock Test - 7 - Question 3

What is the order of the matrix A= 

Detailed Solution for Mathematics: CUET Mock Test - 7 - Question 3

The given matrix A=  has 3 rows and 2 columns. Therefore, the order of the matrix is 3×2.

Mathematics: CUET Mock Test - 7 - Question 4

Which of the following is not a type of matrix?

Detailed Solution for Mathematics: CUET Mock Test - 7 - Question 4

Minor matrix is not a type of matrix. Scalar, diagonal, symmetric are various type of matrices.

Mathematics: CUET Mock Test - 7 - Question 5

Evaluate 

Detailed Solution for Mathematics: CUET Mock Test - 7 - Question 5


Mathematics: CUET Mock Test - 7 - Question 6

(a1, a2) ∈R implies that (a2, a1) ∈ R, for all a1, a2∈A. This condition is for which of the following relations?

Detailed Solution for Mathematics: CUET Mock Test - 7 - Question 6

The above is a condition for a symmetric relation.
For example, a relation R on set A = {1,2,3,4} is given by R={(a,b):a+b=3, a>0, b>0} 1+2 = 3, 1>0 and 2>0 which implies (1,2) ∈ R.
Similarly, 2+1 = 3, 2>0 and 1>0 which implies (2,1)∈R. Therefore both (1, 2) and (2, 1) are converse of each other and is a part of the relation. Hence, they are symmetric.

Mathematics: CUET Mock Test - 7 - Question 7

The given graph is for which equation?

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

The given form of equation can be written as,

The green curve is the graph of y = sinx
The blue curve is the graph for y = |sinx|
As sinx is enclosed by a modulus so the curve that lies in the negative y axis will come to the positive y axis.

Mathematics: CUET Mock Test - 7 - Question 8

Given a matrix A=  which of the elements aij follows the condition i=j.

Detailed Solution for Mathematics: CUET Mock Test - 7 - Question 8

The elements following the condition i=j will have the same row number and column number. The elements are a11, a22, a33 which in the matrix A are 2, 3, 9 respectively.

Mathematics: CUET Mock Test - 7 - Question 9

Find a,b,c,d if  are equal matrices.

Detailed Solution for Mathematics: CUET Mock Test - 7 - Question 9

The two matrices  and  are equal matrices. Comparing the two matrices, we get a=3, b+c=2, c+d=3, b=-1
Solving the above equations, we get a=3, b=-1, c=3, d=0.

Mathematics: CUET Mock Test - 7 - Question 10

Find the value of x if 

Detailed Solution for Mathematics: CUET Mock Test - 7 - Question 10

Given that 
⇒3x2-2x=5(2)-3(3)
⇒3x2-2x=1
Solving for x, we get
x=1, –(1/3).

Mathematics: CUET Mock Test - 7 - Question 11

Evaluate 

Detailed Solution for Mathematics: CUET Mock Test - 7 - Question 11

Expanding along R1, we get


Δ=3(-15+8)+(18-12)+3(-12+15)
Δ=3(-7)+6+9=-6.

Mathematics: CUET Mock Test - 7 - Question 12

What is the value of 

Detailed Solution for Mathematics: CUET Mock Test - 7 - Question 12

Applying R1 → R1 + R2 + R3

This is equal to,

Applying C1 → C1 – C2 and C2 → C2 – C3

= (Σab)3

Mathematics: CUET Mock Test - 7 - Question 13

If f(x) =  then which one among the following is correct?

Detailed Solution for Mathematics: CUET Mock Test - 7 - Question 13

Here, f(x) = 
Multiplying and diving by abc,


= (a – b)(b – c)(c – a)

Mathematics: CUET Mock Test - 7 - Question 14

Which of the following is the formula for finding the area of a triangle with the vertices (x1,y1), (x2,y2), (x3,y3).

Detailed Solution for Mathematics: CUET Mock Test - 7 - Question 14

The area of a triangle with vertices (x1,y1), (x2,y2), (x3,y3) is given by

Mathematics: CUET Mock Test - 7 - Question 15

Which of the following is the formula for cofactor of an element aij?

Detailed Solution for Mathematics: CUET Mock Test - 7 - Question 15

The cofactor of an element aij, denoted by Aij is given by
Aij=(-1)i+j Mij, where Mij is the minor of the element aij.

Mathematics: CUET Mock Test - 7 - Question 16

Evaluate 

Detailed Solution for Mathematics: CUET Mock Test - 7 - Question 16



Δ=1(0-0)-0(0-1)+1(0-0)
Δ=0-0+0=0.

Mathematics: CUET Mock Test - 7 - Question 17

If the system of equation 2x + 5y + 8z = 0, x + 4y + 7z = 0, 6x + 9y – αz = 0 has a non trivial solution then what is the value of α?

Detailed Solution for Mathematics: CUET Mock Test - 7 - Question 17

Here, in L.H.S we have,

So, for trivial roots the above value is = 0
⇒ 
Solving it further we get α = 12

Mathematics: CUET Mock Test - 7 - Question 18

What will be the value of f(x) = 

Detailed Solution for Mathematics: CUET Mock Test - 7 - Question 18

Here, f(x) = f’(x)
⇒ f(x) is purely real.

Mathematics: CUET Mock Test - 7 - Question 19

What is the area of the triangle whose vertices are (0,1), (0,2), (1,5)?

Detailed Solution for Mathematics: CUET Mock Test - 7 - Question 19

The area of the triangle with vertices (0,1), (0,2), (1,5) is given by

Expanding along C1, we get
Δ=1/2{(0-0+1(1-2)}=1/2|-1|=1/2 sq.units.

Mathematics: CUET Mock Test - 7 - Question 20

What is the minor of the element 5 in the determinant Δ= 

Detailed Solution for Mathematics: CUET Mock Test - 7 - Question 20

The minor of element 5 in the determinant Δ=  is the determinant obtained by deleting the row and column containing element 5.
∴ M12 =2(4)-7(6)=-34.

Mathematics: CUET Mock Test - 7 - Question 21

Evaluate |A|2-5|A|+1, if A= 

Detailed Solution for Mathematics: CUET Mock Test - 7 - Question 21

Given that, A= 
|A|=(7(5)-5(4))=35-20=15
|A|2-5|A|+1=(15)2-5(15)+1=225-75+1=151.

Mathematics: CUET Mock Test - 7 - Question 22

What is the value of x if, 

Detailed Solution for Mathematics: CUET Mock Test - 7 - Question 22

Given that,

So, by circular determinant property,
Sum of the elements of a row = 0
So, x + 3 + 6 = 2 + x + 7 = 4 + 5 + x = 0
⇒ x = -9

Mathematics: CUET Mock Test - 7 - Question 23

If, Si = ai + bi + ci then what is the value of 

Detailed Solution for Mathematics: CUET Mock Test - 7 - Question 23

We have, 
So, the value of the  (a – b)(b – c)(c – a)
Now, by circulant determinant,

Multiplying the determinant in row by row,
We get, (a – b)2(b – c)2(c – a)2

Mathematics: CUET Mock Test - 7 - Question 24

Find the minor of the element 2 in the determinant Δ=

Detailed Solution for Mathematics: CUET Mock Test - 7 - Question 24

The minor of the element 2 can be obtained by deleting the first row and the first column
∴M11=9.

Mathematics: CUET Mock Test - 7 - Question 25

Find the minor and cofactor respectively for the element 3 in the determinant Δ=

Detailed Solution for Mathematics: CUET Mock Test - 7 - Question 25

The element 3 is in the second row (i=2) and first column(j=1).
∴ M21=5 (obtained by deleting R2 and C1 in Δ)
A21=(-1)1+2 M21=-1×5 =-5.

Mathematics: CUET Mock Test - 7 - Question 26

Evaluate 

Detailed Solution for Mathematics: CUET Mock Test - 7 - Question 26


Δ=sin⁡ y 
Δ=sin ⁡y (sin⁡ y-cos⁡ x)-0+sin ⁡y (cos⁡ y-sin ⁡y)
Δ=sin2⁡y-sin ⁡y cos⁡ x+sin⁡ y cos ⁡y-sin2⁡y=sin ⁡y (cos⁡ y-cos⁡ x)

Mathematics: CUET Mock Test - 7 - Question 27

Which one of the following is correct if a, b and c are the sides of a triangle ABC and 

Detailed Solution for Mathematics: CUET Mock Test - 7 - Question 27

When a = b or b = c or c = a the determinant reduces to 0
It is not necessary that a = b = c for determinant to be 0
Therefore, the triangle is isosceles.

Mathematics: CUET Mock Test - 7 - Question 28

Let, α and β be real. Find the set of all values of β for which the system of equation βx + sin α*y + cosα*z = 0, x + cosα * y + sinα * z = 0 , -x + sinα*y – cosα * z = 0 has a non-trivial solution. For β = 1 what are all values of α?

Detailed Solution for Mathematics: CUET Mock Test - 7 - Question 28

The given system have non-trivial solution if 
On opening the determinant we get β = sin 2α + cos 2 α
Therefore, -√2 ≤ β ≤ √2
Now, for β = 1,
sin 2α + cos 2 α = 1
⇒(1/√2)sin 2α + (1/√2) cos 2α = (1/√2)
Or, cos(2α – π/4) = 1/√2 = cos(2nπ ± π/4)
⇒ 2α = 2nπ ± π/4 + π/4

Mathematics: CUET Mock Test - 7 - Question 29

Find the value of k for which (1,2), (3,0), (2,k) are collinear.

Detailed Solution for Mathematics: CUET Mock Test - 7 - Question 29

The area of triangle formed by collinear points is zero.

Expanding along C2, we get
1/2 {-2(3-2)+0-k(1-3)}=0
1/2 {-2+2k}=0
∴ k=1

Mathematics: CUET Mock Test - 7 - Question 30

Find the minor of the element 1 in the determinant Δ=

Detailed Solution for Mathematics: CUET Mock Test - 7 - Question 30

The minor of the element 1 can be obtained by deleting the first row and the first column
∴ M11=8.

Mathematics: CUET Mock Test - 7 - Question 31

Find the value of x, if 

Detailed Solution for Mathematics: CUET Mock Test - 7 - Question 31


⇒ 2x-15=3x+5
⇒ x=-20

Mathematics: CUET Mock Test - 7 - Question 32

What is the value of k if 

Detailed Solution for Mathematics: CUET Mock Test - 7 - Question 32

Put the value of x, y, z = 1
Thus, putting the value of x = 1, y = 1 and z = 1 on both sides, we get

So, solving the determinant we get k = 4.

Mathematics: CUET Mock Test - 7 - Question 33

Which one among the following is correct if x, y, z are eliminated from, 

Detailed Solution for Mathematics: CUET Mock Test - 7 - Question 33

 bx – ay – az = 0
 bx – cy + bz = 0
 cx + cy – az = 0

Or, b(ca – bc) + a(-ab – bc) – a(bc + c2) = 0
or, abc – b2c – a2b – abc – abc – ac2 = 0
or, a2b + b2c + c2a + abc = 0 which is the required eliminate.

Mathematics: CUET Mock Test - 7 - Question 34

What is the area of the triangle if the vertices are (0,2), (0, 0), (3, 0)?

Detailed Solution for Mathematics: CUET Mock Test - 7 - Question 34

The area of the triangle (0,2), (0, 0), (3, 0) with vertices is given by

Expanding along R3, we get
Δ= (1/2)  {0-0+3(2-0)}
Δ=3 sq.units.

Mathematics: CUET Mock Test - 7 - Question 35

Find the cofactor of element -3 in the determinant Δ= 

Detailed Solution for Mathematics: CUET Mock Test - 7 - Question 35

The minor of element -3 is given by
 =4(2)-4=4 (Obtained by eliminating R2 and C1)
∴ A21=(-1)2+1 M21=(-1)3 4=-4.

Mathematics: CUET Mock Test - 7 - Question 36

Find the value of x, if 

Detailed Solution for Mathematics: CUET Mock Test - 7 - Question 36

Given that,  -5—(-3)=5x-3x2
-2=5x-3x2
3x2-5x-2=0
Solving for x, we get
x=2, –(1/3).

Mathematics: CUET Mock Test - 7 - Question 37

What will be the value of the given determinant 

Detailed Solution for Mathematics: CUET Mock Test - 7 - Question 37

In the given determinant form the elements are in A.P
Also the common difference of this A.P is 7
Thus the value of the given determinant = 0

Mathematics: CUET Mock Test - 7 - Question 38

The co-ordinates of the vertices of a triangle are [m(m + 1), (m + 1)], [(m + 1)(m + 2), (m + 2)] and [(m + 2)(m + 3), (m + 3)]. Then which one among the following is correct?

Detailed Solution for Mathematics: CUET Mock Test - 7 - Question 38

The area o the triangle with the given point as vertices is,


Now, by performing the row operation R2 = R2 – R1 and R3 = R3 – R2

Now, breaking the determinant we get,
= 1/2 (2m + 2 – 2m – 4)
= -1
Thus, it is independent of m.

Mathematics: CUET Mock Test - 7 - Question 39

Find the equation of the line joining A(2,1) and B(6,3) using determinants.

Detailed Solution for Mathematics: CUET Mock Test - 7 - Question 39

Let C(x,y) be a point on the line AB. Thus, the points A(2,1), B(6,3), C(x,y) are collinear. Hence, the area of the triangle formed by these points will be 0.

Expanding along C3, we get
1/2 {1(6y-3x)-1(2y-x)+1(6-6)}=0
1/2 {6y-3x-2y+x}= 1/2 {4y-2x}=0
⇒ 2y-x=0

Mathematics: CUET Mock Test - 7 - Question 40

Find the determinant of the matrix A=

Detailed Solution for Mathematics: CUET Mock Test - 7 - Question 40

Given that, A = 
⇒ Δ =   = 9(6)-7(8)=54-56 = -2

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