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All questions of Chapter 4 - Determinants for JEE Exam
The value of 
- a)-1
- b)2
- c)0
- d)1
Correct answer is option 'D'. Can you explain this answer?
The value of
a)
-1
b)
2
c)
0
d)
1
|
Anu answered |
(cosФ×cosФ)-(-sinфsinФ) = cos^2Ф-(-sin^2Ф) = cos^2Ф+sin^2Ф=1
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If 
, then the value of |2A| is same as- a)2|A|
- b)4|A|
- c)±2|A|
- d)|A|
Correct answer is option 'B'. Can you explain this answer?
If , then the value of |2A| is same as
, then the value of |2A| is same asa)
2|A|
b)
4|A|
c)
±2|A|
d)
|A|
|
Harshít Bajáj answered |
Pehele |2A| find karo..which is -24.. so, |2A|= -24 _ _ eq (1).. then |A| find kro..which is -6.. so, |A|= -6 _ _ eq (2).. now.. 4|A| = 4 × (-6)= -24 _ _ eq (3).. from eq (1),(3)..we get..|2A|=4|A|..
- a)0
- b)±1
- c)-1
- d)1
Correct answer is option 'B'. Can you explain this answer?
a)
0
b)
±1
c)
-1
d)
1
|
Preeti Iyer answered |
As the value of both determinants are equal,
∴ 1 = x2
x = ±1
∴ 1 = x2
x = ±1
, then the value of x is- a)-2
- b)1
- c)2
- d)-1
Correct answer is option 'B'. Can you explain this answer?
, then the value of x isa)
-2
b)
1
c)
2
d)
-1
|
|
Shreya Singh answered |
(4×2)-(3×2)=(4×X)-(1×2X).8-6= 4X-2X..2=2X.1=X....
The value of 
is - a)(5x + 2) (2 - x)2
- b)(5x + 2)2 (2 - x)
- c)(5x + 2)2 (2 - x)2
- d)(5x + 2) (2 - x)
Correct answer is option 'A'. Can you explain this answer?
The value of is
is a)
(5x + 2) (2 - x)2
b)
(5x + 2)2 (2 - x)
c)
(5x + 2)2 (2 - x)2
d)
(5x + 2) (2 - x)
|
Deepak answered |
We are not preparing for descriptive exam !!
The following system of equations has
x + 3y + 3z = 2
x + 4y + 3z = 1
x + 3y + 4z = 2- a)Infinite Solution
- b)Trivial Solution
- c)Unique Solution
- d)No Solution
Correct answer is option 'C'. Can you explain this answer?
The following system of equations has
x + 3y + 3z = 2
x + 4y + 3z = 1
x + 3y + 4z = 2
x + 3y + 3z = 2
x + 4y + 3z = 1
x + 3y + 4z = 2
a)
Infinite Solution
b)
Trivial Solution
c)
Unique Solution
d)
No Solution
|
Geetika Shah answered |
Let A = {(1,3,3) (1,4,3) (1,3,4)}
|A| = 1(16-9) -3(4-3) +3(3-4)
|A| = 1(7) -3(1) +3(-1)
= 7 - 3 - 3
= 1
Therefore, A is not equal to zero, it has unique solution.
|A| = 1(16-9) -3(4-3) +3(3-4)
|A| = 1(7) -3(1) +3(-1)
= 7 - 3 - 3
= 1
Therefore, A is not equal to zero, it has unique solution.
a)-10b)11c)12d)-13Correct answer is option 'D'. Can you explain this answer?
|
Shreya Hegde answered |
Actually the answer is -13 not +13
I request everyone to recheck
I request everyone to recheck
, then the value of 
is
= 0 , is
- a)(a)2
- b)(a – b)2
- c)1
- d)(a+b)2
Correct answer is option 'D'. Can you explain this answer?
a)
(a)2
b)
(a – b)2
c)
1
d)
(a+b)2
|
Aryan Khanna answered |
Determinant = [(a2 + b2).1 - (-2ab)]
= (a+b)2
= (a+b)2
- a)-3/2
- b)3/2
- c)-1/2
- d)1/2
Correct answer is option 'D'. Can you explain this answer?
a)
-3/2
b)
3/2
c)
-1/2
d)
1/2
|
|
Shreya Singh answered |
(1×1) -(1×1)= 4 × X - 2 × 1.0= 4X-2.4X=2.X=2/4.X=1/2.
Order of a matrix [ 2 5 7 ] is- a)3 x 3
- b)1 x 1
- c)3 x 1
- d)1 x 3
Correct answer is option 'D'. Can you explain this answer?
Order of a matrix [ 2 5 7 ] is
a)
3 x 3
b)
1 x 1
c)
3 x 1
d)
1 x 3
|
|
Utkarsh Pandey answered |
The order of matrix defined by (row × column). The follwing matrix have 1 row and 3 column. so, the correct option is..... (d) 1×3
If A is a square matrix of order 3 and |A| = 7 then |AT| =- a)7
- b)21
- c)1/7
- d)3
Correct answer is option 'A'. Can you explain this answer?
If A is a square matrix of order 3 and |A| = 7 then |AT| =
a)
7
b)
21
c)
1/7
d)
3
|
|
Preeti Khanna answered |
The determinant of a square matrix is the same as the determinant of its transpose.
One root of the equation 
- a)8
- b)2/3
- c)1/3
- d)5/3
Correct answer is option 'B'. Can you explain this answer?
One root of the equation
a)
8
b)
2/3
c)
1/3
d)
5/3
|
Neha Sharma answered |
Apply , R1→R1 +R2+R3,
⇒either (3x -2) = 0
Points (a,a,c),(1,0,1) and (c,c,b) are collinear if- a)a,b,c in GP
- b)a,b,c in AP
- c)C2 = ab
- d)C = ab
Correct answer is option 'C'. Can you explain this answer?
Points (a,a,c),(1,0,1) and (c,c,b) are collinear if
a)
a,b,c in GP
b)
a,b,c in AP
c)
C2 = ab
d)
C = ab
|
Riya Banerjee answered |
a(-c) - a(b-c) + c(c) = 0
- ac - ab + ac + c2 = 0
c2 = ab
- ac - ab + ac + c2 = 0
c2 = ab
The solution of the following system of equation is
2x + 3y = 5
5x – 2y = 3- a)x = 2, y = 3
- b)x = -1, y = -1
- c)x = 1, y = 1
- d)x = 3, y = 2
Correct answer is option 'C'. Can you explain this answer?
The solution of the following system of equation is
2x + 3y = 5
5x – 2y = 3
2x + 3y = 5
5x – 2y = 3
a)
x = 2, y = 3
b)
x = -1, y = -1
c)
x = 1, y = 1
d)
x = 3, y = 2
|
Naincy Tripathi answered |
Its vry easy just simply solve the eq. (2x + 3y = 5) × 5 (5x + 2y = 3) × 2 (10x + 15y = 25) (10x - 4y = 6) (10x will get cancelled ) 19y = 19 y = 1 (put the value of y in any of the two eq. u will get x = 1) (therefore option C is correct )
and A2 + aA + b = O, then the values of a and b are:
If 
, then A-1 =- a)-A
- b)I
- c)A
- d)-I
Correct answer is option 'C'. Can you explain this answer?
If , then A-1 =
, then A-1 =a)
-A
b)
I
c)
A
d)
-I
|
Vinod Kumar answered |
By using inverse formula we get option C is correct answer
- a)-10
- b)11
- c)12
- d)-13
Correct answer is option 'D'. Can you explain this answer?
a)
-10
b)
11
c)
12
d)
-13
|
Siddhesh Ovhal answered |
Using determinant method-9(2x+5)-3(5x+2)=3x+39=0...x=-39/3
If A and B matrices are of same order and A + B = B + A, this law is known as- a)distributive law
- b)commutative law
- c)associative law
- d)cramer's law
Correct answer is option 'B'. Can you explain this answer?
If A and B matrices are of same order and A + B = B + A, this law is known as
a)
distributive law
b)
commutative law
c)
associative law
d)
cramer's law
|
|
Anaya Patel answered |
Commutative law, in mathematics, either of two laws relating to number operations of addition and multiplication, stated symbolically: a + b = b + a and ab = ba
Value of the determinant 
- a)(a-b)2
- b)a2-b2
- c)(a+b)2
- d)a2
Correct answer is option 'A'. Can you explain this answer?
Value of the determinant
a)
(a-b)2
b)
a2-b2
c)
(a+b)2
d)
a2
|
Anshul Pareek answered |
= (a^2 + b^2)×1 - (2a) × b
= a^2 + b^2 - 2ab
= (a - b)^2
i.e. option A
= a^2 + b^2 - 2ab
= (a - b)^2
i.e. option A
Inverse of
, is- a)
- b)
- c)
- d)
Correct answer is option 'A'. Can you explain this answer?
Inverse of , is
, isa)
b)
c)
d)
|
Tanuja Kapoor answered |
A = {(6,7) (8,9)}
|A| = (6 * 9) - (8 * 7)
= 54 - 56
|A| = -2
A-1 = -½{(9,-7) (-8,6)}
A-1 = {(-9/2, 7/2) (4,-3)}
|A| = (6 * 9) - (8 * 7)
= 54 - 56
|A| = -2
A-1 = -½{(9,-7) (-8,6)}
A-1 = {(-9/2, 7/2) (4,-3)}
The operation that will simplify the Determinant
by taking (a+b+c) common from the first Row is- a)R2→R2+R1
- b)R1→R1+R2
- c)R1→R1-R2
- d)R1→R2-R1
Correct answer is option 'B'. Can you explain this answer?
The operation that will simplify the Determinant
by taking (a+b+c) common from the first Row is
a)
R2→R2+R1
b)
R1→R1+R2
c)
R1→R1-R2
d)
R1→R2-R1
|
|
Tejas Verma answered |
R1 ------> R1 + R2, taking (a+b+c) common from the first row, we get the resultant matrix.
Can you explain the answer of this question below:If A and B are invertible matrices of order 3 , then det (adj A) =
- A:
(detA)2
- B:
1
- C:
A−1
- D:
none of these
The answer is d.
If A and B are invertible matrices of order 3 , then det (adj A) =
(detA)2
1
A−1
none of these
|
Sinjini Tiwari answered |
Let A be a non singular square matrix of order n . then , |adj.A| = A−1
The cofactor of 5 in 
- a)3
- b)29
- c)-3
- d)5
Correct answer is option 'C'. Can you explain this answer?
The cofactor of 5 in
a)
3
b)
29
c)
-3
d)
5
|
|
Aryan Khanna answered |
A21 = {(0, -1) (3,4)}
⇒ (0 - (-3)) = 3
A21 = (-1)(2+1) (3)
= -3
⇒ (0 - (-3)) = 3
A21 = (-1)(2+1) (3)
= -3
- a)3 or 3/2
- b)3 or 6
- c)3
- d)none of these
Correct answer is option 'A'. Can you explain this answer?
a)
3 or 3/2
b)
3 or 6
c)
3
d)
none of these
|
Shivani answered |
I uploaded a document..hv a look at it...
System of equations AX = B is inconsistent if- a)│B│ = 0
- b)(adj A) B = 0
- c)(adj A) B ≠ 0
- d)│A│ ≠ 0
Correct answer is option 'C'. Can you explain this answer?
System of equations AX = B is inconsistent if
a)
│B│ = 0
b)
(adj A) B = 0
c)
(adj A) B ≠ 0
d)
│A│ ≠ 0
|
|
Rajesh Gupta answered |
If (adj A) B ≠ 0 (zero matrix), then the solution does not exist. The system of equations is inconsistent. Else, if (adj A) B = 0 then the system will either have infinitely many solutions (consistent system) or no solution (inconsistent system).
A system of linear equations AX = B is said to be inconsistent, if the system of equations has- a)Trivial Solution
- b)Infinite Solutions
- c)No Solution
- d)Unique Solutions
Correct answer is option 'C'. Can you explain this answer?
A system of linear equations AX = B is said to be inconsistent, if the system of equations has
a)
Trivial Solution
b)
Infinite Solutions
c)
No Solution
d)
Unique Solutions
|
|
Geetika Shah answered |
A linear system is said to be consistent if it has at least one solution; and is said to be inconsistent if it has no solution. have no solution, a unique solution, and infinitely many solutions, respectively.
- a)
- b)
- c)
- d)
Correct answer is option 'C'. Can you explain this answer?
a)
b)
c)
d)
|
Rahul Gill answered |
first interchange first and second row and remember negative sign now solving it will give -【(a+2x)(bz-yc)-(b+2y)(az-xc)+(c+2z)(ay-xb)】=【a(bx-yc)-b(az-xc)+c(ay-xb)】+【2x(bx-yc)-2y(az-xc)+2z(ay-xb)】 here secong term is the given determinant in question and first term is what to be calculated so it is clear the right answer is C.
If 
, then the relation between x and y is- a)y = -3x
- b)x = 3y
- c)x = -3y
- d)y = 3x
Correct answer is option 'D'. Can you explain this answer?
If , then the relation between x and y is
, then the relation between x and y isa)
y = -3x
b)
x = 3y
c)
x = -3y
d)
y = 3x
|
|
Poonam Reddy answered |
½{(0,0,1) (1,3,1) (x,y,1)} = 0
{(0,0,1) (1,3,1) (x,y,1)} = 0/(½)
{(0,0,1) (1,3,1) (x,y,1)} = 0
0(3-y) -0(1-x) +1(y-3x) = 0
=> y - 3x = 0
=> y = 3x
{(0,0,1) (1,3,1) (x,y,1)} = 0/(½)
{(0,0,1) (1,3,1) (x,y,1)} = 0
0(3-y) -0(1-x) +1(y-3x) = 0
=> y - 3x = 0
=> y = 3x
If A = 
, and |3A| = k|A|, then the value of k is- a)27
- b)1
- c)25
- d)4
Correct answer is option 'A'. Can you explain this answer?
If A = , and |3A| = k|A|, then the value of k is
, and |3A| = k|A|, then the value of k isa)
27
b)
1
c)
25
d)
4
|
Vikas Kapoor answered |
|kA| = kn|A|
|3A| = (3)n |A|
= 27|A| = k|A|
k = 27
|3A| = (3)n |A|
= 27|A| = k|A|
k = 27
If A and B are square matrices of order 3 , such that Det.A = –1 , Det.B = 3 then the determinant of 3AB is equal to- a)81
- b)–9
- c)–27
- d)-81
Correct answer is option 'D'. Can you explain this answer?
If A and B are square matrices of order 3 , such that Det.A = –1 , Det.B = 3 then the determinant of 3AB is equal to
a)
81
b)
–9
c)
–27
d)
-81
|
|
Nandini Patel answered |
∣3AB∣ = 3^3 ∣AB∣ = 27 x ∣A∣ x ∣B∣
We know,
∣A∣ = −1 and ∣B∣ = 3
So,
∣3AB∣ = 27 x ∣A∣ x ∣B∣ = 27x(−1)x3 = −81
If A is square matrix of order 3 and |A| = 7 then |AT| = ______- a)7
- b)3
- c)1/7
- d)21
Correct answer is option 'A'. Can you explain this answer?
If A is square matrix of order 3 and |A| = 7 then |AT| = ______
a)
7
b)
3
c)
1/7
d)
21
|
|
Nikita Singh answered |
The determinant of a square matrix is the same as the determinant of its transpose. Therefore |A’| = 7
If the value of the determinant 
is equal to 14, then the value of the determinant 
is equal to- a)-42
- b)42
- c)-14
- d)14
Correct answer is option 'B'. Can you explain this answer?
If the value of the determinant is equal to 14, then the value of the determinant is equal to
is equal to 14, then the value of the determinant is equal toa)
-42
b)
42
c)
-14
d)
14
|
|
Aryan Khanna answered |
Taking 3 common from the column I in second determinant, we get the 14 * 3 = 42
- a)−2(a+b+c)3
- b)2(a+b+c)2
- c)4(a+b+c)3
- d)none of these
Correct answer is option 'D'. Can you explain this answer?
a)
−2(a+b+c
)3
b)
2(a+b+c)2
c)
4(a+b+c)3
d)
none of these
|
Ayushi answered |
hint: R1-->R1+R2+R3 and take a+b+c common
If A is a non singular matrix of order 3 , then |adj(adjA)|- a)|A|6
- b)|A|3
- c)|A|4
- d)none of these
Correct answer is 'C'. Can you explain this answer?
If A is a non singular matrix of order 3 , then |adj(adjA)|
a)
|A|6
b)
|A|3
c)
|A|4
d)
none of these
|
Maulik Mehra answered |
where n is order of matrix. Here n = 3.
The system of equations kx + 2y – z = 1,
(k – 1)y – 2z = 2
(k + 2)z = 3 has a unique solution, if k is- a)– 1
- b)– 2
- c)1
- d)0
Correct answer is 'A'. Can you explain this answer?
The system of equations kx + 2y – z = 1,
(k – 1)y – 2z = 2
(k + 2)z = 3 has a unique solution, if k is
(k – 1)y – 2z = 2
(k + 2)z = 3 has a unique solution, if k is
a)
– 1
b)
– 2
c)
1
d)
0
|
|
Neha Sharma answered |
This system of equations has a unique solution, if
The cofactor of an element 9 of the determinant 
is :- a)48
- b)– 48
- c)27
- d)46
Correct answer is option 'B'. Can you explain this answer?
The cofactor of an element 9 of the determinant is :
is :a)
48
b)
– 48
c)
27
d)
46
|
Aditi Keshri answered |
When we will take cofactor of 9 then tahat particular row&column will not be considered rest will be cross multiplied then it will get -48
For a square matrix A in a matrix equation AX = B, if │A│≠ 0, then- a)There exists a unique solution
- b)There exists no solution
- c)There exists infinite number of solutions
- d)The system may or may not be consistent
Correct answer is option 'A'. Can you explain this answer?
For a square matrix A in a matrix equation AX = B, if │A│≠ 0, then
a)
There exists a unique solution
b)
There exists no solution
c)
There exists infinite number of solutions
d)
The system may or may not be consistent
|
|
Kritika Choudhary answered |
Solution:
Given, AX = B, where A is a square matrix.
If A is invertible (i.e., A 0), then there exists a unique solution for X.
Explanation:
When A is invertible, it means that there exists a unique matrix A-1 such that A-1A = I, where I is the identity matrix.
Now, if we multiply both sides of the given equation by A-1, we get:
A-1AX = A-1B
⇒ IX = A-1B (using A-1A = I)
⇒ X = A-1B
Hence, we get a unique solution for X, which is X = A-1B.
This is because the inverse of a matrix is unique, and so there can be only one solution for X.
Therefore, the correct option is (A) - There exists a unique solution.
Given, AX = B, where A is a square matrix.
If A is invertible (i.e., A 0), then there exists a unique solution for X.
Explanation:
When A is invertible, it means that there exists a unique matrix A-1 such that A-1A = I, where I is the identity matrix.
Now, if we multiply both sides of the given equation by A-1, we get:
A-1AX = A-1B
⇒ IX = A-1B (using A-1A = I)
⇒ X = A-1B
Hence, we get a unique solution for X, which is X = A-1B.
This is because the inverse of a matrix is unique, and so there can be only one solution for X.
Therefore, the correct option is (A) - There exists a unique solution.
Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): If the matrix 
is singular, then λ = 4.Reason (R): If A is a singular matrix, then |A|= 0.- a)Both A and R are true and R is the correct explanation of A
- b)Both A and R are true but R is NOT the correct explanation of A
- c)A is true but R is false
- d)A is false and R is True
Correct answer is option 'A'. Can you explain this answer?
Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.
Assertion (A): If the matrix is singular, then λ = 4.
is singular, then λ = 4.Reason (R): If A is a singular matrix, then |A|= 0.
a)
Both A and R are true and R is the correct explanation of A
b)
Both A and R are true but R is NOT the correct explanation of A
c)
A is true but R is false
d)
A is false and R is True
|
|
Varun Kapoor answered |
A matrix is said to be singular if |A| = 0
Hence R is true.
Hence A is true.
R is the correct explanation for A.
If 
, then equals- a)0
- b)–abc
- c)2abc
- d)none of these.
Correct answer is option 'A'. Can you explain this answer?
If , then equals
, then equalsa)
0
b)
–abc
c)
2abc
d)
none of these.
|
Ipsita Sen answered |
Because , the determinant of a skew symmetric matrix of odd order is always zero and of even order is a non zero perfect square.
The system AX = B of n equations in n unknowns has infinitely many solutions if- a)det. A ≠ 0
- b)if det. A = 0 , (adj A) B =O
- c)if det. A ≠ 0 , (adj A) B ≠ O
- d)if det. A = 0 , (adj A) B ≠ O
Correct answer is option 'B'. Can you explain this answer?
The system AX = B of n equations in n unknowns has infinitely many solutions if
a)
det. A ≠ 0
b)
if det. A = 0 , (adj A) B =O
c)
if det. A ≠ 0 , (adj A) B ≠ O
d)
if det. A = 0 , (adj A) B ≠ O
|
Nabanita Singh answered |
Explanation here if det. A = 0 , (adj A) B = O ⇒ The system AX = B of n equations in n unknowns may be consistent with infinitely many solutions or it may be inconsistent.
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