If \(\vec a,\;\vec b\) and \(\vec c\) are the position vectors of the vertices of an equilateral triangle whose orthocentre is at the origin, then which one of the following is correct?

\(\vec a + \vec b + \vec c =\) unit vector

\(\vec a + \vec b + \vec c = \vec 0\)

\(\vec a + \vec b + \vec c =\) unit vector

Let \(\vec a\) and \(\vec b\) be two vectors, which of the following vectors are not perpendicular to each other?

\(\vec a - \vec b\) and \(\vec a \times \vec b\)

\(\left(\vec a \times \vec b\right)\) and \(\vec a\)

\(\left(\vec a + \vec b\right)\) and \(\left(\vec a \times \vec b\right)\)

\(\vec a + \vec b\) and \(\vec a - \vec b\)

\(\vec a - \vec b\) and \(\vec a \times \vec b\)

If a and b are the roots of the equation Px2 - Qx + R = 0, then what is the value of (1/a2) + (1/b2) + (a/b) + (b/a)?

\(\frac{{\left( {{Q^2} - 2R} \right)\left( {2P + R} \right)}}{{{P^2}{R^2}}}\)

\(\frac{{\left( {{Q^2} - 2P} \right)\left( {2R + P} \right)}}{{P{R^2}}}\)

\(\frac{{\left( {{Q^2} - 2PR} \right)\left( {R + P} \right)}}{{P{R^2}}}\)

\(\frac{{\left( {{Q^2} - 2R} \right)\left( {2P + R} \right)}}{{{P^2}{R^2}}}\)

\(\frac{{\left( {{Q^2} - 2PR} \right)\left( {2R + 2P} \right)}}{{{P^2}{R^2}}}\)

If \({x^6} + \frac{1}{{{x^6}}} = k\left( {{x^2} + \frac{1}{{{x^2}}}} \right)\), then k is equal to

\(\left( {{x^4} + 1 + \frac{1}{{{x^4}}}} \right)\)

\(\left( {{x^2} - 1 + \frac{1}{{{x^2}}}} \right)\)

\(\left( {{x^4} - 1 + \frac{1}{{{x^4}}}} \right)\)

\(\left( {{x^4} + 1 + \frac{1}{{{x^4}}}} \right)\)

\(\left( {{x^4} - 1 - \frac{1}{{{x^4}}}} \right)\)

If z = 6 – 2√3, then find the value of \({\left( {\sqrt z - \frac{1}{{\sqrt z }}} \right)^2}\)

\(\frac{{12 - 46\sqrt 3 }}{{24}}\)

\(\frac{{102 - 46\sqrt 3 }}{4}\)

\(\frac{{102 - 46\sqrt 3 }}{2}\)

\(\frac{{102 - 46\sqrt 3 }}{{24}}\)

\(\frac{{12 - 46\sqrt 3 }}{{24}}\)

In the given question, two equations numbered l and II are given. You have to solve both the equations and mark the appropriate answerI. a2 - 8a + 12 = 0II. 8b2 + 10b + 3 = 0

a = b or the relationship cannot be determined

In the following question, two equations numbered I and II are given. You have to solve both the equations and give the answer:I. x2 – x - 12 = 0II. y2 + 5y + 6 = 0

x = y or the relation cannot be determined

In the given question, two equations numbered l and II are given. You have to solve both the equations and mark the appropriate answer.I. 3x2 - 8x + 4 = 0II. 6y2 - 7y - 10 = 0

Either x = y or Relationship between x and y cannot be established

If v1, v2, …., v6 are six vectors in R4, which one of the following statements is FALSE?

If {v1, v3, v5, v6} span R4, then it forms a basis for R4.

It is not necessary that these vectors span R4.

These vectors are not linearly independent

Any four of these vectors form a basis for R4

If {v1, v3, v5, v6} span R4, then it forms a basis for R4.

In the following question, two equations are given. You have to solve both the equations and find the relation between ‘x’ and ‘y’ and mark the correct answer.A. x2 – 16x + 63 = 0B. y2 – 19y + 88 = 0

if x = y or the relationship cannot be established.

1894 + Mcqs in Algebra Page 11 McqOptions

501.	For the matrix \(\left[ {\begin{array}{*{20}{c}} 4&1\\ 1&4 \end{array}} \right]\), the eigen values are
A.	3, -3
B.	-3, -5
C.	3, 5
D.	5, 0
Answer» D. 5, 0

Discussion

502.	If 3X – 3 < 3 + X/2 and X – 2 ≤ 6 + 2X; then X can be take which of the following values?
A.	6
B.	2
C.	10
D.	– 10
Answer» C. 10

Discussion

503.	If P = (√7 - √6)/(√7 + √6), then what is the value of P + (1/P)?
A.	12
B.	13
C.	24
D.	26
Answer» E.

Discussion

504.	In a group of 1300 students, every student reads 5 subjects and every subject is read by 65 students. The number of subjects are:
A.	exactly 100
B.	may be 250
C.	at the most 70
D.	at least 10
Answer» B. may be 250

Discussion

505.	If \(\vec a,\;\vec b\) and \(\vec c\) are the position vectors of the vertices of an equilateral triangle whose orthocentre is at the origin, then which one of the following is correct?
A.	\(\vec a + \vec b + \vec c = \vec 0\)
B.	\(\vec a + \vec b + \vec c =\) unit vector
C.	\(\vec a + \vec b = \vec c\)
D.	\(\vec a = \vec b + \vec c\)
Answer» B. \(\vec a + \vec b + \vec c =\) unit vector

Discussion

506.	If x2 + 8y2 - 12y - 4xy + 9 = 0, then the value of (7x - 8y) is:
A.	12
B.	9
C.	21
D.	5
Answer» C. 21

Discussion

507.	Let \(\vec a\) and \(\vec b\) be two vectors, which of the following vectors are not perpendicular to each other?
A.	\(\left(\vec a \times \vec b\right)\) and \(\vec a\)
B.	\(\left(\vec a + \vec b\right)\) and \(\left(\vec a \times \vec b\right)\)
C.	\(\vec a + \vec b\) and \(\vec a - \vec b\)
D.	\(\vec a - \vec b\) and \(\vec a \times \vec b\)
Answer» D. \(\vec a - \vec b\) and \(\vec a \times \vec b\)

Discussion

508.	If \(A = \left( {\begin{array}{*{20}{c}} 2&3&4\\ 0&4&2\\ 0&0&3 \end{array}} \right)\), the Eigenvalues of adj A and A2 – 2A + I are:
A.	2, 4, 3 and 49, 121, 25
B.	8, 12, 6 and 49, 121, 25
C.	4, 16, 9 and 16, 256, 81
D.	8, 12, 6 and -49, 100, 12
Answer» C. 4, 16, 9 and 16, 256, 81

Discussion

509.	If a and b are the roots of the equation Px2 - Qx + R = 0, then what is the value of (1/a2) + (1/b2) + (a/b) + (b/a)?
A.	\(\frac{{\left( {{Q^2} - 2P} \right)\left( {2R + P} \right)}}{{P{R^2}}}\)
B.	\(\frac{{\left( {{Q^2} - 2PR} \right)\left( {R + P} \right)}}{{P{R^2}}}\)
C.	\(\frac{{\left( {{Q^2} - 2R} \right)\left( {2P + R} \right)}}{{{P^2}{R^2}}}\)
D.	\(\frac{{\left( {{Q^2} - 2PR} \right)\left( {2R + 2P} \right)}}{{{P^2}{R^2}}}\)
Answer» C. \(\frac{{\left( {{Q^2} - 2R} \right)\left( {2P + R} \right)}}{{{P^2}{R^2}}}\)

Discussion

510.	If x + 1 = x2 and x > 0, then 2x4 is
A.	6 + 4 \(\sqrt{5}\)
B.	3 + 5 \(\sqrt{5}\)
C.	5 + 3 \(\sqrt{5}\)
D.	7 + 3 \(\sqrt{5}\)
Answer» E.

Discussion

511.	Mr. Ankit is on tour to Siachin and he has Rs. 360 for his expenditure. If he exceeds his tour by 4 days, he must trim down his daily expenditure by Rs. 3. For how many days is Mr. Ankit is on tour?
A.	20
B.	22
C.	24
D.	26
Answer» B. 22

Discussion

512.	If x + y + z = 0, then the value of (x2 + y2 + z2) ÷ (z2 – xy) is∶
A.	-1
B.	-2
C.	2
D.	1
Answer» D. 1

Discussion

513.	If \({x^6} + \frac{1}{{{x^6}}} = k\left( {{x^2} + \frac{1}{{{x^2}}}} \right)\), then k is equal to
A.	\(\left( {{x^2} - 1 + \frac{1}{{{x^2}}}} \right)\)
B.	\(\left( {{x^4} - 1 + \frac{1}{{{x^4}}}} \right)\)
C.	\(\left( {{x^4} + 1 + \frac{1}{{{x^4}}}} \right)\)
D.	\(\left( {{x^4} - 1 - \frac{1}{{{x^4}}}} \right)\)
Answer» C. \(\left( {{x^4} + 1 + \frac{1}{{{x^4}}}} \right)\)

Discussion

514.	If \(\frac {8 + 2\sqrt 3}{3\sqrt 3 + 5} = a\sqrt 3 - b,\) then the value of a + b is equal to:
A.	15
B.	16
C.	18
D.	24
Answer» D. 24

Discussion

515.	If z = 6 – 2√3, then find the value of \({\left( {\sqrt z - \frac{1}{{\sqrt z }}} \right)^2}\)
A.	\(\frac{{102 - 46\sqrt 3 }}{4}\)
B.	\(\frac{{102 - 46\sqrt 3 }}{2}\)
C.	\(\frac{{102 - 46\sqrt 3 }}{{24}}\)
D.	\(\frac{{12 - 46\sqrt 3 }}{{24}}\)
Answer» D. \(\frac{{12 - 46\sqrt 3 }}{{24}}\)

Discussion

516.	If the equations 3x - ay = 9 and x + y = 3 represent the same line then a =
A.	3
B.	-1
C.	-3
D.	none of these
Answer» D. none of these

Discussion

517.	For how many positive integers ‘n’, n3 - 8n2 + 20n - 13 is a prime?
A.	5
B.	7
C.	2
D.	3
Answer» E.

Discussion

518.	If a3 = 335 + b3 and a = 5 + b, then what is the value of a + b (given that a > 0 and b > 0)?
A.	7
B.	9
C.	16
D.	49
Answer» C. 16

Discussion

519.	If (a + 1⁄a) = 3, then find the value of (a4 + 1⁄a4).
A.	47
B.	12
C.	27
D.	49
Answer» B. 12

Discussion

520.	If x2 + 8y2 + 12y - 4xy + 9 = 0, then the value of (7x + 8y) is:
A.	9
B.	-33
C.	-9
D.	33
Answer» C. -9

Discussion

521.	If a + b = 4 and ab = -21, then what is the value of a3 + b3?
A.	370
B.	158
C.	185
D.	316
Answer» E.

Discussion

522.	In the given question, two equations numbered l and II are given. You have to solve both the equations and mark the appropriate answerI. a2 - 8a + 12 = 0II. 8b2 + 10b + 3 = 0
A.	a < b
B.	a > b
C.	a ≤ b
D.	a ≥ b
E.	a = b or the relationship cannot be determined
Answer» C. a ≤ b

Discussion

523.	If a - b = - 7 and a2 + b2 = 85, then find ab.
A.	18
B.	-30
C.	-44
D.	-60
Answer» B. -30

Discussion

524.	I take a book from a library containing 378 pages to be returned in a week’s time. If I can read 14 pages an hour for three hours daily, for how long should it be renewed so that the book can be fully read?
A.	1 days
B.	3 days
C.	4 days
D.	2 days
Answer» E.

Discussion

525.	If x3 + y3 = 16 and x + y = 4, then the value of x4 + y4 is:
A.	48
B.	32
C.	64
D.	30
Answer» C. 64

Discussion

526.	If \(X^{y^z}=1, Y^{z^x}=125\) and \(Z^{y^x}=243\) (x, y and z are natural numbers), then what is the value of 9x + 10y - 18z?
A.	18
B.	15
C.	12
D.	5
Answer» E.

Discussion

527.	If (2x – 1)3 + (3x – 4)3 + (x – 7)3 = (6x – 3) (3x – 4) (x – 7), then what is the value of x?
A.	5
B.	8
C.	2
D.	3
Answer» D. 3

Discussion

528.	(95)2 – (85)2 = ?
A.	1800
B.	18500
C.	18000
D.	17000
Answer» B. 18500

Discussion

529.	On dividing 15y3 – 30y2 + 12y – 12 by 3y – 6, the remainder is:A) 6B) 36C) 30D) 12
A.	D
B.	C
C.	B
D.	A
Answer» B. C

Discussion

530.	In the following question, two equations numbered I and II are given. You have to solve both the equations and give the answer:I. x2 – x - 12 = 0II. y2 + 5y + 6 = 0
A.	x > y
B.	x ≥ y
C.	x < y
D.	x ≤ y
E.	x = y or the relation cannot be determined
Answer» F.

Discussion

531.	If α and β are the roots of equation x2 – x + 1 = 0, then which equation will have roots α3 and β3?
A.	x2 + 2x + 1 = 0
B.	x2 – 2x – 1 = 0
C.	x2 + 3x – 1 = 0
D.	x2 – 3x + 1 = 0
Answer» B. x2 – 2x – 1 = 0

Discussion

532.	A is an (m × n) matrix with m > n and ‘I’ is Identity matrix. Let A1 = (AT A)-1 AT, Then which of the following statement is false?
A.	AA1A = A
B.	(AA1)2 = AA1
C.	AA1 = I
D.	AA1A = A1
Answer» E.

Discussion

533.	If \(2\left[ {{x^2} + \frac{1}{{{x^2}}}} \right] - 2\left[ {x - \frac{1}{x}} \right] - 8\; = \;0,\;\) then what are the two values of \(x - \frac{1}{x}?\)
A.	-1 or 2
B.	1 or -2
C.	-1 or -2
D.	1 or 2
Answer» B. 1 or -2

Discussion

534.	If x + x-1 = 4, then the value of \(\dfrac{\left(x^3+x^{-1}\right)}{\left(x^2-3x+1\right)}\) is:
A.	14
B.	12
C.	13
D.	11
Answer» B. 12

Discussion

535.	Let M be a real 4 × 4 matrix. Consider the following statements:S1: M has 4 linearly independent eigenvectors.S2: M has 4 distinct eigenvalues.S3: M is non-singular (invertible).Which one among the following is TRUE?
A.	S1 implies S2
B.	S1 implies S3
C.	S2 implies S1
D.	S3 implies S2
Answer» D. S3 implies S2

Discussion

536.	In the given question, two equations numbered l and II are given. You have to solve both the equations and mark the appropriate answer.I. 3x2 - 8x + 4 = 0II. 6y2 - 7y - 10 = 0
A.	x > y
B.	x < y
C.	x ≥ y
D.	x ≤ y
E.	Either x = y or Relationship between x and y cannot be established
Answer» F.

Discussion

537.	\(A = \left[ {\begin{array}{{20}{c}} 3&x\\ 2&y \end{array}} \right]\), \(B = \left[ {\begin{array}{{20}{c}} -2&2\\ z&3 \end{array}} \right]\), \(A + B= \left[ {\begin{array}{*{20}{c}} 1&-4\\ 0&2 \end{array}} \right]\) What is the value of x?
A.	-6
B.	6
C.	1/2
D.	0
Answer» B. 6

Discussion

538.	If v1, v2, …., v6 are six vectors in R4, which one of the following statements is FALSE?
A.	It is not necessary that these vectors span R4.
B.	These vectors are not linearly independent
C.	Any four of these vectors form a basis for R4
D.	If {v1, v3, v5, v6} span R4, then it forms a basis for R4.
Answer» D. If {v1, v3, v5, v6} span R4, then it forms a basis for R4.

Discussion

539.	If y = 5, then what is the value of \(10y\,\sqrt {{y^3} - {y^2}} \)?
A.	50√2
B.	500
C.	200√5
D.	100
Answer» C. 200√5

Discussion

540.	Maria was twice the age of Monica 7 years back. After 5 years, Monica’s age will be two third of Maria’s age. What was Maria’s age 3 years back?
A.	25 years
B.	28 years
C.	31 years
D.	35 years
E.	41 years
Answer» C. 31 years

Discussion

541.	Factorise X2 + 5X – 14.
A.	(X – 7) (X + 2)
B.	(X – 1) (X + 14)
C.	(X + 7) (X – 2)
D.	(X – 14) (X + 1)
Answer» D. (X – 14) (X + 1)

Discussion

542.	If x4 – 83x2 + 1 = 0, then a value of x3 – x-3 can be:
A.	739
B.	737
C.	756
D.	758
Answer» D. 758

Discussion

543.	In a group of 100 students, every student study 8 subjects and every subject is studied by 10 students. The number of subjects is:
A.	Exactly 80
B.	May be 50
C.	At most 30
D.	At least 90
Answer» B. May be 50

Discussion

544.	If \({3^{x^{1/4}}} + \;{4^{x^{1/4}}} = {5^{x^{1/4}}}\) then the value of x is:
A.	2
B.	16
C.	8
D.	4
Answer» C. 8

Discussion

545.	If xa × xb × xc = 1, the the value of a3 + b3 + c3 is
A.	0
B.	a + b + c
C.	abc
D.	3abc
Answer» E.

Discussion

546.	If 3x + 5 = 7, then x - 3 = ?
A.	-9/7
B.	9/7
C.	7//9
D.	-7/3
Answer» E.

Discussion

547.	Consider a 2 × 2 square matrix.\({\rm{A}} = \left[ {\begin{array}{*{20}{c}} {\rm{\sigma }}&{\rm{x}}\\ {\rm{\omega }}&{\rm{\sigma }} \end{array}} \right]\)where x is unknown. If the eigenvalues of the matrix A are (σ + jω) and (σ − jω), then x is equal to
A.	+ jω
B.	− jω
C.	+ω
D.	–ω
Answer» E.

Discussion

548.	A man has equal number of five, ten and twenty rupee notes amounting to Rs. 385. Find the total number of notes?
A.	13
B.	33
C.	15
D.	31
Answer» C. 15

Discussion

549.	A politician distributed 285 kg of sugar among the people of a village counting 1487. Find out how much sugar does each person get.
A.	1.91 kg
B.	191 kg
C.	0.191 kg
D.	19.1 kg
Answer» D. 19.1 kg

Discussion

550.	In the following question, two equations are given. You have to solve both the equations and find the relation between ‘x’ and ‘y’ and mark the correct answer.A. x2 – 16x + 63 = 0B. y2 – 19y + 88 = 0
A.	if x > y
B.	if x ≥ y
C.	if x < y
D.	if x ≤ y
E.	if x = y or the relationship cannot be established.
Answer» F.

Discussion

Explore topic-wise MCQs in General Aptitude.

For the matrix \(\left[ {\begin{array}{*{20}{c}} 4&1\\ 1&4 \end{array}} \right]\), the eigen values are

If 3X – 3 < 3 + X/2 and X – 2 ≤ 6 + 2X; then X can be take which of the following values?

If P = (√7 - √6)/(√7 + √6), then what is the value of P + (1/P)?

In a group of 1300 students, every student reads 5 subjects and every subject is read by 65 students. The number of subjects are:

If \(\vec a,\;\vec b\) and \(\vec c\) are the position vectors of the vertices of an equilateral triangle whose orthocentre is at the origin, then which one of the following is correct?

If x2 + 8y2 - 12y - 4xy + 9 = 0, then the value of (7x - 8y) is:

Let \(\vec a\) and \(\vec b\) be two vectors, which of the following vectors are not perpendicular to each other?

If \(A = \left( {\begin{array}{*{20}{c}} 2&3&4\\ 0&4&2\\ 0&0&3 \end{array}} \right)\), the Eigenvalues of adj A and A2 – 2A + I are:

If a and b are the roots of the equation Px2 - Qx + R = 0, then what is the value of (1/a2) + (1/b2) + (a/b) + (b/a)?

If x + 1 = x2 and x > 0, then 2x4 is

Mr. Ankit is on tour to Siachin and he has Rs. 360 for his expenditure. If he exceeds his tour by 4 days, he must trim down his daily expenditure by Rs. 3. For how many days is Mr. Ankit is on tour?

If x + y + z = 0, then the value of (x2 + y2 + z2) ÷ (z2 – xy) is∶

If \({x^6} + \frac{1}{{{x^6}}} = k\left( {{x^2} + \frac{1}{{{x^2}}}} \right)\), then k is equal to

If \(\frac {8 + 2\sqrt 3}{3\sqrt 3 + 5} = a\sqrt 3 - b,\) then the value of a + b is equal to:

If z = 6 – 2√3, then find the value of \({\left( {\sqrt z - \frac{1}{{\sqrt z }}} \right)^2}\)

If the equations 3x - ay = 9 and x + y = 3 represent the same line then a =

For how many positive integers ‘n’, n3 - 8n2 + 20n - 13 is a prime?

If a3 = 335 + b3 and a = 5 + b, then what is the value of a + b (given that a > 0 and b > 0)?

If (a + 1⁄a) = 3, then find the value of (a4 + 1⁄a4).

If x2 + 8y2 + 12y - 4xy + 9 = 0, then the value of (7x + 8y) is:

If a + b = 4 and ab = -21, then what is the value of a3 + b3?

In the given question, two equations numbered l and II are given. You have to solve both the equations and mark the appropriate answerI. a2 - 8a + 12 = 0II. 8b2 + 10b + 3 = 0

If a - b = - 7 and a2 + b2 = 85, then find ab.

I take a book from a library containing 378 pages to be returned in a week’s time. If I can read 14 pages an hour for three hours daily, for how long should it be renewed so that the book can be fully read?

If x3 + y3 = 16 and x + y = 4, then the value of x4 + y4 is:

If \(X^{y^z}=1, Y^{z^x}=125\) and \(Z^{y^x}=243\) (x, y and z are natural numbers), then what is the value of 9x + 10y - 18z?

If (2x – 1)3 + (3x – 4)3 + (x – 7)3 = (6x – 3) (3x – 4) (x – 7), then what is the value of x?

(95)2 – (85)2 = ?

On dividing 15y3 – 30y2 + 12y – 12 by 3y – 6, the remainder is:A) 6B) 36C) 30D) 12

In the following question, two equations numbered I and II are given. You have to solve both the equations and give the answer:I. x2 – x - 12 = 0II. y2 + 5y + 6 = 0

If α and β are the roots of equation x2 – x + 1 = 0, then which equation will have roots α3 and β3?

A is an (m × n) matrix with m > n and ‘I’ is Identity matrix. Let A1 = (AT A)-1 AT, Then which of the following statement is false?

If \(2\left[ {{x^2} + \frac{1}{{{x^2}}}} \right] - 2\left[ {x - \frac{1}{x}} \right] - 8\; = \;0,\;\) then what are the two values of \(x - \frac{1}{x}?\)

If x + x-1 = 4, then the value of \(\dfrac{\left(x^3+x^{-1}\right)}{\left(x^2-3x+1\right)}\) is:

Let M be a real 4 × 4 matrix. Consider the following statements:S1: M has 4 linearly independent eigenvectors.S2: M has 4 distinct eigenvalues.S3: M is non-singular (invertible).Which one among the following is TRUE?

In the given question, two equations numbered l and II are given. You have to solve both the equations and mark the appropriate answer.I. 3x2 - 8x + 4 = 0II. 6y2 - 7y - 10 = 0

\(A = \left[ {\begin{array}{*{20}{c}} 3&x\\ 2&y \end{array}} \right]\), \(B = \left[ {\begin{array}{*{20}{c}} -2&2\\ z&3 \end{array}} \right]\), \(A + B= \left[ {\begin{array}{*{20}{c}} 1&-4\\ 0&2 \end{array}} \right]\) What is the value of x?

If v1, v2, …., v6 are six vectors in R4, which one of the following statements is FALSE?

If y = 5, then what is the value of \(10y\,\sqrt {{y^3} - {y^2}} \)?

Maria was twice the age of Monica 7 years back. After 5 years, Monica’s age will be two third of Maria’s age. What was Maria’s age 3 years back?

Factorise X2 + 5X – 14.

If x4 – 83x2 + 1 = 0, then a value of x3 – x-3 can be:

In a group of 100 students, every student study 8 subjects and every subject is studied by 10 students. The number of subjects is:

If \({3^{x^{1/4}}} + \;{4^{x^{1/4}}} = {5^{x^{1/4}}}\) then the value of x is:

If xa × xb × xc = 1, the the value of a3 + b3 + c3 is

If 3x + 5 = 7, then x - 3 = ?

Consider a 2 × 2 square matrix.\({\rm{A}} = \left[ {\begin{array}{*{20}{c}} {\rm{\sigma }}&{\rm{x}}\\ {\rm{\omega }}&{\rm{\sigma }} \end{array}} \right]\)where x is unknown. If the eigenvalues of the matrix A are (σ + jω) and (σ − jω), then x is equal to

A man has equal number of five, ten and twenty rupee notes amounting to Rs. 385. Find the total number of notes?

A politician distributed 285 kg of sugar among the people of a village counting 1487. Find out how much sugar does each person get.

In the following question, two equations are given. You have to solve both the equations and find the relation between ‘x’ and ‘y’ and mark the correct answer.A. x2 – 16x + 63 = 0B. y2 – 19y + 88 = 0

\(A = \left[ {\begin{array}{{20}{c}} 3&x\\ 2&y \end{array}} \right]\), \(B = \left[ {\begin{array}{{20}{c}} -2&2\\ z&3 \end{array}} \right]\), \(A + B= \left[ {\begin{array}{*{20}{c}} 1&-4\\ 0&2 \end{array}} \right]\) What is the value of x?