Maths-
General
Easy

Question

The greatest possible difference between two of the roots if  theta element of  [0, 2straight pi] is

  1. 2
  2. 1
  3. square root of 2
  4. 2square root of 2

The correct answer is: 2

Related Questions to study

General
maths-

Statement I : open square brackets table row 5 0 0 row 0 3 0 row 0 0 2 end table close square brackets is a diagonal matrix.
Statement II : A square matrix A = (aij) is a diagonal matrix if aij = 0 .for all straight i times not equal to straight j

Statement I : open square brackets table row 5 0 0 row 0 3 0 row 0 0 2 end table close square brackets is a diagonal matrix.
Statement II : A square matrix A = (aij) is a diagonal matrix if aij = 0 .for all straight i times not equal to straight j

maths-General
General
maths-

Let A be a 2 × 2 matrix with real entries. Let I be the 2 × 2 identity. Denote by tr(A), The sum of diagonal entries of A, Assume that A2 = I.
Statement-I :If Anot equal toI and Anot equal to– I, then det  A= – 1
Statement-II : If A not equal to I and A not equal to – I then tr(A)not equal to0.

Let A be a 2 × 2 matrix with real entries. Let I be the 2 × 2 identity. Denote by tr(A), The sum of diagonal entries of A, Assume that A2 = I.
Statement-I :If Anot equal toI and Anot equal to– I, then det  A= – 1
Statement-II : If A not equal to I and A not equal to – I then tr(A)not equal to0.

maths-General
General
maths-

Suppose A equals open square brackets table row 1 0 row 0 cell negative 1 end cell end table close square brackets, B equals open square brackets table row 2 0 row 0 cell negative 2 end cell end table close square brackets let x be a 2×2 matrix such that X to the power of straight primeAX = B
Statement-I : X is non singular & |x| = ±2
Statement-II : X is a singular matrix

Suppose A equals open square brackets table row 1 0 row 0 cell negative 1 end cell end table close square brackets, B equals open square brackets table row 2 0 row 0 cell negative 2 end cell end table close square brackets let x be a 2×2 matrix such that X to the power of straight primeAX = B
Statement-I : X is non singular & |x| = ±2
Statement-II : X is a singular matrix

maths-General
parallel
General
maths-

If 2 tan invisible function application A equals 3 tan invisible function application B comma then fraction numerator sin invisible function application 2 B over denominator 5 minus cos invisible function application 2 B end fractionis equal to

If 2 tan invisible function application A equals 3 tan invisible function application B comma then fraction numerator sin invisible function application 2 B over denominator 5 minus cos invisible function application 2 B end fractionis equal to

maths-General
General
maths-

Statement-I : If A & B are two 3×3 matrices such that AB = 0, then A = 0 or B = 0
Statement-II : If A, B & X are three 3×3 matrices such that AX = B, |A| not equal to0, then X = A–1B

Statement-I : If A & B are two 3×3 matrices such that AB = 0, then A = 0 or B = 0
Statement-II : If A, B & X are three 3×3 matrices such that AX = B, |A| not equal to0, then X = A–1B

maths-General
General
maths-

Assertion (A): The inverse of the matrix open square brackets table row 1 3 5 row 2 6 10 row 9 8 7 end table close square brackets does not exist.
Reason (R) : The matrix open square brackets table row 1 3 5 row 2 6 10 row 9 8 7 end table close square brackets is singular. [becauseopen vertical bar table row 1 3 5 row 2 6 10 row 9 8 7 end table close vertical bar = 0, since R2 = 2R1]

Assertion (A): The inverse of the matrix open square brackets table row 1 3 5 row 2 6 10 row 9 8 7 end table close square brackets does not exist.
Reason (R) : The matrix open square brackets table row 1 3 5 row 2 6 10 row 9 8 7 end table close square brackets is singular. [becauseopen vertical bar table row 1 3 5 row 2 6 10 row 9 8 7 end table close vertical bar = 0, since R2 = 2R1]

maths-General
parallel
General
maths-

Assertion (A): open square brackets table row 5 0 0 row 0 3 0 row 0 0 9 end table close square brackets is a diagonal matrix
Reason (R) : A square matrix A = (aij) is a diagonal matrix if aij = 0 for all i not equal to j.

Assertion (A): open square brackets table row 5 0 0 row 0 3 0 row 0 0 9 end table close square brackets is a diagonal matrix
Reason (R) : A square matrix A = (aij) is a diagonal matrix if aij = 0 for all i not equal to j.

maths-General
General
maths-

Consider open vertical bar table row cell a subscript 1 end subscript end cell cell b subscript 1 end subscript end cell cell c subscript 1 end subscript end cell row cell a subscript 2 end subscript end cell cell b subscript 2 end subscript end cell cell c subscript 2 end subscript end cell row cell a subscript 3 end subscript end cell cell b subscript 3 end subscript end cell cell c subscript 3 end subscript end cell end table close vertical bar= – 1, where ai. aj + bi. bj + ci.cj = open square brackets table row cell 0 semicolon end cell cell i not equal to j end cell row cell 1 semicolon end cell cell i equals j end cell end table close and i, j = 1,2,3
Assertion(A) : The value of open vertical bar table row cell a subscript 1 end subscript plus 1 end cell cell b subscript 1 end subscript end cell cell c subscript 1 end subscript end cell row cell a subscript 2 end subscript end cell cell b subscript 2 end subscript plus 1 end cell cell c subscript 2 end subscript end cell row cell a subscript 3 end subscript end cell cell b subscript 3 end subscript end cell cell c subscript 3 end subscript plus 1 end cell end table close vertical bar is equal to zero
Reason(R) : If A be square matrix of odd order such that AAT = I, then | A + I | = 0

Consider open vertical bar table row cell a subscript 1 end subscript end cell cell b subscript 1 end subscript end cell cell c subscript 1 end subscript end cell row cell a subscript 2 end subscript end cell cell b subscript 2 end subscript end cell cell c subscript 2 end subscript end cell row cell a subscript 3 end subscript end cell cell b subscript 3 end subscript end cell cell c subscript 3 end subscript end cell end table close vertical bar= – 1, where ai. aj + bi. bj + ci.cj = open square brackets table row cell 0 semicolon end cell cell i not equal to j end cell row cell 1 semicolon end cell cell i equals j end cell end table close and i, j = 1,2,3
Assertion(A) : The value of open vertical bar table row cell a subscript 1 end subscript plus 1 end cell cell b subscript 1 end subscript end cell cell c subscript 1 end subscript end cell row cell a subscript 2 end subscript end cell cell b subscript 2 end subscript plus 1 end cell cell c subscript 2 end subscript end cell row cell a subscript 3 end subscript end cell cell b subscript 3 end subscript end cell cell c subscript 3 end subscript plus 1 end cell end table close vertical bar is equal to zero
Reason(R) : If A be square matrix of odd order such that AAT = I, then | A + I | = 0

maths-General
General
maths-

Assertion(A) : The inverse of the matrix A = [Aij]n × n where aij = 0, i greater or equal than j is B = [aij–1]n× n 
Reason(R): The inverse of singular matrix does not exist

Assertion(A) : The inverse of the matrix A = [Aij]n × n where aij = 0, i greater or equal than j is B = [aij–1]n× n 
Reason(R): The inverse of singular matrix does not exist

maths-General
parallel
General
maths-

Assertion : The product of two diagonal matrices of order 3 × 3 is also a diagonal matrix
Reason : matrix multiplicationis non commutative

Assertion : The product of two diagonal matrices of order 3 × 3 is also a diagonal matrix
Reason : matrix multiplicationis non commutative

maths-General
General
maths-

Assertion : If A is a skew symmetric of order 3 then its determinant should be zero.
Reason : If A is square matrix then det A = det straight A to the power of straight prime = det (–straight A to the power of straight prime)

Assertion : If A is a skew symmetric of order 3 then its determinant should be zero.
Reason : If A is square matrix then det A = det straight A to the power of straight prime = det (–straight A to the power of straight prime)

maths-General
General
maths-

Assertion : There are only finitely many 2 × 2 matrices which commute with the matrix open square brackets table row 1 2 row cell negative 1 end cell cell negative 1 end cell end table close square brackets
Reason : If A is non-singular then it commutes with I, adj A and A–1

Assertion : There are only finitely many 2 × 2 matrices which commute with the matrix open square brackets table row 1 2 row cell negative 1 end cell cell negative 1 end cell end table close square brackets
Reason : If A is non-singular then it commutes with I, adj A and A–1

maths-General
parallel
General
Maths-

Statement-I The equation square root of 3 cos space x minus sin space x equals 2 has exactly one solution in [0, 2straight pi].

Statement-II For equations of type a cos space theta plus b sin space theta equals c to have real solutions in left square bracket 0 comma 2 pi right square bracket comma vertical line c vertical line less or equal than square root of a squared plus b squared end root  should hold true.

In this question, we have to find the statements are the correct or not and statement 2 is correct explanation or not , is same like assertion and reason. Here, Start solving first Statement and try to prove it . Then solve the Statement-II . Remember cos a cosb -sin a sinb = cos ( a + b ) and sin a cosb + cosa sinb = sin( a+ b) .

Statement-I The equation square root of 3 cos space x minus sin space x equals 2 has exactly one solution in [0, 2straight pi].

Statement-II For equations of type a cos space theta plus b sin space theta equals c to have real solutions in left square bracket 0 comma 2 pi right square bracket comma vertical line c vertical line less or equal than square root of a squared plus b squared end root  should hold true.

Maths-General

In this question, we have to find the statements are the correct or not and statement 2 is correct explanation or not , is same like assertion and reason. Here, Start solving first Statement and try to prove it . Then solve the Statement-II . Remember cos a cosb -sin a sinb = cos ( a + b ) and sin a cosb + cosa sinb = sin( a+ b) .

General
maths-

Assertion : If A is a skew symmetric matrix of order 3 then its determinant should be zero.
Reason : If A is square matrix then det A = det straight A to the power of straight prime  = det (–straight A to the power of straight prime)

Assertion : If A is a skew symmetric matrix of order 3 then its determinant should be zero.
Reason : If A is square matrix then det A = det straight A to the power of straight prime  = det (–straight A to the power of straight prime)

maths-General
General
maths-

Assertion : There are only finitely many 2 × 2 matrices which commute with the matrix
open square brackets table attributes columnalign center center columnspacing 1em end attributes row 1 2 row cell negative 1 end cell cell negative 1 end cell end table close square brackets
Reason : If A is non-singular then it commutes with I, adj A and A–1

Assertion : There are only finitely many 2 × 2 matrices which commute with the matrix
open square brackets table attributes columnalign center center columnspacing 1em end attributes row 1 2 row cell negative 1 end cell cell negative 1 end cell end table close square brackets
Reason : If A is non-singular then it commutes with I, adj A and A–1

maths-General
parallel

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