Maths-
General
Easy
Question
Let a, b, c, d R. Then the cubic equation of the type
has either one root real or all three roots are real. But in case of trigonometric equations of the type
can possess several solutions depending upon the domain of x. To solve an equation of the type a
. The equation can be written as
The solution is
where
=
On the domain [–,
] the equation
possess
- only one real root
- three real roots
- our real roots
- six real roots
The correct answer is: six real roots
Related Questions to study
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maths-General
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The products (A) and (B) are:
The products (A) and (B) are:
chemistry-General
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If w is a complex cube root of unity, then the matrix A =
is a-
If w is a complex cube root of unity, then the matrix A =
is a-
maths-General
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Matrix [1 2]
is equal to-
Matrix [1 2]
is equal to-
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maths-
If A –2B =
and 2A – 3B =
, then matrix B is equal to–
If A –2B =
and 2A – 3B =
, then matrix B is equal to–
maths-General
maths-
The value of x for which the matrix A =
is inverse of B =
is
The value of x for which the matrix A =
is inverse of B =
is
maths-General
maths-
The greatest possible difference between two of the roots if [0, 2
] is
The greatest possible difference between two of the roots if [0, 2
] is
maths-General
maths-
Statement I :
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](data:image/png;base64,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)
Statement I :
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](data:image/png;base64,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)
maths-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 A
I and A
– I, then det A= – 1
Statement-II : If A
I and A
– I then tr(A)
0.
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 A
I and A
– I, then det A= – 1
Statement-II : If A
I and A
– I then tr(A)
0.
maths-General
maths-
Suppose
,
let x be a 2×2 matrix such that
AX = B
Statement-I : X is non singular & |x| = ±2
Statement-II : X is a singular matrix
Suppose
,
let x be a 2×2 matrix such that
AX = B
Statement-I : X is non singular & |x| = ±2
Statement-II : X is a singular matrix
maths-General
maths-
If
then
is equal to
If
then
is equal to
maths-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|
0, 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|
0, then X = A–1B
maths-General
maths-
Assertion (A): The inverse of the matrix
does not exist.
Reason (R) : The matrix
is singular. [![because](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAAKCAYAAABSfLWiAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAJufgqOgAAACRJREFUeNpjYMAE/6EYGwiAyi1nIACoYsgoIAzwBTR9DaEPAABHCgvlC8PdSAAAAFB0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bW8+JiN4MjIzNTs8L21vPjwvbWF0aD6HYN/sAAAAAElFTkSuQmCC)
= 0, since R2 = 2R1]
Assertion (A): The inverse of the matrix
does not exist.
Reason (R) : The matrix
is singular. [![because](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAAKCAYAAABSfLWiAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAJufgqOgAAACRJREFUeNpjYMAE/6EYGwiAyi1nIACoYsgoIAzwBTR9DaEPAABHCgvlC8PdSAAAAFB0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bW8+JiN4MjIzNTs8L21vPjwvbWF0aD6HYN/sAAAAAElFTkSuQmCC)
= 0, since R2 = 2R1]
maths-General
maths-
Assertion (A):
is a diagonal matrix
Reason (R) : A square matrix A = (aij) is a diagonal matrix if aij = 0 for all i
j.
Assertion (A):
is a diagonal matrix
Reason (R) : A square matrix A = (aij) is a diagonal matrix if aij = 0 for all i
j.
maths-General
maths-
Consider
= – 1, where ai. aj + bi. bj + ci.cj =
and i, j = 1,2,3
Assertion(A) : The value of
is equal to zero
Reason(R) : If A be square matrix of odd order such that AAT = I, then | A + I | = 0
Consider
= – 1, where ai. aj + bi. bj + ci.cj =
and i, j = 1,2,3
Assertion(A) : The value of
is equal to zero
Reason(R) : If A be square matrix of odd order such that AAT = I, then | A + I | = 0
maths-General