If A = \(\left[ \begin{matrix} 2 & 0 \\ 1 & 5 \end{matrix} \right] \) and B = \(\left[ \begin{matrix} 1 & 4 \\ 2 & 0 \end{matrix} \right] \) then |adj (AB)| = 

(a)

-40

(b)

-80

(c)

-60

(d)

-20

iⁿ+iⁿ⁺¹+iⁿ⁺²+iⁿ⁺³ is

(a)

0

(b)

1

(c)

-1

(d)

i

If \(\alpha \) and \(\beta \) are the roots of x²+x+1 = 0, then \({ \alpha }^{ 2020 }+{ \beta }^{ 2020 }\) is

(a)

-2

(b)

-1

(c)

1

(d)

2

If z = \(\frac { 1 }{ (2+3i)^{ 2 } } \) then |z| = ____________

(a)

\(\frac { 1 }{ 13 } \)

(b)

\(\frac { 1 }{ 5} \)

(c)

\(\frac { 1 }{ 12 } \)

(d)

none of these

lf the root of the equation x³ + bx²+ cx - 1 = 0 form an lncreasing G.P, then ___________

(a)

one of the roots is 2

(b)

one of the roots is 1

(c)

one of the roots is -1

(d)

one of the roots is -2

If sin^-1 x+sin^-1 y+sin^-1 \(z = \frac{3\pi}{2}\), the value of x²⁰¹⁷+y²⁰¹⁸+z²⁰¹⁹\(-\frac { 9 }{ { x }^{ 101 }+{ y }^{ 101 }+{ z }^{ 101 } } \)is

(a)

0

(b)

1

(c)

2

(d)

3

The radius of the circle passing through the point(6, 2) two of whose diameter are x + y = 6 and x + 2y = 4 is

(a)

10

(b)

\( {2} \sqrt {5}\)

(c)

6

(d)

4

If \(\vec { a } ,\vec { b } ,\vec { c } \) are three unit vectors such that \(\vec { a } \) is perpendicular to \(\vec { b } \) and is parallel to \(\vec { c } \) then \(\vec { a } \times (\vec { b } \times \vec { c } )\) is equal to

(a)

\(\vec { a } \)

(b)

\(\vec { b} \)

(c)

\(\vec { c } \)

(d)

\(\vec { 0 } \)

If the planes \(\vec { r } .(2\hat { i } -\lambda \hat { j } +\hat { k } )=3\) and \(\vec { r } .(4\hat{i}+\hat { j } -\mu \hat { k } )=5\) are parallel, then the value of λ and μ are

(a)

\(\frac { 1 }{ 2 } ,-2\)

(b)

\(-\frac { 1 }{ 2 } ,2\)

(c)

\(-\frac { 1 }{ 2 } ,-2\)

(d)

\(\frac { 1 }{ 2 } ,2\)

Which one of the following is not true?

(a)

Negation of a negation of a statement is the statement itself

(b)

If the last column of the truth table contains only T then it is a tautology.

(c)

If the last column of its truth table contains only F then it is a contradiction

(d)

If p and q are any two statements then p↔️q is a tautology.