f(x) = $\left|\begin{array}{ccc}1& \mathrm{x}& \mathrm{x} + 1\\ 2\mathrm{x}& \mathrm{x}\left(\mathrm{x} - 1\right)& \left(\mathrm{x} + 1\right)\mathrm{x}\\ 3\mathrm{x}\left(\mathrm{x} - 1\right)& \mathrm{x}\left(\mathrm{x} - 1\right)\left(\mathrm{x} - 2\right)& \left(\mathrm{x} + 1\right)\mathrm{x}\left(\mathrm{x} - 1\right)\end{array}\right|$ then f(100) is equal to :

• 0

• 1

• 100

• - 100

If ${\mathrm{p\lambda }}^4 + {\mathrm{q\lambda }}^3 + {\mathrm{r\lambda }}^2 + \mathrm{s\lambda } + \mathrm{t} = \left|\begin{array}{ccc}{\mathrm{\lambda }}^2 + 3\mathrm{\lambda }& \mathrm{\lambda } - 1& \mathrm{\lambda } + 3\\ \mathrm{\lambda } + 1& 2 - \mathrm{\lambda }& \mathrm{\lambda } - 3\\ \mathrm{\lambda } - 3& \mathrm{\lambda } + 4& 3\mathrm{\lambda }\end{array}\right|$ then t is equal to :

• 33

• 22

• 21

• - 33

3.

Let A be a square matrix of order 3. If $\left|\mathrm{A}\right|$ = - 2, then the value of determinant of $\left|\mathrm{A}\right|$ adj A is :

• 8

• - 8

• - 1

• 32

If f(x) = $\left|\begin{array}{ccc}\mathrm{x} - 3& 2{\mathrm{x}}^2 - 18& 3{\mathrm{x}}^3 - 81\\ \mathrm{x} - 5& 2{\mathrm{x}}^2 - 50& 4{\mathrm{x}}^3 - 500\\ 1& 2& 3\end{array}\right|$, then f(1) . f(3) + f(3) . f(5) + f(5) . f(1) is equal to

• f(1)

• f(3)

• f(1) + f(3)

• f(1) + f(5)

If A = $\left[\begin{array}{ccc}1& - 1& 1\\ 0& 2& - 3\\ 2& 1& 0\end{array}\right]$ and B = (adj A), and C = 5A, then $\frac{\left|\mathrm{adj} \mathrm{B}\right|}{\left|\mathrm{C}\right|}$ is equal to :

• 5

• 25

• - 1

• 1

The output s as a Boolean expression in the inputs x₁, x₂ and x₃ for the logic circuit in the following figure is

• x₁ x^'₂ + x^'₂ + x₃

• x₁ + x'₂x₃ + x₃

• (x₁x₂)' + x₁x'₂x₃

• x₁x'₂ + x'₂x₃

Let D₇₀ = {1, 2, 57, 10, 14, 35, 70} Define '+', '·' and '" by a + b = lcm (a, b), a . b = gcd (a, b) and a' = $\frac{70}{2}$ for all a, b $\in$ D₇₀. The value of (2 + 7)(14 . 10)' is

• 7

• 14

• 35

• 5

Let a be any element in a Boolean Algebra B. If a + x = 1 and ax = 0, then :

• x = 1

• x = 0

• x = a

• x = a'

then s is equal to :

• x . (y' + z)

• x . (y' + z')

• x . (y + z)

• (x + y) . z

If $\sin \left({\sin }^{-1}\left(\frac{1}{5}\right) + {\cos }^{-1}\left(\mathrm{x}\right)\right) = 1$, then the value of x is :

• - 1

• $\frac{2}{5}$

• $\frac{1}{3}$

• $\frac{1}{5}$