Scalar Matrix

Q. 3 3 3
without actually calculating the cubes, find the value of 30 + 20 - 50

Q. How to calculate (8)^2/5

Q. If A is a square matrix of order n and A=kB, where k is a scalar, then |A|=

1. $|B|$
2. $k|B|$
3. $k^n|B|$
4. $n|B|$

Q. If I is a unit matrix, then 3I will be

1. A unit matrix
2. A triangular matrix
3. A scalar matrix
4. None of these

Q. For any positive real number x, find the value of

${\left(\frac{x^a}{x^b}\right)}^{a+b}\times {\left(\frac{x^b}{x^c}\right)}^{b+c}\times {\left(\frac{x^c}{x^a}\right)}^{c+a}$

Q. Let $\left[x\right]$ denote the greatest integer less than or equal to $x$ for any real number $x$. Then $\underset{n\to \infty }{lim}\frac{\left[n\sqrt{2}\right]}{n}$ is equal to

1. $0$
2. $2$
3. $\sqrt{2}$
4. $1$

Q. If $A=\left[\begin{array}{cc}i& -i\\ -i& i\end{array}\right]$ and $B=\left[\begin{array}{cc}1& -1\\ -1& 1\end{array}\right]$, then $A^8$ equals

1. $4B$
2. $128B$
3. $-128B$
4. $-64B$

Q. Integrate with respect to $x$
$\frac{1}{(x+1)(x+2)}$

Q.

1. By converting into dicimal form

2. By visualization

3. By the process of successive magnification

4. By using Pythogoras Theorem ( Geometrical construction)

Q. The number of real values of $x$ satisfying $\left|\begin{array}{ccc}x& 3x+2& 2x-1\\ 2x-1& 4x& 3x+1\\ 7x-2& 17x+6& 12x-1\end{array}\right|=0$ is

1. 0
2. 1
3. infinite
4. 3

Q. 5^7 x 5^4 divided by 5^8 Is BODMAS applicable here?

Q. If X = { (2^n)-1:n belongs to N} and Y= { 7n:n belongs to N}, then (A) X=Y (B) X is subset of Y (C) Y is subset of X (D) none of these

Q.

If k is scalar $(k\ne 0)$, I is an identity matrix and A is a square matrix . Then which among the following will always be a scalar matrix.

1. kA

2. kI

3. 

4. 

Q. If P, Q and R are subsets of a set A, then R × [(P^c ∪ Q^c)]C is