Identity Matrix

Q.

If $\omega$ is a cube root of unity then the value of $(1-\omega +{\omega }^2{)}^5+(1+\omega -{\omega }^2{)}^5$ is

1. $30$

2. $32$

3. $2$

4. None of these

Q.

p³+ q³ + r³ – 3pqr = ?

1. (p - q - r)³

2. 3pqr

3. (p + q + r)(p² + q² + r² – pq – qr - pr)

4. (p + q +r)³

Q. A matrix with only one column could be called ____ matrix.

1. square
2. identity
3. column
4. row

Q.

If 10^x=64 then what is the value of 10^{(x/2) +1}

Q.

If ab+bc+ac=0, find the value of (1/a^2-bc)+(1/b^2-ca)+(1/c^2-ab)

Q.

The volume of a cube is given by the polynomial p(x)= 27x³+54x²+36x+8 find the possible expression for the side of the cube

Q.

A= {1, 4, 9, 16, 25, 36, 49, 64, 81, 100} write the sets using rule method

Q.

p³+ q³ = ?

1. (p + q)(p² + q² – p q)

2. (p + q)(p² + q² + p q)

3. (p + q)³

4. p³ + q³ + 3pq

Q. Let $A=\left[\begin{array}{ccc}0& 0& -1\\ 0& -1& 0\\ -1& 0& 0\end{array}\right]$. The only correct statement about the matrix A is

1. A is a zero matrix
2. $A^2=I$
3. $A^{-1}$ does not exist.
4. A = (-1)I, where I is a unit matrix.

Q.

Slove using identities (x+1)whole cube -(x-1) whole cube

Q.

x^{​​​​​​6} - 729 (Factorise)

Q. Simplify:

Q. Prove that (5^{125-1)/(5^{25-1) is a composite number.

Q.

Simplify (256)^8

Q. \sqrt{ab}(x^2+1)+x (a+b) is equal to

Q.

(997)² ?

Q.

a³ - b³ equals

1. (a- b)³ 3ab

2. (a + b)(a² - b² - ab)

3. (a – b)(a² + b² + ab)

4. (a + b)(a² + b² + ab)

Q.

Expand each of the following, using suitable identities:

(i) (ii)

(iii) (iv)

(v) (vi)

Q. Let $P=\left[\begin{array}{ccc}1& 0& 0\\ 4& 1& 0\\ 16& 4& 1\end{array}\right]$ and I be the identity matrix of order 3. If $Q=\left[q_{ij}\right]$ is a matrix, such that $P^{50}-Q=I$, then $\frac{q_{31}+q_{32}}{q_{21}}$ equals

1. 52
2. 103
3. 201
4. 205

Q. What is the order of the transpose of a matrix of order 2x9?

1. 2x2
2. 9x9
3. 9x2
4. 2x9

Q.

a³ - b³ equals

1. (a + b)(a² + b² + a b)

2. (a – b)(a² + b² + a b)

3. (a- b)³ 3ab

4. (a + b)(a² - b² - ab)

Q.

Find the value of (12m – 15n)²

1. 122m² – 360mn + 225n²

2. 144m² – 360mn + 225n²

3. 144m² + 360mn + 125n²

4. 144m² – 180mn + 225n²

Q.

Find the value of (12m – 15n)²

1. 122m² – 360mn + 225n²

2. 144m² + 360mn + 125n²

3. 144m² – 360mn + 225n²

4. 144m² – 180mn + 225n²

Q.

Evaluate: (102)²

1. 10404

2. 10440

3. 10044

4. 10444

Q. The average temperature of the first three days of a week is ${27}^{\circ }C$ and the next three days is ${29}^{\circ }C$. If the weekly average is ${28.5}^{\circ }C$, What is the temperature on the last day?

1. ${42}^{\circ }C$
2. ${31.5}^{\circ }C$
3. ${28}^{\circ }C$
4. ${21}^{\circ }C$

Q. If A is a $3\times 3$ non-singular matrix such that $A{A}^{\prime }=A^{\prime }A$ and $B=A^{-1}{A}^{\prime }$ then BB' equals

1. I
2. $B^{-1}$
3. I + B
4. $\left(B^{-1}\right)$

Q.

p³+ q³ = ?

1. (p + q)³

2. (p + q)(p² + q² + p q)

3. (p + q)(p² + q² – p q)

4. p³ + q³ + 3pq

Q.

Evaluate: (102)²

1. 10044

2. 10440

3. 10404

4. 10444

Q. What is the (X+1/X) whole square & (X-1/X)whole square exponent formula??

Q. Solution of $a^{\frac{4}{3}}÷a^{-\frac{2}{3}}$ is $a^2$.

1. True
2. False