NDA MATHEMATICS QUIZ - 11

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Question 1:

If $a + b + c = s$ then the value of the determinant $| \begin{array}{ccc} s + c & a & b \\ c & s + a & b \\ c & a & s + b \end{array} |$ is.

यदि $a + b + c = s$ तो सारणिक $| \begin{array}{ccc} s + c & a & b \\ c & s + a & b \\ c & a & s + b \end{array} |$ का मान है।

s^{3}

s^{3}

2 s^{3}

2 s^{3}

3 s^{3}

3 s^{3}

2 s

2 s

Question 2:

If $X = [\begin{array}{ll} 1 & 2 \\ 2 & 3 \end{array}]$ and $X^{2} - k X - I_{2} = 0$

then $k$ equals.

यदि $X = [\begin{array}{ll} 1 & 2 \\ 2 & 3 \end{array}]$ और $X^{2} - k X - I_{2} = 0$

तो $k$ का मान कौन सा होगा ?

4.0

5.0

2.0

3.0

Question 3:

If $X = [\begin{array}{cc} 3 & - 5 \\ - 4 & 2 \end{array}]$ then the value of $X^{2} - 5 X - 14$ is equal to.

यदि $X = [\begin{array}{cc} 3 & - 5 \\ - 4 & 2 \end{array}]$ है तो $X^{2} - 5 X - 14 I$ का मान कौन सा होगा ?

3 I

3 I

0.0

2 X

2 X

None of these

Question 4:

The determinant $| \begin{array}{ccc} 1 & 1 & 1 \\ a & b & c \\ a^{3} & b^{3} & c^{3} \end{array} |$ where $a \neq b \neq c$ is divisible by .

सरणीक $| \begin{array}{ccc} 1 & 1 & 1 \\ a & b & c \\ a^{3} & b^{3} & c^{3} \end{array} |$ जहां $a \neq b \neq c$ से विभाज्य है।

a b c

a b c

(a - b) (b - c)

(a - b) (b - c)

(a + b + c)

(a + b + c)

(\frac{1}{a} + \frac{1}{b} + \frac{1}{c})

(\frac{1}{a} + \frac{1}{b} + \frac{1}{c})

Question 5:

If $X$ is a square matrix then $X + X^{T}$ is a .

यदि $X$ एक वर्ग आव्यूह है तो $X + X^{T}$ एक है।

Skew symmetric matrix

symmetric matrix

unit matrix

Non-singular matrix

Question 6:

If $A = [\begin{array}{lll} 3 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 3 \end{array}]$ then $A^{5}$ equals .

यदि $A = [\begin{array}{lll} 3 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 3 \end{array}]$ तो $A^{5}$ =

27 A

27 A

9 A

9 A

81 A

81 A

3 A

3 A

Question 7:

If the inverse of matrix $A = [\begin{array}{lll} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 3 & λ & 5 \end{array}]$ exists then $λ$ must not be equal to.

यदि मैट्रिक्स $A = [\begin{array}{llll} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 3 & λ & 5 \end{array}]$ का व्युत्क्रम मौजूद है तो $λ$ के मान किसके बराबर नहीं होना चाहिए ?

2.0

3.0

1.0

4.0

Question 8:

Let X = $[\begin{array}{cc} 1 & \frac{- 1 - \sqrt{3 i}}{2} \\ \frac{- 1 + \sqrt{3} i}{2} & 1 \end{array}]$ then $X^{50}$ equals.

माना X = $[\begin{array}{cc} 1 & \frac{- 1 - \sqrt{3 i}}{2} \\ \frac{- 1 + \sqrt{3} i}{2} & 1 \end{array}]$ तब $X^{50}$ बराबर है |

X^{2}

X^{2}

2^{48}

2^{48}

2^{49} X

2^{49} X

2^{50}

2^{50}

Question 9:

Value of $| \begin{array}{ccc} \frac{1}{x} & x^{2} & y z \\ \frac{1}{y} & y^{2} & x z \\ \frac{1}{z} & z^{2} & x y \end{array} |$ is.

$| \begin{array}{lll} \frac{1}{x} & x^{2} & y z \\ \frac{1}{y} & y^{2} & x z \\ \frac{1}{z} & z^{2} & x y \end{array} |$ का मान कौन सा है ?

1.0

0.0

2 x y z

2 x y z

3 x y z

3 x y z

Question 10:

$Let A = [\begin{array}{cc} \cos \frac{π}{4} & - \sin \frac{π}{4} \\ \sin \frac{π}{4} & \cos \frac{π}{4} \end{array}]$ and $X = [\begin{matrix} \frac{1}{\sqrt{2}} \\ \frac{1}{2} \end{matrix}]$ then $A^{3} X$ is equal to

माना A = $[\begin{array}{cc} \cos \frac{π}{4} & - \sin \frac{π}{4} \\ \sin \frac{π}{4} & \cos \frac{π}{4} \end{array}]$ और $X = [\begin{matrix} \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} \end{matrix}]$ तब $A^{3} X$ का मान कौन सा होगा ?

[\begin{array}{r} - 1 \\ 0 \end{array}]

[\begin{array}{r} - 1 \\ 0 \end{array}]

[\begin{matrix} - 1 \\ 1 \end{matrix}]

[\begin{matrix} - 1 \\ 1 \end{matrix}]

[\begin{matrix} - \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} \end{matrix}]

[\begin{matrix} - \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} \end{matrix}]

[\begin{matrix} \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} \end{matrix}]

[\begin{matrix} \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} \end{matrix}]