Dr.Harswaroop Sharma Mathematics Solution Class 12 Chapter 4 सारणिक (Determinants ) Exercise 4A

       

प्रश्नावली - 4A

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Question 1

निम्नलिखित प्रश्नों के मान ज्ञात कीजिए

1. $\left|\begin{array}{ll}1 & 2 \\ 3 & 4\end{array}\right|$

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Question 2

2. $\left|\begin{array}{cc}2 & 4 \\ -5 & -1\end{array}\right|$

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Question 3

3. $\left|\begin{array}{lll}1 & 3 & 7 \\ 7 & 5 & 9 \\ 2 & 0 & 1\end{array}\right|$

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Question 4

4. $\left|\begin{array}{lll}4 & 3 & 1 \\ 0 & 2 & 2 \\ 1 & 3 & 2\end{array}\right|$

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Question 5

5. $\left|\begin{array}{ll}\sec x & \tan x \\ \tan x & \sec x\end{array}\right|$

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Question 6

6. (i) $\left|\begin{array}{cc}\cos \theta & -\sin \theta \\ \sin \theta & \cos \theta\end{array}\right|$

(ii) $\left|\begin{array}{cc}x^2-x+1 & x-1 \\ x+1 & x+1\end{array}\right|$

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Question 7

7. $\left|\begin{array}{rr}\sin 10^{\circ} & -\cos 10^{\circ} \\ \sin 80^{\circ} & \cos 80^{\circ}\end{array}\right|$

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Question 8

8. $\left|\begin{array}{rrr}1 & \frac{3 \pi}{10} & \frac{2 \pi}{10} \\ 0 & \cos \frac{3 \pi}{10} & \sin \frac{2 \pi}{10} \\ 0 & \sin \frac{3 \pi}{10} & \cos \frac{2 \pi}{10}\end{array}\right|$

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Question 9

9. (i) $\left|\begin{array}{rrr}3 & -1 & -2 \\ 0 & 0 & -1 \\ 3 & -5 & 0\end{array}\right|$

(ii) $\left|\begin{array}{rrr}3 & -4 & 5 \\ 1 & 1 & -2 \\ 2 & 3 & 1\end{array}\right|$

(iii) $\left|\begin{array}{rrr}0 & 1 & 2 \\ -1 & 0 & -3 \\ -2 & 3 & 0\end{array}\right|$

(iv) $\left|\begin{array}{rrr}2 & -1 & -2 \\ 0 & 2 & -1 \\ 3 & -5 & 0\end{array}\right|$

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Question 10

10. यदि $\left|\begin{array}{rrr}3 & 1 & -4 \\ 3 & 2 & 5 \\ 1 & -1 & 3\end{array}\right|=49$ हो, तो $\left|\begin{array}{rrr}6 & 3 & -16 \\ 6 & 6 & 20 \\ 2 & -3 & 12\end{array}\right|$ का मान बताओ।

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Question 11

11. यदि $A=\left[\begin{array}{ll}1 & 2 \\ 4 & 2\end{array}\right]$, तो दिखाइए $|2 A|=4|A|$.

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Question 12

12. यदि $A=\left[\begin{array}{lll}1 & 0 & 1 \\ 0 & 1 & 2 \\ 0 & 0 & 4\end{array}\right]$, तो दिखाइए $|3 A|=27|A|$.

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Question 13

13. $\left|\begin{array}{lll}13 & 16 & 19 \\ 14 & 17 & 20 \\ 15 & 18 & 21\end{array}\right|=0$

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Question 14

14. $\left|\begin{array}{lll}38 & 7 & 63 \\ 16 & 3 & 29 \\ 27 & 5 & 46\end{array}\right|=0$

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Question 15

15. यदि $A=\left[\begin{array}{lll}1 & 1 & -2 \\ 2 & 1 & -3 \\ 5 & 4 & -9\end{array}\right]$, तो $|A|$ का मान ज्ञात कीजिए।

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Question 16

x के मान ज्ञात कीजिए यदि

(i) $\left|\begin{array}{cc}-6 & 2 \\ 3 & x\end{array}\right|=18$

(ii) $\left|\begin{array}{cc}2 & -3 \\ x & 9\end{array}\right|=30$

(iii) $\left|\begin{array}{ll}1 & 5 \\ 6 & 3\end{array}\right|=\left|\begin{array}{rr}7 x & 4 \\ 5 & -x\end{array}\right|$

(iv) $\left|\begin{array}{ll}1 & 4 \\ 2 & 6\end{array}\right|=\left|\begin{array}{cc}x & 2 \\ 3 x & 4\end{array}\right|$

(v) $\left|\begin{array}{ll}2 & 4 \\ 5 & 1\end{array}\right|=\left|\begin{array}{rr}2 x & 4 \\ 6 & x\end{array}\right|$

(vi) $\left|\begin{array}{ll}2 & 3 \\ 4 & 5\end{array}\right|=\left|\begin{array}{rr}x & 3 \\ 2 x & 5\end{array}\right|$