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

        

प्रश्नावली - 4F

निम्नलिखित प्रश्नों में दी गयी समीकरण निकायों को संगत अथवा असंगत के रुव में वर्गीकरण कीजिए :

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Question 1

1. $\begin{array}{r}x+2 y=2 \\ 2 x+3 y=3\end{array}$

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Question 2

2. $\begin{array}{r}2 x-y=5 \\ x+y=4\end{array}$

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Question 3

3. $\begin{array}{r}x+3 y=5 \\ 2 x+6 y=8\end{array}$

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Question 4

4. $\begin{array}{r}x+y+z=1 \\ 2 x+3 y+2 z=2 \\ a x+a y+2 a z=4\end{array}$

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Question 5

5. $\begin{aligned} 3 x-y-2 z & =2 \\ 2 y-z & =-1 \\ 3 x-5 y & =3\end{aligned}$

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Question 6

6. $\begin{aligned} 5 x-y+4 z & =5 \\ 2 x+3 y+5 z & =2 \\ 5 x-2 y+6 z & =-1\end{aligned}$

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Question 7

7. $\begin{array}{r}
x+2 y=4 \\
2 x+5 y=9
\end{array}$

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Question 8

8. $\begin{aligned}
& 4 x-3 y=11 \\
& 3 x+7 y=-1
\end{aligned}$

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Question 9

9. $\begin{aligned} x+y+2 z & =4 \\ x+2 y+z & =1 \\ x+y+z & =2\end{aligned}$

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Question 10

10. $\begin{aligned} & 5 x+2 y=4 \\ & 7 x+3 y=5\end{aligned}$

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Question 11

11. $\begin{aligned} 2 x-y & =-2 \\ 3 x+4 y & =3\end{aligned}$

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Question 12

12. $\begin{aligned} & 4 x-3 y=3 \\ & 3 x-5 y=7\end{aligned}$

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Question 13

13. $\begin{array}{r}5 x+2 y=3 \\ 3 x+2 y=5\end{array}$

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Question 14

14. $\begin{aligned} x+y+z & =3 \\ x+2 y+3 z & =4 \\ x+4 y+9 z & =6\end{aligned}$

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Question 15

15. $\quad \begin{aligned} 5 x+3 y+z & =16 \\ 2 x+y+3 z & =19 \\ x+2 y+4 z & =25\end{aligned}$

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Question 16

16. $\begin{aligned} x+y+z & =6 \\ x+y-z & =0 \\ 2 x+y+2 z & =10\end{aligned}$

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Question 17

17. $\begin{aligned} & x+3 y+3 z=16 \\ & x+4 y+3 z=18 \\ & x+3 y+4 z=19\end{aligned}$

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Question 18

18. $\begin{aligned} 2 x+y+z & =1 \\ x-2 y-z & =\frac{3}{2} \\ 3 y-5 z & =9\end{aligned}$

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Question 19

19. $\begin{array}{r}x-y+z=4 \\ 2 x+y-3 z=0 \\ x+y+z=2\end{array}$

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Question 20

20. $\begin{aligned} 2 x+3 y+3 z & =5 \\ x-2 y+z & =-4 \\ 3 x-y-2 z & =3\end{aligned}$

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Question 21

21. $\begin{aligned}
x-y+2 z & =7 \\
3 x+4 y-5 z & =-5 \\
2 x-y+3 z & =12
\end{aligned}$

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Question 22

22. $\begin{aligned} x-2 y+3 z & =11 \\ 3 x+y-z & =2 \\ 5 x+3 y+2 z & =3\end{aligned}$

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Question 23

23. $\begin{array}{r}x+y+z=6 \\ x-y+z=2 \\ 2 x+y-z=1\end{array}$

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Question 24

24. $\begin{aligned} 9 x+8 y-7 z & =14 \\ 6 x-5 y+4 z & =4 \\ -3 x+2 y+z & =-10\end{aligned}$

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Question 25

25. यदि $A=\left[\begin{array}{ccc}2 & -3 & 5 \\ 3 & 2 & -4 \\ 1 & 1 & -2\end{array}\right]$ है तो $A^{-1}$ ज्ञात कीजिए। $A^{-1}$ का प्रयोग कसे निम्नलिखित समीकरण निकाय को हल कीजिए:

$\begin{aligned} 2 x-3 y+5 z & =11 \\ 3 x+2 y-4 z & =-5 \\ x+y-2 z & =-3\end{aligned}$

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Question 26

26. 4 किग्रा प्याज, 3 किग्रा गेहूँ और 2 किग्रा चावल का मूल्य ₹ 60 है। 2 किग्रा प्याज, 4 किग्रा गेहूँ और 6 किग्रा चावल का मूल्य ₹ 90 है। 6 किग्रा प्याज, 2 किग्रा गेहूँ और 3 किग्रा चावल का मूल्य ₹ 70 है। आव्यूह विधि द्वारा प्रत्येक का मूल्य प्रति किग्रा ज्ञात कीजिए।