Bihar Board Mathematics 2017 Questions Paper

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Download Bihar Board 2018 Math Questions of Intermediate 

Q 01. यदि [latex]A=\left\{ 1,2,3\right\}[/latex] तो [latex]\left( 1,2\right)[/latex] को शामिल करते हुए कितने तुल्यता संबंध [latex]A[/latex] पर परिभाषित हो सकते हैं?

  1. [latex]2[/latex]
  2. [latex]3[/latex]
  3. [latex]8[/latex]
  4. [latex]6[/latex]

Q 02. यदि [latex]n\left( A\right)=3[/latex] तथा [latex]n\left( B\right) =2[/latex] तो [latex]n\left( A\times B\right) =\ldots \ldots?[/latex]

  1. [latex]6[/latex]
  2. [latex]4[/latex]
  3. [latex]2[/latex]
  4. [latex]0[/latex]

Q 3. यदि f:R→R जहां f(x)=3x-4 तो f-1(x) निम्नलिखित में कौन है?

  1. [latex]\dfrac {x+4}{3}[/latex] 
  2. [latex]\dfrac {1}{3}x-4[/latex]
  3. [latex]3x-4[/latex]
  4. [latex]3x+5[/latex]

Q 4. [latex]\dfrac {d}{dx}\left( \sin \right) =[/latex]

  1. [latex]\cos x[/latex]
  2. [latex]-Sinx[/latex]
  3. [latex]-\cos x[/latex]
  4. [latex]\tan x[/latex]

Q 05. [latex]\dfrac {d}{dx}\left( \tan ax\right) =[/latex]

  1. [latex]a\tan ax[/latex]
  2. [latex]a\sec ^{2}ax[/latex]
  3. [latex]a\sec x[/latex]
  4. [latex]a\cotax[/latex]

Q 06. [latex]\begin{vmatrix} 1 & 1 & 2 \\ 2 & 2 & 4 \\ 3 & 5 & 6 \end{vmatrix}=\ldots .?[/latex]

  1. [latex]5[/latex]
  2. [latex]7[/latex]
  3. [latex]0[/latex]
  4. [latex]9[/latex]

Q 07. [latex]ta\eta ^{-1}\left( 1\right) =\ldots \ldots ?[/latex]

  1. [latex]\dfrac {\pi }{4}[/latex]
  2. [latex]\dfrac {\pi }{2}[/latex]
  3. [latex]\dfrac {\pi }{3}[/latex]
  4. [latex]\dfrac {\pi }{8}[/latex]

Q 08. [latex]\tan ^{-1}\dfrac {1}{2}+\tan ^{-1}\dfrac {1}{4}=[/latex]

  1. [latex]\tan ^{-1}\dfrac {3}{2}[/latex]
  2. [latex]\tan ^{-1}\dfrac {6}{7}[/latex]
  3. [latex]\tan ^{-1}\dfrac {5}{6}[/latex]
  4. [latex]\tan ^{-1}\dfrac {1}{2}[/latex]

9. [latex]\begin{vmatrix} x & 5 \\ 5 & x \end{vmatrix}=0[/latex]

  1. [latex]\pm 5[/latex]
  2. [latex]6[/latex]
  3. [latex]0[/latex]
  4. [latex]4[/latex]

11. यदि [latex]A=\begin{vmatrix} 9 & 10 & 11 \\ 12 & 13 & 14 \end{vmatrix}B=\begin{vmatrix} 11 & 10 & 9 \\ 8 & 7 & 6 \end{vmatrix} [/latex]

  1. [latex]\begin{bmatrix} 20 & 20 & 20 \\ 20 & 20 & 20 \end{bmatrix}[/latex]
  2. [latex]\begin{vmatrix} 10 & 10 & 10 \\ 10 & 10 & 10 \end{vmatrix}[/latex]
  3. [latex]\begin{vmatrix} 10 & 5 & 10 \\ 5 & 10 & 10 \end{vmatrix}[/latex]
  4. [latex]\begin{vmatrix} 25 & 10 & 15 \\ 15 & 10 & 25 \end{vmatrix}[/latex]

12. [latex]\dfrac {d}{a}\left( \sec x\right) =[/latex]

  1. [latex]\sec ^{2}x[/latex]
  2. [latex]\tan ^{2}x[/latex]
  3. [latex]\sec x\cdot \tan x[/latex]
  4. [latex]0[/latex]

13. [latex]\dfrac {d}{dx}\sin ^{-1}=\ldots \ldots[/latex]

  1. [latex]\dfrac {1}{1+x^{2}}[/latex]
  2. [latex]\dfrac {1}{1-x^{2}}[/latex]
  3. [latex]\dfrac {1}{\sqrt {1-x^{2}}}[/latex]
  4. [latex]\dfrac {1}{\sqrt {1+x^{2}}}[/latex]

Q 14. [latex]\dfrac {d}{dx}\left( \sin x^{-1}+\cos ^{-1}x\right) =?[/latex]

  1. [latex]\dfrac {2}{1+x^{2}}[/latex]
  2. [latex]0[/latex]
  3. [latex]2[/latex]
  4. [latex]1[/latex]

Q 15. [latex]y=\sin ^{-1}\left( \log x\right) \dfrac {dy}{dx}=[/latex]

  1. [latex]\dfrac {1}{x}\cos x\left( \log x\right)[/latex]
  2. [latex]\dfrac {1}{x}\sin x\left( \log x\right)[/latex]
  3. [latex]0[/latex]
  4. [latex]1[/latex]

Q 16. [latex]y=x^{5}[/latex] तो [latex]\dfrac {dy}{dx}=[/latex]

  1. [latex]5x[/latex]
  2. [latex]6x[/latex]
  3. [latex]5x^{4}[/latex]
  4. [latex]5x^{2}[/latex]

Q 17. [latex]\int x^{5}dx=?[/latex]

  1. [latex]\dfrac {x^{6}}{6}+k[/latex]
  2. [latex]\dfrac {x^{5}}{5}+k[/latex]
  3. [latex]\dfrac {x^{7}}{7}+k[/latex]
  4. [latex]\dfrac {x^{8}}{8}+k[/latex]

Q 18. [latex]\int 0\cdot dx=?[/latex]

  1. [latex]\dfrac {y^{2}}{2}-\dfrac {x^{2}}{2}=k[/latex]
  2. [latex]\dfrac {y^{2}}{2}+\dfrac {x^{2}}{2}=k[/latex]
  3. [latex]1[/latex]
  4. [latex]-1[/latex]

Q. 19. [latex]\int 0\cdot dx[/latex]

  1. [latex]x+k[/latex]
  2. [latex]\dfrac {1}{x^{2}}+k[/latex]
  3. [latex]-\dfrac {1}{x^{2}}+k[/latex]
  4. [latex]\log x+k[/latex]

Q 20. [latex]\int ^{a}_{b}x^{3}dx=?[/latex]

  1. [latex]\dfrac {b^{3}-a^{3}}{3}[/latex]
  2. [latex]\dfrac {b^{4}-a^{4}}{4}[/latex]
  3. [latex]\dfrac {b^{2}-a^{2}}{2}[/latex]
  4. [latex]0[/latex]

Q 21. [latex]\dfrac {dy}{dx}=\dfrac {x}{y}[/latex]  का हल है-

  1. [latex]\dfrac {y^{2}}{2}-\dfrac {x^{2}}{2}=k[/latex]
  2. [latex]\dfrac {y^{2}}{2}+\dfrac {x^{2}}{2}=k[/latex]
  3. [latex]\dfrac {x-y}{2}=k[/latex]
  4. [latex]\dfrac {x+y}{2}=k[/latex]

Q 22. अवकल समीकरण [latex]\dfrac {dy}{dx}=e^{x-y}[/latex] का हल है-

  1. [latex]e^{x}+e^{-y}+k=0[/latex]
  2. [latex]e^{2x}=ke^{y}[/latex]
  3. [latex]e^{x}-e^{y}=k[/latex]
  4. [latex]e^{x+y}=k[/latex]

Q 23. अवकल समीकरण [latex]\dfrac {dy}{dx}+4y=2x[/latex]

  1. [latex]0[/latex]
  2. [latex]1[/latex]
  3. [latex]2[/latex]
  4. [latex]3[/latex]

Q 24. समीकरण [latex]\left( \dfrac {d_{2}y}{dx^{2}}\right) ^{3}-4\dfrac {dx}{dy}=2[/latex] का घात है-

  1. [latex]0[/latex]
  2. [latex]1[/latex]
  3. [latex]2[/latex]
  4. [latex]3[/latex]

Q 25. बिंदु [latex]4,5,6[/latex] की राशि सदिश है-

  1. [latex]\overrightarrow {4j}+\overrightarrow {5j}+6\overrightarrow {k}[/latex]
  2. [latex]\overrightarrow {4j}-\overrightarrow {5j}-6\overrightarrow {k}[/latex]
  3. [latex]2\overrightarrow {i}+\overrightarrow {j}+\overrightarrow {k}[/latex]
  4. [latex]\overrightarrow {i}+\overrightarrow {j}+\overrightarrow {k}[/latex]

Q 26. [latex]\left| 2\overrightarrow {i}-3\overrightarrow {j}+\overrightarrow {k}\right|=?[/latex]

  1. [latex]14[/latex]
  2. [latex]\sqrt {14}[/latex]
  3. [latex]\sqrt {3}[/latex]
  4. [latex]2[/latex]

Q 27. यदि [latex]\overrightarrow {OA}=2\overrightarrow {i}+5\overrightarrow {j}-2\overrightarrow {k}[/latex] तथा [latex]\overrightarrow {OB}=3\overrightarrow {i}+6\overrightarrow {j}+5\overrightarrow {k}[/latex] तो [latex]\overrightarrow {AB}=?[/latex]

  1. [latex]\overrightarrow {j}+\overrightarrow {j}+7\overrightarrow {k}[/latex]
  2. [latex]5\overrightarrow {i}+2\overrightarrow {j}+\overrightarrow {k}[/latex]
  3. [latex]\overrightarrow {i}+2\overrightarrow {j}-7\overrightarrow {k}[/latex]
  4. [latex]\overrightarrow {i}-\overrightarrow {j}-\overrightarrow {k}[/latex]

Q 28. [latex]\overrightarrow {a}=\overrightarrow {i}+\overrightarrow {j}+3\overrightarrow {k}[/latex];[latex]\overrightarrow {b}=2\overrightarrow {i}+3\overrightarrow {j}-5\overrightarrow {k}[/latex] तब [latex]\overrightarrow {a}\cdot \overrightarrow {b}=?[/latex]

[latex]20[/latex]

[latex]-10[/latex]

[latex]20[/latex]

[latex]5[/latex]

Q 29. यदि [latex]\overrightarrow {a}[/latex]और [latex]\overrightarrow {b}[/latex] परस्पर लंबवत हो तो [latex]\overrightarrow {a}\cdot \overrightarrow {b}=?[/latex]

[latex]1[/latex]

[latex]0[/latex]

[latex]2[/latex]

[latex]3[/latex]

Q 30. [latex]\overrightarrow {j}\times \overrightarrow {k}=[/latex]

  1. [latex]\overrightarrow {i}[/latex]
  2. [latex]-\overrightarrow {i}[/latex]
  3. [latex]\overrightarrow {0}[/latex]
  4. [latex]1[/latex]

Q 31. [latex]z[/latex]-अक्ष की दिक् कोज्याएं होती है-

[latex]0,0,0[/latex]

[latex]1,0,0[/latex]

[latex]0,0,1[/latex]

[latex]0,1,0[/latex]

Q 34. [latex]\overrightarrow {k}\times \overrightarrow {k}=[/latex]

[latex]1[/latex]

[latex]0[/latex]

[latex]2[/latex]

[latex]1[/latex]

Q 33. दो सरल रेखाओं के अनुपात [latex]l_{1},m_{1},n_{1}[/latex] और [latex]l_{2},m_{2},n_{2}[/latex] दोनों सरल रेखाएं परस्पर लंबवत होगी यदि

[latex]l_{1}l_{2}+m_{1}m_{1}+n_{1}n_{1}=0[/latex]

[latex]l_{1}l_{2}+m_{1}m_{1}+n_{1}n_{1}=1[/latex]

[latex]\dfrac {l_{1}}{l_{2}}=\dfrac {m_{1}}{m_{2}}=\dfrac {n_{1}}{n_{2}}[/latex]

[latex]\dfrac {l_{1}}{l_{2}}=\dfrac {m_{1}}{m_{2}}+\dfrac {n_{1}}{n}=0[/latex]

Q 34. यदि किसी सरल रेखा का दिक् अनुपात [latex]a,b,c[/latex] है तो उसकी दिक् कोज्याएं होगी-

  1. [latex]\dfrac {a}{\sqrt {\Sigma a^{2}}},\dfrac {b}{\sqrt {\sum a^{2}}},\dfrac {c}{\sqrt {\sum a^{2}}}[/latex]
  2. [latex]\dfrac {1}{\sqrt {\Sigma a^{2}}},\dfrac {1}{\sqrt {\sum a^{2}}},\dfrac {1}{\sqrt {\sum a^{2}}}[/latex]
  3. [latex]\dfrac {1}{a},\dfrac {1}{b},\dfrac {1}{c}[/latex]
  4. [latex]\dfrac {a}{\sqrt {\Sigma a^{2}}},\dfrac {b}{\sqrt {\sum b^{2}}},\dfrac {c}{\sqrt {\sum c^{2}}}[/latex]

Q 35. एक सरल रेखा [latex]a,\beta ,\gamma[/latex] से गुजरती है और इसके दिक् कोज्याएं [latex]l,m,n[/latex] है| सरल रेखा के समीकरण है-

[latex]\dfrac {x}{l}=\dfrac {\gamma }{m}=\dfrac {z}{n}[/latex]

[latex]\dfrac {x-a}{l}=\dfrac {y-\beta }{m}=\dfrac {z-\gamma }{n}[/latex]

[latex]\dfrac {x+a}{l}=\dfrac {y+\beta }{m}=\dfrac {z+\gamma }{n}[/latex]

[latex]\dfrac {x-a}{l}=\dfrac {y+\beta }{m}=\dfrac {z-\gamma }{n}[/latex]

 

Q 36. जब 7x+4y-2z+5=0 पर अभिलंब के दिक् अनुपात है-

  1. 7,4,-2
  2. 7,4,5
  3. 7,4,2
  4. 4,-2,5

Q 37. यदि A और B दो स्वतंत्र घटनाएं हो, तो [latex]P\left( A\cap B\right)=?[/latex]

  1. P(A).P(B)
  2. P(A/B)
  3. P(A)+P(B)
  4. P(A)+P(B)-P(A∩B)

Q 38. यदि S कोई प्रतिदर्श समष्टि तथा E कोई घटना है तो घटना E की प्रतिक्रिया P(E)=?

[latex]\dfrac {n\left( E\right) }{n\left( s\right) }[/latex]

[latex]\dfrac {n\left( s\right) }{n\left( E\right) }[/latex]

[latex]n\left( E\right)[/latex]

[latex]n\left( s\right)[/latex]

Q 39.  यदि A, B और C दो तीन स्वतंत्र घटनाएं हो तो P(A∩B∩C)=?

  1. P(A)+P(B)+P(C)
  2. P(A)-P(B)+P(C)
  3. P(A)+P(B)-P(A∩B)
  4. P(A)P(B)P(C)

Q 40.  यदि P(A)=3/8:P(B)=1/2 और P(A∩B)=1/4 हो, तो P(A∪B)=?

  1. 0
  2. 5/8
  3. 1
  4. 4

गैर वस्तुनिष्ठ प्रश्न

लघु उत्तरीय प्रश्न

Q 1. यदि फलन [latex]f:\mathbb{R} \rightarrow \mathbb{R} ,f\left( x\right) =x^{2}[/latex]  द्वारा परिभाषित हो तो दिखलावे की फलन f many one into है|

Q 2. यदि [latex]A=\begin{vmatrix} 2 & 5 \\ 3 & 1 \end{vmatrix}[/latex] तथा [latex]B=\begin{vmatrix} 1 & 5 \\ 6 & 2 \end{vmatrix}[/latex] तब (A+B) तथा (A-B)ज्ञात करें|

Q 3. साबित करे कि [latex]\tan ^{-1}x+\cot ^{-1}x=\dfrac {\pi }{2}[/latex]

Q 4. अगर [latex]y=\tan \left( \sin ^{-1}x\right)[/latex] तब [latex]\dfrac {dx}{dy}[/latex] का मान निकाले|

Q 5. अगर [latex]y=\sin \left[ \cos \left\{ \tan \left( \cot x\right) \right\} \right][/latex] तब [latex]\dfrac {dx}{dy}[/latex] का मान निकाले|

Q 6. समाकलन करें [latex]\int \sin ^{2}x\cdot \cos ^{2}xdx[/latex]

Q 7. मान निकाले [latex]\int _{0}\dfrac {a_{xdx}}{\sqrt {a^{2}-x^{2}}}[/latex]

Q 8. यदि [latex]\overrightarrow {a}=\overrightarrow {i}-2\overrightarrow {j}-3\overrightarrow {k}[/latex]; [latex]\overrightarrow {b}=2\overrightarrow {i}+2\overrightarrow {j}-\overrightarrow {k}[/latex] तथा [latex]\overrightarrow {c}=\overrightarrow {i}+3\overrightarrow {j}-2\overrightarrow {k}[/latex] तो [latex]\overrightarrow {a}\times \left( \overrightarrow {b}\times \overrightarrow {c}\right)[/latex] मान निकाले|

 

Q 9. यदि [latex]x^{x^{x^{t_{o}\infty }}}[/latex] तो साबित करे कि [latex]\dfrac {dy}{dx}=\dfrac {y^{2}}{x\left( 1-y\log x\right) }[/latex]

Q 10. हल करें [latex]\dfrac {dy}{dx}-\dfrac {xy}{1-x^{2}}=\dfrac {1}{1-x^{2}}[/latex]

Q 11. उस सरल रेखा के समीकरण ज्ञात करें, जो सरल रेखाओ [latex]\dfrac {x-1}{1}=\dfrac {y}{1}=\dfrac {z-a}{1}[/latex] और [latex]\dfrac {x+1}{1}=\dfrac {y}{1}=\dfrac {z+a}{1}[/latex] को प्रतिछेद करती है और [latex]\dfrac {x-a}{2}=\dfrac {y-a}{1}=\dfrac {z-2a}{3}[/latex]सरल रेखा के समांतर है|

 

 

 

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