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CBSE

Gujarati JEE Mathematics : નિશ્વાયક

Multiple Choice Questions

61. જો a,b,c સમાંતર શ્રેણીમાં હોય તો $open vertical bar table row cell bold x bold plus bold 1 end cell cell bold x bold plus bold 2 end cell cell bold x bold plus bold a end cell row cell bold x bold plus bold 2 end cell cell bold x bold plus bold 3 end cell cell bold x bold plus bold b end cell row cell bold x bold plus bold 3 end cell cell bold x bold plus bold 4 end cell cell bold x bold plus bold c end cell end table close vertical bar bold space bold space bold equals bold space bold space bold. bold. bold. bold. bold. bold.$

2x
x+a+b+c
0
x

62.

જો (2,-6), (5, 4) અને (k, 4) શિરોબિંદુઓવાળા ત્રિકોણનું ક્ષેત્રફળ 35 હોય, તો k = ...........

12
-2
-12 અથવા - 2
12 અથવા - 2

63.

y = m₁x + c₁;y=m₂x + c₂ અને x = 0 બાજુઓવાળા ત્રિકોણનું ક્ષેત્રફળ ....... છે. (c₁#c₂)

$fraction numerator bold left parenthesis bold c subscript bold 1 bold space bold minus bold space bold c subscript bold 2 bold right parenthesis bold space over denominator bold 2 bold left parenthesis bold m subscript bold 1 bold space bold minus bold space bold m subscript bold 2 bold right parenthesis bold space end fraction$
$fraction numerator bold left parenthesis bold c subscript bold 1 bold comma bold space bold minus bold space bold c subscript bold 2 bold right parenthesis to the power of bold 2 bold space over denominator bold 2 bold left parenthesis bold m subscript bold 1 bold space bold minus bold space bold m subscript bold 2 bold right parenthesis bold space end fraction$
$fraction numerator bold left parenthesis bold c subscript bold 1 bold space bold minus bold space bold c subscript bold 2 bold right parenthesis to the power of bold 2 over denominator bold 2 bold left parenthesis bold m subscript bold 2 bold space bold minus bold space bold m subscript bold 1 bold right parenthesis bold space end fraction$
$fraction numerator bold left parenthesis bold c subscript bold 1 bold space bold minus bold space bold c subscript bold 2 bold right parenthesis to the power of bold 2 over denominator bold 2 open vertical bar table row cell bold m subscript bold 1 bold space bold minus bold space bold m subscript bold 2 end cell end table close vertical bar end fraction$

64.

જો $bold f bold left parenthesis bold x bold right parenthesis bold space bold equals bold space open vertical bar table row cell bold x bold plus bold 1 end cell cell bold x bold plus bold 2 end cell cell bold x bold plus bold 3 end cell row cell bold P presubscript bold x bold plus bold 1 end presubscript subscript bold x bold plus bold 1 end subscript end cell cell bold P presubscript bold x bold plus bold 2 end presubscript subscript bold x bold plus bold 2 end subscript end cell cell bold P presubscript bold x bold plus bold 3 end presubscript subscript bold x bold plus bold 3 end subscript end cell row cell bold C presubscript bold x bold plus bold 1 end presubscript subscript bold x bold plus bold 1 end subscript end cell cell bold C presubscript bold x bold plus bold 2 end presubscript subscript bold x bold plus bold 2 end subscript end cell cell bold C presubscript bold x bold plus bold 3 end presubscript subscript bold x bold plus bold 3 end subscript end cell end table close vertical bar$ તો f(x) એ .................. વડે વિભાજ્ય છે.

(x+1)!
(x+2)!
(x+3)!
(x+4)!

65.

open vertical bar table row bold x bold y cell bold x bold plus bold y end cell row bold y cell bold x bold plus bold y end cell bold x row cell bold x bold plus bold y end cell bold x bold y end table close vertical bar bold space bold equals bold space bold k bold space bold left parenthesis bold x to the power of bold 3 bold space bold plus bold space bold y to the power of bold 3 bold right parenthesis bold space bold ત ો bold space bold k bold space bold equals bold space bold. bold. bold. bold. bold. bold. bold. bold. bold. bold. bold. bold. bold. bold. bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold left parenthesis bold x bold space bold plus bold space bold y bold space bold # bold 0 bold right parenthesis

0
1
2
-2

66.

જો $bold f bold left parenthesis bold x bold right parenthesis bold space bold equals bold space open vertical bar table row bold sinx bold cosx bold sinx row bold 1 bold 2 bold 3 row bold 5 bold 2 bold 4 end table close vertical bar bold space bold ત ો bold space bold f bold " bold left parenthesis bold x bold right parenthesis bold space bold. bold. bold. bold. bold. bold. bold. bold. bold. bold. bold. bold space$

f'(x)
f"(x)
f(x)
-f(x)

67.

bold જ ો bold space bold f bold left parenthesis bold x bold right parenthesis bold space bold equals bold space open vertical bar table row bold cosx bold 1 bold 1 row cell bold 2 bold sinx end cell bold x cell bold 2 bold x end cell row bold tanx bold 1 bold 1 end table close vertical bar bold space bold ત ો bold space table row bold lim row cell bold x bold rightwards arrow bold 0 end cell end table bold space fraction numerator bold f bold left parenthesis bold x bold right parenthesis over denominator bold x end fraction bold space bold equals bold space bold. bold. bold. bold. bold.

0
-1
1
2

68. જો $bold P bold space bold equals bold space table row bold cosθ row bold integral row bold 1 end table fraction numerator bold t bold space bold dt over denominator bold 1 bold plus bold t to the power of bold 2 end fraction bold space bold અન ે bold space bold space bold Q bold equals bold space table row bold secθ row bold integral row bold 1 end table bold space fraction numerator bold dt over denominator bold t bold left parenthesis bold 1 bold plus bold t to the power of bold 2 bold right parenthesis end fraction bold comma bold ત ો bold space bold space open vertical bar table row bold P cell bold P to the power of bold 2 end cell bold Q row cell bold 2 bold P to the power of bold 2 bold Q end cell cell bold Q to the power of bold 2 end cell cell bold minus bold 1 end cell row bold 1 cell bold P to the power of bold 2 bold plus bold Q to the power of bold 2 end cell cell bold minus bold 1 end cell end table close vertical bar$ નું મુલ્ય ........ છે.