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Gujarati JEE Mathematics : નિશ્વાયક

Multiple Choice Questions

1. a ની કઈ કિંમત માટે સમીકરણ સંહિત
ax + y + z = a - 1
x+ ay + z = a - 1
x + y + az = a - 1 ને એક પણ ઉકેલ નથી.

-2
2 અથવા 1
-2 સિવાય
1

2. જો $open vertical bar table row bold a bold b cell bold ax bold plus bold by end cell row bold b bold c cell bold ax bold plus bold cy end cell row cell bold ax bold plus bold by end cell cell bold bx bold plus bold cy end cell bold 0 end table close vertical bar bold space bold equals bold space bold 0$ અને ax² + 2bxy + cy² ≠ 0 તો.........

a, b, cસમગુણોત્તર શ્રેણીમાં છે.
a, b, c સમાંતર શ્રેણીમાં છે.
a, b, c સ્વરિત શ્રેણીમાં છે.
a, b, c એ સમગુણોત્તર, સમાંતર કે સ્વરિત શ્રેણીમાં નથી.

a, b, cસમગુણોત્તર શ્રેણીમાં છે.

Tips: -

$open vertical bar table row bold a bold b cell bold ax bold plus bold by end cell row bold b bold c cell bold ax bold plus bold cy end cell row cell bold ax bold plus bold by end cell cell bold bx bold plus bold cy end cell bold 0 end table close vertical bar bold space bold equals bold space bold 0 bold therefore bold space open vertical bar table row bold a bold b bold 0 row bold b bold c bold 0 row cell bold ax bold plus bold by end cell cell bold bx bold plus bold y end cell cell bold minus bold ax to the power of bold 2 bold minus bold 2 bold bxy bold minus bold cy to the power of bold 2 end cell end table close vertical bar bold space bold equals bold space bold 0 bold space bold therefore bold space bold left parenthesis bold minus bold ax to the power of bold 2 bold space bold minus bold space bold 2 bold bxy bold space bold minus bold space bold cy to the power of bold 2 bold right parenthesis bold space bold left parenthesis bold ac bold space bold minus bold space bold b to the power of bold 2 bold right parenthesis bold space bold equals bold space bold 0 bold space bold therefore bold space bold ac bold space bold minus bold space bold b to the power of bold 2 bold space bold equals bold space bold 0 bold space bold therefore bold space bold ac bold space bold equals bold space bold b to the power of bold 2$

∴ a, b, c સમગુણોત્તર શ્રેણીમાં છે.

જો a²+ b² + c² + 2 = 0 અને $bold f bold left parenthesis bold x bold right parenthesis bold space bold equals bold space open vertical bar table row cell bold 1 bold plus bold a to the power of bold 2 bold x end cell cell bold left parenthesis bold 1 bold plus bold b to the power of bold 2 bold right parenthesis bold x end cell cell bold left parenthesis bold 1 bold plus bold c to the power of bold 2 bold right parenthesis bold x end cell row cell bold left parenthesis bold 1 bold plus bold a to the power of bold 2 bold right parenthesis bold x end cell cell bold 1 bold plus bold b to the power of bold 2 bold x end cell cell bold left parenthesis bold 1 bold plus bold c to the power of bold 2 bold right parenthesis bold x end cell row cell bold left parenthesis bold 1 bold plus bold a to the power of bold 2 bold right parenthesis bold x end cell cell bold left parenthesis bold 1 bold plus bold b to the power of bold 2 bold right parenthesis bold x end cell cell bold 1 bold plus bold c to the power of bold 2 bold x end cell end table close vertical bar$ તો, f(x) એ ..........ઘાતવાળી બહુપદી થાય.

4. જો s = p + q + r, તો $open vertical bar table row cell bold s bold plus bold r end cell bold p bold q row bold r cell bold s bold plus bold p end cell bold q row bold r bold p cell bold s bold plus bold q end cell end table close vertical bar$ ની કિંમત ....... છે.

s³
2s³
2s²
3s³

5. જો $bold D bold space bold equals bold space open vertical bar table row bold 1 bold 1 bold 1 row bold 1 cell bold 1 bold plus bold x end cell bold 1 row bold 1 bold 1 cell bold 1 bold plus bold y end cell end table close vertical bar$ જ્યાં x ≠ 0, y ≠ 0 તો D એ ....... x, y ∈ N

x અને y વડે વિભાજ્ય છે.
x વડે વિભાજ્ય છે પરંતુ y વડે વિભાજ્ય નથી.
x વડે વિભાજ્ય નથી પરંતુ y વડે વિભાજ્ય છે.
x અને y પૈકી એક પણ વડે વિભાજ્ય નથી.

જો a < 0 અને ax² + 2bx + c નો વિવેચક ઋણ હોય, તો $open vertical bar table row bold a bold b cell bold ax bold plus bold b end cell row bold b bold c cell bold bx bold plus bold c end cell row cell bold ax bold plus bold b end cell cell bold bx bold plus bold c end cell bold 0 end table close vertical bar$ નું મૂલ્ય ......... છે.

ઋણ
(ac-b²) (ax²+2bx+c)
0
ધન

જો x + 2ay + az = 0; x + 3by + bz = 0, x + 4cz + cz = 0 સમીકરણો સુસંગત હોય, તો a, b, c એ ........ છે.

સ્વરિત શ્રેણીમાં
સમાંતર શ્રેણીમાં
સમગુણોત્તર શ્રેણીમાં
ત્રણમાંથી એક પણ નહી

8. જો 1, w, w² એ 1 નાં ઘન મુળ હોય, તો $open vertical bar table row bold 1 cell bold w to the power of bold n end cell cell bold w to the power of bold 2 bold n end exponent end cell row cell bold w to the power of bold n end cell cell bold w to the power of bold 2 bold n end exponent end cell bold 1 row cell bold w to the power of bold 2 bold n end exponent end cell bold 1 cell bold w to the power of bold n end cell end table close vertical bar bold space bold equals bold space bold. bold. bold. bold. bold. bold. bold. bold. bold. bold. bold.$

જો $open vertical bar table row bold a cell bold a to the power of bold 2 end cell cell bold 1 bold plus bold a to the power of bold 3 end cell row bold b cell bold b to the power of bold 2 end cell cell bold 1 bold plus bold b to the power of bold 3 end cell row bold c cell bold c to the power of bold 2 end cell cell bold 1 bold plus bold c to the power of bold 3 end cell end table close vertical bar bold space bold equals bold space bold 0$ અને સદિશો (1, a, a²) ; (1, b, b²) અને (1, c, c²) એ સમતલીય હોય, તો abc = ......

1
2
0
-1

10. જો, w એ 1 નું ઘન મૂળ હોય, અને w ≠ 1 $open vertical bar table row bold 1 cell bold 1 bold plus bold i bold plus bold w to the power of bold 2 end cell cell bold w to the power of bold 2 end cell row cell bold 1 bold minus bold i end cell cell bold minus bold 1 end cell cell bold w to the power of bold 2 bold minus bold 1 end cell row cell bold minus bold i end cell cell bold minus bold 1 bold plus bold w bold minus bold i end cell cell bold minus bold 1 end cell end table close vertical bar bold space bold equals bold space bold. bold. bold. bold. bold. bold. bold. bold. bold space$

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Gujarati JEE Mathematics : નિશ્વાયક

Multiple Choice Questions

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