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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 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

2s³

Tips: -

bold D bold space bold equals bold space 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 bold equals bold space open vertical bar table row cell bold s bold plus bold p bold plus bold q bold plus bold r end cell bold p bold q row cell bold s bold plus bold p bold plus bold q bold plus bold r end cell cell bold s bold plus bold p end cell bold q row cell bold s bold plus bold p bold plus bold q bold plus bold r end cell bold p cell bold s bold plus bold q end cell end table close vertical bar 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 table row cell bold C subscript bold 21 bold space bold left parenthesis bold 1 bold right parenthesis bold space bold C subscript bold 31 bold space bold left parenthesis bold 1 bold right parenthesis end cell row cell bold left square bracket bold C subscript bold 1 bold space bold rightwards arrow bold space bold C subscript bold 2 bold space bold plus bold space bold C subscript bold 2 bold space bold C subscript bold 1 bold space bold rightwards arrow bold space bold C subscript bold 1 bold space bold plus bold space bold C subscript bold 3 bold right square bracket end cell end table bold space bold equals bold space bold 2 bold s bold space open vertical bar table row bold 1 bold p bold q row bold 1 cell bold s bold plus bold p end cell bold q row bold 1 bold p cell bold s bold plus bold q end cell end table close vertical bar 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 C subscript bold 1 open parentheses fraction numerator bold 1 over denominator bold 2 bold s end fraction close parentheses bold space bold left parenthesis bold s bold space bold equals bold space bold p bold space bold plus bold space bold q bold space bold plus bold space bold r bold comma bold right parenthesis bold space bold equals bold space bold 2 bold s bold space open vertical bar table row bold 0 cell bold minus bold s end cell bold 0 row bold 1 cell bold s bold plus bold p end cell bold q row bold 0 cell bold minus bold s end cell bold s end table close vertical bar 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 space bold space bold space bold space bold space bold space bold space bold space bold space table row cell bold R subscript bold 21 bold left parenthesis bold minus bold 1 bold right parenthesis bold space bold R subscript bold 23 bold left parenthesis bold minus bold 1 bold right parenthesis end cell row cell bold left square bracket bold R subscript bold 1 bold space bold rightwards arrow bold space bold R subscript bold 1 bold space bold plus bold space bold left parenthesis bold minus bold 1 bold right parenthesis bold space bold R subscript bold 2 end cell row cell bold R subscript bold 3 bold rightwards arrow bold R subscript bold 3 bold plus bold R subscript bold 2 bold left parenthesis bold minus bold 1 bold right parenthesis bold right square bracket end cell end table bold equals bold space bold 2 bold s to the power of bold 3

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

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

1
2
0
-1

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

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

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.

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

10. 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.

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Gujarati JEE Mathematics : નિશ્વાયક

Multiple Choice Questions

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