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Q 1. If {tex} \mathrm { p } \times \mathrm { q } = \mathrm { p } + \mathrm { q } + \frac { \mathrm { p } } { \mathrm { q } } , {/tex} the value of {tex} 8 \times 2 {/tex} is:
6
10
14
16
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Q 2. Two numbers {tex} x {/tex} and {tex} y ( x > y ) {/tex} are such that their sum is equal to three times their difference. Then value of {tex} \frac { 3 x y } { 2 \left( x ^ { 2 } - y ^ { 2 } \right) } {/tex} will be:
{tex} \frac { 2 } { 3 } {/tex}
1
{tex} 1 \frac { 1 } { 2 } {/tex}
{tex} 1 \frac { 2 } { 3 } {/tex}
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Q 3. The value of
{tex} \left( 1 + \frac { 1 } { x } \right) \left( 1 + \frac { 1 } { x + 1 } \right) \left( 1 + \frac { 1 } { x + 2 } \right) \left( 1 + \frac { 1 } { x + 3 } \right) {/tex}
{tex} 1 + \frac { 1 } { x + 4 } {/tex}
{tex} x + 4 {/tex}
{tex} \frac { 1 } { x } {/tex}
{tex} \frac { x + 4 } { x } {/tex}
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Q 4. If {tex} \frac { 2 a + b } { a + 4 b } = 3 {/tex}, then find the value of {tex} \frac { a + b } { a + 2 b } {/tex}
{tex} \frac { 5 } { 9 } {/tex}
{tex} \frac { 2 } { 7 } {/tex}
{tex} \frac { 10 } { 9 } {/tex}
{tex} \frac { 10 } { 7 } {/tex}
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Q 5. If {tex} a * b = a + b + a b {/tex}, then {tex} 3 * 4 - 2 * 3 {/tex} is equal to :
6
8
10
12
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Q 6. If {tex} \quad x = 7 - 4 \sqrt { 3 } {/tex}, then the value of {tex} \left( x + \frac { 1 } { x } \right) {/tex} is :
{tex} 3 \sqrt { 3 } {/tex}
{tex} 8 \sqrt { 3 } {/tex}
{tex} 14 + 8 \sqrt { 3 } {/tex}
{tex} 14{/tex}
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Q 7. If {tex} \frac { a } { 3 } = \frac { b } { 4 } = \frac { c } { 7 } {/tex} then {tex} \frac { a + b + c } { c } {/tex} is equal to
0
1
2
3
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Q 8. If {tex} \frac { 144 } { 0.144 } = \frac { 14.4 } { x } , {/tex} then the value of {tex} x {/tex} is
144
14.4
1.44
0.0144
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Q 9. If a {tex} \otimes \mathrm { b } = ( a \times b ) + b {/tex}, then {tex} 5 \otimes{/tex} 7 equals to
12
35
42
50
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Q 10. If {tex}47.2506 = 4 \mathrm { A } + \frac { 7 } { \mathrm { B } } + 2 \mathrm { C } + \frac { 5 } { \mathrm { D } } + 6 \mathrm { E } {/tex}, then the value of {tex} 5 \mathrm { A } {/tex} {tex} + 3 \mathrm { B } + 6 \mathrm { C } + \mathrm { D } + 3 \mathrm { E } {/tex} is
53.6003
53.603
153.6003
213.0003
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Q 11. If {tex} \frac { 2 p } { p ^ { 2 } - 2 p + 1 } = \frac { 1 } { 4 } , p \neq 0 {/tex}
then the value of {tex} p + \frac { 1 } { p } {/tex} is
4
5
10
12
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Q 12. If {tex} 5 ^ { 5 x + 5 } = 1 , {/tex} then {tex} x {/tex} equals
{tex} 0{/tex}
{tex} - 1 {/tex}
{tex} 1{/tex}
{tex} - \frac { 4 } { 5 } {/tex}
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Q 13. If {tex} 3 ^ { x + 3 } + 7 = 250 , {/tex} then {tex} x {/tex} is equal
5
3
2
1
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Q 14. If {tex} \frac { 1 } { 4 } \times \frac { 2 } { 6 } \times \frac { 3 } { 8 } \times \frac { 4 } { 10 } \times \frac { 5 } { 12 } \times {/tex} {tex} \ldots \times \frac { 31 } { 64 } = \frac { 1 } { 2 ^ { x } } , {/tex} the value of {tex} x {/tex} is
31
32
36
37
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Q 15. The value of
{tex} \frac { ( 243 ) ^ { \frac { n } { 5 } } \cdot 3 ^ { 2 n + 1 } } { 9 ^ { n } \cdot 3 ^ { n - 1 } } {/tex} is
1
9
3
{tex} 3 ^ { n } {/tex}
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Q 16. If {tex} x = 0.5 {/tex} and {tex} y = 0.2 , {/tex} then value of {tex} \sqrt { 0.6 } \times ( 3 y ) ^ { x } {/tex} is equal to
1.0
0.5
0.6
1.1
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Q 17. If {tex} x ^ { x \sqrt { x } } = ( x \sqrt { x } ) ^ { x } , {/tex} then {tex} x {/tex} equals
{tex} \frac { 4 } { 9 } {/tex}
{tex} \frac { 2 } { 3 } {/tex}
{tex} \frac { 9 } { 4 } {/tex}
{tex} \frac { 3 } { 2 } {/tex}
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Q 18. If {tex} 7 ^ { x } = \frac { 1 } { 343 } , {/tex} then the value of {tex} x {/tex}
3
-3
{tex} \frac { 1 } { 3 } {/tex}
{tex} \frac { 1 } { 7 } {/tex}