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Question
SSCCGLENQA12042256
Wired Faculty App

If left parenthesis square root of 3 right parenthesis to the power of 5 space cross times space 9 squared space equals space 3 to the power of straight n space cross times space 3 square root of 3 comma then find the value of n.

  • 2

  • 3

  • 4

  • 5

Solution

D.

5

We have, left parenthesis square root of 3 right parenthesis to the power of 5 cross times 9 squared space equals space 3 to the power of straight n cross times 3 square root of 3
rightwards double arrow space space space 3 to the power of 5 cross times 1 half end exponent space cross times space left parenthesis 3 squared right parenthesis squared space equals space 3 to the power of straight n space cross times space 3 to the power of 1 space cross times space 3 to the power of 1 half end exponent rightwards double arrow space space space space space 3 to the power of 5 over 2 end exponent space cross times space 3 to the power of 4 space equals space 3 to the power of straight n plus 3 over 2 end exponent rightwards double arrow space space space space space space 3 to the power of 5 over 2 plus 4 end exponent space equals space 3 to the power of straight n plus 3 over 2 end exponent rightwards double arrow space space space space space space space space 3 to the power of 12 over 2 end exponent space equals space 3 space to the power of straight n plus 3 over 2 end exponent
If base will be same, then comparing the exponent,
therefore                 straight n plus 3 over 2 space equals space 13 over 2
                              straight n space equals space 13 over 2 space minus space 3 over 2 space equals space 10 over 2 space equals space 5

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Question
SSCCGLENQA12042255
Wired Faculty App

The value of open curly brackets open parentheses straight n square root of straight x squared end root close parentheses to the power of straight n over 2 end exponent close curly brackets squared is

  • x

  • straight x to the power of straight n divided by 2 end exponent
  • straight x squared
  • 1 over straight x squared

Solution

C.

straight x squared
open curly brackets open parentheses straight n square root of straight x squared end root close parentheses to the power of straight n over 2 end exponent close curly brackets squared space equals space open square brackets left parenthesis straight x squared right parenthesis to the power of 1 over straight n cross times straight n over 2 end exponent close square brackets squared space equals space open square brackets straight x to the power of 2 space cross times space 1 half end exponent close square brackets squared equals space straight x squared

Question
SSCCGLENQA12042321
Wired Faculty App

The value of left parenthesis straight d to the power of straight s plus straight t end exponent space divided by space straight d to the power of straight s right parenthesis space divided by space straight d to the power of straight t would be

  • straight d to the power of 2 left parenthesis straight s plus straight t right parenthesis end exponent

  • 1

  • 0

  • straight d to the power of straight s plus straight t end exponent

Solution

B.

1

left parenthesis straight d to the power of straight s plus straight t end exponent space divided by space straight d to the power of straight s right parenthesis space divided by space straight d to the power of straight t space equals space open parentheses straight d to the power of straight s plus straight t end exponent over straight d to the power of straight s close parentheses space divided by space space straight d to the power of straight t
                        equals space left parenthesis straight d to the power of straight s plus straight t minus straight s end exponent right parenthesis divided by straight d to the power of straight t space equals space straight d to the power of straight t over straight d to the power of straight t space equals space 1

Question
SSCCGLENQA12042554
Wired Faculty App

When xm is multiplied by xn ,product is 1. The relation between m and n is

  • mn = 1

  • m = n

  • m + n = 1

  • m = - n

Solution

D.

m = - n

straight x to the power of straight m space cross times space space straight x to the power of straight n space equals space 1
rightwards double arrow space space straight x to the power of straight m plus straight n end exponent space equals space straight x to the power of 0 rightwards double arrow space space space straight m space plus space straight n space equals space 0 rightwards double arrow space space space space straight m space equals space minus straight n

Question
SSCCGLENQA12043725
Wired Faculty App

If 2x+4 - 2x+2 = 3,  then the value of 'x' is

  • 0

  • 2

  • -1

  • -2

Solution

D.

-2

Shortcut Method:
Start putting the value of option which equates the equation.
e.g. put x = -2
2x+4 - 2x+2 = 3
2-2+4 - 2-2+2 = 3
22 - 20 = 3
4 - 1 = 3

 

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