Questions on indices for IPM, MTSE, IMO for STD VII

Questions on indices for IPM, MTSE, IMO for STD VII

indices

If p =100.48, q =100.70 and pz = q2, then the value of z is:

indices

 

JMO indicies

(6561)^(1/2) + (6561)^(1/4) + (6561)^(1/8) = .......................

JMO STD V and STD VI

JMO, indices, number

In the sum 23¹⁵ + 19¹⁷ + 27³⁵, find the digit in the unit place.

JMO STD V and STD VI

indices

indicies

indicies

Indicies

indicies/ factors

Express as factors: x^-2c + x^-c – 20

Express as factors: x^3m + 27  

indicies / factors

Express as factors: a + 7√a + 12

Express as factors: x – 4x^-½ - 12

Express as factors: x^a – 49  

Express as factors: 3a^½  + 5a^¼  + 2

indicies

11-indicies

Prove that X = 3ⁿ⁺².2ⁿ⁺³ + 3ⁿ⁺¹. 2ⁿ⁺⁴ is divisible by 720, given that n ε N.

10-indicies

Show that 2²⁰¹³ – 2²⁰¹² - 2²⁰¹¹ – 2²⁰¹⁰ is a perfect square.

9- indicies

Prove that X = 4ⁿ⁺¹.9ⁿ⁺² + 6²ⁿ⁺¹.9 - 2²ⁿ.9ⁿ⁺¹ is divisible by 369. Given that n ε N.

8-indicies

Find the value of k in the expression

64 + 2.64 + 3.64 + 4.64 + 5.64 + ....49.64 = k²

7-indicies

Find the value of x for which a= 2¹⁰⁰ + (2⁵⁰)² + (2²⁵)⁴ + (2⁵)²⁰ and b = 2⁹⁹ + (2³³)³ + (2¹¹)⁹ + (2³)³³ +2⁹⁹.x are equal (a = b).

6-indicies

Show that 25ⁿ⁺¹.3ⁿ⁺¹ – 3ⁿ⁺².5²ⁿ⁺¹ + 5ⁿ.15ⁿ where n is a natural number, is completely divisible by 31.

5-indicies

Prove that X = 4²ⁿ⁺³.3²ⁿ⁺³ - 6²ⁿ⁺³.2²ⁿ⁺¹ is a perfect square.

4-indicies

If,  (x – 2)^2x-4. 2³ = 8^17. Then find the value of x