12. Mallapragada's Mathematics.(Surds and Indices-2)

Surds and Indices-1

1.If 2ⁿ⁺⁴  - 2ⁿ⁺²  = 3 Then n is equal to:

(a)         -2         (b) -1        (c)2        (d) 0

2. If 2^n-1 + 2ⁿ⁺¹ = 320 then n is equal to:

(a) 5        (b) 8        (c)6        (d) 7

3. If 3^x – 3^x-1  = 18,. Then the value of x^x

(a)  8       (b)  3     (c) 216   ( d) 27

4. If 2x = 4y =8z and 1/2x +1/4y + 1/6z = 24/7, then the value of z

(a)7/16     (b) 7/32   (c) 7/64     (d)  7/48

5.a^x =b, b^y=c and c^z=a, then the value of xyz is:

(a) 0    (b)  abc      (c) 1/abc)    ( d)1

6. If a^x =b^y=c^z and b²=ac, then y equals:   

(a)  2xz/(x+z)( b) xz/2(x-z)  (c) xz/x+z (d) xz/2(z-x)

7. 5^x+3= (25)^3x-4 then the value of x

(a) 13/5   (b) 5/11  (c) 11/5   (d)  11/3

8. 2^x x 8^1/5 = 2^1/5 then x is equal to

(a) 1/5   (b) -1/5)  (c) 2/5  (d) -2/5

9. 2x = 3root of 32 then x is equal to:

(a) 5/3  (b) 3/5   (c) 5     (d)  3

 10.(9/4)^x (8/27)^x-1  = 2/3 then the value of x

(a) 1     (b)  2   (c)  3    (d)  4

11. 3^x-y =27 and 3^x+y = 243 then x is equal to

(a) 6   (b)   4   (c)  2   (d)   1

12. If abc =1                                                                                                                                           then {1/1+a+b^-1} + {1/1+b+c^-1} +{1/1=c+a^-1}=?

(a) ab   (b) 1/abc   (c)  1   (d)  0

13. (x^a/x^b)^1/ab (x^b/x^c)^1/bc (x^c/x^a)^1/ca ?

(a)1        (b) x ^1/abc  (c) 0  (d) x ^1/(ab+bc+ca)

13. (x^a/x^b)^a+b (x^b/x^c)^b+c (x^c/x^a)^c+a ?

(a) 1   (b)  0   (c) x^abc  (d) x^a+b+c

14. (x^a/x^b)^a+b-c (x^b/x^c)^b+c-a (x^c/x^a)^c+a-b ?

(a) x^abc   (b) 1  (c) x^a+b+c  (d) x^ab+bc+ca

15. 1/1+a^(n-m)  + 1/1+a^(m-n)  = ?

(a) 1   (b) ½    (c) a^(m+n)     (d)  0

16. If m and n are whole numbers such that mⁿ=121, then the value of (m-1)ⁿ⁺¹

(a) 1000   (b) 10  (c) 1   (d) 121

17. Which is larger root 2 or three root three ?

18. Find the largest from among 4^th root 6, root 2,and cube root of 4

19. (243)^n/5. 3²ⁿ⁺¹/9ⁿ . 3^n-1 = ?

20. Find the value of[5{81/3+271/3}3]1/4