For any two rational numbers a and `b ,\ a^5x\ b^5` is equal to `(a\ x\ b)^0` (b) `(a\ x\ b)^(10)` (c) `(a\ x\ b)^5` (d) `(a\ x\ b)^(25)`

4 a 2 b 3 x 3a b 2 x 5 a 3 b is equal to: (a) 60 a 3 b 5 (b) 60 a 6 b 5 (c) 60 a 6 b 6 (d) a 6 b 5

If x is a real number and |x| =5 b.-5

4 a 2 b 3 x 3a b 2 x 5 a 3 b is equal to: 60 a 3 b 5 (b) 60 a 6 b 5 (c) 60 a 6 b 6 (d) a 6 b 5

If (b + c) (y + z) - ax = b - c, (c + a) (z + x) - by = c - a and (a + b) (x + y) - cz = a - b , where a + b + c ne 0, then x is equal to a) (c + b)/(a + b + c) b) (c - b)/(a + b + c) c) (a - b)/(a + b + c) d) (a + b)/(a + b + c)

If x_(1) and x_(2) are two distinct roots of the equation a cos x+b sin x=c, then tan((x_(1)+x_(2))/(2)) is equal to (a)(a)/(b) (b) (b)/(a) (c) (c)/(a) (d) (a)/(c)

If x+2 is a factor of x^2+a x+2b and a+b=4 , then (a) a=1,\ b=3 (b) a=3,\ b=1 (c) a=-1,\ b=5 (d) a=5,\ b=-1

If |a a x m m m b x b|=0,\ then x may be equal to- a. a b. b c. a+b d. m

In the figure, if A B=A C ,/_B A D=30^0 and A E=A D , then x is equal to a) 15^0 (b) 10^0 (c) 12. 5^0 (d) 7. 5^0

Assuming that x is a positive real number and a ,\ b ,\ c are rational numbers, show that: ((x^a)/(x^b))^(a+b)\ ((x^b)/(x^c))^(b+c)((x^c)/(x^a))^(c+a)=1