Home
Class 14
MATHS
r is a non-zero real number such that r^...

r is a non-zero real number such that `r^(75) gt r^(90)`. This is possible only when

A

`-1 lt r lt 0`

B

`0 lt r lt 1`

C

`1 lt r`

D

`-1 lt r lt 1`

Text Solution

Verified by Experts

Promotional Banner

Similar Questions

Explore conceptually related problems

Suppose p,q,r and real number such that q=p(4-p),r=q(4-q),p=r(4-r) . The maximum possible value of p+q+r is

Let R_(0) denote the set of all non-zero real numbers and let A=R_(0)xx R_(0) .If * is a binary operation on A defined by (a,b)*(c,d)=(ac,bd) for all (a,b),(c,d)in A* show that * is both commutative and associative on A( ii) Find the identity element in A

Let R_(0) denote the set of all non-zero real numbers and let A=R_(0)xx R_(0). If * is a binary operation on A defined by (a,b)*(c,d)=(ac,bd) for all (a,b),(c,d)in A. Find the invertible element in A.

Consider the following statements : 1. "cos"^(2)theta=1-(p^(2)+q^(2))/(2pq) , where p, q are non-zero real numbers, is possible only when p = q. 2. "tan"theta=(4pq)/((p+q)^(2))-1 , where p, q are non-zero real numbers, is possible only when p = q. Which of the statements given above is/are correct ?

Show that the function f:R_(0)rarr R_(0), defined as f(x)=(1)/(x), is one-one onto,where R_(0) is the set of all non-zero real numbers.Is the result true,if the domain R_(0) is replaced by N with co-domain being same as R_(0)?

The value of lim_(n to oo) ([r]+[2r] +….+[nr])/(n^(2)) , where r is a non-zero real number and [r] denotes the greatest integer less than or equal to r, is equal to :

Write the identity element for the binary operations* on the set R_(0) of all non-zero real numbers by the rule a*b=(ab)/(2) for all a,b in R_(0)

If R is the set of real numbers prove that a function f:R rarr R,f(x)=e^(x),x in R is one to one mapping.