If `a, bgt0,a+b=1`, then the least value of `(1+(1)/(a))(1+(1)/(b))`, isA. 3B. 6C. 9D. 12

If `a, bgt0,a+b=1`, then the least value of `(1+(1)/(a))(1+(1)/(b))`,

1.	If `a, bgt0,a+b=1`, then the least value of `(1+(1)/(a))(1+(1)/(b))`, isA. 3B. 6C. 9D. 12
Answer» Correct Answer - C We have, `(1+(1)/(a))(1+(1)/(b))=((a+1)(b+1))/(ab)=(1+(a+b)+ab)/(ab)=(2+ab)/(ab)` `implies" "(1+(1)/(a))(1+(1)/(b))=1+(2)/(ab)` Now, `A.M. geG.M.` `implies" "(a+b)/(2)gesqrt(ab)` `implies" "(1)/(2)gesqrt(ab)implies(1)/(ab)ge4implies1+(2)/(ab)ge9implies(1+(1)/(a))(1+(1)/(b))ge9` Hence, the least value of `(1+(1)/(a))(1+(1)/(b))` is 9.

If a, b, c are positive integers, then `((a^(2)+b^(2)+c^(2))/(a+b+c))^(a+b+c)gta^(x)b^(y)c^(z)`, thenA. `x=a, y=b, z=c`B. `x=b, y=a, z=c`C. `x=(1)/(a),y=(1)/(b),z=(1)/( c )`D. `x=y=z=1`
For all positive values of x and y, the value of `((1+x+x^(2))(1+y+y^(2)))/(xy)`,isA. `le9`B. `lt9`C. `ge9`D. `gt9`
If `agt1,bgt1,cgt1,dgt1` then the minimum value of `log_(b)a+log_(a)b+log_(d)c+log_(c)d`, isA. 1B. 2C. 3D. 4
If `x_(n)gt1` for all `n in N`, then the minimum value of the expression `log_(x_(2))x_(1)+log_(x_(3))x_(2)+...+log_(x_(n))x_(n-1)+log_(x_(1))x_(n)` is
Number of integers, which satisfy the inequality `((16)^(1/ x))/((2^(x+3))) gt1,` is equal to
The number of solution of the equation `16(x^(2)+1)+pi^(2)=|tanx|+8pix` is equal toA. 2B. 4C. 1D. infinite
The numbers of integral solutions of the equations `y^(2)(5x^(2)+1)=25(2x^(2)+13)" where "x, y inI`, isA. 2B. 4C. 8D. infinite
The least value of `2^(sinx)+2^(cosx)`, isA. `2^(1//sqrt(2))`B. `2^(1-2^(-1//2))`C. `2^(1+2^(-1//2))`D. `2^(1-sqrt(2))`
If `0ltxlt(pi)/(2)`, then the minimum value of `(sinx+cosx+cosec2x)`,isA. 27B. `(27)/(2)`C. `(25)/(4)`D. none of these
Number of solutions of `|(1)/(|x|-1)|=x+sinx,` isA. 1B. 2C. 3D. none of these