If log xlog y k-0 where x- k -0-1 then y -A- 0- xB- 0- kC- k- 1D- R -

Define $x % a$ as the remainder obtained when $x$ is divided by $a$ .
Let $f : Z \to R$ be defined as $f (x) = x % k$ , where $k ϵ N$ . If Y is the range of $f (x)$ , then

Q. If the area of the region bounded by the lines

y - x = 0

x = 0

and the normal to

y = e^{x}

(0, 1)

\frac{1}{k}

, then k is equal to ________.

Q. If the system of equations

x + y - 3 = 0, (1 + K) x + (2 + K) y - 8 = 0

x - (1 + K) y + (2 + K) = 0

is consistent then the value of K may be

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If logx(logyk)>0 where x,k∈(0,1) then y∈

The correct option is C (k, 1)logyk<1 case 1 : if y > 1 ⇒ k < y for logyk>0⇒k>1 which is not possible case 2 : if y < 1 ⇒ k > y and for logyk>0⇒k<1 which is true

If $l o g_{x} (l o g_{y} k) > 0$ where $x, k \in (0, 1)$ then $y \in$

The correct option is C (k, 1)
$l o g_{y} k < 1$
case 1 : if y > 1 $\Rightarrow$ k < y
for $l o g_{y} k > 0 \Rightarrow k > 1$ which is not possible
case 2 : if y < 1 $\Rightarrow$ k > y
and for $l o g_{y} k > 0 \Rightarrow k < 1$ which is true