IPMAT Indore > Modern Math > Logarithms PYQs

$(2,5)$

$(-5,-2)$

$(5,\infty)$

Null set

$\frac{1}{y-a}$ is proportional to $x^{b}$

$y-a$ is proportional to $x^{b}$

$e^{y}$ is proportional to $x^{b}$

$\log _{e} y$ is proportional to $x$

4

16

2

8

$\dfrac{a + b}{2}$

$\dfrac{a - b}{2ab}$

$\dfrac{a + b}{2ab}$

$\dfrac{a + b}{2(a - b)}$

1987

2025

2065

2000

8

$\frac{5}{2}$

5

$\frac{7}{2}$

$(b-a)^n=(c-b)$

$a^n+b^n=c^n$

$a+b=c$

$(a^n+b)^n=ac$

$n\pi + \dfrac{\pi}{4}, n$ is an integer

$2n\pi + \dfrac{\pi}{4}, n$ is an integer

$\dfrac{n\pi}{4}, n$ is an integer

$\dfrac{n\pi}{4} + \dfrac{\pi}{4}, n$ is an integer

$[2,81)$

$(2,27)$

$[2,81]$

$(2,27]$

105

71

89

37

2$\sqrt{2}$

$\sqrt{2}$

2

3

0.5

30

2

1

$f(x) > g(x) > 0$ for $0 < a < 1$ and $g(x) > f(x) > 0$ for $a > 1$

$g(x) > f(x) > 0$ for $0 < a < 1$ and $f(x) > g(x) > 0$ for $a > 1$

$f(x) > g(x) > 0$ for $a > 0$

$g(x) > f(x) > 0$ for $a > 0$

$x \in \left( \frac{1}{3}, 1 \right)$

$x \in \left( \frac{1}{3}, 2 \right)$

$x \in \left( 0, \frac{1}{3} \right) \cup \left( 1, 2 \right)$

$x \in \left( -\infty, 1 \right)$