IPMAT Indore 2024 (MCQ) PYQs

$\dfrac{(1-q)\log(p)-(1-p)\log(q)}{p-q}$

$\dfrac{(1-q)\log(q)-(1-p)\log(p)}{p-q}$

$\dfrac{(1-q)\log(p)+(1-p)\log(q)}{p-q}$

$\dfrac{(1-q)\log(q)+(1-p)\log(p)}{p-q}$

$1.5 \, \text{cm}$ or $13 \, \text{cm}$

$2.5 \, \text{cm}$

$3.5 \, \text{cm}$

$2.5 \, \text{cm}$ or $6.5 \, \text{cm}$

$\frac{1}{5}$

$\frac{1}{2}$

$\frac{1}{7}$

2

1

4

3

2

$2^{300}$

$3^{200}$

$2^{100} + 3^{100}$

$4^{100}$

4

5

7

6

$9000 \leq n < 10000$

$8000 \leq n < 9000$

$7000 \leq n < 8000$

$6000 \leq n < 7000$

8

$\frac{5}{2}$

5

$\frac{7}{2}$

27

100

200

25

$\dfrac{k^2 \sin \theta}{2} + k \sin \theta \sqrt{c^2 + k^2 \sin^2 \theta}$

$\dfrac{k^2 \sin 2\theta}{2} + k \sin \theta \sqrt{c^2 - k^2 \sin^2 \theta}$

$\dfrac{k^2 \cos 2\theta}{2} + k \sin \theta \sqrt{c^2 - k^2 \sin^2 \theta}$

$\dfrac{k^2 \cos \theta}{2} + k \sin \theta \sqrt{c^2 + k^2 \sin^2 \theta}$

$60^\circ$

$30^\circ$

$10^\circ$

$15^\circ$

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

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

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

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

$\frac{1}{7}$

$\frac{2}{7}$

$\frac{3}{5}$

$\frac{1}{4}$

190

210

180

220

22.5 km downstream of A

20 km downstream of A

15 km downstream of A

12.5 km downstream of A

20200

19200

19600

18400

1987

2025

2065

2000

$\frac{4}{5}$

$\frac{2}{5}$

$\frac{3}{4}$

$\frac{20}{21}$

$\sqrt{10}$

$2\sqrt{5}$

$\sqrt{7}$

$2\sqrt{7}$

$15(\sqrt{5} + 1)$

$20(\sqrt{3} + 1)$

$30$

$10(\sqrt{3} + 1)$

6

2

4

5

$\left(3\sqrt{3} + \pi\right) \frac{k^2}{24}$

$\left(3\sqrt{3} + \pi\right) \frac{k^2}{6}$

$\left(3\sqrt{3} - \pi\right) \frac{k^2}{24}$

$\left(3\sqrt{3} + \pi\right) \frac{k^2}{6}$

1111

1000

1100

1130

75

60

100

50

1

-1

7

-7