IPM Indore 2022

Instructions

For the following questions answer them individually

Question 11

The number of triangles that can be formed by choosing points from 7 points on a line and 5 points on another parallel line is_________.

Backspace
789
456
123
0.-
Clear All
Video Solution
Question 12

A new sequence is obtained from the sequence of positive integers (1, 2, 3,...) by deleting all the perfect squares. Then the $$2022^{nd}$$ term of the new sequence is___________.

Backspace
789
456
123
0.-
Clear All
Video Solution
Question 13

When Geeta increases her speed from 12 km/hr to 20 km/hr, she takes one hour less than the usual time to cover the distance between her home and office. The distance between her home and office is________km.

Backspace
789
456
123
0.-
Clear All
Video Solution
Question 14

The $$3^{rd}, 14^{th}$$ and $$69^{th}$$ terms of an arithmetic progression form three distinct and consecutive terms of a geometric progression. If the next terms of the geometries progression is the $$n^{th}$$ term of the arithmetic progression, then n quals____________.

Backspace
789
456
123
0.-
Clear All
Video Solution
Question 15

Given that
$$f(x)=|x|+2|x−1|+|x−2|+|x−4|+|x−6|+2|x−10|$$, $$x \epsilon (-\infty, \infty)$$
the minimum value of f(x) is _________.

Backspace
789
456
123
0.-
Clear All
Video Solution
Question 16

The sum of the first 15 terms in an arithmetic progression in 200, while the sum of the next 15 terms in 350, then the common difference is

Video Solution
Question 17

For $$0 < \theta < \frac{\pi}{4}$$, let
$$a = ((\sin \theta)^{\sin \theta}) (\log_{2} \cos \theta)$$, $$b = ((\cos \theta)^{\sin \theta}) (\log_{2} \sin \theta)$$
$$c = ((\sin \theta)^{\cos \theta}) (\log_{2} \cos \theta)$$ and $$d = ((\sin \theta)^{\sin \theta}) (\log_{2} \sin \theta)$$
Then, the median value in the sequence a, b, c, d is

Video Solution
Question 18

In a right-angled triangle ABC, the hypotenuse AC is of length 13 cm. A line drawn connecting the midpoints D and E of sides AB and AC is found to be 6 cm in length. The length of BC is

Video Solution
Question 19

In a room, there are n persons whose average height is 160 cm. If m more persons, whose average height is 172 cm, enter the room, then the average height of all persons in the room becomes 164 cm. Then m : n is

Video Solution
Question 20

The number of four-digit integers which are greater than 1000 and divisible by both 2 and 3, but not by 5, is

Video Solution
cracku

Boost your Prep!

Download App