This page contains solutions to the IISER Aptitude test Sample 1. Currently the solutions are only for Maths and Physics sections. Other sections will be uploaded soon.
Some Mnemonics and tricks to solve Permutation and Combination type Problems. Link
1) If ;
then equals ?
2) We have a sequence and so on…..
Which is the largest value in the sequence ?
3) Assuming interchange of limit and integration is permisssible, the value of
4) Let f: R→R be a function such that |f(x)-f(y)| for all .
If f(3)=6 then, f(6) equals ?
5)Let be the area bounded by curve y=x & in 1st quadrant. Then, the value of is.
6) In how many ways can 4 distinguishable pieces be placed on a 8*8 chessboard so that no two pieces are in the same row or column?
7) A and B are playing a game by alternately rolling a die,with A starting first. Each player’s score is the numbers obtained on his last roll. The ends when the sum of scores of the two players is 7, and the last player to roll the die wins. What is the probability that A wins the game ?
8) The binomial coefficient where
9) The Sum of infinite series is ?
10) The integer values of k for which the equation has real solutions is ?
11) The complex solutions of lie on :
12) How many 2*2 matrices A satisfy both and , where denotes the 2*2 identity matix and denotes the transpose of A ?
Solution: Proof of why the inverse is unique is left to be written but it can be found easily on Google or any Linear Algebra Text Book.
13) Let C be the circle that touches the X-Axis and whose centre coincides with the circum-centre of the triangle defined by ; . How many points with both co-ordinates integers are there in the interior of C?
14) Let P and Q be the centres of the circles that pass through (0,2) and (0,8) and touch the X-Axis. Then the equation of the ellipse with P and Q as focii and touching X-Axis is ?
15 Let f: R→R be a function such that f(x+y) + f(x-y)= f(xy) for all . Then f is ?