# IISER Aptitude Test Sample Paper 2 Solution

his page contains solutions to the IISER Aptitude test Sample 2. Currently the solutions are only for Maths and Physics sections. Other sections will be uploaded soon.

• MATH
• PHYSICS
• BIOLOGY
• CHEMISTRY

### MATH

1) The equations of two lines are x+2y=1 and 2x-y=3. what is the nature between two lines ?

Solution:

2) Suppose the matrix $\begin{bmatrix} 2 &a \\ 3&b \end{bmatrix}$ with a and b integers has determinant 1. A possible value for b is ?

Solution:

3) There are 5 students. Arul and Neeraj are Mathematics students. Sunny likes Biology. Mathematics students dislike Chemistry. Students who like Biology cannot dislike Chemistry. Students who want to take Physics must like all other subjects. Swati and Manas want to take Physics. The number of students who dislike Chemisty is?

Solution:

4) Let $a_1,a_2,.....,a_10$ be 10 observations with median 3. Then

Solution:

5) The value of the $\int^1_-1 (x^2 + \frac{x^{2013}}{x^2+2|x|+1})\,dx$ is ?

Solution:

6) The sum of the infinite series $\frac{9}{10} + \frac{9}{100} + \frac{9}{1000} +.....$ is

Solution:

7) The angle between the tangents to the circles $x^2 +y^2 =1$  and  $x^2 + {(y-1)}^2=2$ at the point (1,0) is ?

Solution:

8) The length of the shortest path in space between the z-axis and the line given by the equations z=0 and y=1 is ?

Solution:

9) Consider the inequalities x+y<3 , x-y<5, 5x-3y<15 and 2x+y>2. The region in the plae that consists of the points satisfying these inequalities is ?

Solution:

10) The number of the solutions of $\tan{x} = x - x^2$ with $-1 \leq x \leq 1$ is ?

Solution:

11)