Q1:
Algebra>Progression & Series
Medium
Given that $1 + \frac{1}{2^2} + \frac{1}{3^2} + \frac{1}{4^2} + ... = \frac{\pi^2}{6}$, the value of $1 + \frac{1}{3^2} + \frac{1}{5^2} + \frac{1}{7^2} + ...$ is
Correct Answer
Option 4
Correct Answer
IPMAT Indore 2025 PYQsMultiple Choice (Quants). Free, no login required.
Q2:
Modern Math>Logarithms
Medium
If $y=a+b \log _{e} x$ then which of the following is true?
Correct Answer
Option 3
Correct Answer
Q3:
Algebra>Polynomials
Medium
If $a_1, a_2, ..., a_8$ are the roots of the equation $x^8 + x^7 + ... + x + 1 = 0$, then the value of $a_1^{2025} + a_2^{2025} + ... + a_8^{2025}$ is
Correct Answer
Option 3
Correct Answer
Q4:
Arithmetic>Mean, Median & Mode
Medium
Suppose $a, b$ and $c$ are three real numbers such that Max$(a, b, c) \ +$ Min$(a, b, c) = 15$, and Median$(a, b, c) \ -$ Mean$(a, b, c) = 2.$ Then the median of $a, b$ and $c$ is
Correct Answer
Option 2
Correct Answer
Q5:
Modern Math>Logarithms
Easy
If $\log_{25} [5 \log_3 (1+\log_3(1+2\log_2x))] = \frac12$ then $x$ is:
Correct Answer
Option 2
Correct Answer
Q6:
Number System>Miscellaneous
Medium
A natural number $n$ lies between $100$ and $400$, and the sum of its digits is $10$. The probability that $n$ is divisible by $4$, is
Correct Answer
Option 2
Correct Answer
Q7:
Geometry>Triangles
Medium
In triangle $ABC, AB = AC = x, ∠ABC = \theta$ and the circumradius is equal to $y$. Then $\frac{x}{y}$ equals
Correct Answer
Option 4
Correct Answer
Q8:
Algebra>Polynomials
Medium
If $8x^2 - 2kx + k = 0$ is a quadratic equation in $x$, such that one of its roots is $p$ times the other, and $p, k$ are positive real numbers, then $k$ equals
Correct Answer
Option 3
Correct Answer
Q9:
Geometry>Straight Lines
Medium
Let $A(1,3)$ and $B(5,1)$ be two points. If a line with slope $m$ intersects $AB$ at an angle of $45°$, then the possible values of $m$ are
Correct Answer
Option 3
Correct Answer
Q10:
Algebra>Polynomials
Hard
Let $P(x)$ be a quadratic polynomial such that $\left|\begin{array}{ll} P(0) & P(1) \\ P(0) & P(2) \end{array}\right|=0$ Let $P(0)=2$ and $P(1)+P(2)+P(3)=14$. Then $P(4)$ equals
Correct Answer
Option 3
Correct Answer
Q11:
Geometry>Circles
Medium
A circle touches the y-axis at $(0, 4)$ and passes through the point $(-2, 0)$. Then the radius of the circle is
Correct Answer
Option 2
Correct Answer
Q12:
Geometry>Triangles
Medium
Consider a triangle with side lengths 4 meters, 6 meters, and 9 meters. A dog runs around the triangle in such a way that the shortest distance of the dog from the triangle is exactly 1 meter. The total distance covered (in meters) by the dog in one round is
Correct Answer
Option 2
Correct Answer
Q13:
Arithmetic>Simple & Compound Interest
Medium
Anindita invests a total of $1$ lakh rupees distributed across three schemes A, B and C for a period of two years. These schemes offer an interest rate of $10\%$, $8\%$ and $12\%$ per annum, respectively, each compounded annually. If the initial investment amount in scheme A is $30000$ rupees and the total interest earned from all the three schemes during the first year is $10600$ rupees, then the total interest earned, in rupees, from all the three schemes for the second year is
Correct Answer
Option 2
Correct Answer
Q14:
Algebra>Polynomials
Easy
Let $f(x) = a^2x^2 + 2bx + c$ where, $a \neq 0$, $b, c$ are real numbers and $x$ is a real variable then
Correct Answer
Option 2
Correct Answer
Q15:
Geometry>Straight Lines
Medium
The area of the triangle, formed by the straight lines $y = 0, 12x - 5y = 0,$ and $3x + 4y = 7$ is
Correct Answer
Option 2
Correct Answer
Q16:
Geometry>Polygons
Easy
Area of a regular octagon inscribed in a circle of radius 1 unit is:
Correct Answer
Option 1
Correct Answer
Q17:
Arithmetic>Time, Speed & Distance
Hard
Two swimmers, Ankit and Bipul, start swimming from the opposite ends of a swimming pool at the same time. Ankit can cover the length of the pool once in 10 minutes. Bipul can cover the length of the pool once in 15 minutes. They swim back and forth for 80 minutes without stopping. The number of times they meet each other is
Correct Answer
Option 3
Correct Answer
Q18:
Algebra>Progression & Series
Medium
The sum of the first 5 terms of a geometric progression is the same as the sum of the first 7 terms of the same progression. If the sum of the first 9 terms is 24, then the 4th term of the progression is
Correct Answer
Option 2
Correct Answer
Q19:
Modern Math>Logarithms
Medium
The set of all values of $x$ satisfying the inequality $\log _{\left(x+\frac{1}{x}\right)}\left[\log _{2}\left(\frac{x-1}{x+2}\right)\right]>0$ is
Correct Answer
Option 4
Correct Answer
Q20:
Algebra>Progression & Series
Medium
Let $S_1 = \{100, 105, 110, 115, ... \}$ and $S_2 = \{100, 95, 90, 85, ... \}$ be two series in arithmetic progression. If $a_k$ and $b_k$ are the $k$-th terms of $S_1$ and $S_2$, respectively, then $\sum_{k=1}^{20} a_k b_k$ equals __________.
Correct Answer
Option 2
Correct Answer
Q21:
Modern Math>Probability
Medium
A and B take part in a rifle shooting match. The probability of A hitting the target is 0.4, while the probability of B hitting the target is 0.6. If A has the first shot, post which both strike alternately, then the probability that A hits the target before B hits it is
Correct Answer
Option 2
Correct Answer
Q22:
Number System>Divisibility Rules
Medium
Which of the following numbers is divisible by $3^{10} + 2$?
Correct Answer
Option 4
Correct Answer
Q23:
Modern Math>Set Theory
Medium
Let A and B be two finite sets such that $n(A - B)$, $n(A\cap B)$, $n(B - A)$ are in an arithmetic progression. Here $n(X)$ denotes the number of elements in a finite set $X$. If $n(A\cup B) = 18$, then $n(A) + n(B)$ is ____
Correct Answer
Option 1
Correct Answer
Q24:
Modern Math>Permutation & Combination
Easy
The number of integers greater than 5000 and divisible by 5 that can be formed with the digits 1, 3, 5, 7, 8, 9 where no digit is repeated is
Correct Answer
Option 1
Correct Answer
Q25:
Number System>Remainder
Medium
The remainder when $11^{1011} + 1011^{11}$ is divided by $9$ is
Correct Answer
Option 2
Correct Answer
Q26:
Data Interpretation>Tabular Data
Medium
Correct Answer
Option 4
Correct Answer
Q27:
Data Interpretation>Tabular Data
Medium
Correct Answer
Option 3
Correct Answer
Q28:
Data Interpretation>Tabular Data
Medium
Correct Answer
Option 1
Correct Answer
Q29:
Data Interpretation>Tabular Data
Medium
Correct Answer
Option 2
Correct Answer
Q30:
Data Interpretation>Tabular Data
Medium
Correct Answer
Option 2
Correct Answer
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