ISI MS(QMBA) 2018 Question Paper with Solutions: 46 Questions, Answer Key & Section-wise Analysis

ISI MS(QMBA) 2018 previous year paper: 46 questions with answer key and detailed solutions, section-wise breakdown and free sample questions.

Paper breakdown

46 questions · 120 marks · 248 minutes. Algebra and Number Theory: 21 · Calculus: 10 · Linear Algebra: 6 · Probability, Statistics and Analytical Reasoning: 5 · Geometry and Trigonometry: 4

Free sample questions from ISI MS(QMBA) 2018 Question Paper

Question 1 · Geometry and Trigonometry MCQ

The area lying in the first quadrant and bounded by the circle

$x^{2} + y^{2} = 4$

and lines

$x = 0 and x = 1$

is given by

A.
$\frac{π}{3} + \frac{3}{2}$
B.
$\frac{π}{6} + \frac{3}{4}$
C.
$\frac{π}{3} - \frac{3}{2}$
D.
$\frac{π}{6} + \frac{3}{2}$

Question 2 · Calculus SUB

Let $f$ be a real valued function defined on the interval $(- 1, 1)$ such that $e^{- x} f (x) = 2 + \int_{0}^{1} 1 + t^{4} d t$ , for all $x \in (- 1, 1)$ . And let $f^{- 1}$ be the inverse function of $f$ . Then find the value of $(f^{- 1})^{'} (2)$ , where $(f^{- 1})^{'} (2)$ is the value of first order derivative of $f^{- 1}$ at 2.

Question 3 · Linear Algebra SUB

a_{1}, a_{2}, a_{3}, \dots, a_{n}, \dots

are in Geometric Progression, then show that the value of

det A

is equal to zero, where

A = lo g a_{n} l o g a_{n + 3} l o g a_{n + 6} lo g a_{n + 1} lo g a_{n + 4} lo g a_{n + 7} lo g a_{n + 2} lo g a_{n + 5} lo g a_{n + 8}

Question 4 · Geometry and Trigonometry MCQ

If $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ are the opposite endpoints of a diameter of a circle, then the equation of the circle is given by

A.
$(x - x_{1}) (y - y_{1}) + (x - x_{2}) (y - y_{2}) = 0$
B.
$(x - x_{1}) (y - y_{2}) + (x - x_{2}) (y - y_{1}) = 0$
C.
$(x - x_{1}) (x - x_{2}) + (y - y_{1}) (y - y_{2}) = 0$
D.
$(x - x_{1}) (x - x_{2}) = (y - y_{1}) (y - y_{2}) = 0$

Question 5 · Algebra and Number Theory SUB

Show that $1 9^{93} - 1 3^{99}$ is divisible by 162.

Question 6 · Calculus SUB

Evaluate $\int \frac{x + 3}{5 - 4 x - x ^{2}} d x$ .

Question 7 · Algebra and Number Theory MCQ

If $α, β$ and $γ$ are the roots of the equation $x^{3} + 3 x^{2} - 8 x + 1 = 0$ , then an equation whose roots are $α + 1, β + 1$ and $γ + 1$ is given by

A.
$y^{3} - 11 y + 11 = 0$
B.
$y^{3} - 11 y - 11 = 0$
C.
$y^{3} + 13 y + 13 = 0$
D.
$y^{3} + 6 y^{2} + y - 3 = 0$

Other ISI MS(QMBA) papers

ISI MS(QMBA)

Previous Year Papers

Verified Solutions Included

ISI MS(QMBA) 2018 Question Paper with Solutions: 46 Questions, Answer Key & Section-wise Analysis

ISI MS(QMBA) 2018 previous year paper: 46 questions with answer key and detailed solutions, section-wise breakdown and free sample questions.

46 Qs

Total Questions

120 Marks

Total Marks

248 Mins

Duration

+3 / -1 / 0

Marking Scheme

Section-wise Paper Structure

Algebra and Number Theory

21 Qs

46% of total marks

Calculus

10 Qs

22% of total marks

Linear Algebra

6 Qs

13% of total marks

Probability, Statistics and Analytical Reasoning

5 Qs

11% of total marks

Geometry and Trigonometry

4 Qs

9% of total marks

Free Solved Questions with Step-by-Step Solutions

Authentic examination problems with detailed derivations and answer keys.

Question 1

The area lying in the first quadrant and bounded by the circle x^{2} + y^{2} = 4 and lines x = 0 and x = 1 is given by

Question 2

Let f be a real valued function defined on the interval (- 1, 1) such that e^{- x} f (x) = 2 + \int_{0}^{1} 1 + t^{4} d t, for all x \in (- 1, 1) . And let f^{- 1} be the inverse function of f . Then find the value of (f^{- 1})^{'} (2), where (f^{- 1})^{'} (2) is the value of first order derivative of f^{- 1} at 2.

Question 3

If a_{1}, a_{2}, a_{3}, \dots, a_{n}, \dots are in Geometric Progression, then show that the value of det A is equal to zero, where A = lo g a_{n} l o g a_{n + 3} l o g a_{n + 6} lo g a_{n + 1} lo g a_{n + 4} lo g a_{n + 7} lo g a_{n + 2} lo g a_{n + 5} lo g a_{n + 8}

Question 4

If (x_{1}, y_{1}) and (x_{2}, y_{2}) are the opposite endpoints of a diameter of a circle, then the equation of the circle is given by

Question 5

Show that 1 9^{93} - 1 3^{99} is divisible by 162.

Question 6

Evaluate \int \frac{x + 3}{5 - 4 x - x ^{2}} d x .

Question 7

If α, β and γ are the roots of the equation x^{3} + 3 x^{2} - 8 x + 1 = 0, then an equation whose roots are α + 1, β + 1 and γ + 1 is given by

Unlock All 46 Questions in Real Examination Mode

Practice with the authentic timer, on-screen calculator, instant percentile ranking, and section-wise analytics.

More ISI MS(QMBA) Previous Year Papers

ISI MS(QMBA) 2025

47 Questions with Solutions

ISI MS(QMBA) 2024

46 Questions with Solutions

ISI MS(QMBA) 2023

47 Questions with Solutions

ISI MS(QMBA) 2022

46 Questions with Solutions

ISI MS(QMBA) 2021

46 Questions with Solutions

ISI MS(QMBA) 2020

46 Questions with Solutions

ISI MS(QMBA) 2019

46 Questions with Solutions

Free preview ends here

Login to view the complete paper and solutions

Creating an account is free. You get the rest of this chapter, step-by-step solutions, and a study plan built around the topics you are actually weak at.

Why MastersUp

Personalised first. High quality throughout.

Most platforms hand everyone the same content. Here the content moves with your performance, topic by topic.

Built around you, not around a syllabus PDF

Every answer you give moves your topic-level intelligence rate. The next question, the next revision card and tomorrow's plan all change with it.

Revision that hits your weak spots

We only revise topics you have actually attempted and are still below the safe bar on — never the same chapter on repeat.

Questions calibrated to the real exam

Each question carries a measured toughness. You are served a rung above your current level, so practice keeps stretching you.

Notes written for recall, not for volume

Full lesson cards for first study, curated short-note cards for the last mile — with derivations, traps and exam patterns marked.

One place for everything

Notes, chapter practice, previous-year questions, test series and full-length papers — all feeding one picture of your preparation.

Honest progress

No vanity streaks. Progress here means chapters mastered and accuracy that held up on harder questions.

Unlock the whole course

Full notes and short notes, the complete question bank with worked solutions, mock tests, full-length papers, and an adaptive plan that rebuilds itself as you improve.

View all plans Start free