ISI MS(QMBA) 2021 Question Paper with Solutions: 46 Questions, Answer Key & Section-wise Analysis

Let $A=(1,-1),B=(-2,0),C=(1,2)$ and $D$ be the vertices of a parallelogram in the $X-Y$ plane listed clockwise. Then the point $D$ is

Three real numbers are in Arithmetic Progression, the first term is 9. If 2 is added to the second term and 20 is added to the third term, the resulting three numbers are in Geometric Progression. What is the smallest possible value for the third term of the Geometric Progression?

Let $z=(1-t^2)+i\sqrt{1-t^2}$ be a complex number where $t$ is a real number such that $|t|<1$. Then the locus of $z$ in the complex plane is

There are 4 Red, 5 Black and 6 Blue balls in an urn. 4 balls are drawn at random without replacement from this urn. What is the probability that these 4 balls will contain at least one ball of each colour?

Let ${\int }_1^2{e}^{x^2}dx=a$. Then the value of ${\int }_e^{e^4}\sqrt{{\log }_{e}x}dx$ is