GATE CS question library

If $V_1$ and $V_2$ are $4$-dimensional subspaces of a $6$-dimensional vector space $V$, then the smallest possible dimension of $V_1 \cap V_2$ is _____.

Which one of the following statements is TRUE about every $n \times n$ matrix with only real eigenvalues?

Let $G$ be a group with $15$ elements. Let $L$ be a subgroup of $G$. It is known that $L \neq\ G$ and that the size of $L$ is at least $4$. The size of $L$ is __________.

Let $X$ and $Y$ be finite sets and $f:X \to Y$ be a function. Which one of the following statements is TRUE?

Consider the following statements: P: Good mobile phones are not cheap Q: Cheap mobile phones are not good L: P implies Q M: Q implies P N: P is equivalent to Q Which one of the following about L, M, and N is CORRECT?

Consider the equation: $(7526)_8 − (Y)_8 = (4364)_8$, where $(X)_N$ stands for $X$ to the base $N$. Find $Y$.

The ratio of male to female students in a college for five years is plotted in the following line graph. If the number of female students in $2011$ and $2012$ is equal, what is the ratio of male students in $2012$ to male students in $2011$?

By the beginning of the $20^{\text{th}}$ century, several hypotheses were being proposed, suggesting a paradigm shift in our understanding of the universe. However, the clinching evidence was provided by experimental measurements of the position of a star which was directly behind our sun. Which of the following inference(s) may be drawn from the above …

A dance programme is scheduled for $10.00$ a.m. Some students are participating in the programme and they need to come an hour earlier than the start of the event. These students should be accompanied by a parent. Other students and parents should come in time for the programme. The instruction you think that is appropriate for this is

The table below has question-wise data on the performance of students in an examination. The marks for each question are also listed. There is no negative or partial marking in the examination. …

Which number does not belong in the series below? $\qquad2, 5, 10, 17, 26, 37, 50, 64$

Choose the word that is opposite in meaning to the word “coherent”.

If she _______________ how to calibrate the instrument, she _______________ done the experiment.

$\underset{\text{I}}{\underline{\text{While trying to collect}}}$ an envelope $\underset{\text{II}}{\underline{\text{from under the table,}}}$ $\underset{\text{III}}{\underline{\text{Mr. X fell down}}}$ and $\underset{\text{IV}}{\underline{\text{was losing consciousness.}}}$ Which one of the above underlined parts of the sentence is NOT appropriate?