GATE CS question library

At what time between $6$ a. m. and $7$ a. m. will the minute hand and hour hand of a clock make an angle closest to $60^{\circ}$?

The security system at an IT office is composed of $10$ computers of which exactly four are working. To check whether the system is functional, the officials inspect four of the computers picked at random (without replacement). The system is deemed functional if at least three of the four computers inspected are working. Let the probability that the system …

If $x$ is real and $\mid x^2-2x+3 \mid = 11$, then possible values of $\mid -x^3+x^2-x\mid$ include

Number of people diagnosed with dengue fever (contracted from the bite of a mosquito) in North India is twice the number diagnosed last year. Municipal authorities have concluded that measures to control the mosquito population have failed in this region. Which one of the following statements, if true, does not contradict this conclusion?

The old city of Koenigsberg, which had a German majority population before World War 2, is now called Kaliningrad. After the events of the war, Kaliningrad is now a Russian territory and has a predominantly Russian population. It is bordered by the Baltic Sea on the north and the countries of Poland to the south and west and Lithuania to the east …

The value of $\sqrt{12+\sqrt{12+\sqrt{12+\dots}}}$is

What is the average of all multiples of $10$ from $2$ to $198$?

Match the columns. …

Who ___________ was coming to see us this evening?

Choose the most appropriate phrase from the options given below to complete the following sentence. India is a post-colonial country because

Let $\oplus$ denote the exclusive OR (XOR) operation. Let '$1$' and '$0$' denote the binary constants. Consider the following Boolean expression for $F$ over two variables $P$ and $Q$: $$F(P,Q)=\left( \left(1 \oplus P \right) \oplus \left( P \oplus Q \right )\right ) \oplus \left(\left(P \oplus Q\right) \oplus \left(Q \oplus 0\right)\right)$$ The …

Consider the following relational schema: employee (empId,empName,empDept) customer (custId,custName,salesRepId,rating) salesRepId is a foreign key referring to empId of the employee relation. Assume that each employee makes a sale to at least one customer. What does the following query return? SELECT empName FROM employee E WHERE NOT EXISTS (SELECT custId …

The CORRECT formula for the sentence, "not all Rainy days are Cold" is

If $G$ is the forest with $n$ vertices and $k$ connected components, how many edges does $G$ have?

Let $\delta$ denote the minimum degree of a vertex in a graph. For all planar graphs on $n$ vertices with $\delta \geq 3$, which one of the following is TRUE?

There are two elements $x,\:y$ in a group $(G,*)$ such that every element in the group can be written as a product of some number of $x$'s and $y$'s in some order. It is known that $$x*x=y*y=x*y*x*y=y*x*y*x=e$$ where $e$ is the identity element. The maximum number of elements in such a group is ____.

Consider the set of all functions $f:\{0,1, \dots,2014\} \to \{0,1,\dots, 2014\}$ such that $f\left(f\left(i\right)\right)=i$, for all $0 \leq i \leq 2014$. Consider the following statements: $P$. For each such function it must be the case that for every $i,f(i) = i$. $Q$. For each such function it must be the case that for some $i,f(i)=i$. …

Let $S$ be a sample space and two mutually exclusive events $A$ and $B$ be such that $A \cup B = S$. If $P(.)$ denotes the probability of the event, the maximum value of $P(A)P(B)$ is_____.

With respect to the numerical evaluation of the definite integral, $K = \int \limits_a^b \:x^2 \:dx$, where $a$ and $b$ are given, which of the following statements is/are TRUE? The value of $K$ obtained using the trapezoidal rule is always greater than or equal to the exact value of the definite integral. The value of $K$ obtained using the …

The value of the integral given below is $$\int \limits_0^{\pi} \: x^2 \: \cos x\:dx$$