Recent questions tagged tifr2019

Let $X$ be a set with $n$ elements. How many subsets of $X$ have odd cardinality?$n$ $2^n$$2^{n/2}$$2^{n-1}$Can not be determined w...

How many proper divisors (that is, divisors other than $1$ or $7200$) does $7200$ have ?$18$$20$$52$$54$$60$

$A$ is $n \times n$ square matrix for which the entries in every row sum to $1$. Consider the following statements:The column vector $[1,1,\ldots,1]^T$ is an eigen vector...

What are the last two digits of $1! + 2! + \dots +100!$?$00$$13$$30$$33$$73$

Consider the following toy model of traffic on a straight , single lane, highway. We think of cars as points, which move at the maximum speed $v$ that satisfies the follo...

Let $A$ and $B$ be two containers. Container $A$ contains $50$ litres of liquid $X$ and container $B$ contains $100$ litres of liquid $Y$. Liquids $X$ and $Y$ are solub...

Consider the integral$$\int^{1}_{0} \frac{x^{300}}{1+x^2+x^3} dx$$What is the value of this integral correct up to two decimal places?$0.00$$0.02$$0.10$$0.33$$1.00$

A drawer contains $9$ pens, of which $3$ are red, $3$ are blue, and $3$ are green. The nine pens are drawn from the drawer one at at time (without replacement) such that ...

Which of the following decimal numbers can be exactly represented in binary notation with a finite number of bits ?$0.1$$0.2$$0.4$$0.5$All the above

How many distinct minimum weight spanning trees does the following undirected, weighted graph have ?$8$$16$$32$$64$None of the above

A graph is $d$ – regular if every vertex has degree $d$. For a $d$ – regular graph on $n$ vertices, which of the following must be TRUE?$d$ divides $n$Both $d$ and $n$ ar...

Given the following pseudocode for function $\text{printx()}$ below, how many times is $x$ printed if we execute $\text{printx(5)}?$void printx(int n) { if(n==0){ printf...

Consider the following program fragment:var a,b : integer; procedure G(c,d: integer); begin c:=c-d; d:=c+d; c:=d-c end; a:=2; b:=3; G(a,b);If both parameters to $G$ are p...

Consider the following program fragment:var x, y: integer; x := 1; y := 0; while y < x do begin x := 2*x; y := y+1 end;For the above fragment , which of the following is ...

Let the language $D$ be defined in the binary alphabet $\{0,1\}$ as follows:$D:= \{ w \in \{0,1\}^* \mid \text{ substrings 01 and 10 occur an equal number of times in w}...

Consider the following non-deterministic automaton,where $s_1$ is the start state and $s_4$ is the final (accepting) state. The alphabet is $\{a,b\}$. A transition with l...

A row of $10$ houses has to be painted using the colours red, blue, and green so that each house is a single colour, and any house that is immediately to the right of a r...

Consider directed graphs on $n$ labelled vertices $\{1,2, \dots ,n\}$, where each vertex has exactly one edge coming in and exactly one edge going out. We allow self-loo...