GATE EC question library

“By giving him the last _______ of the cake, you will ensure lasting _______ in our house today.” The words that best fill the blanks in the above sentence are

“Even though there is a vast scope for its _______, tourism has remained a/an ________ area.” The word that best fill the blanks in the above sentence are

If the number $715\blacksquare423$ is divisible by $3(\blacksquare$ denotes the missing digit in the thousandths place$),$ then the smallest whole number in the place of $\blacksquare$ is _________.

What is the value of $1+\frac{1}{4}+\frac{1}{16}+\frac{1}{256}+ \cdots?$

A $1.5$ m tall person is standing at a distance of $3$ m from a lamp post. The light from the lamp at the top of the post casts her shadow. The length of the shadow is twice her height. What is the height of the lamp post in meters?

Leila aspires to buy a car worth Rs.$10,00,000$ after $5$ years. What is the minimum amount in Rupees that she should deposit now in a bank which offers $10\%$ annual rate of interest, if the interest was compounded annually?

Two alloys $A$ and $B$ contain gold and copper in the ratios of $2:3$ and $3: 7$ by mass, respectively. Equal masses of alloys $A$ and $B$ are melted to make an alloy $C.$ The ratio of gold to copper in alloy $C$ is$:$

The Cricket Board has long recognized John's potential as a leader of the team. However, his on-field temper has always been a matter of concern for them since his junior days. While this aggression has filled stadia with die-hard fans. it has taken a toll on his own batting. Until recently, it appeared that he found it difficult to convert his aggression …

A cab was involved in a hit and run accident at night. You are given the following data about the cabs in the city and the accident. 85% of cabs in the city are green and the remaining cabs are blue. A witness identified the cab involved in the accident as blue. It is known that a witness can conectly identify the cab colour only 80% of the tune. Which of …

A coastal region with unparalleled beauty is home to many species of animals. It is dotted with coral reefs and unspoilt white sandy beaches. It has remained inaccessible to tourists due to poor connectivity and lack of accommodation. A company has spotted the opportunity and is planning to develop a luxury resort with helicopter service to the nearest major …

Two identical $\text{nMOS}$ transistors $M_{1}$ and $M_{2}$ are connected as shown below. The circuit is used as an amplifier with the input connected between $\text{G and S}$ terminals and the output taken between $D\: \text{and}\: S$ terminals. $V_{bias}$ and $V_{D}$ are so adjusted that both transistors are in saturation. The …

In the circuit shown below, the op-amp is ideal and Zener voltage of the diode is $2.5\: volts$. At the input, unit step voltage is applied, i.e. $v_{IN}\left ( t \right ) = u\left ( t \right )\:volts$. Also, at $t = 0$, the voltage across each of the capacitors is zero. The time $t$, in milliseconds, at which the output voltage $v_{OUT}$ crosses …

A good transimpedance amplifier has

Let the input be $u$ and the output be $y$ of a system, and the other parameters are real constants. Identify which among the following systems is not a linear system:

The Nyquist stability criterion and the Routh criterion both are powerful analysis tools for determining the stability od feedback controllers. Identify which of the following statements is FALSE:

Consider $p(s)=s^{3}+ a_{2}s^{2}+a_{1}s+a_{0}$ with all real coefficients. It is known that its derivatives ${p}'(s)$ has no real roots. The number of real roots of $p(s)$ is

In a $\text{p-n}$ junction diode at equilibrium, which one of the following statements is NOT TRUE?

The logic function $f(X, Y)$ realized by the given circuit is

A function $F(A, B, C)$ defined by three Boolean variables $\text{A, B and C}$ when expressed as sum of products is given by $$F=\overline{A}\:.\overline{B}\:.\overline{C}+\overline{A}\:.B\:.\overline{C}+A\:.\overline{B}\:.\overline{C}$$ where, $\overline{A}\:,\overline{B}\:,and\:\overline{C}$ are the complements of the respective variables. The …

The points $\text{P, Q, and R}$ shown on the Smith chart (normalized impedance chart) in the following figure represent: