Electronics and Communication Gate 2018 Questions with Answer

Ques 27 GATE 2018

In the circuit shown below, the (W/L) value for M₂ is twice that for M₁. The two nMOS transistors are otherwise identical. The threshold voltage V_T for both transistors is 1.0V. Note that V_GS for M₂ must be > 1.0 V.

Ques 28 GATE 2018

Two identical nMOS transistors M₁ and M₂ are connected as shown below. The circuit is used as an amplifier with the input connected between G and S terminals and the output taken between D and S terminals. V_bias and V_D are so adjusted that both transistors are in saturation. The transconductance of this combination is defined as g_m=∂i_D/∂v_GS where i_D is the current flowing into the drain of M₂. while the output resistance is r_o=∂v_DS/∂i_D, Let g_m1, g_m2 be the transconductances and r_o1, r_o2 be the output resistances of transistors M₁ and M₂, respectively.

Ques 29 GATE 2018

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

Ques 30 GATE 2018

A p-n step junction diode with a contact potential of 0.65 V has a depletion width of 1μm at equilibrium. The forward voltage (in volts, correct to two decimal places) at which this width reduces to 0.6μm is

Ques 31 GATE 2018

There are two photolithography systems: one with light source of wavelength λ₁=156 nm (System 1) and another with light source of wavelength λ₂=325 nm (System 2). Both photolithography systems are otherwise identical. If the minimum feature sizes that can be realized using System1 and System2 are L_min1 and L_min2 respectively, the ratio L_min1/L_min2 (correct to two decimal places) is

Ques 32 GATE 2018

Red (R), Green (G) and Blue (B) Light Emitting Diodes (LEDs) were fabricated using p-n junctions of three different inorganic semiconductors having different band-gaps. The built-in voltages of red, green and blue diodes are V_R, V_G and V_B, respectively. Assume donor and acceptor doping to be the same (N_A and N_D respectively) in the p and n sides of all the three diodes. Which one of the following relationships about the built-in voltages is TRUE?

Ques 33 GATE 2018

A solar cell of area 1.0 cm², operating at 1.0 sun intensity, has a short circuit current of 20 mA, and an open circuit voltage of 0.65 V. Assuming room temperature operation and thermal equivalent voltage of 26 mV, the open circuit voltage (in volts, correct to two decimal places) at 0.2 sun intensity is

Ques 34 GATE 2018

A junction is made between p- Si with doping density N_A1=10¹⁵cm^-3 and p Si with doping density N_A2=10¹⁷cm^-3. Given: Boltzmann constant k=1.38 x 10^-23 J·K^-1, electronic charge q=1.6×10^-19 C. Assume 100% acceptor ionization. At room temperature (T=300K), the magnitude of the built-in potential (in volts, correct to two decimal places) across this junction will be

Ques 35 GATE 2018

Consider p(s)=s³+a₂s²+a₁s+a₀ with all real coefficients. It is known that its derivative p'(s) has no real roots. The number of real roots of p(s) is

Ques 36 GATE 2018

Let M be a real 4x4 matrix. Consider the following statements:
S1: M has 4 linearly independent eigenvectors.
S2: M has 4 distinct eigenvalues.
S3: M is non-singular (invertible).
Which one among the following is TRUE?

Ques 37 GATE 2018

Let f(x,y)=(ax²+by²)/xy where a and b are constants. If ∂f/∂x=∂f/∂y at x=1 and y=2, then the relation between a and b is

Ques 38 GATE 2018

Consider matrix A=[[k, 2k],[k²-k, k²]] and vector x=[[x₁],[x₂]]. The number of distinct real values of k for which the equation Ax=0 has infinitely many solutions is

Ques 39 GATE 2018

Taylor series expansion of f(x)=∫₀^xe^-(t2/2)dt around x=0 has the form f(x)=a₀+a₁x+a₂x²+••• The coefficient a₂ (correct to two decimal places) is equal to