Algebra - General Aptitude - General Aptitude (GA) Previous Year Questions

1

2012 · General Aptitude (GA) · General Aptitude · Algebra

Instrumentation Engineering (IN) 2012

The average power delivered to an impedance \((4-j3) \Omega\) by a current \(5\cos(100\pi t+100)\)A is

A

44.2 W

B

50 W

C

62.5 W

D

125 W

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2

2012 · General Aptitude (GA) · General Aptitude · Algebra

Instrumentation Engineering (IN) 2012

The maximum value of \( f(x) = x^3 - 9x^2 + 24x + 5 \) in the interval [1, 6] is

A

21

B

25

C

41

D

46

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3

2012 · General Aptitude (GA) · General Aptitude · Algebra

Instrumentation Engineering (IN) 2012

The Fourier transform of a signal \( h(t) \) is \( H(j\omega) = (2\cos\omega)(\sin2\omega)/\omega \). The value of \( h(0) \) is

A

1/4

B

1/2

C

1

D

2

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4

2012 · General Aptitude (GA) · General Aptitude · Algebra

Instrumentation Engineering (IN) 2012

Let \( y[n] \) denote the convolution of \( h[n] \) and \( g[n] \), where \( h[n] = (1/2)^n u[n] \) and \( g[n] \) is a causal sequence. If \( y[0] = 1 \) and \( y[1] = 1/2 \), then \( g[1] \) equals

A

0

B

1/2

C

1

D

3/2

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5

2012 · General Aptitude (GA) · General Aptitude · Algebra

Instrumentation Engineering (IN) 2012

The input x(t) and output y(t) of a system are related as y(t) = \int_{-\infty}^{t} x(\tau) \cos(3\tau) d\tau. The system is

A

time-invariant and stable

B

stable and not time-invariant

C

time-invariant and not stable

D

not time-invariant and not stable

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6

2012 · General Aptitude (GA) · General Aptitude · Algebra

Instrumentation Engineering (IN) 2012

The open loop transfer function of a unity negative feedback control system is given by G(s) = 150 / (s(s + 9)(s + 25)). The gain margin of the system is

A

10.8 dB

B

22.3 dB

C

34.1 dB

D

45.6 dB

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7

2012 · General Aptitude (GA) · General Aptitude · Algebra

Instrumentation Engineering (IN) 2012

G_c(s) is a lead compensator if

A

a = 1, b = 2

B

a = 3, b = 2

C

a = -3, b = -1

D

a = 3, b = 1

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8

2012 · General Aptitude (GA) · General Aptitude · Algebra

Instrumentation Engineering (IN) 2012

Rajju has 14 currency notes in his pocket consisting of only Rs. 20 notes and Rs. 10 notes. The total money value of the notes is Rs. 230. The number of Rs. 10 notes that Rajju has is

A

5

B

6

C

9

D

10

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9

2015 · General Aptitude (GA) · General Aptitude · Algebra

Instrumentation Engineering (IN) 2015

The double integral \(\int_{0}^{a} \int_{0}^{y} f(x,y) \, dx \, dy\) is equivalent to

A

\(\int_{0}^{a} \int_{0}^{y} f(x,y) \, dx \, dy\)

B

\(\int_{0}^{a} \int_{x}^{a} f(x,y) \, dx \, dy\)

C

\(\int_{0}^{a} \int_{x}^{a} f(x,y) \, dy \, dx\)

D

\(\int_{0}^{a} \int_{0}^{x} f(x,y) \, dx \, dy\)

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10

2015 · General Aptitude (GA) · General Aptitude · Algebra

Instrumentation Engineering (IN) 2015

The highest frequency present in the signal \(x(t)\) is \(f_{max}\). The highest frequency present in the signal \(y(t) = x^2(t)\) is

A

\(\frac{1}{2} f_{max}\)

B

\(f_{max}\)

C

\(2 f_{max}\)

D

\(4 f_{max}\)

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11

2015 · General Aptitude (GA) · General Aptitude · Algebra

Instrumentation Engineering (IN) 2015

The output frequency of an $LC$ tank oscillator employing a capacitive sensor acting as the capacitor of the tank is 100 kHz. If the sensor capacitance increases by 10 %, the output frequency in kilo-hertz becomes __________ kHz.

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12

2015 · General Aptitude (GA) · General Aptitude · Algebra

Instrumentation Engineering (IN) 2015

The signal \( x[n] = \sin(\pi n/6)/(\pi n) \) is processed through a linear filter with the impulse response \( h[n] = \sin(\omega_c n)/(\pi n) \) where \( \omega_c > \pi/6 \). The output of the filter is

A

\(\sin(2\omega_c n)/(\pi n) \)

B

\(\sin(\pi n/3)/(\pi n) \)

C

\([\sin(\pi n/6)/(\pi n)]^2 \)

D

\(\sin(\pi n/6)/(\pi n) \)

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13

2015 · General Aptitude (GA) · General Aptitude · Algebra

Instrumentation Engineering (IN) 2015

Consider a low-pass filter module with a pass-band ripple of \( \delta \) in the gain magnitude. If \( M \) such identical modules are cascaded, ignoring the loading effects, the pass-band ripple of the cascade is

A

\(1 - (1 - \delta)^M \)

B

\(\delta^M \)

C

\((1 - \delta^M) \)

D

\((1 - \delta)^M \)

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14

2015 · General Aptitude (GA) · General Aptitude · Algebra

Instrumentation Engineering (IN) 2015

The fundamental period of the signal \( x(t) = 2 \cos\left(\frac{2\pi t}{3}\right) + \cos(\pi t) \), in seconds, is __________ s.

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15

2016 · General Aptitude (GA) · General Aptitude · Algebra

Instrumentation Engineering (IN) 2016

A straight line is fit to a data set $(\ln x, y)$. This line intercepts the abscissa at $\ln x = 0.1$ and has a slope of $-0.02$. What is the value of $y$ at $x = 5$ from the fit?

A

-0.030

B

-0.014

C

0.014

D

0.030

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16

2024 · General Aptitude (GA) · General Aptitude · Algebra

Instrumentation Engineering (IN) 2024

If the sum of the first 20 consecutive positive odd numbers is divided by \(20^2\), the result is

A

1

B

20

C

2

D

1/2

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17

2024 · General Aptitude (GA) · General Aptitude · Algebra

Instrumentation Engineering (IN) 2024

The ratio of the number of girls to boys in class VIII is the same as the ratio of the number of boys to girls in class IX. The total number of students (boys and girls) in classes VIII and IX is 450 and 360, respectively. If the number of girls in classes VIII and IX is the same, then the number of girls in each class is

A

150

B

200

C

250

D

175

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18

2025 · General Aptitude (GA) · General Aptitude · Algebra

Instrumentation Engineering (IN) 2025

If \( P e^{x} = Q e^{-x} \) for all real values of \( x \), which one of the following statements is true?

A

\(P = Q = 0 \)

B

\(P = Q = 1 \)

C

\(P = 1; Q = -1 \)

D

\(\frac{P}{Q} = 0 \)

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19

2020 · General Aptitude (GA) · General Aptitude · Algebra

Instrumentation Engineering (IN) 2020

The sum of the first \(n\) terms in the sequence 8, 88, 888, 8888, … is _____.

A

\(\frac{81}{80}(10^n - 1) + \frac{9}{8}n\)

B

\(\frac{81}{80}(10^n - 1) - \frac{9}{8}n\)

C

\(\frac{80}{81}(10^n - 1) + \frac{8}{9}n\)

D

\(\frac{80}{81}(10^n - 1) - \frac{8}{9}n\)

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20

2020 · General Aptitude (GA) · General Aptitude · Algebra

Instrumentation Engineering (IN) 2020

Select the graph that schematically represents BOTH \(y = x^m\) and \(y = x^{1/m}\) properly in the interval \(0 \le x \le 1\), for integer values of \(m\), where \(m > 1\).

A

B

C

D

Graph (D)

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