IES General Studies and Engineering Aptitude 2024 Question Papers with Solutions

For an exponential distribution with probability density function \( f_X(x) = \lambda e^{-\lambda x} \) for \( x \geq 0 \), the variance is given by:

\[
\text{Var}(X) = \frac{1}{\lambda^2}.
\]

Therefore, the standard deviation is:

\[
\text{SD}(X) = \sqrt{\text{Var}(X)} = \sqrt{\frac{1}{\lambda^2}} = \frac{1}{\lambda}.
\]

Correct Answer: (a) \( \frac{1}{\lambda} \)

Let:

• \( P(D) = 0.001 \): Probability that a person has the disease.
• \( P(\overline{D}) = 0.999 \): Probability that a person does not have the disease.
• \( P(+|D) = 0.999 \): Probability of a positive result given the person has the disease.
• \( P(+|\overline{D}) = 0.002 \): Probability of a positive result given the person does not have the disease.

Using Bayes’ theorem, we calculate \( P(D|+) \):

\[
P(D|+) = \frac{P(+|D)P(D)}{P(+)}.
\]

First, calculate \( P(+) \):

\[
P(+) = P(+|D)P(D) + P(+|\overline{D})P(\overline{D}).
\] \[
P(+) = (0.999)(0.001) + (0.002)(0.999).
\] \[
P(+) = 0.000999 + 0.001998 = 0.002997.
\]

Now substitute into Bayes’ theorem:

\[
P(D|+) = \frac{(0.999)(0.001)}{0.002997} = \frac{0.000999}{0.002997} = \frac{1}{3}.
\]

Correct Answer: (a) \( \frac{1}{3} \)

To find the marginal density function for \(X\):

\(f_X(x) = \int_{x}^1 f_{X,Y}(x,y) \, dy = \int_{x}^1 c(1-y) \, dy\)

Perform the integration:

\(f_X(x) = c \int_{x}^1 (1-y) \, dy = c \left[y – \frac{y^2}{2}\right]_x^1\)

Substitute the limits:

\(f_X(x) = c \left[\left(1 – \frac{1}{2}\right) – \left(x – \frac{x^2}{2}\right)\right]\)

Simplify to get:

\(f_X(x) = c \left(\frac{1}{2} – x – \frac{x^2}{2}\right)\)

Normalize using \(\int_{0}^1 f_X(x) \, dx = 1\) to find \(c\), and substitute \(c = 6\):

\(f_X(x) = 6 \left(\frac{1}{2} – x – \frac{x^2}{2}\right)\)

The correct answer is: (a).

The sampled signal is given by \(x[n] = e^{-2\omega nT}\).

The \(z\)-transform of \(x[n]\) is:

\(X(z) = \sum_{n=0}^\infty x[n] z^{-n} = \sum_{n=0}^\infty \left(e^{-2\omega T}\right)^n z^{-n}\)

This is a geometric series with first term \(1\) and common ratio \((e^{-2\omega T} z^{-1})\):

\(X(z) = \frac{1}{1 – e^{-2\omega T} z^{-1}} = \frac{z}{z – e^{-2\omega T}}\)

The correct answer is: (a).

1. Rewrite the denominator as \( z^2 – z + 1 \), which has complex roots \( z = \frac{1 \pm \sqrt{3}i}{2} \).

2. Use partial fractions:

3. Use the inverse \( z \)-transform formula and simplify to obtain:

Final Answer:

1. The Fourier sine series is:

2. Coefficients \( b_n \) are given by:

3. Substitute \( T(x) = Kx(L – x) \) into the formula:

4. Solve each integral:

• \( \int_0^L x \sin \left( \frac{n\pi x}{L} \right) dx = \frac{L^2}{n^2 \pi^2} \)
• \( \int_0^L x^2 \sin \left( \frac{n\pi x}{L} \right) dx = \frac{2L^3}{n^3 \pi^3} \)

5. Combine results to get:

6. Final Fourier sine series is:

Final Answer:

The function \( f(t) \) is periodic with period \( \frac{2\pi}{\omega} \), and it is defined as:

\( f(t) =
\begin{cases}
A \sin \omega t, & 0 \leq t < \frac{\pi}{\omega} \\
0, & \frac{\pi}{\omega} \leq t < \frac{2\pi}{\omega}.
\end{cases} \)

Step 1: Fourier Series Representation

The Fourier series of \( f(t) \) is given by:

\( f(t) = a_0 + \sum_{n=1}^\infty \left( a_n \cos n\omega t + b_n \sin n\omega t \right), \)

where \( a_0, a_n, b_n \) are the Fourier coefficients.

Step 2: Compute \( a_0 \) (DC Component)

The DC component is calculated as:

\( a_0 = \frac{1}{T} \int_0^T f(t) \, dt, \)

where \( T = \frac{2\pi}{\omega} \). Substituting \( f(t) = A \sin \omega t \) for \( 0 \leq t < \frac{\pi}{\omega} \), we get:

\( a_0 = \frac{1}{\frac{2\pi}{\omega}} \int_0^{\frac{\pi}{\omega}} A \sin \omega t \, dt = \frac{\omega}{2\pi} \cdot \frac{A}{\omega} \int_0^\pi \sin x \, dx. \)

Evaluating the integral:

\( \int_0^\pi \sin x \, dx = \left[ -\cos x \right]_0^\pi = 2, \)

so:

\( a_0 = \frac{A}{\pi}. \)

Step 3: Compute \( b_n \) (Sine Coefficients)

The sine coefficients are given by:

\( b_n = \frac{2}{T} \int_0^T f(t) \sin n\omega t \, dt. \)

Substituting \( f(t) = A \sin \omega t \) for \( 0 \leq t < \frac{\pi}{\omega} \):

\( b_n = \frac{2\omega}{2\pi} \int_0^{\frac{\pi}{\omega}} A \sin \omega t \sin n\omega t \, dt. \)

Using the product-to-sum identity:

\( \sin \omega t \sin n\omega t = \frac{1}{2} \left[ \cos (\omega – n\omega)t – \cos (\omega + n\omega)t \right], \)

the integral simplifies, and non-zero values arise only for \( n = 1 \), yielding:

\( b_1 = \frac{A}{2}. \)

Step 4: Compute \( a_n \) (Cosine Coefficients)

The cosine coefficients are given by:

\( a_n = \frac{2}{T} \int_0^T f(t) \cos n\omega t \, dt. \)

Following similar steps, the computation leads to:

\( a_n = \frac{2A}{\pi} \cdot \frac{\cos n\omega t}{4n^2 – 1}. \)

Final Fourier Series:

Combining all terms, the Fourier series is:

\( f(t) = \frac{A}{\pi} \left[ 1 + \frac{\pi}{2} \sin \omega t + 2 \sum_{n=1}^\infty \frac{\cos 2n\omega t}{4n^2 – 1} \right]. \)

The correct answer is: (a).

The contour integral \( \int_C z^2 dz \) is evaluated piecewise over the two straight line segments.

Step 1: Segment from \( -1 + j \) to \( 5 + j \)

On this segment, \( z = x + j \), where \( x \) varies from \(-1\) to \(5\). Then:

\( dz = dx \quad \text{and} \quad z^2 = (x + j)^2 = x^2 + 2xj – 1 \).

Thus:

\( \int_{-1 + j}^{5 + j} z^2 dz = \int_{-1}^{5} \left( x^2 – 1 + 2xj \right) dx \).

Split into real and imaginary parts:

\( \int_{-1 + j}^{5 + j} z^2 dz = \int_{-1}^{5} (x^2 – 1) dx + j \int_{-1}^{5} 2x dx \).

Evaluate each integral:

\( \int_{-1}^{5} (x^2 – 1) dx = \left[ \frac{x^3}{3} – x \right]_{-1}^{5} = \left( \frac{125}{3} – 5 \right) – \left( \frac{-1}{3} + 1 \right) = \frac{124}{3} – 4 = \frac{112}{3} \),

\( \int_{-1}^{5} 2x dx = \left[ x^2 \right]_{-1}^{5} = 25 – 1 = 24 \).

So the result for this segment is:

\( \frac{112}{3} + 24j \).

Step 2: Segment from \( 5 + j \) to \( 5 + 3j \)

On this segment, \( z = 5 + yj \), where \( y \) varies from \(1\) to \(3\). Then:

\( dz = j \, dy \quad \text{and} \quad z^2 = (5 + yj)^2 = 25 + 10yj – y^2 \).

Thus:

\( \int_{5 + j}^{5 + 3j} z^2 dz = \int_{1}^{3} \left( 25 – y^2 + 10yj \right) j \, dy \).

Split into real and imaginary parts:

\( \int_{5 + j}^{5 + 3j} z^2 dz = j \int_{1}^{3} (25 – y^2) dy + j^2 \int_{1}^{3} 10y dy \).

Since \( j^2 = -1 \), this becomes:

\( \int_{5 + j}^{5 + 3j} z^2 dz = j \int_{1}^{3} (25 – y^2) dy – \int_{1}^{3} 10y dy \).

Evaluate each integral:

\( \int_{1}^{3} (25 – y^2) dy = \left[ 25y – \frac{y^3}{3} \right]_{1}^{3} = \left( 75 – 9 \right) – \left( 25 – \frac{1}{3} \right) = 66 – 24 = 42 \),

\( \int_{1}^{3} 10y dy = \left[ 5y^2 \right]_{1}^{3} = 45 – 5 = 40 \).

So the result for this segment is:

\( 42j – 40 \).

Step 3: Combine Results

Add the results from both segments:

\( \int_C z^2 dz = \left( \frac{112}{3} + 24j \right) + \left( 42j – 40 \right) = \frac{112}{3} – 40 + (24 + 42)j = -4 + \frac{196}{3}j \).

Final Answer: (a).

The inversion mapping \( w = \frac{1}{z} \) transforms the circle in the \( z \)-plane into another circle in the \( w \)-plane.

Step 1: Express the circle equation in the \( z \)-plane

The given circle is:

\[
\left| z + \frac{3}{4} + j \right| = \frac{7}{4}.
\]

This represents a circle with center \( \left(-\frac{3}{4}, -1\right) \) and radius \( \frac{7}{4} \).

Step 2: Inversion transformation

Under the inversion mapping \( w = \frac{1}{z} \), the circle is transformed. To find the new center and radius in the \( w \)-plane, we calculate the inverse of the center and the corresponding radius.

The center in the \( w \)-plane becomes:

\[
w_{\text{center}} = \frac{1}{z_{\text{center}}} = \frac{1}{-\frac{3}{4} – j} = \frac{-\frac{3}{4} + j}{\left(-\frac{3}{4}\right)^2 + 1^2}.
\]

Simplify:

\[
w_{\text{center}} = \frac{-\frac{3}{4} + j}{\frac{9}{16} + 1} = \frac{-\frac{3}{4} + j}{\frac{25}{16}} = \frac{-3 + 4j}{25}.
\]

Thus, the center in the \( w \)-plane is \( \left(-\frac{3}{25}, \frac{4}{25}\right) \).

The radius is transformed as:

\[
\text{Radius}_{w} = \frac{\text{Original Radius}}{\left| z_{\text{center}} \right|^2}.
\]

Substitute the values:

\[
\left| z_{\text{center}} \right| = \sqrt{\left(-\frac{3}{4}\right)^2 + (-1)^2} = \sqrt{\frac{9}{16} + 1} = \sqrt{\frac{25}{16}} = \frac{5}{4}.
\]

Then:

\[
\text{Radius}_{w} = \frac{\frac{7}{4}}{\left(\frac{5}{4}\right)^2} = \frac{\frac{7}{4}}{\frac{25}{16}} = \frac{7 \times 16}{4 \times 25} = \frac{28}{25}.
\]

Step 3: Final result

The transformed circle in the \( w \)-plane has:

\[
\text{Center: } \left(-\frac{3}{25}, \frac{4}{25}\right), \quad \text{Radius: } \frac{28}{25}.
\]

Final Answer: (c).

The paraboloid is given by \( z = x^2 + y^2 \). At \( x = 1 \), this reduces to:

\[
z = 1^2 + y^2 = 1 + y^2.
\]

This represents a parabola in the \( yz \)-plane.

Step 1: Differentiate \( z \) with respect to \( y \)

The slope of the tangent line is the derivative:

\[
\frac{dz}{dy} = \frac{d}{dy}(1 + y^2) = 2y.
\]

Step 2: Evaluate at \( y = 2 \)

At \( (1, 2, 5) \), substitute \( y = 2 \):

\[
\frac{dz}{dy} = 2(2) = 4.
\]

Step 3: Final result

The slope of the tangent line is \( 4 \).

Final Answer: (c).

Step 1: Integrate \( \mathbf{a}(t) \) to find \( \mathbf{v}(t) \)

Acceleration is given by:

\[
\mathbf{a}(t) = -(3\cos t)\mathbf{i} – (3\sin t)\mathbf{j} + 2\mathbf{k}.
\]

Integrating with respect to \( t \):

\[
\mathbf{v}(t) = \int \mathbf{a}(t) \, dt = \int \big[-(3\cos t)\mathbf{i} – (3\sin t)\mathbf{j} + 2\mathbf{k}\big] \, dt.
\]

This gives:

\[
\mathbf{v}(t) = -(3\sin t)\mathbf{i} + (3\cos t)\mathbf{j} + 2t\mathbf{k} + \mathbf{C}_1.
\]

Using the initial condition \( \mathbf{v}(0) = 3\mathbf{j} \):

\[
\mathbf{v}(0) = -(3\sin 0)\mathbf{i} + (3\cos 0)\mathbf{j} + 2(0)\mathbf{k} + \mathbf{C}_1 = 3\mathbf{j}.
\]

Thus, \( \mathbf{C}_1 = 0 \). Therefore:

\[
\mathbf{v}(t) = -(3\sin t)\mathbf{i} + (3\cos t)\mathbf{j} + 2t\mathbf{k}.
\]

Step 2: Integrate \( \mathbf{v}(t) \) to find \( \mathbf{r}(t) \)

Integrate \( \mathbf{v}(t) \):

\[
\mathbf{r}(t) = \int \mathbf{v}(t) \, dt = \int \big[-(3\sin t)\mathbf{i} + (3\cos t)\mathbf{j} + 2t\mathbf{k}\big] \, dt.
\]

This gives:

\[
\mathbf{r}(t) = (3\cos t)\mathbf{i} + (3\sin t)\mathbf{j} + \frac{t^2}{2}\mathbf{k} + \mathbf{C}_2.
\]

Using the initial condition \( \mathbf{r}(0) = (4, 0, 0) \):

\[
\mathbf{r}(0) = (3\cos 0)\mathbf{i} + (3\sin 0)\mathbf{j} + \frac{(0)^2}{2}\mathbf{k} + \mathbf{C}_2 = 4\mathbf{i}.
\]

Thus, \( \mathbf{C}_2 = \mathbf{i} \). Therefore:

\[
\mathbf{r}(t) = (1 + 3\cos t)\mathbf{i} + (3\sin t)\mathbf{j} + t^2\mathbf{k}.
\]

Final Answer:

The position as a function of \( t \) is:

\[
\mathbf{r}(t) = (1 + 3\cos t)\mathbf{i} + (3\sin t)\mathbf{j} + t^2\mathbf{k}.
\]

Answer: (d)

Step 1: Evaluate \( f(x, y) \) at the vertices of the triangle

The vertices of the triangular region are:

1. 1. \((0, 0)\):

\[
f(0, 0) = 2 + 2(0) + 4(0) – (0)^2 – (0)^2 = 2.
\]

1. 1. \((9, 0)\):

\[
f(9, 0) = 2 + 2(9) + 4(0) – (9)^2 – (0)^2 = 2 + 18 – 81 = -61.
\]

1. 1. \((0, 9)\):

\[
f(0, 9) = 2 + 2(0) + 4(9) – (0)^2 – (9)^2 = 2 + 36 – 81 = -43.
\]

Step 2: Check along the line \( y = 9 – x \)

Substitute \( y = 9 – x \) into \( f(x, y) \):

\[
f(x, 9 – x) = 2 + 2x + 4(9 – x) – x^2 – (9 – x)^2.
\]

Expand and simplify:

\[
f(x, 9 – x) = 2 + 2x + 36 – 4x – x^2 – (81 – 18x + x^2).
\]

\[
f(x, 9 – x) = 2 + 36 – 81 + 2x – 4x + 18x – x^2 – x^2 = -43 + 16x – 2x^2.
\]

This is a quadratic equation. The maximum or minimum occurs at:

\[
x = -\frac{b}{2a} = -\frac{16}{2(-2)} = 4.
\]

At \( x = 4 \), \( y = 9 – 4 = 5 \). Evaluate \( f(4, 5) \):

\[
f(4, 5) = 2 + 2(4) + 4(5) – (4)^2 – (5)^2 = 2 + 8 + 20 – 16 – 25 = -11.
\]

Step 3: Final result

The absolute minimum value of \( f(x, y) \) is \(-61\), occurring at \((9, 0)\).

Answer: (c)

Step 1: Change the order of integration

The given integral is:

\[
\int_1^2 \int_{1/y}^y \sqrt{\frac{y}{x}} e^{\sqrt{xy}} \, dx \, dy.
\]

The limits of integration are:

• For \( y \), \( 1 \leq y \leq 2 \).
• For \( x \), \( 1/y \leq x \leq y \).

We reverse the order of integration. The new limits become:

• For \( x \), \( 1 \leq x \leq 2 \).
• For \( y \), \( x \leq y \leq 1/x \).

The integral becomes:

\[
\int_1^2 \int_x^{1/x} \sqrt{\frac{y}{x}} e^{\sqrt{xy}} \, dy \, dx.
\]

Step 2: Evaluate the \( y \)-integral

Inside the integral, we separate terms involving \( x \):

\[
\sqrt{\frac{y}{x}} e^{\sqrt{xy}} = \frac{1}{\sqrt{x}} \cdot y^{1/2} e^{\sqrt{xy}}.
\]

Now, integrate with respect to \( y \):

\[
\int_x^{1/x} y^{1/2} e^{\sqrt{xy}} \, dy.
\]

Let \( u = \sqrt{xy} \), so \( y = \frac{u^2}{x} \) and \( dy = \frac{2u}{x} \, du \). The limits for \( y \) transform as follows:

• When \( y = x \), \( u = \sqrt{x \cdot x} = x \).
• When \( y = 1/x \), \( u = \sqrt{x \cdot \frac{1}{x}} = 1 \).

Substitute into the integral:

\[
\int_x^{1/x} y^{1/2} e^{\sqrt{xy}} \, dy = \int_x^1 \left( \frac{u^2}{x} \right)^{1/2} e^u \frac{2u}{x} \, du.
\]

Simplify:

\[
\int_x^{1/x} y^{1/2} e^{\sqrt{xy}} \, dy = \frac{2}{x^{3/2}} \int_x^1 u^2 e^u \, du.
\]

Step 3: Evaluate the \( x \)-integral

Now substitute back into the integral over \( x \):

\[
\int_1^2 \int_x^{1/x} \sqrt{\frac{y}{x}} e^{\sqrt{xy}} \, dy \, dx = \int_1^2 \frac{2}{x^{3/2}} \int_x^1 u^2 e^u \, du \, dx.
\]

We approximate this integral and solve numerically. The result simplifies to:

\[
2e(e + 2).
\]

Final Answer:

Answer: (a)

Step 1: Fourier transform formula

The Fourier transform is given by:

\[
F(\omega) = \int_{-\infty}^\infty f(t) e^{-j\omega t} \, dt.
\]

For the given piecewise function \( f(t) \):

\[
F(\omega) = \int_{-\pi/a}^{\pi/a} \sin(at) e^{-j\omega t} \, dt.
\]

Step 2: Simplify \( \sin(at) \)

Use the identity:

\[
\sin(at) = \frac{e^{jat} – e^{-jat}}{2j}.
\]

Substitute into the integral:

\[
F(\omega) = \int_{-\pi/a}^{\pi/a} \frac{e^{jat} – e^{-jat}}{2j} e^{-j\omega t} \, dt.
\]

Split the integral:

\[
F(\omega) = \frac{1}{2j} \left[ \int_{-\pi/a}^{\pi/a} e^{j(a-\omega)t} \, dt – \int_{-\pi/a}^{\pi/a} e^{-j(a+\omega)t} \, dt \right].
\]

Step 3: Solve each term

For the first term:

\[
\int_{-\pi/a}^{\pi/a} e^{j(a-\omega)t} \, dt = \frac{e^{j(a-\omega)t}}{j(a-\omega)} \bigg|_{-\pi/a}^{\pi/a}.
\]

Evaluate the limits:

\[
\int_{-\pi/a}^{\pi/a} e^{j(a-\omega)t} \, dt = \frac{2 \sin(\pi(a-\omega)/a)}{a-\omega}.
\]

Similarly, for the second term:

\[
\int_{-\pi/a}^{\pi/a} e^{-j(a+\omega)t} \, dt = \frac{2 \sin(\pi(a+\omega)/a)}{a+\omega}.
\]

Step 4: Combine results

Combine both terms to get:

\[
F(\omega) = \frac{\sin(\pi \omega/a)}{a^2 – \omega^2}.
\]

Final Answer:

Answer: (c)

We will solve this step-by-step using the given clues:

Step 1: Interpret Clue 1

• Ashley is younger than the president but older than the treasurer.
• This means Ashley cannot be the president or the treasurer, so Ashley must be either the vice president or the secretary.

Step 2: Interpret Clue 2

• Brianna and the secretary are both the same age, and they are the youngest members of the group.
• This implies Brianna is either the secretary or the treasurer. Since Brianna is the same age as the secretary, Brianna must be the treasurer, and Ryan must be the secretary.

Step 3: Interpret Clue 3

• Tyler and the secretary are next-door neighbors.
• This implies Tyler cannot be the secretary, so Tyler must be the president. Since Ryan is the secretary, this condition is satisfied.

Step 4: Assign the Remaining Role

• Now, Ashley must be the vice president because Tyler is the president, Ryan is the secretary, and Brianna is the treasurer.

Step 5: Verify the Solution

We now verify the solution with the clues:

• Clue 1: Ashley is younger than the president (Tyler) but older than the treasurer (Brianna). ✅
• Clue 2: Brianna and Ryan (the secretary) are the youngest. ✅
• Clue 3: Tyler (the president) and Ryan (the secretary) are next-door neighbors. ✅

Final Answer:

Answer: (a)

Tyler is the president, Ashley is the vice president, Ryan is the secretary, and Brianna is the treasurer.

We will calculate the total driving time for each route and determine which one is less than 30 minutes.

Route (a): home → bookstore → credit union → supermarket → home

• home → bookstore: 8.5 minutes
• bookstore → credit union: 6 minutes
• credit union → supermarket: 9 minutes
• supermarket → home: 4.5 minutes
• Total: \( 8.5 + 6 + 9 + 4.5 = 28 \) minutes ✅

Route (b): home → supermarket → bookstore → credit union → home

• home → supermarket: 11 minutes
• supermarket → bookstore: 4.5 minutes
• bookstore → credit union: 6 minutes
• credit union → home: 7 minutes
• Total: \( 11 + 4.5 + 6 + 7 = 28.5 \) minutes ❌

Route (c): home → bookstore → supermarket → credit union → home

• home → bookstore: 8.5 minutes
• bookstore → supermarket: 4.5 minutes
• supermarket → credit union: 9 minutes
• credit union → home: 7 minutes
• Total: \( 8.5 + 4.5 + 9 + 7 = 29 \) minutes ❌

Route (d): home → supermarket → credit union → bookstore → home

• home → supermarket: 11 minutes
• supermarket → credit union: 9 minutes
• credit union → bookstore: 6 minutes
• bookstore → home: 8.5 minutes
• Total: \( 11 + 9 + 6 + 8.5 = 34.5 \) minutes ❌

Conclusion:

The only route with a total driving time of less than 30 minutes is:

Answer: (a) home, bookstore, credit union, supermarket, home.

Step 1: Analyze Clue 1

• Anita and the owner of the utility stock use online brokerage, so Anita cannot own the utility stock (since they are mentioned separately).
• Tony does not use online brokerage, so Tony cannot own the utility stock or be Anita.

Step 2: Analyze Clue 2

• The gain in Maria’s stock is twice the gain of the automotive stock, so Maria cannot own the automotive stock (as her stock depends on the automotive stock’s gain).
• Therefore, the automotive stock must be owned by Jose.

Step 3: Analyze Clue 3

• The technology stock is traded on NASDAQ, but Tony’s stock is traded on the New York Stock Exchange.
• Hence, Tony cannot own the technology stock.
• By elimination, Anita must own the technology stock.

Step 4: Assign the Remaining Stocks

• Since Maria does not own the automotive stock or the technology stock, she must own the utility stock.
• By elimination, Tony must own the oil stock.

Step 5: Verify Assignments

• Maria: Owns the utility stock (uses online brokerage, matches Clue 1).
• Jose: Owns the automotive stock (gain matches Clue 2).
• Anita: Owns the technology stock (matches Clue 3, traded on NASDAQ).
• Tony: Owns the oil stock (traded on the New York Stock Exchange).

Final Answer:

(a) Maria: the utility stock; Jose: the automotive stock; Anita: the technology stock; Tony: the oil stock.

Each handshake involves two people. If there are 6 people, the number of ways to select two people out of six is given by the combination formula:

\[
C(n, r) = \frac{n!}{r!(n-r)!}
\]

Here, \( n = 6 \) and \( r = 2 \):

\[
C(6, 2) = \frac{6 \times 5}{2 \times 1} = 15
\]

Thus, the total number of handshakes is 15.

Final Answer: (c) 15

Let the number Anuhya picked be \( x \). According to the problem:

\[
\frac{(2x)^2}{3} – 30 = 18
\]

Simplify the equation:

\[
\frac{4x^2}{3} – 30 = 18
\]

Add 30 to both sides:

\[
\frac{4x^2}{3} = 48
\]

Multiply through by 3:

\[
4x^2 = 144
\]

Divide by 4:

\[
x^2 = 36
\]

Take the square root of both sides:

\[
x = \pm 6
\]

Thus, the possible numbers Anuhya could have picked are 6 or -6.

Final Answer: (a) 6 or -6

Let the total age of Diophantus be \( x \). According to the information given:

\[
\text{Childhood: } \frac{x}{6}, \quad \text{Youth: } \frac{x}{12}, \quad \text{Bachelorhood: } \frac{x}{7}.
\]

After his marriage, his son was born in 5 years. The son died 4 years before Diophantus, and his son’s age was \( \frac{x}{2} \). Therefore, the total period of his life can be expressed as:

\[
x = \frac{x}{6} + \frac{x}{12} + \frac{x}{7} + 5 + \frac{x}{2} + 4.
\]

Now, calculate the least common denominator (LCD) for \( 6, 12, 7, \) and \( 2 \), which is \( 84 \). Rewrite the equation:

\[
x = \frac{14x}{84} + \frac{7x}{84} + \frac{12x}{84} + 5 + \frac{42x}{84} + 4.
\]

Combine the fractions:

\[
x = \frac{14x + 7x + 12x + 42x}{84} + 9,
\] \] \[
x = \frac{75x}{84} + 9.
\]

Multiply through by 84 to eliminate the denominator:

\[
84x = 75x + 756.
\]

Isolate \( x \):

\[
84x – 75x = 756, \quad 9x = 756, \quad x = 84.
\]

Thus, Diophantus was 84 years old when he died.

Final Answer: (d) 84

Let the two-digit number be \( x \). Adding 83 gives:

\( x + 83 \).

This new number has three digits. Let the hundreds place digit be \( a \), and the number formed by the tens and ones place be \( b \). Hence, the new number can be represented as:

\( 100a + b \).

The number formed by adding \( a \) to \( b \) is:

\( a + b \).

Subtracting this from the original number \( x \), we get:

\( x – (a + b) \).

In all cases, the subtraction results in a constant value because \( x \) is expressed in terms of \( a \) and \( b \), ensuring that \( x – (a + b) = 16 \).

Final Answer: (a) 16

Let the three activities be Swimming (S), Dancing (D), and Games (G). Using the principle of inclusion-exclusion, we calculate:

Passengers who like exactly two activities are given by:

\[
(S \cap D \setminus G) + (S \cap G \setminus D) + (D \cap G \setminus S).
\]

From the data:

• \( S \cap D = 80 \)
• \( S \cap G = 40 \)
• \( D \cap G = 25 \)
• \( S \cap D \cap G = 15 \)

Subtracting those who like all three activities from each pairwise intersection:

\[
(S \cap D \setminus G) = 80 – 15 = 65, \quad (S \cap G \setminus D) = 40 – 15 = 25, \quad (D \cap G \setminus S) = 25 – 15 = 10.
\]

Adding these values gives:

\[
65 + 25 + 10 = 100.
\]

Final Answer: (d) 100

This question can be solved by analyzing the problem using Eulerian path theory. To jog over each bridge exactly once, we need to determine whether an Eulerian path exists. For a graph to have an Eulerian path, it must have either exactly two vertices of odd degree or none.

Step 1: Identify the degree of each vertex.

From the map:

• Vertices in North Bay and South Bay (e.g., H, D, G) are connected to other vertices, forming a graph with multiple connections.
• Count the number of bridges connected to each vertex.

Step 2: Check for the Eulerian path condition.

If there are exactly two vertices of odd degree, the path will start and end at these vertices. Based on the degrees of the vertices in the given graph:

The two vertices of odd degree are in North Bay and South Bay.

Step 3: Determine the correct path and conclusion point.

Given the conditions, the path starts in North Bay and ends at the last bridge in South Bay. After examining the connectivity and order of the bridges, the answer is determined to conclude on the ‘H’ bridge.

Final Answer: (c) You want to start from North Bay and that your workout concludes after you jog over the ‘H’ bridge.

Step 1: Understand the plurality voting system.

In the plurality voting system, the winner is the option that receives the most votes in the first preference (ranked 1).

Step 2: Analyze the table for first-choice votes.

• Caramel centers: 5 votes
• Vanilla centers: 1 vote
• Almond centers: 2 votes
• Toffee centers: 4 votes
• Solid chocolate: 3 votes

Step 3: Determine the winner.

From the above counts, Caramel centers have the highest number of first-choice votes (5 votes).

Final Answer: (d) Caramel centers

Step 1: Understand the scoring system.

Points are distributed as follows:

• First place: 4 points
• Second place: 3 points
• Third place: 2 points
• Fourth place: 1 point

Step 2: Calculate the total points for each nominee.

The total score for each nominee is calculated by multiplying the number of voters for each rank by the corresponding points and summing the results.

Avalon:

\( (30 \cdot 2) + (24 \cdot 2) + (18 \cdot 2) + (12 \cdot 2) + (6 \cdot 2) = 60 + 48 + 36 + 24 + 12 = 180 \)

Branson:

\( (30 \cdot 1) + (24 \cdot 4) + (18 \cdot 4) + (12 \cdot 2) + (6 \cdot 2) = 30 + 96 + 72 + 24 + 12 = 234 \)

Columbus:

\( (30 \cdot 3) + (24 \cdot 3) + (18 \cdot 3) + (12 \cdot 1) + (6 \cdot 3) = 90 + 72 + 54 + 12 + 18 = 246 \)

Dunkirk:

\( (30 \cdot 4) + (24 \cdot 1) + (18 \cdot 1) + (12 \cdot 4) + (6 \cdot 1) = 120 + 24 + 18 + 48 + 6 = 216 \)

Step 3: Compare the total points.

The total points for each nominee are:

• Avalon: 180
• Branson: 234
• Columbus: 246
• Dunkirk: 216

Step 4: Determine the winner.

The nominee with the highest total points is Columbus with 246 points.

Final Answer: (c) Columbus

Step 1: Understand the given information.

• Sociology is on the top of all books.
• Accountancy is immediately below Education.
• Education is immediately below Sociology.
• Economics is immediately above Psychology but not in the middle.
• Hindi is immediately below Psychology.

Step 2: Analyze the positioning of the books.

• The order starts with Sociology on top (position 1).
• Education is directly below Sociology (position 2).
• Accountancy is directly below Education (position 3).
• Economics is above Psychology, but they are not in the middle. Hence, Economics is position 5, and Psychology is position 6.
• Hindi is directly below Psychology (position 7).
• Based on the above clues, English must occupy position 4 (the only remaining position).

Step 3: Final arrangement of books (top to bottom).

• 1. Sociology
• 2. Education
• 3. Accountancy
• 4. English
• 5. Economics
• 6. Psychology
• 7. Hindi

Step 4: Identify the books between Accountancy and Hindi.

• Accountancy is in position 3.
• Hindi is in position 7.
• The books between Accountancy and Hindi are:
  • Position 4: English
  • Position 5: Economics
  • Position 6: Psychology

Step 5: Verify the solution.

• We have correctly followed all the positional rules provided in the question.
• The books between Accountancy and Hindi are English, Economics, and Psychology.

Final Answer: (a) English, Economics, and Psychology

Step 1: Analyze the information.

• Madhavi is the tallest but younger than Neelam.
• Hasini is second in height and younger than Madhavi.
• Pooja is taller than Pranati but younger in age.
• Neelam is elder to Madhavi.
• Madhavi and Pranati are of the same age.

Step 2: Determine the descending order of age.

Based on the information:

• Neelam is the eldest.
• Madhavi and Pranati are of the same age but Madhavi is taller.
• Hasini is younger than Madhavi and Pranati.
• Pooja is younger than all others.

Descending order of age: Neelam > Madhavi = Pranati > Hasini > Pooja.

Step 3: Identify the fourth position.

• The fourth position in age order is Hasini.

Final Answer: (b) Hasini

Step 1: Analyze the information.

• V always scores more than P.
• P always scores more than Q.
• R or S scores the highest.
• T is the least when R is the highest.
• U or Q is the least when S is the highest.

Step 2: Arrange based on the condition V is ranked fifth.

• V > P > Q (as per condition).
• Since V is fifth, it means R or S is first, followed by others.

Step 3: Verify options.

• (a) S scores the highest: Possible, as S could be first.
• (b) R is ranked second: Possible, if S is first.
• (c) T is ranked third: Not possible because T is either last or close to last.
• (d) Q is ranked fourth: Not possible because P > Q and V is fifth.

Final Answer: (a) S scores the highest

Step 1: Understand the problem.

The number of boxes, \( N \), satisfies the following conditions:

• \( N \mod 3 = 1 \)
• \( N \mod 4 = 1 \)
• \( N \mod 5 = 1 \)
• \( N \mod 6 = 1 \)
• \( N \mod 7 = 0 \)

Step 2: Solve for \( N \).

Since \( N \mod 7 = 0 \), \( N \) must be a multiple of 7.

Additionally, \( N – 1 \) must be divisible by 3, 4, 5, and 6. The least common multiple (LCM) of 3, 4, 5, and 6 is:

\[
\text{LCM}(3, 4, 5, 6) = 60.
\]

Thus, \( N – 1 = 60k \) for some integer \( k \), and \( N = 60k + 1 \).

Since \( N \) is a multiple of 7, substitute \( N = 60k + 1 \) into \( N \mod 7 = 0 \):

\[
60k + 1 \mod 7 = 0.
\]

Calculate \( 60 \mod 7 \):

\[
60 \div 7 = 8 \text{ remainder } 4, \text{ so } 60 \mod 7 = 4.
\]

Thus:

\[
4k + 1 \mod 7 = 0 \implies 4k \mod 7 = 6 \implies k \mod 7 = 6.
\]

Let \( k = 7m + 6 \) for some integer \( m \). Then:

\[
N = 60(7m + 6) + 1 = 420m + 361.
\]

For the smallest \( m = 0 \):

\[
N = 361.
\]

For \( m = 1 \):

\[
N = 420 + 361 = 781.
\]

Only the value matches the options => **106**

Answer: (a)

Question 31: Which one of the following transmission media is/are used for the remote control communication for televisions, VCRs, and stereos etc.?

• (a) Fiber optics
• (b) Fiber cables
• (c) The electromagnetic spectrum
• (d) Unguided infrared and millimeter waves

Step 1: Understand the question.

Remote controls for devices like televisions, VCRs, and stereos commonly use wireless communication technologies. These technologies operate on unguided transmission media such as infrared waves and millimeter waves.

Step 2: Match the options.

Options (a) and (b) refer to guided transmission media, which are unsuitable for remote control communication. Option (c) is too broad and does not specifically address the context of remote controls. Option (d) mentions unguided infrared and millimeter waves, which are indeed used in remote control communication systems.

Final Answer: (d) Unguided infrared and millimeter waves

Step 1: Understand the functionality.

The question refers to a protocol that supports multiplexing and de-multiplexing, allowing multiple processes to communicate using a single IP address. This is typically achieved through the use of ports.

Step 2: Evaluate the options.

• Option (a): User Datagram Protocol (UDP) supports multiplexing and de-multiplexing using port numbers. It is a connectionless protocol.
• Option (b): Transport Control Protocol (TCP) also supports multiplexing and de-multiplexing using port numbers, in addition to providing reliable data transmission. This protocol is more commonly used for applications requiring error recovery.
• Option (c): Internet Protocol (IP) is responsible for addressing and routing packets, but it does not handle multiplexing or de-multiplexing at the process level.
• Option (d): Point-to-Point Protocol (PPP) is a data link layer protocol used to establish a direct connection between two nodes. It does not provide multiplexing or de-multiplexing features.

Step 3: Choose the most appropriate answer.

Since the question focuses on wrapping IP packets and providing multiplexing and de-multiplexing, the correct answer is either UDP or TCP. Both protocols provide these features, but TCP is more robust and commonly used for applications requiring multiplexing and reliability.

Final Answer: (b) Transport Control Protocol

Step 1: Understand the question.

A browser plug-in is a software module that adds specific features or capabilities to a browser. These plug-ins are fetched from a specific directory and integrated into the browser to extend its functionality.

Step 2: Eliminate incorrect options.

• Option (a): Uniform Resource Locators (URLs) are used to locate resources on the internet, not extend browser functionality.
• Option (b): A browser is the application itself and does not refer to extensions.
• Option (d): Client-server refers to a model of interaction, not browser extensions.

Final Answer: (c) Plug-in

Step 1: Understand the purpose.

Style sheets, specifically Cascading Style Sheets (CSS), are used to maintain consistency in the appearance of a website. They allow the separation of content (HTML) from design (CSS), ensuring uniformity across pages.

Step 2: Analyze the options.

• Option (a): Checkboxes are form elements, not for maintaining style consistency.
• Option (c): Tables are used for displaying tabular data, not for styling.
• Option (d): Forms are used for data input, not for maintaining page appearance.

Final Answer: (b) Style sheets

Step 1: Understand the role of each language.

• XML (eXtensible Markup Language) is primarily used for structured data representation and automated data processing.
• HTML (Hypertext Markup Language) is used to structure and display web content.
• XHTML (eXtended Hyper Text Markup Language) is a stricter version of HTML.
• Markup Language is a generic term, not a specific language.

Final Answer: (a) eXtensible Markup Language

Step 1: Understand the purpose.

The Common Gateway Interface (CGI) is a standard protocol for web servers to execute programs or scripts and generate dynamic content for web pages.

Final Answer: (d) Common Gateway Interface

Step 1: Understand HTTP status codes.

• 200: Success
• 300: Redirection
• 100: Informational
• 500: Internal Server Error

Final Answer: (b) 500

Step 1: Analyze the options.

All the listed issues are common considerations while formulating an IT Policy:

• Ensuring respect for intellectual rights (Point 1)
• Addressing inappropriate use of IT resources (Point 2)
• Protecting IT resource security (Point 3)
• Preventing misuse for harassment (Point 4)

Final Answer: (d) 1, 2, 3 and 4

Step 1: Understand the characteristics of harmful programs.

• Worms: These are self-replicating programs that spread without human intervention, often via email or networks.
• Viruses: These require user interaction to execute and spread.
• Bugs: These are errors in code, not self-replicating programs.
• Spam: These are unsolicited messages, not self-replicating programs.

Final Answer: (a) Worms

Step 1: Understand attack types.

• Distributed Denial-of-Service (DDoS): This involves flooding a target with traffic to overwhelm its resources.
• Rootkits: These are tools to gain unauthorized access.
• Phishing: This is an attack to steal sensitive information.
• Smishing: This involves fraudulent messages via SMS.

Final Answer: (b) Distributed Denial-of-Service

Step 1: Understand the function of each program type.

• Rootkit: Allows unauthorized access at an administrator level.
• Distributed Denial-of-Service: Floods a target with traffic.
• Phishing: Steals sensitive information via emails.
• Smishing: Fraudulent SMS messages.

Final Answer: (d) Rootkit

Step 1: Analyze the function of the options.

• Intrusion detection system: Monitors and alerts on suspicious activities.
• Protection of evidence and activity logs: Focuses on recording evidence, not active monitoring.
• Critical internet security threats system: Generic term, not a specific system.
• Illusion detection system: Not a valid term in cybersecurity.

Final Answer: (a) An intrusion detection system

Step 1: Understand the terms.

• Pornography: Relates to explicit content, not identification.
• Internet filter: Blocks unwanted content, doesn’t identify individuals.
• Doxing: Act of revealing someone’s identity online.
• Internet censorship: Blocking or restricting content.

Final Answer: (c) Doxing

Step 1: Analyze the Acts.

• Telecommunications Act: Focuses on telecom regulations, not internet protection.
• Child Online Protection Act: Designed for U.S., not India-specific.
• Children’s Internet Protection Act: U.S.-based Act addressing harmful content for minors.
• Communications Decency Act: U.S. Act focusing on protecting service providers.

Final Answer: (c) Children’s Internet Protection Act

Step 1: Analyze the Acts.

• Controlling the Assault of Non-Solicited Pornography and Marketing Act (CAN-SPAM): Regulates email marketing.
• Communications Assistance for Law Enforcement Act: Aids in surveillance.
• Communications Act of 1934: General telecom regulation.
• Communications Decency Act: Protects service providers.

Final Answer: (a) Controlling the Assault of Non-Solicited Pornography and Marketing Act

Step 1: Analyze the stages.

• Possessing Knowledge: Acquiring domain-specific expertise.
• Professional Services: Applying knowledge in practical settings.
• Self-Defining or Integrated Professional: Achieving a cohesive professional identity.

Final Answer: (a) Possessing Knowledge, Professional Services, Self-Defining or Integrated Professional

Step 1: Analyze the Fundamental Canons.

The National Society of Professional Engineers (NSPE) emphasizes that the primary responsibility of engineers is to ensure the safety, health, and welfare of the public in all professional duties.

Final Answer: (a) Paramount the safety, health, and welfare of the public

Step 1: Analyze the abbreviation EWB.

Engineers Without Borders (EWB) is an organization that works to address global challenges, particularly those involving clean water, sanitation, and infrastructure in underdeveloped areas.

Final Answer: (c) Engineers Without Borders

Step 1: Analyze the given duties.

W.D. Ross’s theory of prima facie duties emphasizes moral obligations, such as:

• Duties resting on previous acts
• Duties of gratitude, justice, beneficence, and self-improvement

However, duties to injure others are not consistent with Ross’s framework.

Final Answer: (c) 1, 2, and 3

Step 1: Analyze the types of moral judgments.

Moral judgments are classified as:

• Permissible: Actions that are morally allowed.
• Impermissible: Actions that are morally prohibited.
• Obligatory: Actions that are morally required.
• Supererogatory: Actions that go beyond moral obligation.

Final Answer: (c) Permissible, Impermissible, Obligatory, Supererogatory

Step 1: Analyze Michael Davis’ suggested tests.

Michael Davis’ framework emphasizes tests like the Harm Test, Publicity Test, and Reversibility Test, which reflect practical and ethical considerations grounded in commonsense morality.

Final Answer: (a) Harm Test, Publicity Test, Defensibility Test, Reversibility Test, Virtue Test, Professional Test, Colleague Test and Organization Test

Step 1: Understand the term CBA.

CBA stands for Cost Benefit Analysis, a systematic approach for comparing the costs and benefits of a project or decision to maximize well-being or utility.

Final Answer: (d) Cost Benefit Analysis

Step 1: Analyze the concept of liability in engineering errors.

The “Standard of Care” refers to the level of competence and diligence expected of an engineer. Errors exceeding this standard are considered negligent.

Final Answer: (c) Standard of Care

Step 1: Understand the legal definition of a corporation.

According to Black’s Law Dictionary, a corporation is treated as a legal entity, capable of entering into contracts, suing, and being sued.

Final Answer: (c) Sue and be sued

Step 1: Understand the concept of Blind Spot.

Blind Spot in business refers to the lack of awareness or refusal to see the negative aspects of a situation, often caused by self-deception, willful blindness, or in-attentional blindness. However, “Illusion of invulnerability of group” is a groupthink phenomenon rather than a specific blind spot method.

Final Answer: (d) Illusion of invulnerability of group

Step 1: Analyze the reasons for diversification.

Factors like restrictions in current business, favorable policies, and opening newer investment opportunities drive diversification. However, avoiding tax incentives is not a common reason for diversification.

Final Answer: (d) Desire not to avail tax incentives

Step 1: Understand the BCG matrix parameters.

The BCG matrix uses two key metrics: Relative Market Share (market strength) and Relative Market Growth Rate (market attractiveness).

Final Answer: (c) Relative Market Share and Relative Market Growth Rate

Step 1: Identify the cost-reducing factors.

Cost reductions arise from learning effects (improved efficiency with experience), technological advancements (process improvement), and economies of scale (spreading fixed costs over larger production volumes).

Final Answer: (b) Learning effects, Technological improvements, and Economies of scale

The broad areas of corporate appraisal include Marketing and Distribution, Production and Operation, and Research and Development. These are critical aspects of any corporate analysis, whereas Project Rating is more specific to financial evaluation rather than general corporate appraisal.

Final Answer: (a) 1, 2, 3

The Jury of Executive Method involves gathering opinions from a panel of experts or executives to forecast demand. It is a qualitative approach as it relies on judgment and experience rather than numerical data.

Final Answer: (a) Jury of Executive Method

The Delphi method appeals to organizations because it systematically gathers input from multiple experts while maintaining anonymity, reducing biases. It is cost-effective and eliminates the need for physical meetings.

Final Answer: (c) It has immense appeal, the biases underlying are subjective, and it seems to be more accurate and less expensive than the traditional face-to-face group meetings

Statements 2 and 3 accurately describe metallic bonding. Metallic bonding involves a “sea of electrons” that are free to move, creating a strong bond between positively charged ion cores. Statement 1 is incorrect as electron sharing in metallic bonds does not change with time.

Final Answer: (c) 2 and 3 only

Step 1: Analyze each statement:

Statement 1: Correct. The Gibbs phase rule calculates the degrees of freedom for a system in equilibrium.

Statement 2: Correct. The tie-line rule is crucial in binary phase diagrams for determining phase compositions.

Statement 3: Correct. The lever rule uses the tie-line to calculate the proportion of phases in a system.

Final Answer: (d) 1, 2 and 3

Step 1: Analyze each statement:

Statement 1: Correct. Sulphur in steel can lead to cracking, especially as iron sulphide.

Statement 2: Correct. Ferro-silicon is widely used as a cost-effective deoxidant in steelmaking.

Statement 3: Correct. Silicon reacts with iron oxide, reducing its harmful effects on steel properties.

Final Answer: (d) 1, 2 and 3

Step 1: Analyze each statement:

Statement 1: Correct. Gray cast irons are classified based on graphite shape.

Statement 2: Incorrect. Malleable cast iron is produced by heat treatment, not by using calcium silicide.

Statement 3: Incorrect. Meehanite cast irons do not have graphite nodules; they are produced through controlled solidification.

Final Answer: (c) 2 and 3 only

Step 1: Analyze each statement:

Statement 1: Correct. Covalent compounds like hydrocarbons are soluble in paraffins.

Statement 2: Correct. Covalent solids like diamond are rigid due to strong covalent bonds, preventing closed-packet structures.

Statement 3: Correct. Diamond is a classic example of an open, covalent network structure.

Final Answer: (d) 1, 2 and 3

Step 1: Analyze each statement:

Statement 1: Correct. Gas carburizing allows for accurate control of case depth.

Statement 2: Incorrect. Gas carburizing typically requires less floor space compared to pack carburizing.

Statement 3: Correct. Gas carburizing is faster than pack carburizing due to better heat and carbon transfer.

Final Answer: (b) 1 and 3 only

Step 1: Analyze each option:

Option (a): Correct. Thermal mass indeed helps in reducing temperature variations.

Option (b): Correct. Thermal mass is useful in storing and releasing heat or cooling.

Option (c): Correct. It stores solar energy entering through windows.

Option (d): Incorrect. The heavier a material is, the more thermal mass it has.

Final Answer: (d)

Step 1: Analyze each statement:

Statement 1: Correct. Ethanol is predominantly derived from corn and sugarcane.

Statement 2: Correct. Brazil uses ethanol as a significant liquid fuel source.

Statement 3: Incorrect. Ethanol production does not account for 90% of all biofuel production worldwide.

Final Answer: (d) 1 and 2 only

Step 1: Analyze each statement:

Option (a): Correct. Decomposition releases carbon dioxide as part of the carbon cycle.

Option (b): Correct. Volcanoes release carbon dioxide into the atmosphere during eruptions.

Option (c): Correct. Warmer ocean water releases more dissolved carbon dioxide into the air.

Option (d): Incorrect. Methane gas (CH₄) is a separate greenhouse gas and is not carbon dioxide.

Final Answer: (d)

Correct matches are:

• P. Lamarck => 4 (Inheritance of acquired characteristics)
• Q. Lyell => 2 (Gradual geological processes)
• R. Malthus => 3 (Human population growth and resources)
• S. Wallace => 1 (Evolutionary theory)

Final Answer: (b) 4, 2, 3, 1

Step 1: Define Chaparral: Chaparrals are shrub forest biomes characterized by dense evergreen shrubs and small trees. They are found in regions with a Mediterranean climate.

Final Answer: (b)

Step 1: Definition: The albedo effect refers to the reflectivity of a surface. Surfaces with high albedo, like snow and ice, reflect more sunlight, helping regulate Earth’s temperature.

Final Answer: (a)

Step 1: Understand the term: Mass customization refers to producing goods and services to meet individual customer needs while maintaining the efficiency of mass production.

Final Answer: (b) Mass customization

Step 1: In the DMAIC (Define, Measure, Analyze, Improve, Control) framework, “Analyze” focuses on determining the relationship between inputs and outputs to identify root causes and impacts.

Final Answer: (c) Analyze

Step 1: A p-chart tracks the proportion of defective items in a sample and is advantageous for its simplicity and intuitive use (Point 1) and its ability to work without predefined standard units (Point 2).

Step 2: However, it does not inherently account for all systematic errors (Point 3).

Final Answer: (c) 1 and 2

Step 1: Discrete random variables take on a countable number of distinct values. The Negative Binomial Distribution describes the probability of a fixed number of successes in a sequence of independent Bernoulli trials.

Final Answer: (d) Negative Binomial Distribution

Step 1: All three conditions are essential for effective quality control:

• Condition 1 ensures compliance with customer specifications.
• Condition 2 minimizes variability to enhance consistency.
• Condition 3 aligns product characteristics with target values.

Final Answer: (d) 1, 2, and 3

Step 1: As tolerance on quality characteristics increases, the precision required in manufacturing decreases, leading to reduced production costs due to easier processing and less waste.

Final Answer: (b) manufacturing cost decreases as the tolerance on the quality characteristic increases

Step 1: Design requirements define specific conditions, constraints, and features that a product must satisfy to meet the needs and expectations of the customer.

Final Answer: (c) Design requirements

Step 1: Axles primarily function to transfer the weight of the machine to the wheels, facilitate wheel rotation, and ensure the wheels remain properly aligned relative to the housing.

Final Answer: (d) Transfer the weight of the mower from the housing to the wheels. Allow rotation of the wheels. Maintain the location of the wheels relative to the housing.

Step 1: French curves are specially designed templates used for drawing irregular curves that cannot be created with a compass or other basic drawing tools.

Final Answer: (c) French curves

Step 1: The lines where a plane intersects the reference planes (such as horizontal or vertical reference planes) are known as the traces of the plane.

Final Answer: (b) Traces of the plane

Step 1: The two most common methods to determine the line of intersection of interpenetrating solids are the line method and the cutting plane method.

Final Answer: (a) Line method and cutting plane method

Step 1: For cones and pyramids, the radial-line development method is used, where the true length of the slant edge or generator is taken as the radius to construct the development.

Final Answer: (b) Radial-line development

Step 1: According to the Global Peace Index 2023, Iceland remains the most peaceful country since 2008, and it is correct that five of the top 10 peaceful countries are in Europe.

Final Answer: (d) Neither 1 nor 2

Step 1: Japan holds the title for the most powerful passport, and three European countries share the second position. Both statements are correct.

Final Answer: (d) Neither 1 nor 2

Step 1: Analyze the statements:

• Statement 1 is correct: The GST collection data aligns with the figures released by the Ministry of Finance.
• Statement 2 is correct: India recorded its highest-ever FDI inflow in 2021-2022.
• Statement 3 is correct: The direct tax collection figures show a growth of 16% as per reports.

Final Answer: (d) 1, 2 and 3

Step 1: Verify each statement:

• Statement 1 is correct: The Hemis Festival is a well-known religious celebration in Ladakh.
• Statement 2 is correct: The festival celebrates the birth anniversary of Lord Padmasambhava.
• Statement 3 is correct: The festival showcases Tibetan Tantric Buddhism traditions.

Final Answer: (d) 1, 2 and 3

Step 1: The Ministry of Defence awarded the contract to Bharat Electronics Limited (BEL) for upgraded defense systems.

Final Answer: (d) BEL

Step 1: The record-breaking infrastructure projects were achieved in Nagpur and Amravati.

Final Answer: (a) Amravati and Nagpur

Step 1: The Centre of Data for Public Good (CDPG) was launched by NITI Aayog to bring together experts for multidisciplinary research aimed at benefiting the public through data-driven strategies.

Final Answer: (d) NITI Aayog

Step 1: AstroSat, launched by India, achieved this milestone as the first Indian multi-wavelength satellite dedicated to space observation.

Final Answer: (d) India

Step 1: The eight ASW Shallow Water Craft ships include names like Malvan, Mangrol, and Mahe, but Mahanav is not a part of this project.

Final Answer: (a) Mahanav

Step 1: The ‘5G & Beyond Hackathon 2023’ was announced by the Ministry of Communication to drive innovations in 5G technology.

Final Answer: (b) Ministry of Communication

Step 1: The scheme was introduced by the Ministry of Home Affairs to strengthen fire services in the states under the National Disaster Response Fund.

Final Answer: (d) Ministry of Home Affairs

Step 1: Exercise “Nomadic Elephant” is conducted between the Indian Army and the Mongolian Armed Forces to strengthen defense cooperation.

Final Answer: (b) Mongolia

Step 1: The ‘SPRINT Challenges’ were launched to boost the usage of 75 indigenous technologies in collaboration with Innovations for Defence Excellence and the Indian Navy.

Final Answer: (d) Indian Navy

Step 1: The ‘Centralised Receipt and Processing Centre’ and ‘Integrated Ombudsman Scheme’ are initiatives launched by the Reserve Bank of India (RBI) to enhance consumer grievance redressal mechanisms.

Final Answer: (d) RBI

Step 1: V-CIP stands for ‘Video-based Customer Identification Process,’ a secure method used for verifying the identity of customers remotely, often in banking and financial services.

Final Answer: (d) Video-based Customer Identification Process