GATE 2025 CE (Set 1) question paper PDF and answer key

The minute hand gains on the hour hand at

$$6-0.5=5.5^\circ/\text{min}.$$

Successive coincidences require a relative gain of $360^\circ$, so the interval is

$$\frac{360}{5.5} = \frac{720}{11} = 65\frac5{11}\text{ min}.$$

Therefore, the correct answer is Option C.

The model is the subtractive CMY color model:

• Yellow + Magenta gives Red.
• Magenta + Cyan gives Blue.
• Cyan + Yellow gives Green.
• Yellow + Magenta + Cyan gives Black.

Only option (A) places all four derived colors in the corresponding overlap regions.

Therefore, the correct answer is Option A.

From the Mohr circle, the principal stresses at failure are

$$\sigma_3=50\text{ kPa}, \qquad \sigma_1=100\text{ kPa}.$$

For a normally consolidated clay in a drained test, take $c'=0$. Then

$$\sin\phi' = \frac{\sigma_1-\sigma_3}{\sigma_1+\sigma_3}.$$

Hence

$$\sin\phi' = \frac{100-50}{100+50} = \frac13.$$

Therefore,

$$\phi'=\sin^{-1}\left(\frac13\right).$$

Therefore, the correct answer is Option B.

A second-order linear homogeneous PDE must:

1. contain derivatives up to second order,
2. be linear in the dependent variable and all its derivatives, and
3. have zero forcing term.

Option (B),

$$u_{xx}+u_{yy}+u_{zz}=0,$$

satisfies all three requirements.

Option (A) contains the nonzero forcing term $xy$, so it is nonhomogeneous. Option (C) is only first order. Option (D) is nonlinear because a second derivative is squared.

Therefore, the correct answer is Option B.

For fineness modulus, add the cumulative percentages retained on the standard sieves and divide by 100.

The cumulative percentages retained are:

• 4.75 mm: $0$
• 2.36 mm: $30$
• 1.18 mm: $30+35=65$
• 600 µm: $80$
• 300 µm: $100$
• 150 µm: $100$

Therefore,

$$FM = \frac{0+30+65+80+100+100}{100} = 3.75.$$

Therefore, the answer is 3.75 (official accepted range 3.74 to 3.76).