GATE 2026 CE (Set 2) question paper PDF and answer key

The natural grammatical sequence is:

• a pit
• an elephant
• bewildered and miserable
• look up at a crowd

Thus the completed sequence is a; an; and; at.

Therefore, the correct answer is Option B.

Let the quantity of T be $t$. Then

$$Q=4t,\qquad R=3t,\qquad S=2t.$$

If $p$ units of P were sold, the total item count gives

$$p+4t+3t+2t+t=250,$$

so

$$p+10t=250.$$

Total sales revenue is

$$250(60)=15000.$$

Using the unit prices,

$$100p+50(4t)+40(3t)+60(2t)+60t=15000,$$

or

$$100p+500t=15000.$$

Substitute $p=250-10t$:

$$100(250-10t)+500t=15000.$$

Hence $t=20$ and

$$p=250-200=50.$$

Therefore, the correct answer is Option B.

Because G and J are internal hinges, span GJ can be treated as a simply supported segment for vertical equilibrium.

On GJ, the $30$ kN load acts at the midpoint, 2 m from either hinge. The $20$ kN load acts directly at hinge G and therefore produces no moment about G.

Taking moments about G for span GJ:

$$R_J(4)=30(2),$$

so

$$R_J=15\text{ kN}.$$

Thus the right segment JL receives a downward hinge force of $15$ kN at J.

The $4$ kN/m UDL acts only over KL, a length of 2 m, so its resultant is

$$4(2)=8\text{ kN}.$$

Vertical equilibrium of segment JL gives

$$R_L=15+8=23\text{ kN}.$$

Therefore, the correct answer is Option A.

Any twice-differentiable function of $x+y$ satisfies the equation because, for $u=F(x+y)$,

$$u_{xx}=F''(x+y)=u_{yy}.$$

Therefore both

$$(x+y)^5$$

and

$$\cos(x+y)$$

are solutions.

For $u=F(x-2y)$,

$$u_{xx}=F'', \qquad u_{yy}=4F'',$$

so

$$u_{xx}-u_{yy}=-3F'',$$

which is nonzero for the cubic and sine choices given.

Therefore, the correct answers are Options A and C.

The determinant of a square matrix is the product of its eigenvalues:

$$\det(A)=\lambda_1\lambda_2\lambda_3.$$

Therefore,

$$|\det(A)| = |(-1.547)(12.330)(4.711)| \approx89.86.$$

Therefore, the answer is 89.86 (official accepted range 89.00 to 91.00).