GATE 2022 CE (Set 1) question paper PDF and answer key

Under the conventional family-relation interpretation of this question, Q and R are S’s parents. P is Q’s sister, and T is P’s husband, making T an uncle of S: B. Strictly, the statements do not explicitly say Q is S’s father; the keyed relationship uses that usual family-puzzle assumption. No numerical calculation applies.

Therefore, the correct answer is B.

The radius $RQ$ is perpendicular to tangent $PQ$. Thus $PR^2=PQ^2+RQ^2$. The square PXWR has side PR, SPQT has side PQ, and RUVZ has side RZ, with $RZ=RQ$. Therefore $A_{SPQT}=PQ^2=PR^2-RZ^2=A_{PXWR}-A_{RUVZ}$. Hence B.

Therefore, the correct answer is B.

Cut at Q and isolate segment HQ. Resolve the applied horizontal load along the tangent and normal at Q; at 45° both components have magnitude $P/\sqrt2$. The perpendicular distance from Q to the horizontal line of action of P is $R\sin45^\circ=R/\sqrt2$, so $|M_Q|=PR/\sqrt2$. Hence A. The bending moment is not zero merely because the load acts horizontally.

Therefore, the correct answer is A.

The branches intersect where $3-x=x-1$, giving $x=2$ and $f=1$. Equivalently $f(x)=1+|x-2|$. It is continuous on all real numbers and has a strict local (also global) minimum at 2. Its left and right derivatives there are −1 and +1, so it is not differentiable throughout its domain. Hence A and B.

Therefore, the correct answers are A, B.

Euler’s update is $y_{n+1}=y_n+0.2[4(x_n+2)-y_n]$. First, $y(1.2)\approx3+0.2(12-3)=4.8$. Next, $y(1.4)\approx4.8+0.2[4(3.2)-4.8]=4.8+1.6=6.4$. This is the requested discrete Euler approximation, not the exact ODE solution.

Therefore, the answer lies in the range 6.3 to 6.5.