Analytical & Spatial Aptitude

Subtopic: Spatial Reasoning & Paper Folding

A paper shown in Panel I is folded along the dashed lines (- - -) to construct a cube. The shaded regions shown in Panel I appear on the outer surface of the cube. Referring to cubes shown in Panel II, which one of the options is correct?

Subtopic: Logical Puzzles & Sequences

Consider the cube shown below with its 8 corners labelled a, b, c, d, e, f, g, and h. The figure is representative. All corners are to be colored such that any two corners that are connected by an edge must be of different colors. The minimum number of colors required to achieve this is ________

Subtopic: Spatial Reasoning & Paper Folding

A rectangular paper sheet of dimensions 54 cm × 4 cm is taken. The two longer edges of the sheet are joined together to create a cylindrical tube. A cube whose surface area is equal to the area of the sheet is also taken. Then, the ratio of the volume of the cylindrical tube to the volume of the cube is

Subtopic: Spatial Reasoning & Paper Folding

A rectangular paper of 20 cm × 8 cm is folded 3 times. Each fold is made along the line of symmetry, which is perpendicular to its long edge. The perimeter of the final folded sheet (in cm) is

Subtopic: Spatial Reasoning & Paper Folding

A line of symmetry is defined as a line that divides a figure into two parts in a way such that each part is a mirror image of the other part about that line. The given figure consists of 16 unit squares arranged as shown. In addition to the three black squares, what is the minimum number of squares that must be coloured black, such that both PQ and MN form lines of symmetry? (The figure is representative)

Subtopic: Logical Puzzles & Sequences

Which one of the following shapes can be used to tile (completely cover by repeating) a flat plane, extending to infinity in all directions, without leaving any empty spaces in between them? The copies of the shape used to tile are identical and are not allowed to overlap.

Subtopic: Spatial Reasoning & Paper Folding

Equal sized circular regions are shaded in a square sheet of paper of 1 cm side length. Two cases, case M and case N, are considered as shown in the figures below. In the case M, four circles are shaded in the square sheet and in the case N, nine circles are shaded in the square sheet as shown. What is the ratio of the areas of unshaded regions of case M to that of case N? case M case N

Subtopic: Spatial Reasoning & Paper Folding

PHYLAXIS The mirror image of the above text about the horizontal X-axis (placed below the text) is:

Subtopic: Logical Puzzles & Sequences

Two identical cube shaped dice each with faces numbered 1 to 6 are rolled simultaneously. The probability that an even number is rolled out on each dice is:

Subtopic: Logical Puzzles & Sequences

Four persons P, Q, R and S are to be seated in a row. R should not be seated at the second position from the left end of the row. The number of distinct seating arrangements possible is:

Subtopic: Logical Puzzles & Sequences

On a planar field, you travelled 3 units East from a point O. Next you travelled 4 units South to arrive at point P. Then you travelled from P in the North-East direction such that you arrive at a point that is 6 units East of point O. Next, you travelled in the North-West direction, so that you arrive at point Q that is 8 units North of point P. The distance of point Q to point O, in the same units, should be:

Subtopic: Logical Puzzles & Sequences

Five numbers 10, 7, 5, 4 and 2 are to be arranged in a sequence from left to right following the directions given below: 1. No two odd or even numbers are next to each other. 2. The second number from the left is exactly half of the left-most number. 3. The middle number is exactly twice the right-most number. Which is the second number from the right?

Subtopic: Logical Puzzles & Sequences

The phenomenon of rudder lock in conventional low speed aircraft is primarily due to

Subtopic: Logical Puzzles & Sequences

The streamlines of a potential line vortex is concentric circles with respect to the vortex center as shown in figure. Velocity along these streamlines, outside the core of the vortex can be written as, vv$\theta \theta$ = $\Gamma$ 2$\pi \pi \pi \pi$, where strength of the vortex is $\Gamma$ 2$\pi \pi$ and r is radial direction. The value of circulation along the curve shown in the figure is:

Subtopic: Logical Puzzles & Sequences

The directional derivative of the function 22 (, ) 5 x xyfx y  in the direction ˆˆ24ija at (, ) ( 1 , 1 )xy  is

Subtopic: Logical Puzzles & Sequences

Consider the function f(x1, x^2) = x1^2 + 2x2^2 + e^(x1 - x^2). The vector pointing in the direction of maximum increase of the function at (1, -1) is:

Subtopic: Logical Puzzles & Sequences

A thin rectangular plate made of isotropic maerial which satisfies the octahedral (i.e.. Von Mises/ Distortion energy) failure criterion has yield strength of 200 MPa under uniaxial tension. As shown in the figure. if it is loaded with uniform tension of 1S0 MPa along the x-direction, the maximum uniform tensile stress that can be applied along the y-direction before the plate starts yielding is about 1111ttt111, * 0. = 150 MPa THTFTTITTT