geometry

In the diagram, the lines QR and ST are parallel to each other. The shortest distance between these two lines is half the shortest distance between the point P and line QR. What is...

In the given figure, PQRS is a square of side 2 cm and PLMN is a rectangle. The corner L of the rectangle is on the side QR. Side MN of the rectangle passes through the corner S of...

A rectangular paper sheet of dimensions 54 cm x 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 equa...

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 shee...

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 i...

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 folde...

Looking at the surface of a smooth 3-dimensional object from the outside, which one of the following options is TRUE?

We have 2 rectangular sheets of paper, M and N, of dimensions 6 cm $$\times$$ 1 cm each. Sheet M is rolled to form an open cylinder by bringing the short edges of the sheet togethe...

A polygon is convex if, for every pair of points. P and Q belonging to the polygon, the line segment PQ lies completely inside or on the polygon. Which one of the following is NOT...

If $$\theta$$ is the angle, in degrees, between the longest diagonal of the cube and any one of the edges of the cube, then cos $$\theta$$ = _______

Two straight lines are drawn perpendicular to each other in X-Y plane. If $$\alpha $$ and $$\beta $$ are the acute angles the straight lines make with the X-axis, then $$\alpha $$...

The area of a square is $$𝑑.$$ What is the area of the circle which has the diagonal of the square as its diameter?

A cube is built using $$64$$ cubic blocks of side one unit. After it is built, one cubic block is removed from every corner of the cube. The resulting surface area of the body (in...