Mega Quiz 30 & Weekly Revision || Quantitative Aptitude || CAT 2021 || 10 October

In the diagram, M is the midpoint of YZ, ∠XMZ = 32°, and ∠XYZ = 16°. The measure of ∠XZY is:

The corners of an equilateral triangle ABC whose side is 15 cm are cut to form a regular hexagon PQRSTU. Then, what is the length of side of the hexagon?

In an isosceles triangle ABC with AB = AC and AD is perpendicular to BC, if AD = 6 cm and the perimeter of ∆ABC is 36 cm, then the area of ∆ABC is:

In a ∆PQR, I is incentre and O is the orthocenter, and ∠QIR : ∠QOR is 61: 58. ∠PQR is 44° more than ∠PRQ. X is the point of intersection of external angle bisectors of ∠P and ∠R. If C is the circum-center of ∆PQR, then find the ratio ∠PXR : ∠PCQ. 

In the figure two circles intersect at two points M and N. Through M two-line segments AMD and PMQ are drawn to intersect the circles at A, D and P, Q respectively. If ∠ANP = 45° then what is the value of ∠QND?

In the given figure, BT and CT′ are two tangents at points B and C on the circle and ∠BPC = 80°. If O is the centre of the circle, then ∠BAC is equal to:

ABCD is a rectangle. P is a point inside the rectangle such that AP = 3 cm, PC = 4√2 cm and DP = 5 cm. If ∠APB = 90°, what is the length of rectangle?

In a trapezium ABCD, the two non-parallel sides AD and BC are equal in length each being of 13 cm. The parallel sides AB and CD are at a distance of 12 cm apart. If the smaller side of the parallel sides is of length 11 cm, then the sum of the lengths of the diagonals of the trapezium is: