SSC CGL 21st April 2022 Shift-2

In $$\triangle$$ ABC , the perpendiculars drawn from A, B and C meet the opposite sides at points D, E and F, respectively. AD, BE and CF intersect at point P. If $$\angle EPD = 110^{\circ}$$ and the bisectors of $$\angle$$ A and $$\angle$$ B meet at point Q, then $$\angle$$ AQB?

AB is the diameter of a circle with centre O. C and D are two points on the circle on either side of AB, such that $$\angle CAB = 52^{\circ}$$ and $$\angle ABD = 47^{\circ}$$. What is the difference (in degrees) between the measures of $$\angle$$ CAD and $$\angle$$ CBD?

Two trains are running on parallel tracks in the same direction at the speed of 80 km/h and 90 km/h, respectively. The trains crossed each other in 3 minutes. If the length of one train is 230 m, then what is the length (in m) of the other train?

If $$\frac{\sin^{2} \theta-3\sin \theta +2}{\cos^{2} \theta}=1$$, where $$0^{\circ} < \theta < 90^{\circ}$$, then what is the value of $$\left(\cos2 \theta-\sin3 \theta+\cosec2 \theta\right)$$

In the following figure AD bisects angle BAC. Find the length (in cm) of BD.

Simplify $$\left[\left(5\frac{1}{4}\div3\frac{1}{2}\times\frac{5}{12}\right)-\frac{3}{16}\right]\div \left(3\frac{4}{7}\div\frac{5}{14} of 6\frac{2}{3}\right)$$ of $$1\frac{1}{3}$$

Study the graph and answer the question that follows.

What is the ratio of the total number of workers whose daily wages are less than ₹450 to the total number of workers  whose daily wages are ₹650 and above?

A solid cone of radius 7 cm and height 7 cm was melted along with two solid spheres of radius 7 cm each to form a solid cylinder of radius 7 cm. What is the curved surface area (in $$cm^{2}$$) of the cylinder?
(User $$\pi = \frac{22}{7}$$)

The given pie chart shows the percentage of students in five schools and the table shows the ratio of
boys and girls in each school.
Study the pie chart and table and answer the question that follows.

The below table shows the ratio of girls and boys in the given five schools.

The number of girls in school D is what percentage less than the number of boys in school B ( correct to the nearest integer)?

What is the compound interest (in ₹) on a sum of ₹62,500 for 2 years at 12% p.a., if the inerest is compounded 8- monthly?