SSC CGL Tier-2 8th August 2022 Maths

ABC is an isosceles right angle triangle. Angle ABC = 90 degree and AB = 12 cm. What is the ra tio of the radius of the circle inscribed in it to the radius of the circle circumscribing triangle ABC ?

A alone can do a work in 11 days. B alone can do the same work in 22 days. C alone can do the same work in 33 days.
They work in the following manner:
Day 1 : A and B work.
Day 2: B and C work.
Day 3: C and A work.
Day 4: A and B work. And so on.
In how many days will the work be completed?

What is the sum of all the common terms between the given series S1 and S2?
S1 = 2, 9, 16 ...... 632
S2 = 7, 11 15, ..... , 743

ABC is an equilateral triangle. If the area of the triangle is $$36\sqrt{3}$$ , then what is the radius of circle circumscribing the triangle ABC?

What is the value of $$\frac{3 \sin 58^\circ}{\cos 32^\circ} + \frac{3 \sin 42^\circ}{\cos 48^\circ}$$

What is the value of $$\frac{\cos 50^\circ}{\sin 40^\circ} + \frac{3 \cosec 80^\circ}{\sec 10^\circ} - 2 \cos 50^\circ.\cosec 40^\circ$$ ?

Which of the following is equal to $$\left[\frac{\tan \theta + \sec \theta - 1}{\tan \theta - \sec \theta + 1}\right]$$?

Two circles each of radius 36 cm are intersecting each other such that each circle is passing through the centre of the other circle. What is the length of common chord to the two circles?

The height of a cylinder is 45 cm. If circumference of its base is 132 cm, then what is the curved surface of this cylinder? ( use $$\pi = \frac{22}{7}$$)

The slant height ofa cone is 20 cm. If area of its base is 616 cm$$^2$$, then what is the cmv ed smface area of this cone? (use $$\pi = \frac{22}{7}$$)