SSC CHSL 16th April 2021 Shift-3

Simplify the following expression.
$$\cos^2 30^\circ + \cos^2 40^\circ + \cos^2 50^\circ + \cos^2 60^\circ$$

If $$5k = \tan \theta$$ and $$\frac{5}{k} = \sec \theta$$, then what is the value of $$10\left(k^2 - \frac{1}{k^2}\right)$$?

The lengths of three sides ofa triangle are in the ratio 3 : 4 : 5. Among three sides, the difference between the largest side and the smallest side of this triangle is 3.6 cm. The area (in cm$$^2$$) of the triangle is:

If $$21 \tan \theta = 20$$, then $$(1 + \sin \theta - \cos \theta):(1 - \sin \theta + \cos \theta)$$ is equal to:

A,B and C can independently complete the same task in 4, 6 and 12 days, respectively. In how many dayswill they be able to complete the sametask if they work together?

IfA is 28% less than B and C is 25% less than the sum of A and B, then by what percentage will C be more than A (correct to one decimal place)?

The average score of 84 students (boys and girls) in a test is 95. The ratio of the numberof boys to that of girls is 10: 11. The average score of the boys is 20% less than that of the girls. What is the average score of the boys in the test?

The simple interest on a certain sum for $$3\frac{1}{2}$$ years at the rate of 10% per annum is ₹2,940. What will be the compound interest (in ₹) on the same sum for $$1\frac{1}{2}$$ years at the same rate wheninterest is compounded half-yearly (nearest to a rupee)?

The ratio of the ages of A and B, four years ago. was 4 : 5. Eight years hence, the ratio of the ages ofA and B will be 11 : 13, What is theratio of their present ages?

Some persons went on an outstation tour. The histogram shows their ages.

If the children of age less than 15 years got concession, then how many persons got the concession?