SSC CPO 4th Oct 2023 Shift 1

The total surface area of a square-based right pyramid is 1536 $$m^{2}$$, of which 37.5% is the area of the base of the pyramid. What is the volume (in $$m^{3}$$) of this pyramid?

If $$\sin A + \sin^{2} A = 1$$, then the value of $$\cos^{4} A + \cos^{6} A$$ is:

The radius of a circle is 1.75 cm. What is the circumference of the circle?

(Take $$ \pi = \frac{22}{7}$$)

Let the HCF of m and n be ‘a’ and let n = ab, LCM of m and n is given by:

Study the given pie-chart and answer the question that follows.
The pie-chart shows the number of students (boys and girls) studying in standard 10 of various schools (X, Y, Z in the year 2022).

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What is the difference between the total number of students (boys and girls) in school Y and Z together and the total number of students (boys and girls) in school X and Y together?

The radius of the base of a right circular cone is 5 cm. Its slant height is 13 cm.
What is its volume (in $$cm^{3}$$ , rounded off to 1 decimal place)? (Take $$ \pi = \frac{22}{7}$$)

A sum of money was invested at 10% interest per year, compounded half-yearly, for 18 months. If the amount payable on maturity was ₹64,827, what was the sum invested?

Let C be a circle with centre O and radius 5 cm. Let PQ be a tangent to the circle and A be the point of tangency. Let B be a point on PQ such that the length of AB is 12 cm. If the line joining O and B intersects the circle at R, find the length of BR (in cm).

The value of $$1\frac{2}{5} - [3\frac{3}{4} \div {1\frac{1}{4} \div \frac{1}{2} (1\frac{1}{2} \times 3\frac{1}{3} \div 1\frac{1}{3})}]$$

When A alone does a piece of work, he takes 25 days more than the time taken by A and B to do the work together. On the other hand, B alone takes 16 days more than the time taken by A and B to do the work together. How many days will A and B, working together, take to do the work?