SSC CGL 13th April 2022 Shift-3

The length of the shadow on the ground of a tall tree of height 45 m is $$15\sqrt{3}$$ m. What is the angle (in degrees) of elevation of the sun?

What is the least number which when decreased by 7 is divisible by 15, 24, 28 and 32?

An isosceles $$\triangle$$ MNP is inscribed in a circle. If MN= MP= $$165\sqrt{5}$$cm, and NP= 32 cm, what is the radius (in cm) of the circle?

Study the given pie-chart and answer the question that follows.
The chart represents the percentage-wise distribution of total number of vanilla cakes and chocolate cakes sold every day in a week. Total number of cakes sold in a week = 10500.

The ratio of vanilla cakes sold to chocolate cakes sold on Friday is 4 : 3. If the selling price of one vanilla cake is ₹9 and that of one chocolate cake is ₹10, then the total amount earned (in ₹) by selling all the vanilla cakes and chocolate cakes on Friday is:

Let $$\triangle ABC \sim \triangle PQR$$ and $$\frac{ar\left(\triangle ABC\right)}{ar\left(\triangle QPR\right)} = \frac{64}{169}$$. If AB = 10 cm, BC = 7 cm and AC = 16 cm, then PR (in cm) is equal to:

Find the value of $$\left(1.6\right)^{3} - \left(0.9\right)^{3} - \left(0.7\right)^{3}$$

The base of a triangle is increased by 40%. By what percentage (correct to two decimal places) should its height be increased so that the area increases by 60%?

A shopkeeper allows 28% discount on the marked price of an article and still makes a profit of 30%. If he gains ₹30.90 on the sale of one article, then what is the marked price (to the nearest ₹) of the article?

The average of 46 numbers is 50.5. The average of the first 25 numbers is 45 and that of the last 18 numbers is 56. The $$28^{th}$$ number is 67. If the $$26^{th}$$ and $$27^{th}$$ numbers are excluded, then what is the average of the remaining numbers?

If x + y + z = 2 , xy + y z + zx = - 11 , and xyz = -12 , then what is the value of $$x^{3} + y^{3} + z^{3}$$ ?