SSC CGL 13th April Shift 3 - QA

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 △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.

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

Find the value of (1.6)³ - (0.9)³ - (0.7)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 28th number is 67. If the 26th and 27th 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 x³ + y³ + z³?

A person travels 5x distance at a speed of 5 km/h, x distance at a speed of 5 km/h, and 4x distance at a speed of 6 km/h, and takes a total of 112 minutes. What is the total distance (in km) travelled by the person?

Person A can do one-fifth of the work in 3 days, while B's efficiency is half of that of A. In how many days A and B working together can do half of the work?

Study the given histogram that shows the marks obtained by students in an examination and answer the question that follows.

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The number of students who obtained less than 200 marks is what percentage less than the number of students who obtained 400 or more marks ( correct to one decimal place)?

If sin² θ - cos² θ - 3 sin θ + 2 = 0, 0° < 0 < 90°, then what is the value of 1 + sec θ + tan θ​​​​​​​?

What is the value of p, if 25(3 + 4p) + 12 of 5 - 3 8 = 6?

Let x cm² be the surface area and y cm³ be the volume of a sphere such that y = 14x. What is the radius (in cm) of the sphere?

A shopkeeper bought 40 pieces of an article at a rate of ₹50 per item. He sold 35 pieces with 20% profit. The remaining 5 pieces were found to be damaged and he sold them with 10% loss. Find his overall profit percentage.

The curved surface area of a right circular cylinder is 616 cm² and the area of its base is 38.5 cm². What is the volume (in of the cylinder?

(Take π = 22/7).

The sides PQ and PR of △PQR are produced to points S and T, respectively. The bisectors of ∠SQR and ∠TRQ meet at point U. If ∠QUR = 69°, then the measure of ∠P is:

A, B and C start a business. A invests 33$\frac{1}{3}$% of the total capital, B invests 25% of the remaining, and C invests the rest. If the total profit at the end of the year is ₹1,86,000, then A's share of the profit (in ₹) is:

(sec θ − tan θ)² (1 + sin θ )² + cos² θ = ?

Study the given bar graph and answer the question that follows.
The bar graph shows the exports of cars of type A and B (in ₹ millions) from 2014 to 2018.

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What is the ratio of the total exports of cars of type A in 2016 and 2018 to the total exports of cars of type B in 2015 and 2017?

If Seema invests ₹17,650 in an account that yields 8.5% p.a. simple interest, then how much (to nearest ₹) will she have after 5 years?

The following bar graph shows the total number of youth (in lakhs) and the number of employed youth (in lakhs) in 5 states A, B, C, D and E.
What is the percentage of employed youth in states A and E taken together?

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If the nine-digit number 9m2365n48 is completely divisible by 88, what is the value of (m² × n²), for the smallest value of n, where m and n are natural numbers?