SSC CGL Tier-2 18-February-2018 Maths

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For the following questions answer them individually
SSC CGL Tier-2 18-February-2018 Maths - Question 3

If N = 0.369369369369… and M = 0.531531531531…, then what is the value of $$(\frac{1}{N}) + (\frac{1}{M})$$?

SSC CGL Tier-2 18-February-2018 Maths - Question 5

If $$A = \frac{1}{1 \times 2} + \frac{1}{1 \times 4} + \frac{1}{2 \times 3} + \frac{1}{4 \times 7} + \frac{1}{3 \times 4} + \frac{1}{7 \times 10}...$$ upto 20 terms, then what is the value of $$A?$$

SSC CGL Tier-2 18-February-2018 Maths - Question 7

If $$A = 3\frac{1}{4} \times 4 \frac{1}{4} \div 34 - \frac{47}{32} + \frac{47}{16}$$ and $$B = 2\frac{1}{2} \times 5 \frac{1}{2} \div 55 - \frac{11}{10}$$, then what is the value of $$A - B?$$

SSC CGL Tier-2 18-February-2018 Maths - Question 11

Which of the following statement(s) is/are true?

$$I. (65)^{\frac{1}{6}} > (17)^{\frac{1}{4}} > (12)^{\frac{1}{3}}$$
$$II. (17)^{\frac{1}{4}} > (65)^{\frac{1}{6}} > (12)^{\frac{1}{3}}$$
$$III. (12)^{\frac{1}{3}} > (17)^{\frac{1}{4}} > (65)^{\frac{1}{6}}$$

SSC CGL Tier-2 18-February-2018 Maths - Question 13

If $$x = (\surd5) + 1$$ and $$y = (\surd5) - 1$$, then what is the value of $$\left(\frac{x^2}{y^2}\right) + \left(\frac{y^2}{x^2}\right) + 4[\left(\frac{x}{y}\right) + \left(\frac{y}{x}\right)] + 6$$?

SSC CGL Tier-2 18-February-2018 Maths - Question 14

If $$x = 2 +\surd3, y = 2 - \surd3$$ and $$z = 1$$, then what is the value of $$\left(\frac{x}{yz}\right) + \left(\frac{y}{xz}\right) + \left(\frac{z}{xy}\right) + 2 \left[\left(\frac{1}{x}\right) + \left(\frac{1}{y}\right) + \left(\frac{1}{z}\right)\right]$$?

SSC CGL Tier-2 18-February-2018 Maths - Question 15

A root of equation $$ax^2 + bx + c = 0$$ (where $$a, b$$ and $$c$$ are rational numbers) is $$5 + 3\surd3$$. What is the value of $$\frac{(a^2 + b^2 + c^2)}{(a + b + c)}$$?

SSC CGL Tier-2 18-February-2018 Maths - Question 16

If $$x = (\frac{a}{b}) + (\frac{b}{a}), y = (\frac{b}{c}) + (\frac{c}{b})$$ and $$z = (\frac{c}{a}) + (\frac{a}{c})$$, then what is the value of $$xyz - x^2 - y^2 - z^2$$?

SSC CGL Tier-2 18-February-2018 Maths - Question 17

If $$\left[a + (\frac{1}{a})\right]^2 - 2\left[a - (\frac{1}{a})\right] = 12$$, then which of the following is a value of '$$a$$'?

SSC CGL Tier-2 18-February-2018 Maths - Question 20

$$A = \frac{(x^8 - 1)}{(x^4 + 1)}$$ and $$B = \frac{(y^4 - 1)}{(y^2 + 1)}$$. If $$x = 2$$ and $$y = 9$$, then what is the value of $$A^2 + 2AB + A(A+B)^2$$?

SSC CGL Tier-2 18-February-2018 Maths - Question 22

If $$(\frac{x}{a}) + (\frac{y}{b}) = 3$$ and $$(\frac{x}{b}) - (\frac{y}{a}) = 9$$, then what is the value of $$\frac{x}{y}$$?

SSC CGL Tier-2 18-February-2018 Maths - Question 23

In the given figure, $$OX, OY$$ and $$OZ$$ are perpendicular bisectors of the three sides of the triangle. If $$\angle QPR = 65^\circ$$ and $$\angle PQR = 60^\circ$$, then what is the value (in degrees) of $$\angle QOR + \angle POR$$? 

SSC CGL Tier-2 18-February-2018 Maths - Question 27

A line cuts two concentric circles. The lengths of chords formed by that line on the two circles are 4 cm and 16 cm. What is the difference (in $$cm^2$$) in squares of radii of two circles?

SSC CGL Tier-2 18-February-2018 Maths - Question 28

In the given figure, a circle touches the sides of the quadrilateral $$PQRS$$. The radius of the circle is 9 cm. $$\angle RSP = \angle SRQ = 60^\circ$$ and $$\angle PQR = \angle QPS = 120^\circ$$. What is the perimeter (in cm) of the quadrilateral ?

SSC CGL Tier-2 18-February-2018 Maths - Question 29

In the given figure, from the point $$P$$ two tangents $$PA$$ and $$PB$$ are drawn to a circle with centre $$O$$ and radius 5 cm. From the point $$O, OC$$ and $$OD$$ are drawn parallel to $$PA$$ and $$PB$$ respectively. If the length of the chord $$AB$$ is 5 cm. then what is the value (in degrees) of $$\angle COD$$?

SSC CGL Tier-2 18-February-2018 Maths - Question 30

In the given figure, $$AB$$ is a diameter of the circle with centre $$O$$ and $$XY$$ is the tangent at a point $$C$$. If $$\angle ACX = 35^\circ$$. then what is the value (in degrees) of $$\angle CAB$$?

SSC CGL Tier-2 18-February-2018 Maths - Question 31

In the given figure. $$PQ$$ is a diameter of the semicircle $$PABQ$$ and $$O$$ is its center. $$\angle AOB = 64^\circ$$. $$BP$$ cuts $$AQ$$ at $$X$$. What is the value (in degrees) of $$\angle AXP$$?

SSC CGL Tier-2 18-February-2018 Maths - Question 33

In the given figure, in a right angle triangle $$ABC, AB = 12 cm$$ and $$AC = 15 cm$$. A square is inscribed in the triangle. One of the vertices of square coincides with the vertex of triangle. What is the maximum possible area (in $$cm^2$$) of the square?

SSC CGL Tier-2 18-February-2018 Maths - Question 34

In the given figure, $$PQRS$$ is a square of side 8 cm. $$\angle PQO = 60$$°. What is the area (in $$cm^2$$) of the triangle $$POQ$$?

SSC CGL Tier-2 18-February-2018 Maths - Question 35

In the given figure. two squares of sides 8 cm and 20 cm are given. What is the area (in $$cm^2$$) of the shaded part?

SSC CGL Tier-2 18-February-2018 Maths - Question 36

The area of a regular hexagon is equal to the area of the square. What is the ratio of the perimeter of the regular hexagon to the perimeter of square?

SSC CGL Tier-2 18-February-2018 Maths - Question 37

In the given figure, $$ABCDEF$$ is a regular hexagon of side 12 cm. $$P, Q$$ and $$R$$ are the mid points of the sides $$AB, CD$$ and $$EF$$ respectively. What is the area (in $$cm^2$$) of triangle $$PQR$$?

SSC CGL Tier-2 18-February-2018 Maths - Question 40

A regular hexagonal base prism has height 8 cm and side of base is 4 cm. What is the total surface area (in $$cm^2$$) of the prism?

SSC CGL Tier-2 18-February-2018 Maths - Question 41

A cube is placed inside a cone of radius 20 cm and height 10 cm, one of its face being on the base of the cone and vertices of opposite face touching the cone. What is the length (in cm) of side of the cube?

SSC CGL Tier-2 18-February-2018 Maths - Question 43

A right circular cylinder has height 28 cm and radius of base 14 cm. Two hemispheres of radius 7 cm each are cut from each of the two bases of the cylinder. What is the total surface area (in $$cm^2$$) of the remaining part?

SSC CGL Tier-2 18-February-2018 Maths - Question 44

Two spheres of equal radius are taken out by cutting from a solid cube of side $$(12 + 4\surd3)$$ cm. What is the maximum volume (in $$cm^3$$) of each sphere?

SSC CGL Tier-2 18-February-2018 Maths - Question 45

Three toys are in a shape of cylinder, hemisphere and cone. The three toys have same base. Height of each toy is $$2\surd2$$ cm. What is the ratio of the total surface areas of cylinder, hemisphere and cone respectively?

SSC CGL Tier-2 18-February-2018 Maths - Question 47

A regular square pyramid has side of its base 20 cm and height 45 cm is melted and recast into regular triangular pyramids of equilateral base of side 10 cm and height $$10\surd3$$ cm. What are the total numbers of regular triangular pyramid?

SSC CGL Tier-2 18-February-2018 Maths - Question 53

What is the value of $$[(\sin 59$$° $$\cos 31$$° + $$\cos 59$$° $$\sin 31$$°) $$\div$$ ($$\cos 20$$° $$\cos 25$$° - $$\sin 20$$° $$\sin 25$$°$$)]$$?

SSC CGL Tier-2 18-February-2018 Maths - Question 55

Two trees are standing along the opposite sides of a road. Distance between the two trees is 400 metres. There is a point on the road between the trees. The angle of depressions of the point from the top of the trees are 45° and 60°. If the height of the tree which makes 45°angle is 200 metres, then what will be the height (in metres) of the other tree?

SSC CGL Tier-2 18-February-2018 Maths - Question 56

A tower stands on the top of a building which is 40 metres high. The angle of depression of a point situated on the ground from the top and bottom of the tower are found to be 60° and 45° respectively. What is the height (in metres) of tower?

SSC CGL Tier-2 18-February-2018 Maths - Question 57

From a point P, the angle of elevation of a tower is such that its tangent is $$\frac{3}{4}$$. On walking 560 metres towards the tower the tangent of the angle of elevation of the tower becomes $$\frac{4}{3}$$. What is the height (in metres) of the tower?

Read the information given in the table below and answer the questions:

The table below shows the sales of milk in six different states as a percentage of total sales. In each state only two milkmen A and B sell the milk. The table below shows the sales of salesman A as percentage of total sale of milk in each state. The total sales of milk is 200000 litres.

For the following questions answer them individually
SSC CGL Tier-2 18-February-2018 Maths - Question 63

A beaker contains acid and water in the ratio 1 : x. When 300 ml of the mixture and 150 ml of water are mixed, the ratio of acid and water becomes 2 : 5. What is the value of x?

SSC CGL Tier-2 18-February-2018 Maths - Question 64

A mixture is composed of 11 parts of pure milk and 2 parts of water. If 35 litres of water were added to the mixture then the new mixture will contain twice as much pure milk as water, then how many litres of pure milk does the original mixture contain?

SSC CGL Tier-2 18-February-2018 Maths - Question 65

A starts a taxi service by investing Rs 25 lakhs. After 3 months, B joins the business by investing Rs 40 lakhs then 4 months after B joined, C too joins them by investing Rs 50 lakhs. One year after A started the business they make Rs 2,73,000 in profit. What is C's share of the profit (in Rs)?

SSC CGL Tier-2 18-February-2018 Maths - Question 66

A, B and C invest in a business in the ratio 4 : 5 : 7. C is a sleeping partner, so his share of profits will be half of what it would have been if he were a working partner. If they make Rs 36,000 profit of which 25% is reinvested in the business, how much does B get (in Rs)?

SSC CGL Tier-2 18-February-2018 Maths - Question 67

A can do a work in 36 days and B in 12 days. If they work on it together for 3 days, then what fraction of work is left?

SSC CGL Tier-2 18-February-2018 Maths - Question 69

A,B and C together can finish a task in 7.5 days. C is thrice as productive as A and B alone can do the task in 15 days. In how many days can A and C do the job if B goes on leave?

SSC CGL Tier-2 18-February-2018 Maths - Question 70

A, B and C can do job in 9, 12 and 36 days respectively if they worked alone. A leaves after they have worked together for 3 days. In how many days can B and C do the rest of the job?

SSC CGL Tier-2 18-February-2018 Maths - Question 78

According to the will, the wealth of Rs 11,50,000 was to be divided between the son and the daughter in the ratio $$\frac{2}{3} : \frac{5}{4}$$. How much share did the son get (in Rs lakhs)?

SSC CGL Tier-2 18-February-2018 Maths - Question 80

Bunty had candies and chewing gums in his sweet box in the ratio 7 : 13. After he has eaten 8 candies and 11 chewing gums the ratio became 1 : 2. How many candies does he have now?

SSC CGL Tier-2 18-February-2018 Maths - Question 82

Rita buys 5 sarees at an average cost of Rs 2250. If she buys three more sarees at an average cost of Rs 2750, what will be the average (in Rs) of all the sarees she buys?

SSC CGL Tier-2 18-February-2018 Maths - Question 83

In a one day match of 50 overs in an innings the team A had a run rate of 5.3 runs per over. Team B is playing and 5 overs are left and the required run rate to tie the match is 7.2 per over to match the score of Team A. What is team B's score?

SSC CGL Tier-2 18-February-2018 Maths - Question 86

A wholesaler sells a watch to a retailer at a profit of 8% and the retailer sells it to a customer at a profit of 12%. If the customer pays Rs. 8,448 what had it cost (approximately) to the wholesaler (in Rs)?

SSC CGL Tier-2 18-February-2018 Maths - Question 87

A trader had 2000 kgs of rice. He sold a part of it at 10% profit and the rest at 16% profit, so that he made a total profit of 14.2%. How much rice (in kg) did he sell at 10% profit?

SSC CGL Tier-2 18-February-2018 Maths - Question 88

A used car dealer sells a car for Rs 7.6 lakhs and makes some loss. If he had sold it for Rs 9.2 lakhs his profit would have been thrice his loss. What was the cost price of the car (in Rs lakhs)?

SSC CGL Tier-2 18-February-2018 Maths - Question 95

Two cyclists A and B start cycling at 21 km/hr and 24 km/hr towards each other. They meet after 1 hour and 12 minutes. How far (in km) were they from each other when they started?

SSC CGL Tier-2 18-February-2018 Maths - Question 97

If in 3 years at simple interest the principal increases by 15%. What will be the approximate compound interest earned (in Rs lakhs) on Rs 15 lakhs in 3 years at the same rate?

SSC CGL Tier-2 18-February-2018 Maths - Question 98

If the amount received at the end of $$2^{nd}$$ and $$3^{rd}$$ year at compound Interest on a certain Principal is Rs 9,600 and Rs 10,272 respectively, what is the rate of interest (in %)?

SSC CGL Tier-2 18-February-2018 Maths - Question 99

A invested an amount of x rupees in a bank for 2 years which gave 5% interest in year 1 and 6% interest in year 2. The amount received after 2 years is Rs 24,486. What is the value of x?

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