How many three digit numbers are there in which all the digits are odd?
SSC CGL Tier-2 18-February-2018 Maths
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If the sum of ten different positive integers is 100, then what is the greatest possible number among these 10 numbers?
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If N = 0.369369369369… and M = 0.531531531531…, then what is the value of $$(\frac{1}{N}) + (\frac{1}{M})$$?
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If $$A = \frac{0.216 + 0.008}{0.36 + 0.04 - 0.12}$$ and $$B = \frac{0.729 - 0.027}{0.81 + 0.09 + 0.27}$$, then what is the value of $$(A^2 + B^2)^2?$$
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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 $$A?$$
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If $$56 \times 75 \times 60 \times 84 \times 210 = 2^p \times 3^q \times 5^r \times 7^s$$, then what is the value of $$\left[\frac{(p + q)}{s}\right] + r$$?
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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 $$A - B?$$
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What is the sum of all natural numbers between 100 and 400 which are divisible by 13?
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If the least common multiple of two numbers, 1728 and K is 5184, then how many values of K are possible?
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If $$(3^{33} + 3^{33} + 3^{33})(2^{33} + 2^{33}) = 6^x$$, then what is the value of x?
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Which of the following statement(s) is/are true?
$$I. (65)^{\frac{1}{6}} > (17)^{\frac{1}{4}} > (12)^{\frac{1}{3}}$$
$$II. (17)^{\frac{1}{4}} > (65)^{\frac{1}{6}} > (12)^{\frac{1}{3}}$$
$$III. (12)^{\frac{1}{3}} > (17)^{\frac{1}{4}} > (65)^{\frac{1}{6}}$$
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If $$P = 7 + 4\surd3$$ and $$PQ = 1$$, then what is the value of $$\left( \frac{1}{P^2} \right) + \left(\frac{1}{Q^2}\right)$$?
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If $$x = (\surd5) + 1$$ and $$y = (\surd5) - 1$$, then what is the value of $$\left(\frac{x^2}{y^2}\right) + \left(\frac{y^2}{x^2}\right) + 4[\left(\frac{x}{y}\right) + \left(\frac{y}{x}\right)] + 6$$?
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If $$x = 2 +\surd3, y = 2 - \surd3$$ and $$z = 1$$, then what is the value of $$\left(\frac{x}{yz}\right) + \left(\frac{y}{xz}\right) + \left(\frac{z}{xy}\right) + 2 \left[\left(\frac{1}{x}\right) + \left(\frac{1}{y}\right) + \left(\frac{1}{z}\right)\right]$$?
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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 $$\frac{(a^2 + b^2 + c^2)}{(a + b + c)}$$?
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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 $$xyz - x^2 - y^2 - z^2$$?
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 '$$a$$'?
If $$x^2 - 4x + 1 = 0$$, then what is the value of $$x^9 + x^7 - 194x^5 - 194x^3$$?
If $$x + y = 3$$, then what is the value of $$x^3 + y^3 + 9xy$$?
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$$A = \frac{(x^8 - 1)}{(x^4 + 1)}$$ and $$B = \frac{(y^4 - 1)}{(y^2 + 1)}$$. If $$x = 2$$ and $$y = 9$$, then what is the value of $$A^2 + 2AB + A(A+B)^2$$?
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If $$x - 4y = 0$$ and $$x + 2y = 24$$, then what is the value of $$\frac{(2x + 3y)}{(2x - 3y)}$$?
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If $$(\frac{x}{a}) + (\frac{y}{b}) = 3$$ and $$(\frac{x}{b}) - (\frac{y}{a}) = 9$$, then what is the value of $$\frac{x}{y}$$?
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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 $$\angle QOR + \angle POR$$?
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In a triangle $$PQR$$, $$\angle PQR = 90$$°, $$PQ$$ = 10 cm and $$PR$$ = 26 cm, then what is the value (in cm) of inradius of incircle?
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In the given figure, if $$\frac{QR}{XY} = \frac{14}{9}$$ and $$PY = 18$$ cm, then what is the value (in cm) of $$PQ$$ ?
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In a triangle $$PQR, PX, QY$$ and $$RZ$$ be altitudes intersecting at $$O$$. If $$PO$$ = 6 cm, $$PX$$ = 8 cm and $$QO$$ = 4 cm, then what is the value (in cm) of $$QY$$?
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?
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 ?
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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 $$\angle COD$$?
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 $$\angle CAB$$?
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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 $$\angle AXP$$?
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In the given figure. $$E$$ and $$F$$ are the centers of two identical circles. What is the ratio of area of triangle $$AOB$$ to the area of triangle $$DOC$$?
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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?
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 $$POQ$$?
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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?
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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?
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 $$PQR$$?
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A man is running at the speed of 20 km/hr. What is time (in seconds) taken by man to cover one round of a circular garden of radius 350 metres?
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In the given figure, four identical semicircles are drawn in a quadrant. XA = 7 cm. What is the area (in $$cm^2$$) of shaded region?
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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?
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?
A cylinder of radius 4.5 cm and height 12 cm just fits in another cylinder completely with their axis perpendicular. What is the radius (in cm) of second cylinder?
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?
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?
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?
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A solid cube is cut into 27 identical cubes. What is the percentage increase in the total surface area?
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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?
What is the value of $$[(\sin 7x - \sin 5x) \div (\cos 7x + \cos 5x)] - [(\cos 6x - \cos 4x) \div (\sin 6x + \sin 4x)]$$?
What is the value of $$[(\cos^3 2\theta + 3 \cos 2\theta) \div (\cos^6 \theta - \sin^6 \theta)]$$?
What is the value of $$\tan \left(\frac{\pi}{4} + A\right) \times \tan \left(\frac{3\pi}{4} + A\right)?$$
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What is the value of $$\left[(\sec 2\theta + 1)\sqrt{\sec^2 \theta -1}\right] \times \frac{1}{2} (\cot \theta - \tan \theta)$$
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What is the value of sin $$(630$$° + $$A) + \cos A$$?
What is the value of $$[(\sin 59$$° $$\cos 31$$° + $$\cos 59$$° $$\sin 31$$°) $$\div$$ ($$\cos 20$$° $$\cos 25$$° - $$\sin 20$$° $$\sin 25$$°$$)]$$?
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What is the value of $$\cos (90 - B) \sin (C - A) + \sin (90 + A) \cos (B + C) - \sin (90 - C) \cos (A + B)$$?
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?
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?
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.
What are the average sales of milk (in litres) by the salesmen A in all the given states?
What is the respective ratio of sales of milk in state P and Q by salesmen B and the sales of milk in state R and T by salesmen A?
What will be the central angle (in degrees) formed by the average sale of milk in state Q, T and S together?
What will be difference (in litres) in the sale of milk in state T by salesmen B and the total sale of milk in state R and S together?
What is the difference (in litres) between the sale of milk in state R by salesmen A and the sale of milk in the same state by the salesmen B?
For the following questions answer them individually
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?
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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?
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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)?
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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)?
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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?
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A can paint a house in 45 days and B can do it in 15 days. Along with C, they did the job in 5 days only. Then, C alone can do the job in how many days?
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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?
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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?
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Giving two successive discounts of 40% is equal to giving one discount of ________%.
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If a website is selling smartphone at Rs 18,000 which is marked at Rs 25,000, then what is the discount (in %) at which the smartphone is being sold?
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If on an item there is 12% discount on the marked price of Rs 10,000 but the item is sold at Rs 8,360 only then what additional discount (in %) did the customer get?
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A shopkeeper marks up his wares by 125% and offers 25% discount. What will be the selling price if the cost price (in Rs) is Rs 640?
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Priya's marks in History and Geography are in the ratio 5 : 7. If she got 14 marks more in Geography than in History, what are her History marks?
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The ratio of present ages of Rahul and his sister is 3 : 4. Before 10 years the ratio of their ages was 13:19. What is Rahul's present age (in years)?
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What is the third proportional to 9 and 15?
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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)?
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If Rs 7,800 is to be divided between A, B and C in the ratio $$\frac{1}{2} : \frac{1}{3} : \frac{1}{4}$$, then how much share will B get (in Rs)?
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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?
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The average weight of P, Q and R is 71 kg. If the average weight of P and Q be 66 kg and that of Q and R be 76.5 kg, then the weight (in kg) of Q is.
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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?
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?
Average of all even numbers between 104 and 148 is __________.
A vendor buys bananas at 4 for Rs 3 and sells at 3 for Rs 4. What will be the result?
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)?
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?
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)?
0.09% of 25% of 1200 is equal to____________.
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When a number is increased by 20, it becomes 116% of itself. What is the number?
Two numbers are 50% and 75% lesser than a third number. By how much percent is the second number to be enhanced to make it equal to the first number?
Price of petrol increased from Rs 60/liter to Rs 75/liter. How much should the consumption of petrol be reduced (in %) so as to increase expenditure by only 10%?
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A train has to cover a distance of 900 km in 25 hours. What should be its average speed in meters/second?
If a boat goes upstream at a speed of 18 km/hr and comes back the same distance at 30 km/hr. What is the average speed (in km/hr) for the total journey?
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?
Excluding stoppages, the speed of a bus is 60 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour?
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?
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 %)?
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?
What is the difference (in Rs) in Compound interest earned in 1 year on a sum of Rs 10,000 at 40% per annum compounded quarterly and annually?
