Let $$ 0 < x < 1$$. Then the correct inequality is
SSC CGL Tier-2 01-December-2016 Maths
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Three bells ring at interval of 36 seconds, 40 seconds and 48 seconds respectively. They start ringing together at a particular time. They will ring together after every
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f the sum of the digits of a three digit numberis subtracted from that number, then it will always be divisible by
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Which ofthe following is correct ?
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The greater of the two numbers whose product is 900 and sum exceeds their difference by 30 is
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The smallest fraction, which should be added to the sum of $$ 2 \frac{1}{2} , 3 \frac{1}{3} ,4 \frac{1}{4} and 5\frac{1}{5} $$ to make the result a whole number, is
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Find the cube root of (-13824)
OR
Find the value of $$ \sqrt[3]{-13824} $$
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The sum of three positive numbersis 18 and their product is 162. If the sum of two numbersis equal to the third then the sum of squares of the numbersis
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The sum of three consecutive even numbers is 28 more than the average of these three numbers. Then the smallest of these three numbers is
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In a division sum, the divisor 'd' is 10 times the quotient 'q' and 5 times the remainder'r'. If r = 46, the dividend will be
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A man can do a piece of workin 30 hours. If he works with his son then the same piece of work is finished in 20 hours. If the son works alone he can do the work in
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A water tap fills a tub in 'p' hours and a sink at the bottom empties it in 'q' hours. If p < q and both tap and sink are open, the tank is filled in 'r' hours; then
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John does $$ \frac{1}{2} $$ piece of work in 3 hours, Joe does $$ \frac{1}{4} $$ of the remaining work in 1 hour and George finishes remaining work in 5 hours. How long would it have taken the three working together to do the work ?
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A does $$ \frac{2}{5} $$ of a work in 9 days. Then B joined him and they together completed the remaining work in 6 days. B alone can finish the whole work in
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The daily wagesof A and B respectively are Rs.3.50 and 2.50 . When A finishes a certain work, he gets a total wage of Rs. 63. When B does the same work, he gets a total wage Rs.75. If both of them do it together what is the cost of the work ?
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A man does double the work done by a boy in the same time. The number of days that 3 men and 4 boys will take to finish a work which can be done by 10 men in 8 days is
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The marked price of an article is 30% higher than the cost price. If a trader sells the articles allowing 10% discount to customer, then the gain percent will be
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A merchant marked the price of an article by increasing its production cost by 40%. Now he allows 20%discount and gets a profit of Rs. 48 after selling it. The production cost is
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A watch dealer pays 10% customs duty on a watch which costs Rs.500 abroad. He desires to make a profit of 20% after giving a discount of 25% to the buyer, The marked price should be
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A shopkeeper allows 20% discount on his advertised price and to make a profit of 25% on his outlay. What is the advertised price (in Rs.) on which he gains Rs.6000?
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Rs.2420 were divided among A, B, C so that A: B=5 : 4 and B : C = 9 : 10 then C gets
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49 Kg of blended tea contain Assam and Darjeeling tea in the ratio 5 : 2. Then the quantity of Darjeeling tea is to be added to the mixture to make the ratio of Assam to Darjeeling tea 2 : 1 is
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Among 132 examineesof a certain school, the ratio of successful to unsuccessful students is 9 : 2, Had 4 more students passed, then the ratio of successful to unsuccessful students will be
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Ina regiment the ratio between the numberofofficers to soldiers was 3 : 31 before battle. In a battle 6 officers and 22 soldiers werekilled and theratio became 1 : 13, the number of officers in the regiment before battle was
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Three containers have their volumesin the ratio 3 : 4: 5. They are full of mixtures of milk and water. The mixtures contain milk and water in the ratio of(4:1), (3 : 1) and (5 : 2) respectively. The contents ofall these three containers are poured into a fourth container. The ratio of milk and water in the fourth container is
In what proportion must a grocer mix sugar at Rs.12 a kg and Rs.7 a kg so as to make a mixture worth Rs.8 a kg ?
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Fifteen movie theatres average 600 customers per theatre per day.If six of the theatres close down but the total theatre attendence stays the same,then the average daily attendence per theatre among the remaining theatres is
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The average weight of A, B and C is 45 kg. If the average weight of A and B be 40 kg andthat of B and C be 43 kg, then the weight of B is:
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The batting average for 40 innings of a cricket player is 50 runs. His highest score exceeds his lowest score by 172 runs, If these twoinnings are excluded, the average of the remaining 38 innings is 48 runs. The highest score of the player is
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The average of 7 consecutive numbersis 20. The largest of these numbersis
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Mukesh has twice as much money as Soham, Soham has 50% more moneythan Pankaj. If the average money with them is Rs.110, then Mukesh has
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The average daily income of 7 men, 11 womenand 2 boysis Rs.257.50. If the average daily income of the men is Rs.10 more than that of women and the average daily income of the womenis Rs.10 more than that of boys, the average daily income of a man is
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The profit on selling an article for Rs.425 is the same as the loss on selling it for Rs.355, then the cost price of the article is
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A & B jointly made a profit of Rs.1650 and they decided to share it such that $$ \frac{1}{3} $$ of A's profit is equal to $$ \frac{2}{5} $$of B's profit. Then profit of B is
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4%of the selling price of an article is equal to 5% of its cost price. Again 20% of the selling price is Rs.120 more than 22%ofits cost price. The ratio ofcostprice & selling price is
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Due to 25% fall in the rate of eggs, one can buy 2 dozen eggs morethan before by investing Rs.162. Then the orignal rate per dozen of the eggsis
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Last year Mr. A bought two paintings. This year he sold them for Rs, 20,000 each. On one, he made a 25% profit and on the other he had a 25% loss.Then his net profit or loss is
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A shopkeeper sells rice at 10% profit and uses weight 30% less than the actual measure. His gain percent is
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What % of a day is 30 minutes ?
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A businessman's earning increase by 25%in one year but decreases by 4%in the next. Goingby this pattern, after 5 years, his total earnings would be Rs.72000. Whatis his present earning?
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In an examination 73%of the candidates passed in quantitative aptitude test, 70% passed in General awareness and 64% passedin both. If 6300 failed in both subjects the total number of examinees were
A man spends 75% of his income. His income increases by 20% and his expenditure also increases by 10%. Find the percentage increase in his savings.
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On river, Q is the mid-point between two points P and R on the same bank ofthe river. A boat can go from P to Q and back in 12 hours, and from P to R in 16 hours 40 min. How long would it take to go from R to P ?
A car can finish a certain journey in 10 hours at a speed of 42 kmph. In order to cover the same distance in 7 hours, the speed of the car (km/h) must be increased by
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A man travels 450 km to his home partly by train and partly by car. He takes 8 hrs 40 minsif he travels 240 km bytrain and rest by car. He takes 20 mins moreif he travels 180 km by train and the rest by car. The speed of the car in km/hr is
A train 'B' speeding with 100 kmph crosses another train C, running in the same direction, in 2 mins. If the length of the train B and C be 150m and 250m respectively, what is the speed of the train C (in kmph) ?
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The compound interest on Rs. 30,000 at 7%per annum for n years is Rs. 4347. The value of n is
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If A borrowed Rs. P at x% and B borrowed Rs. Q (>P) at y% per annum at simple interest at the same time, then the amountof their debts will be equal after
A man invested a sum of money at compoundinterest. It amounted to Rs. 2420 in 2 years and to Rs. 2662 in 3 years. Find the sum.
if a sum of money becomes 4000 in 2 yrs and 5500 in 4 yrs 6 months at the same rate of simple interest per annum. Then the rate of simple interest is
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A hollow cylindrical tube 20 cm long is madeofiron andits external and internal diameters are 8 cm and 6 cm respectively. The volume (in cubic cm) of iron used in making the tube is (Take $$ \pi = \frac{22}{7} $$)
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If the areas of three adjacent faces of a rectangular box which meet in a corner are $$ 12 cm^2, 15 cm^2 and 20 cm^2$$ respectively. Then the volume of the box is
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The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundaryof the park at the speed of 12 km/hour completes one round in 8 minutes, then the area of the park is
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If the radius of a right circular cylinder open at both the ends, is decreased by 25% and the height of the cylinder is increased by 25%. Then the curved surface areaofthe cylinder thus formed
A cylindrical pencil of diameter 1.2 cm has one of its end sharpened into a conical shape of height 1.4 cm. The volume of the material removed is
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A rectangular park 60 m long and 40 m wide has two concrete crossroads running in the middle of the park and rest of the park has been used as a lawn. If the area of the lawn is 2109 $$m^2$$ then the width of the road is
Four circles of equal radii are described about the four corners of a square so that each touches two of the other circles. If each side of the square is 140 cm then area of the space enclosed between the circumference of the circle is (take $$\pi = \frac{22}{7}$$)
The amount of concrete required to build a concrete cylindrical pillar whose base has a perimeter 8.8 metre and curved surface area 17.6 sq. metre, is (Take $$\pi = \frac{22}{7}$$)
A hemispherical bowlof internal radius 9 cm, contains a liquid. This liquid is to befilled into small cylindrical bottles of diameter 3 cm and height 4 cm.Then the numberof bottles necessary to empty the bowlis
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A rectangular water tank is 80 m $$x\times$$ 40 m. Water flows into it through a pipe of 40 sq.cm at the opening at a speed of 10 km/hr. The water level will rise in the tank in half an hour is
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A square and a regular hexagon are drawn such that all the vertices of the square and the hexagon are on circle of radius r cm. The ratio of area of the square and the hexagon is
A solid cylinder has the total surface area 231 sq.cm. If its curved surface area is $$\frac{2}{3}$$ of the total surface area, then the volume of the cylinder is
The lateral surface area of frustum of a right circular cone,if the area of its base is $$16 \pi cm^2$$ and the diameter of circular upper surface is 4 cm and slant height 6 cm, will be
The diameter of a sphere is twice the diameter of another sphere, The surface area ofthefirst sphere is equal to the volume of the second sphere, The magnitude of the radius ofthefirst sphereis
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A right circular cylinder having diameter 21 cm & height 38 cm is full of ice cream. The ice cream is to be filled in cones of height 12 cm and diameter 7 cm having a hemispherical shape on the top. The numberof such conesto befilled with ice cream is
The Simplified value of $$ \left(1 - \frac{2xy}{x^2 + y^2}\right) \div \left(\frac{x^3 - y^3}{x - y} - 3xy\right)$$ is
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If $$a + b + c = 0$$ then the value of $$\frac{1}{(a + b)(b + c)} + \frac{1}{(b + c)(c + a)} + \frac{1}{(c + a)(a + b)}$$ is
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If $$x^2 + y^2 + 2x + 1 = 0$$, then the value of $$x^{31} + y{35}$$ is
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If $$x = \frac{\sqrt{5} + 1}{\sqrt{5} - 1} and y = \frac{\sqrt{5} - 1}{\sqrt{5} + 1}$$, the value of $$\frac{x^2 + xy + y^2}{x^2 - xy + y^2}$$ is
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If $$\left(x - \frac{1}{x}\right)^2 = 3$$, then the value of $$x^6 + \frac{1}{x^6}$$ equals
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If $$x^4 + 2x^3 + ax^2 + bx + 9$$ is a perfect square, where a and b are positive real numbers,then the value of a and b are
If $$a^2 + b^2 + c^2 = 16, x^2 + y^2 + z^2 = 25 and ax + by + cz = 20$$, then the value of $$\frac{a + b + c}{x + y + z}$$
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The value of x which satisfies the equation $$\frac{x + a^2 + 2c^2}{b + c} + \frac{x + b^2 + 2a^2}{c + a} + \frac{x + c + 2b^2}{a + b} = 0$$ is
If $$a^3 = 117 + b^3$$ and $$a = 3 + b$$, then the value of $$a + b$$ is:
If $$a + \frac{1}{a} = -2$$ then the value of $$a^{1000} + a^{-1000}$$ is
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$$\triangle ABC$$ is similar to $$\triangle DEF$$. If area of $$\triangle ABC$$ is 9 sq.cm. and area of $$\triangle DEF$$ is 16 sq.cm. and BC = 2.1 cm. Then the length of EF will be
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A chord of a circle is equal to its radius. The angle subtended by this chord at a point on the circumference is
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Let two chords AB and AC of the larger circle touch the smaller circle having same centre at X and Y. Then XY = ?
Let G be the centroid of the equilateral triangle ABC of perimeter 24 cm. Then the length of AG is
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A and B are the centres of two circles with radii 11 cm and 6 cm respectively. A common tangent touches these circles at P & Q respectively. If AB =13 cm, then the length of PQ is
ABC is an isosceles triangle inscribed in a circle. If $$AB = AC = 12\surd5$$ and $$BC = 24 cm$$ then radius of circle is
ABC is an isosceles triangle where AB = AC whichis circumscribed abouta circle. If P is the point where the circle touches the side BC, then which of the following is true ?
If D and E are the mid points of AB and AC respectively of $$\triangle$$ABC, then the ratio of the areas of ADE and BCED is ?
O is the circumcentre of the isosceles $$\triangle$$ABC. Given that AB = AC = 17 cm and BC = 6 cm. The radius of the circle is
$$B_1$$ is a point on the side $$AC$$ of $$\triangle ABC$$ and $$B_1B$$ is joined. line is drawn through A parallel to $$B_1B$$ meeting $$BC$$ at $$A_1$$ and another line is drawn through $$C$$ parallel to $$B_1B$$ meeting $$AB$$ produced at $$C_1$$. Then
The value of the expression $$(1 + \sec 22^\circ + \cot 68^\circ)(1 - \cosec 22^\circ + \tan 68^\circ)$$is
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If $$x \sin^3 \theta + y \cos^3 \theta = \sin \theta \cos \theta and x \sin \theta - y \cos \theta = 0$$, then the value of $$x^2 + y^2$$ equals
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If $$\sec \theta + \tan \theta = m (>1)$$, then the value of $$\sin \theta is (0^\circ < \theta < 90^\circ)$$
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If $$(a^2 - b^2)\sin \theta + 2ab \cos \theta = a^2 + b^2$$, then $$\tan \theta =$$
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A person from the top of a hill observes a vehicle moving towards him at a uniform speed. It takes 10 minutes for the angle of depression to change from $$45^\circ$$ to $$60^\circ$$. After this the time required by the vehicle to reach the bottom of the hill is
If $$2y \cos \theta = x \sin \theta and 2x \sec \theta - y \cosec \theta = 3$$, then the value of $$x^2 + 4y^2$$ is
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From the top of a cliff 100 metre high, the angles of depression of the top and bottom of a tower are $$45^\circ$$ and $$60^\circ$$ respectively. The height of the tower is
A vertical tower stands on a horizontal plane and is surmounted by a vertical flag staff of height h. At a point on the plane, the angle of elevation of the bottom of the flag staff is $$\alpha$$ and that of the top of the flag staff is $$\beta$$. Then the height of the tower is
A man on the top of a tower, standing on the sea-shore, finds that a boat coming towards him takes 10 minutes for the angle of depression to change from $$30^\circ$$ to $$60^\circ$$. How soon the boat reach the sea-shore ?
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The expression of $$\frac{\cot \theta + \cosec \theta - 1}{\cot \theta + \cosec \theta + 1}$$ is equal to
The following pie-chart shows the monthly expenditure of a family on various items. If the family spends Rs. 825 on clothing, answer the question
Whatis the total monthly income of the family ?
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What percent of the total income does the family save
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Whatis the ratio of expenses on food and miscellaneous ?
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Whatis the average of expensesonclothing and rent?
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The ratio of average of expenses on food, clothing and miscellaneous items to the average of expenses on savings and rent is
