N solid metallic spherical balls are melted and recast into a cylindrical rod whose radius is 3 times that of a spherical ball and height is 4 times the radius of a spherical ball. The value of N is:
SSC CGL Tier-2 13th September 2019 Maths
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If x is the remainder when $$3^{61284}$$ is divided by 5 and y is the remainder when $$4^{96}$$ is divided by 6, then what is the value of (2x - y)?
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What is the area (in square units) of the triangular region enclosed by the graphs of the equations x + y = 3, 2x + 5y = 12 and the x-axis?
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The value of $$\sqrt{28+10\sqrt{3}}-\sqrt{7-4\sqrt{3}}$$ is closest to:
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If $$\sec\theta+\tan\theta=p,\left(p>1\right)$$ then $$\frac{\operatorname{cosec}\theta+1}{\operatorname{cosec}\theta-1} = ?$$
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The value $$\cosec(67^\circ + \theta) - \sec(23^\circ - \theta) + \cos 15^\circ \cos 35^\circ \cos 55^\circ \cos 60^\circ \cos 75^\circ$$ is:
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35% of goods were sold at a profit of 65%, while the remaining were sold at x% loss. If the overall loss is 12%, then what is the value of x ? (correct to one decimal place)
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In a circle with centre O, ABCD isa cyclic quadrilateral and AC is the diameter. Chords AB and CD are produced to meet at E. If $$\angle CAE = 34^\circ$$ and $$\angle E = 30^\circ$$, then $$\angle CBD$$ is equal to:
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$$ab(a - b) + bc(b - c) + ca(c - a)$$ is equal to:
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The radius of the base of a right circular cylinder is increased by 20%. By what per cent should its height be reduced so that its volume remains the same as before?
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A is as efficient as B and C together. Working together A and B can complete a work in 36 days and C alone can complete it in 60 days. A and C work together for 10 days. B alone will complete the remaining work in:
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If $$2\cos^2 \theta + 3\sin \theta = 3$$, where $$0^\circ < \theta < 90^\circ$$, then what is the value of $$\sin^2 2\theta + \cos^2 \theta + \tan^2 2\theta + \cosec^2 2\theta$$?
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The radius and the height of a right circular cone are in the ratio 5 : 12. Its curved surface area is 816.4 $$cm^2$$, What is the volume (in $$cm^3$$) of the cone? (Take $$\pi = 3.14$$)
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Given that $$(5x - 3)^3 + (2x + 5)^3 + 27(4 - 3x)^3 = 9(3 - 5x)(2x + 5)(3x - 4)$$, then the value of $$(2x + 1)$$ is:
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The sides of a triangle are 12 cm, 35 cm and 37 cm. What is the circumradius of the triangle
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The base of a right pyramid is an equilateral triangle with area $$16\sqrt{3}cm^2$$. If the area of one of its lateral facesis 30 $$cm^2$$, then its height (in cm) is:
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A vessel contains a 32 litre solution of acid and water in which the ratio of acid and water is 5 : 3, If 12 litres of the solution are taken out and $$7\frac{1}{2}$$ litres of water are added to it, then what is the ratio of acid and water in the resulting solution?
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A sphere of maximum volume is cut out from a solid hemisphere. What is the ratio of the volume of the sphere to that of the remaining solid?
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If $$5\sqrt{5}x^3 + 2\sqrt{2}y^3 = (Ax + \sqrt{2}y)(Bx^2 + 2y^2 + Cxy)$$, then the value of $$(A^2 + B^2 - C^2 )$$ is:
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The value of $$(1 + \cot \theta - \cosec \theta )(1 + \cos \theta + \sin \theta)\sec \theta = ?$$
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S is the incenter of $$\triangle PQR$$. If $$\angle PSR = 125^\circ$$, then the measure of $$\angle PQR$$ is:
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The value of $$0.4\overline{7} + 0.5\overline{03} - 0.3\overline{9} \times 0.\overline{8}$$ is:
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If in $$\triangle ABC$$, D and E are the points on AB and BC respectively such that DE $$\parallel$$ AC, and AD : AB = 3: 8, then (area of $$\triangle BDE$$) : ( area of quadrilateral DECA) = ?
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Monika spends 72% of her income. If her income increases by 20% and savings increase by 15%, then her expenditure increases by: (correct to 1 decimal place)
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A. B and C started a business with their capitals in the ratio 2 : 3 : 5. A increased his capital by 50% after 4 months, B increased his capital by $$33\frac{1}{3}\%$$ after 6 months and C withdrew 50% of his capital after 8 months, from the start of the business. If the total profit at the end of a year was ₹86,800,then the difference between the shares of A and C in the profit was:
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The graph of the equations $$5x - 2y + 1 = 0$$ and $$4y - 3x + 5 = 0$$, interest at the point $$P(\alpha, \beta)$$, What is the value of $$(2\alpha - 3\beta)$$?
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An article was sold at a profit of 14%. Hadit been sold for ₹121 less, a loss of 8% would have been incurred. If the same article would have been sold for ₹536.25, then the profit/loss per cent would have been:
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A shopkeeper allows 18% discount on the marked price of an article and still makes a profit of 23%. If he gains ₹18.40 on the sale of the article, then what is the marked price of the article?
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The value of $$\frac{\sec^2 \theta}{\cosec^2 \theta} + \frac{\cosec^2 \theta}{\sec^2 \theta} - (\sec^2 \theta + \cosec^2 \theta)$$ is:
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The given graph shows the weights of students in a school on a particular day.
The number of students weighing less than 50 kg is what per centless than the number of students weighing 55 kg or more?
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A right prism has height 18 cm and its base is a triangle with sides 5 cm, 8 cm and 12 cm. What is its lateral surface area (in $$cm^2$$) ?
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A can do one-third of a work in 15 days, B can do 75% of the same work in 18 days and C can do the same work in 36 days. B and C work together for 8 days. In how many days will A alone complete the remaining work?
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A person buys 80 kg of rice and sells it at a profit of as much money as he paid for 30 kg. His profit per cent is:
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To cover a distance of 416 km, a train A takes $$2\frac{2}{3}$$ hours more than train B. If the speed of A is doubled, it would take $$1\frac{1}{3}$$ hours less than B, What is the speed (in km/h) of train A?
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The value of $$\frac{2\sqrt{10}}{\sqrt{5} + \sqrt{2} - \sqrt{7}} - \sqrt{\frac{\sqrt{5} - 2}{\sqrt{5} + 2}} - \frac{3}{\sqrt{7} - 2}$$ is:
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The price of oil is increased by 20%. However, its consumption decreased by $$8\frac{1}{3}\%$$. What is the percentage increase or decrease in the expenditure on it?
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The average age of 120 students in a group is 13.56 years. 35% of the number of students are girls and the rest are boys. If the ratio of the average age of boys and girls is 6 : 5, then what is the average age (in years)of the girls?
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The marked price of an article is ₹1500. If two successive discounts, each of x% . on the marked price is equal to a single discount of ₹587.40, then what will be the selling price ofthe articleif a single discount of x% is given on the marked price?
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Two parallel chords on the same side of the centre of a circle are 12 cm and 20 cm long and the radius of the circle is $$5\sqrt{13}$$ cm. What is the distance (in cm) between the chords?
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Study the following bar graph and answer the question given.
The ratio of the total demand of motor cycles of companies A, C and E to the total production of motorcycles of B and C is:
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A circle touches the side BC of $$\triangle$$ABC at D and AB and AC are produced to E and F, respectively. If AB = 10 em, AC = 8.6 cm and BC = 6.4 cm, then BE =?
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If the measure of each exterior angle of a regular polygon is $$\left(51\frac{3}{7}\right)^\circ$$ then the ratio of the number of its diagonals to the number of its sides is:
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Two numbers are in the ratio 3 : 5. If 13 is subtracted from each, the new numbers are in the ratio 10 : 21, If 15 is added to each ofthe original numbers, then the ratio becomes:
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Pipes A and B are filling pipes while pipe C is an emptying pipe. A and B can fill a tank in 72 and 90 minutes respectively. When all the three pipes are opened together, the tank gets filled in 2 hours. A and B are opened together for 12 minutes, then closed and C is opened, The tank will be empty after:
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The LCM of two numbers x and yis 204 times their HCF. If their HCF is 12 and the difference between the numbers is 60, then x + y = ?
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In $$\triangle ABC, BE \perp AC, CD \perp AB$$ and $$BE$$ and $$CD$$ intersect each other at O. The bisectors of $$\angle OBC$$ and $$\angle OCB$$ meet at P. If $$\angle BPC = 148^\circ$$, then what is the measure of $$\angle A$$?
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The value of $$\frac{2(\sin^6 \theta + \cos^6 \theta) - 3(\sin^4 \theta + \cos^4 \theta)}{\cos^4 \theta - \sin^4 \theta - 2 \cos^2 \theta}$$ is:
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The value of $$24 \times 2 \div 12 + 12 \div 6 of 2 \div (15 \div 8 \times 4) of (28 \div 7 of 5)$$ is:
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A person covers 40% of the distance from A to B at 8 km/h, 40% of the remaining distance at 9 km/h and the rest at 12 km/h. His average speed (in km/h) for the journey is:
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A 15 m deep well with radius 2.8 m is dug and the earth taken out from it is spread evenly to form platform of breadth 8 m and height 1.5 m. What will be the length of the platform? (Take $$\pi = \frac{22}{7}$$)
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In $$\triangle PQR, \angle Q > \angle R, PS$$ is the bisectors of $$\angle P$$ and $$PT \perp PQ$$. If $$\angle SPT = 28^\circ$$ and $$\angle R = 23^\circ$$, then the measure of $$\angle Q$$ is:
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25 persons can complete a work in 60 days. They started the work. 10 persons left the work after x days. If the whole work was completed in 80 days, then whatis the value of x ?
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The value of $$\sin^2 64^\circ + \cos 64^\circ \sin 26^\circ + 2 \cos 43^\circ \cosec 47^\circ$$ is:
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A tank is in the form of a cuboid with length 12 m. If 18 kilolitre of water is removed from it, the water level goes down by 30cm. Whatis the width (in m) of the tank?
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In finding the HCF of two numbers by division method, the last divisor is 17 and the quotients are 1. 11 and 2, respectively. What is sum of the two numbers?
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A person invested one-fourth of the suum of ₹25,000 at a certain rate of simple interest and the rest at 4% p.a. higher rate. If the total interest received for 2 years is ₹4,125, whatis the rate at which the second sum was invested?
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The radius of the base of a right circular cylinder is 3 cm and its curved surface area is $$60 \pi cm^2$$ , The volume of the cylinder (in $$cm^3$$) is:
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If $$\frac{3(x^2 + 1) - 7x}{3x} = 6,$$ x ≠ 0, then the value of $$\sqrt{x} + \frac{1}{\sqrt{x}}$$ is:
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Basir’s working hours per day were increased by 15% and his wages per hour were increased by 20%. By how much per cent did his daily earings increase?
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A student was asked to find the value of $$9\frac{4}{9}\div11\frac{1}{3} of \frac{1}{6} + \left(1\frac{1}{3} \times 1\frac{4}{5} \div \frac{3}{5}\right) \times 2\frac{1}{6} of \frac{2}{3} \div \frac{4}{3} of \frac{2}{3}$$. His answer was $$19\frac{1}{4}$$. What is the difference between his answer and the correct answer
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If a 10-digit number 5 4 3 2 y 1 7 4 9 x is divisible by 72, then what is the value of (5x - 4y)?
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What is the remainder when $$(127^{97} + 97^{97})$$ is divided by 32?
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The value of $$\frac{(\sin \theta - \cos \theta)(1 + \tan \theta + \cot \theta)}{1 + \sin \theta \cos \theta} = ?$$
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A, B and C spend 80%, 85% and 75% of their incomes, respectively. If their savings are in the ratio 8 : 9 : 20 and the difference between the incomes of A and C is ₹18,000, then the income of B is:
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If 25% of half of x is equal to 2.5 times the value of 30% of one-fourth of y. then x is what percent more or less than y?
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The value of $$\frac{\sin \theta + \cos \theta - 1}{\sin \theta - \cos \theta + 1} \times \frac{\tan^2 \theta(\cosec^2 \theta -1)}{\sec \theta - \tan \theta}$$ is:
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In an examination, A obtained 10% more marks than B, B obtained 20% more marks than C and C obtained 32% less marks than D. If A obtained 272 more marks than C, then the marks obtained by B is:
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In quadrilateral $$ABCD, \angle C = 72^\circ$$ and $$\angle D = 28^\circ$$. The bisectors of $$\angle A$$ and $$\angle B$$ meet in O. What is the measure of $$\angle AOB$$?
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a, b and c are three fractions such that a < b < c. If c is divided by a, the result is $$\frac{9}{2}$$, which exceeds b by $$\frac{23}{6}$$. The sum of a, b and c is $$\frac{19}{12}$$ , What is the value of (2a + b - c)?
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How many kg of salt costing ₹28 per kg must be mixed with 39.6 kg of salt costing ₹16 per kg, so that selling the mixture at ₹29.90, there is a gain of 15%?
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Study the following bar graph and answer the question given.
The total production of motorcycles of companies C, D and E is what per cent less than the total demand of motor cycles of all the companies during five years?
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A, B and C started a business, Thrice the investment of A is equalto twice the investment of B and also equal to four times the investment of C, If C’s share out of the total profit is ₹4,863,then the share ofA in the profit is:
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Two positive numbers differ by 2001, When the larger number is divided by the smaller number, the quotient is 9 and the remainder is 41. The sum of the digits ofthe larger number is:
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Let $$x = \sqrt[6]{27} - \sqrt{6\frac{3}{4}}$$ and $$y = \frac{\sqrt{45} + \sqrt{605} + \sqrt{245}}{\sqrt{80} + \sqrt{125}}$$, then the value of $$x^2 + y^2$$ is:
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If $$(5x + 2y) : (10x + 3y) = 5 : 9$$, then $$(2x^2 + 3y^2) : (4x^2 + 9y^2) = ?$$
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The average of 18 numbers is 37.5. If six numbers of average X are added to them, then the average of all the numbers increases by one, The value of x is:
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In an office, $$\frac{5}{8}$$ of the total number of employees are males and the rest are females. $$\frac{2}{5}$$ of the number of males are non technical workers while $$\frac{2}{3}$$ of the number of females are technical workers, What fraction of the total number of employees are technical workers?
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A solid cylinder of base radius 12 cm and height 15 cm is melted and recast into m toys each in the shape of a right circular cone of height 9 cm mounted on a hemisphere of radius 3 cm. The value of n is:
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In $$\triangle ABC, D$$ and $$E$$ are the points on $$AB$$ and $$AC$$ respectively such that $$AD \times AC = AB \times AE.$$ If $$\angle ADE = \angle ACB + 30^\circ$$ and $$\angle ABC = 78^\circ$$, then $$\angle A = ?$$
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P and Q are two points on the ground on either side of a pole. The angles of elevation of the top of the pole as observed from P and Q are $$60^\circ$$ and $$30^\circ$$, respectively and the distance between them is $$84\sqrt3$$ m. What is the height (in m) of the pole?
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If in $$\triangle PQR, \angle P = 120^\circ, PS \perp QR$$ at $$S$$ and $$PQ + QS = SR$$. then the measure of $$\angle Q$$ is:
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The given pie-chart shows the break-up of total marks obtained by a student in five subjects A, B, C, D and E. The maximum marks in each subject is 150 and he obtained total of 600 marks.
In how many subjects did the student obtain more than his average score?
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Walking at 60% of his usual speed, a man reaches his destination 1 hour 40 minuteslate, His usual time (in hours) to reach the destination is:
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A man can row a distance of 900 metres against the stream in 12 minutes and returns to the starting point in 9 minutes. What is the speed (in km/h) of the man in still water?
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If $$x + y + z = 6, xyz = -10$$ and $$x^2 + y^2 + z^2 = 30$$, then what is the value of $$(x^3 + y^3 + z^3)$$?
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The value of $$\frac{(4.6)^4 + (5.4)^4 + (24.84)^2}{4.6)^2 + (5.4)^2 + 24.84}$$ is:
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If $$\frac{\sin \theta}{1 + \cos \theta} + \frac{1 + \cos \theta}{\sin \theta} = \frac{4}{\sqrt{3}}, 0^\circ < \theta < 90^\circ$$, then the value of $$(\tan \theta + \sec \theta)^{-1}$$ is:
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Sudha bought 80 articlesat the same price. She sold some of them at 8% profit and the remaining at 12% loss resulting in an overall profit of 6%. The mimber of items sold at 8% profit is:
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The given pie-chart shows the break-up of total marks obtained by a student in five subjects A, B, C, D and E. The maximum marks in each subject is 150 and he obtained total of 600 marks.
The total marks obtained by the student in subjects C and E is approximately how much per cent more than what he obtained in A and D together?
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If the selling price of an article is 32% more than its cost price and the discount offered on its marked price is 12%, then what is the ratio of its cost price to the marked price?
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Study the following bar graph and answer the question given.
The number of companies whose production of motorcycles is equal to or more than the average demand of motorcycles (per year) overfive years is:
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The internal diameter of a hollow hemispherical vessel is 24 cm. It is made of a steel sheet which is 0.5 cm thick, What is the total surface area (in $$cm^2$$) of the vessel?
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The bisector of $$\angle A$$ in $$\triangle ABC$$ meets $$BC$$ in $$D$$. If $$AB = 15 cm, AC = 13 cm$$ and $$BC = 14 cm$$, then $$DC = ?$$
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A certain loan was retumed in two equal half yearly instalments each of ₹6,760, If the rate of interest was 8% p.a., compounded yearly, how much was the interest paid on the loan?
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A sum is divided among A, B, C and D such that the ratio of the shares of A and is 2 : 3, that of B and C is 1 : 2 and that of C and D is 3 : 4. If the difference between the shares of A and is ₹648,then the sum of their shares is:
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The given pie-chart shows the break-up of total marks obtained by a student in five subjects A, B, C, D and E. The maximum marks in each subject is 150 and he obtained total of 600 marks.
What is the difference between the marks obtained by the student in subjects B and D?
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A sector of radius 10.5 cm with the central angle $$120^\circ$$ is folded to form a cone by joining the two bounding radii of the sector. What is the volume (in $$cm^3$$) of the cone so formed?
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A certain sum amounts to ₹4,205.55 at 15% p.a. in $$2\frac{2}{5}$$ years, interest compounded yearly. The sum is:
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In $$\triangle ABD, C$$ is the midpoint of $$BD$$. If $$AB = 10 cm, AD = 12 cm$$ and $$AC = 9 cm$$, then $$BD = ?$$
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A sum of ₹10,500 amounts to ₹13,825 in $$3\frac{4}{5}$$ years at a certain rate per cent per annum simple interest. What will be the simple interest on the same sum for 5 years at double the earlier rate?
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