$$ \frac{6^2 + 7^2 + 8^2 + 9^2 + 10^2}{\sqrt{7} + 4\sqrt{3} - \sqrt{4} + 2\sqrt{3}} $$ is equal to
SSC CGL Tier-2 25-October-2015 Maths
For the following questions answer them individually
The bar graph given below shows the percentage distribution of the total production of a car manufacturing company into various models over two years.
Percentage of Six different types of Cars manufactured by a Company over Two Years
The total producton of Type P vehicles in the years 2008 and 2011 is what percent of total production of Type Q vehicles in 2010 and 2014?
The total production of Type P vehicles in the years 2008 and 2011 is what percent of total production of Type Q vehicles in 2010 and 2014?
Approximate percentage decrease in production of Type Q vehicles from 2010 to 2011 is
The ratio of total production of Type P vehicles to total production of Type Q vehicles over the years is
In how many of the given years, was the production of Type P vehicles of the company more than the average production of this type vehicles in the given years?
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For the following questions answer them individually
If $$ 3 ( a^2 + b^2 + c^2) = ( a + b + c)^2 $$, then the relation between a,b and c is
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A car covers four successive 7 km distances at speeds of 10 km/hour, 20 km/hour, 30 km/hr, 60 km/hour respectively. Its average speed over this distance is
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A cylinder with base radius 8 cm and height 2 cm is melted to form a cone of height 6 cm, The radius of the cone will be
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A dealer fixed the price of an article 40% above the cost of production. While selling it he allows a discount of 20% and makes a profit of 48. The cost of production (in %) of the article is
Average of n numbers is a. Thefirst number is increased by 2, second one is increased by 4, the third one is increased by 8 and so on. The average of the new number is
If $$ x = a sin\theta - b cos \theta, y = a cos \theta + b sin \theta $$ , then which of the following is true?
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Let $$ x = \frac{\sqrt{13} + \sqrt{11}}{\sqrt{13} - \sqrt{11}} and y = \frac{1}{x} $$, then the value of $$ 3x^2 - 5xy + 3y^2 is $$
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If 64 buckets of water are removed from a cubical shaped water tank completely filled with water, 1/3 of the tank remains filled with water. The length of each side of the tank is 1.2 m. Assuming that all buckets are of the same measures then the volume (in litres) of water contained by each bucketis
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In trapezium ABCD,AB|| CD and AB = 2CD.Its diagonals intersect at O. If the area of $$ \triangle AOB = 84 cm^2$$, then the area of $$ \triangle $$COD is equalto
latek
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Water tax is increased by 20% but its consumption is decreased by 20%. Then the increase or decrease in the expenditure of the money is
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A number when divided by 361 gives a remainder 47. If the same number is divided by 19, the remainder obtained is
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If $$ \left(\frac{p^{-1} q^2}{p^3 q^{-2}}\right) + \left(\frac{p^{5} q^{-3}}{p^{-2} q^{3}}\right)^\frac{1}{3} = p^a q^b $$, then the value of a + b, where p and q are different positive primes, is
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In triangle ABC, DE || BC where D is a point on AB and is a point on AC. DE divides the area of A ABC into two equal parts. Then DB : AB is equal to
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A and B have their monthly incomes in the ratio 8:S, While their monthly expenditures are in the ratio S : 3. If they have saved = 12,000 and & 10,000 monthly respectively, then the difference in their monthly income is
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ABCDis a cyclic quadrilateral, AB and DC when produced meet at P, if PA = 8 cm, PB = 6 cm, PC = 4 cm, then the length (in cm) of PDis
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In a school there were 1554 students and the ratio of the number of the boys and girls was 4 : 3, After few days, 30 girls joined the school but few boys left; as a result the ratio of the boys and girls became 7 : 6. The number of boys who left the school is
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If $$ 7sin^2 \theta + 3cos^2\theta = 4 $$, then the value of $$ tan \theta is ( \theta $$ is acute)
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If $$ (Bx — 2y) : (2x + 3y) = 5: 6,$$ then one of value of $$ \left(\frac{\sqrt[3]{x} + \sqrt[3]{y}}{{\sqrt[3]{x} - \sqrt[3]{y}}}\right)^2 $$ is?
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If $$ \tan A = n \tan B and \sin A = m \sin B,$$ then the value of $$ \cos^2 A$$ is
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In an office, 40% of the staff is female. 70%of the female staff and 50% of the male staff are married, The percentage of the unmarried staff in the office is
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In an examination average mark obtained by the girls of a class is 85 and the average mark obtained by the boys of the same class is 87. If the girls and boys are in the ratio 4 : 5, average marks of the whole class (approx.) is closest to
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Articles are marked at a price which gives a profit of 25%. After allowing a certain discount the profit reduces to $$ 12\frac{1}{2} \% $$. The discount percent is
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If \sin A + \sin^A = 1,$$ then the value of $$ \cos^A + \cos^4 A is
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A manufacturer fixes his selling price at 33% over the cost of production. If cost of production goes up by 12% and manufacturer raises his selling price by 10%, his percentage profit is
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A boat moves downstream at the rate of 1 km in $$ 7\frac{1}{2} $$ minutes and upstream at the rate of 5 km an hour, What is the speed (in km/hour) of the boat in the still water?
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The greatest number among $$ 3^{50}, 4^{40}, 5^{30}, 6^{20}$$ is
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Give that the ratio of altitudes of two triangles is 4 : 5, ratio of their areas is 3: 2. The ratio of their corresponding bases is
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If $$ \sec \theta - \tan \theta = \frac{1}{\sqrt{3}} $$ then value of $$ \sec\theta \tan \theta$$ is
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A man sells an article at 5% above its cost price.\f he had bough tit at 5% less than what he had paid for it and sold it at 2 less, he would have gained 10%. The cost price of the article is
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The value of $$ \frac{(0.67 \times 0.67 \times0.67) \times (0.33 \times 0.33 \times 0.33)}{(0.67 \times 0.67) \div (0.67 \times 0.33) \div (0.33 \times 0.33)} $$
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If a +b =1, find the value of $$ a^3 + b^3 - ab - (a^2 - b^2)^2 $$
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AB and CD are two parallel chords of a circle of lengths 10 cm and 4 cm respectively. If the chords are on the same side of the centre and the distance between them is 3 cm, then the diameter of the circle is
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Let x be the least number, which when divided by 5, 6, 7 and 8 leaves a remainder 3 in each case but when divided by 9 leaves no remainder. The sum of digits of x is
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Three science classes A, B and C take a Life Science test. The average score of class A is 83. The average score of class B is 76. The average score of class C is 85. The average score of class A and B is 79 and average score of class B and CG is 81. Then the average score of classes A, B and C is.
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Two blends of a commodity costing ₹35 and ₹40 per kg respectively are mixed in the ratio 2:3 by weight. If one-fifth of the mixture is sold at ₹46 per kg and the remaining at the rate of ₹55 per kg, the profit percent is
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If$$x^{2}+ y^{2}+ z^{2} $$= xy + yx + zx, then the value of $$\frac{3x^{4}+7y^{4}+5z^{4}}{5x ^{2}y^{2}+7y ^{2}z^{2}+3z^{2}x^{2}}$$
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Ram solid two horses at the same price, In one he gets a profit 10% and in the other he gets a loss of 10%. Then Ram gets
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A and B can do a given piece of work in 8 days, Band C can do the same work in 12 days and A, B, C together complete it in 6 days. Number of days required to finish the work by A and C is
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Pipe A can fill an empty tank in 6 hours and pipe B in 8 hours. If both the pipes are opened and after 2 hours pipe A is dosed, how much time B will take to fill the remaining tank?
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There is a number consisting of two digits, the digit in the units place is twice that in the tens place and if 2 be subtracted from the sum of the digits, the difference is equal to$$ \frac{1}{6}$$ thof the number. The number is
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The value of
$$ cot41^\circ. cot42^\circ. cot43^\circ.co44. cot45^\circ. cot46^\circ.cot47^\circ.cot48^\circ. cot49^\circ $$
A man purchases some orangesat the rate of 3 for 40 and the same quantity at 5 for £60.If he sells all the oranges at the rate of 3 for %50,find his gain orloss percent(to the nearest integer).
The perimeter of a rhombus is 60 cm and one ofits diagonal is 24cm. The area (in sq.cm) of therhombus is
A sum of money is paid back in two annual instalments of %17,640 each, allowing 5% compound interest compounded annually. The sum borrowed was
A man starts from a place P and reaches the place Q in 7 hours. He travels $$\frac{1}{4}$$ th of the distance at 10 km/hour and the remaining distance at 12 km/hour. The distance, in kilometre, between P and Qis
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If O is the circumcentre of a tnangle ABC lying inside the triangle, then equal to
The simple interest on a sum of money is$$\frac{8}{25}$$ of the sum. If the number of years is numerically half the rate percent per annum, then the rate percent per annum is
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. In $$ \triangle$$ ABC ,$$ \angle BAC=$$90^\circ$$ and $$AD \perp BC$$.If BD= 3 cm and CD= 4 cm then the length (in cms) of AD is
Three glasses of equal volume contains acid mixed with water, The ratio of acid and water are 2: 3,3: 4 and 4: 5 respectively. Contents of these glasses are poured in a large vessel. The ratio of acid and water in the large vessel is
IfA: B=2: 3 and B: C = 3: 7 thenA+B:B+C:C+Ais
The numerical values of the volume and the area of the lateral surface of a right circular cone are equal. If the height of the cone be h and radius, be r, then the value of $$\frac{1}{h^{2}}$$+$$\frac{1}{r^{2}}$$ is
Two places P and Q are 162 km apart. A train leaves P for Q and simultaneously another train leaves Q for P. They meet at the end of 6 hours. If the former train travels 8km/hour faster then the other, then speed of train from Qis
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If $$tan\theta-cot\theta=0$$ and $$\theta$$ is positive acute angle then the value of $$ \frac{tan(\theta+15)}{tan(\theta-15)}$$
The portion of a ditch 48 m long, 16.5 m wide and 4 m deep that can be filled with stones and earth available during excavation of a tunnel, cylindrical in shape, of a diameter 4 m and length S6 mis
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If $$ (x^{3}-y^{3}):(x^{2}+xy+y^{2})$$=5:1 and $$(x^{2}-y^{2}):(x-y)$$=7:1 then the value of 2x:3y equals
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If x=$$a^{\frac{1}{2}}+a^{\frac{-1}{2}}$$, y=$$a^{\frac{1}{2}}-a^{\frac{-1}{2}}$$ then the value of$$ (x^{4}-x^{2}y^{2}-1)+(y^{4}-x^{2}y^{2}+1)$$
The marked price of a tape recorder is $12,600. A festival discount of 5%is allowed onit. Further for cash payment, a second discount of 2%is given. The cash payment, in rupees, that is to be made for buying it is
A man walks at the rate of Skm/hour, he misses a train by 7 minutes. However,if he walks at the rate of Gkm/hour, he reaches the station 5 minutes before the arrival of the train. The distance covered by him to reach the station is
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If $$x-\sqrt{3}-\sqrt{2}=0$$ and $$y-\sqrt{3}+\sqrt{2}=0$$ then the value of $$(x^{3}-20\sqrt{2})-(y^{3}+2\sqrt{2})$$
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The radil of two solid iron spheres are 1 cm and6 cm respectively. A hollow sphere is made bymelting the two s pheres. If the external radius of the hollow sphere is 3 cm, then its thickness (in cm) is
There is a wooden sphere of radius 6 $$\sqrt{3}$$ cm. The surface area of the largest possible cube cut outfrom the sphere will be
If 60% of A = 30 % of B , B = 40 % of C and C = x % of A, then value of x is
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Aand B can do piece of work in 30 and 36 days respectively. They began the work together but A
leaves after some days and B finished the remaining work in 25 days. After how many days did A leave?
A sum of money placed at compound interest doubles itself in S years. It will amount to eight times Itself at the same rate of interest in
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Quadnlateral ABCD is circumscribed about a
circle. If the lengths of AB, BC, CD are 7 cm, 85
cm and 9.2 cm respectively, then the length
{in cm) of DA i
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A right prism has a triangular base whose sides are 13 cm, 20 cm and 21 cm. If the altitude of the prism is 9 cm, then its volume is
300 gramsof sugar solution has 40% of sugar in it. How much sugar should be added to make it 50 % in the solution?
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The area of isosceles trapezium is 176 $$cm^{2}$$ and the height h is$$ \frac{2}{11}$$ th of the sum of its parallel sides if the ratio of the length of the parallel sides is 4:7, then the length of a diagonal {in cm) is
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A and B are centres of twocircles of radii 11 cm and 6 cm, respectively. PQ is a direct common tangent to the circles. If $$\bar {AB}$$ = 13 cm, then length of $$\bar {PQ}$$ will be
A, B and C can do work separately in 16, 32 and48 days respectively. They started the work together but B leaving off & days and C six daysbefore the completion of the work. In what time is the work finished?
AD is perpendicular to the internal bisector of$$ \angle ABC $$ of $$ \triangle$$ ABC. DE is drawn through D and parallel to BC to meet AC at E. If the length of AC is 12 cm, then the length of AE (in cm)is
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The average of five consecutive positive integers is n, If the next two integers are also included, the
average of all these integers will
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If a-$$\frac{1}{a-3}$$=5 then the value of $$(a-3)^{3}-\frac{1}{(a-3)^{3}}$$
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.A plane divides a night circular cone into two parts of equal volume. If the plane is parallel to the base, then the ratio, in which the height of the coneis divided, is
Let x be the smallest number, which when added to 2000 makes the resulting number divisible by 12, 16, 18 and 21. The sum of the digits of x is
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The diameter of each wheel of a car is 70 cm. If each wheel rotates 400 times per minute, then the speed of the car(in km/hr)is
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The average age of 30.students of a class is 14 years 4 months. After admission of 5 new students in the class the average becomes 13 years 9 months. The youngest one of the five new students is 9 years 11 months old. The average age of the remaining 4 new studentsis
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P and Q together can do a job in 6 days. Q and Rcan finish the same job in 60/7 days. P started the work and worked for 3 days. Q and R continued for 6 days. Then the difference of days in which R and P can complete the job is
Telegraph post is bent at a point above the ground due to storm. Its top just touches the ground at a distance of 10$$\sqrt{3}$$m from its foot and makes an angle of $$30^\circ$$ with the horizontal. Then height (in metres) of the telegraph post is
If $$5 cos\theta+ 12 sin\theta$$=13, $$0<\theta<90^\circ$$ then value of $$sin\theta$$
if a+$$\frac{1}{b}$$ =b+$$\frac{1}{c}$$=c+$$\frac{1}{a}$$ where as a≠b≠c≠0 then the value of $$a^{2}b^{2}c^{2}$$ is
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The H.C.F and L.C.M of two numbers are 21 and 84 respectively. If the ratio of the two numbers is 1: 4, then the larger of the two numbers is
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If 90 men can do a certain job in 16 days, working 12 hours/day, then the part of that work which can be completed by 70 men in 24 days, working 8hours/dayis
A sum of 7,930 is divided into 3 parts and given on loan at 5% simple interest to A, B and C for 2,3 and 4 years respectively. If the amounts of all three are equal after their respective periods of loan, then the A received a loan of
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The value of (coseca — sina) (seca — cosa) (tana + cota)
There would be a 10% loss,if rice is sold at RS.54 per kg. To earn a profit of 20%, the price of rice per kg will be
If a hemisphere is melted and four spheres of equal volume are made, the radius of each sphere will be equal to
60 kg of an alloy A is mixed with 100 kg of alloyB. If alloy A has lead and tin in the ratio 3 ; 2 and alloy B has tin and copperin the ratio 1: 4, the amount of tin in the new alloy is
Base of a right pyramid is a square of side 10cm. If the height of the pyramid is 12cm, then its total surface area is
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If a shopkeeper wants to give 20% discount on a toy, he has to sell it for Rs.300. If he sells it at Rs.405, then his gain percentage is
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The unit digit in the product $$(2467)^{153} \times (841)^{72}$$is
The interior angle of a regular polygon exceedsits extenior angle by $$108^\circ$$, The numberof sides ofthe polygonis
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The value of $$4-\frac{5}{1+\frac{1}{3+\frac{1}{2+\frac{1}{4}}}}$$
The centroid of a $$ \triangle ABC$$ is G. The area of $$\triangle abc $$ is 50$$ cm^{2}$$, The area of $$ \triangle GBC$$ is
