If sec θ - tan θ = 1/√3, the value of sec θ tan θ is
A sum of money placed at compound interest doubles itself in 5 years. It will amount to eight times itself at the same rate of interest in
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 substracted from the sum of the digits, the difference is equal to 1/6th of the number. The number is
The average of five consecutive positive integers is n. If the next two integers are also included, the average of all these integers will
A and B are centres of two circles of radii I I cm and 6 cm, respectively. PQ is a direct common tangent to the circles. If AB=13 cm, then length of PQ will be
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
A man starts from a place P and reaches the place Q in 7 hours. He travels 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 Q is
A car covers four successive 7 km distances at speeds of 10 km/hour, 20 km/ hour, 30 km/hour, 60 km/hour respectively. Its average speed over his distance is
If a shopkeeper wants to give 20% discount on a toy. he has to sell it for INR 300. If he sells it at INR 405, then his gain percent is
Ram sold two horses at the same price. In one he gets a profit of 10% and in the other he gets a loss of 10%. Then Ram gets
300 grams of sugar solution has 40% of sugar in it. How much sugar should be added to make it 50% in the solution
Given 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
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
Two blends of a commodity costing INR 35 and INR 40 per kg respectively are mixed in the ratio 2:3 by weight. If one-fifth of the mixture is sold at INR 46 per kg and the remaining at the rate of INR 55 per kg, the profit percent is
If x=a sin θ - b cos θ, y = a cos θ + b sin θ then which of the following is true
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
A plane divides a right 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 cone is divided, 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 8 km/hour faster than the other, then speed of train from Q is
The area of an isosceles trapezium is 176 cm2 and the height is 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
In an examination average marks obtained by the girls of a class is 85 and the average marks 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
In triangle ABC, DE || BC where D is a point on AB and E is a point on AC. DE divides the area of Δ ABC into two equal parts. Then DB : AB is equal to
In trapezium ABCD, AB || CD and AB = 2CD. Its diagonals intersect at O. If the area of Δ AOB = 84 cm2, then the area of Δ COD is equal to
Average of n numbers is a. The first 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 numbers is
The unit digit in the product (2467)153×(341)72 is
If a man walks at the rate of 5 km/hour, he misses a train by 7 minutes. However if he walks at the rate of 6 km/hour, he reaches the station 5 minutes before the arrival of the train. The distance covered by him to reach the station is
If 60% of A = 30% of B, B = 40% of C and C = x% of A, then value of x is
If a-1/a-3=5, then the value of (a-3)3-1/(a-3)3 is
If O is the circumcentre of a triangle ABC lying inside the triangle, then ∠ OBC +∠ BAC is equal to
The interior angle of a regular polygon exceeds its exterior angle by 1080. The number of sides of the polygon is
The marked price of a tape recorder is INR 12600. A festival discount of 5% is allowed on it. Further for cash payment, a second discount of 2% is given. The cash payment, in rupees, is to be made for buying it is
If A:B = 2:3 and B:C = 3:7, then A+B : B+C :C+A is
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
Water tax is increased by 20% but its consumption is decreased by 20%. Then the increase of decrease in the expenditure of the money is
A and B have their monthly incomes in the ratio 8:5, while their monthly expenditures are in the ratio 5:3. If they have saved INR 12000 and INR 10000 monthly respectively, then the difference in their monthly incomes is
If a+1/b = b+1/c = c+1/a, where a ≠ b ≠ c ≠ 0, then the value of a2b2c2 is
If tan A = n tan B and sin A = m sin B, then the value of cos2 A is
If tan θ - cot θ = 0 and θ is positive acute angle, then the value of tan (θ+150)/tan (θ-15) is
Directions :
The following graph shows production (in thousands) of two types (P and Q) of vehicles by a factory over the years 2009 to 2014. Study the graph and answer five questions:
The production of Type Q vehicles in 2010 was approximately what percent of Type P vehicles in 2014
The ratio of total production of Type P vehicle 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
The total prodcution of Type P vehicles in the years 2009 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 and 2011 is
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
If sin A + sin 2 A = 1, then the value of cos 2 A + cos 4 A is
A and B can do a piece of work in 30 and 36 days respectively. They began the work together but A leaves after some days and B finished the reamaining work in 25 days. After how many days did A leave
A man purchases some oranges at the rate of 3 for INR 40 and the same quantity at 5 for INR 60. If he sells all the oranges at the rate of 3 for INR 50, find his gain or loss percent (to the nearest integer).
A right prism has a traingular base whose sides are 13 cm, 20 cm and 21 cm. If the altitude of the prism is 9 cm, then its volume is
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
If = pa qb,
then the value of a+b, where p and q are different positive primes, is
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 C is 81. Then the average score of classes A, B and C is
The value of
4 - ...........
1 + ..........
3 + ..........
2 + 1/4
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 closed, how much time B will take to fill the remaining tank
Quadrilateral ABCD is circumscribed about a circle. If the lengths of AB, BC, CD are 7 cm, 8.5 cm and 9.2 cm respectively, then the length (in cm) of DA is
62+72+82+92+102/√7+4√3-√4+2√3 is equal to
A man sells an article at 5% above its cost price. If he had bought it at 5% less than what he had paid for it and sold it at INR 2 less, he would have gained 10%. The cost price of the article is
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 INR 48. The cost of production (in INR) of the article is
The greatest number among 350: 440 : 530 and 620 is
P and Q together can do a job in 6 days. Q and R can 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
ABCD is 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 PD is
AD is perpendicular to the internal bisector of ∠ ABC of Δ 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
Base of a right pyramid is a square of side 10 cm. If the height of the pyramid is 12 cm, then its total surface area is
The centroid of a Δ ABC is G. The area of Δ ABC is 60 cm2. The area of Δ GBC is
If x2+y2+z2 = xy+yz+zx, then the value of
3x4+7y4+5z4/5x2y2+7y2z2+3z2x2 is
If 3(a2+b2+c2) = (a+b+c)2, then the relation between a, b and c is
A boat moves downstream at the rate of 1 km in 7 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
If (3x-2y) : (2x+3y) 5:6 then one of the value of [3√x+3√y/3√x-3y]2 is
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 [Take ∏ = 22/7]
In a school there were 1554 students and the ratio on 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
There would be a 10% loss, if rice is sold at INR 54 per kg. To earn a profit of 20%, the price of rice per kg will be
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 diameter 4 m and length 56 m is
[Take∏=22/7]
A sum of money is paid back in two annual instalments of INR 17640 each allowing 5% compound interest compounded annually. The sum borrowed was
If 5 cos θ + 12 sin θ = 13, 00 < θ < 900, then the value of sin θ is
If a hemisphere is melted and four spheres of equal volume are made, the radius of each sphere will be equal to
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 8 hours/day is
The perimeter of a rhombus is 60 cm and one of its diagonal is 24 cm. The area (in sq.cm) of the rhombus is
If x - √3- √2 = 0 and y- √3+√2 = 0, then value of (x3-20√2)-(y3+2√2)
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
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
A number when divided by 361 gives a remainder 47. If the same number is divided by 19, the remainder obtained is
There is a wooden sphere of radius 6 √3 cm. The surface area of the largest possible cube cut out from the sphere will be
60 kg of an alloy A is mixed with 100 kg of alloy B. If alloy A has lead and tin in the ratio 3 : 2 and alloy B has tin and copper in the ratio 1 : 4, the amount of tin in the new alloy is
A telegraph post is bent at a point above the ground due to storm. Its top just touches the ground at a distance of 10 √3 m from its foot and makes an angle of 300 with the horizontal. Then height (in metres) of the telegraph post is
The radii of two solid iron spheres are 1 cm and 6 cm respectively. A hollow sphere is made by melting the two spheres. If the external radius of the hollow sphere is 9 cm, then its thickness (in cm) is
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 students is
cot 410 . cot 420 . cot 430 . cot 440 . cot 450 . cot 460 . cot 470 . cot 480 . cot 490
The simple interest on a sum of money is 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
Let x = √13+√11/√13-√11 and y = 1/x, then the value of 3x2-5xy+3y2 is
A sum of INR 7930 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
(067×0.67×0.67)-(0.33×0.33×0.33)/(067×067)+((067×0.33)+(0.33×0.33)
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, the value of 1/h2+1/r2 is
If (x3-y3) : (x2+xy+y2) = 5:1 and (x2-y2) : (x-y) = 7:1, then the ratio 2x:3y equals
A, B and C can do a work seperately in 16, 32 and 48 days respectively. They started the work together but B leaving off 8 days and C six days before the completion of the work. In what time is the work finished
If x = a1/2+a-1/2, y=a1/2-a-1/2 then value of (x4-x2y2-1)+(y4-x2y2+1)
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 measure, then the volume (in litres) of water contained by each bucket is
A and B can do a given piece of work in 8 days, B and C can do the same work in 12 days and A, B, C complete it in 6 days. Number of days required to finish the work by A and C is
In Δ ABC, ∠ BAC = 900 and AD ⊥ BC. If BD = 3 cm and CD = 4 cm, then the length (in cm) of AD is
Articles are marked at a price which gives a profit of 25%. After allowing a certain discount the profit reduces to 12 1/2%. The discount percent is
If a + b = 1, find the value of a3+b3-ab-(a2-b2)2
If 7 sin2θ+3cos2θ=4, then the value of tan θ is (θ is acute)
(cosec a - sin a) (sec a-cod a) (tan a + cot a)