Exam Details
2016 Elementary Mathematics
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100
Duration
180 mins
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Combined Defence Services Examination (II) - Previous Year Papers
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PYP
2016 Elementary Mathematics
What is the solution of
log_{10} \left[ 1- \left\{ 1- \left( 1-x^{2} \right)^{-1} \right\}^{-1} \right]^{-1/2} = 1 ?
PYP
2016 Elementary Mathematics
If \lambda is an integer and \alpha, \beta are the roots of 4x^{2} - 16x + \lambda/4 = 0 such that 1 < \alpha < 2 and 2 < \beta < 3, then how many values can \lambda take ?
PYP
2016 Elementary Mathematics
What is \frac{6^{2} + 7^{2} + 8^{2} + 9^{2} + 10^{2}}{√{7 + 4√{3}} - √{4 + 2√{3}}} equal to ?
PYP
2016 Elementary Mathematics
If x^{2} = y + z, y^{2} = z + x and z^{2} = x + y, then what is the value of 1/x+1 + 1/y+1 + 1/z+1 ?
PYP
2016 Elementary Mathematics
What would be the maximum value of Q in the equation 5P9 + 3R7 + 2Q8 = 1114 ?
PYP
2016 Elementary Mathematics
A is a set of positive integers such that when divided by 2, 3, 4, 5 and 6 leaves the remainder 1, 2, 3, 4 and 5 respectively. How many integers between 0 and 100 belong to the set A ?
PYP
2016 Elementary Mathematics
In an examination, a student was asked to divide a certain number by 8. By mistake he multiplied it by 8 and got the answer 2016 more than the correct answer. What was the number ?
PYP
2016 Elementary Mathematics
In the quadratic equation x^{2} + ax + b = 0, a and b can take any value from the set \{1, 2, 3, 4\}. How many pairs of values of a and b are possible in order that the quadratic equation has real roots ?
PYP
2016 Elementary Mathematics
The sum of the squares of two positive integers is 208. If the square of the larger number is 18 times the smaller number, then what is the difference of the larger and smaller numbers ?
PYP
2016 Elementary Mathematics
Let A = {7, 8, 9, 10, 11, 12} and B = {7, 10, 14, 15}. What is the number of elements in (A - B) and (B - A) respectively ?
PYP
2016 Elementary Mathematics
A boy saves Rs. 4.65 daily. What is the least number of days in which he will be able to save an exact number of rupees ?
PYP
2016 Elementary Mathematics
Two men, A and B run a 4 km race on a course 0.25 km round. If their speeds are in the ratio 5 : 4, how often does the winner pass the other ?
PYP
2016 Elementary Mathematics
Which one of the following rational numbers has non-terminating and repeating decimal expansion ?
PYP
2016 Elementary Mathematics
If α and β are the two zeros of the polynomial 25x2 - 15x + 2, then what is a quadratic polynomial whose zeros are (2α)−1 and (2β)−1 ?
PYP
2016 Elementary Mathematics
What is the remainder when 2100 is divided by 101 ?
PYP
2016 Elementary Mathematics
In an office, one-third of the workers are women, half of the women are married and one-third of the married women have children. If three-fourth of the men are married and one-third of the married men have children, then what is the ratio of married women to married men ?
PYP
2016 Elementary Mathematics
A can do 50% more work than B in the same time. B alone can do a piece of work in 30 hours. B starts working and had already worked for 12 hours when A joins him. How many hours should B and A work together to complete the remaining work?
PYP
2016 Elementary Mathematics
When the speed of a train is increased by 20%, it takes 20 minutes less to cover the same distance. What is the time taken to cover the same distance with the original speed?
PYP
2016 Elementary Mathematics
A candidate scoring x% marks in an examination fails by a marks, while another candidate who scores y% marks gets b marks more than the minimum required pass marks. What is the maximum marks for the examination?
PYP
2016 Elementary Mathematics
If p and q are the roots of x2 + px + q = 0, then which one of the following is correct?
PYP
2016 Elementary Mathematics
The cost of 2·5 kg rice is Rs. 125. The cost of 9 kg rice is equal to that of 4 kg pulses. The cost of 14 kg pulses is equal to that of 1·5 kg tea. The cost of 2 kg tea is equal to that of 5 kg nuts. What is the cost of 11 kg nuts?
PYP
2016 Elementary Mathematics
Which one of the following is correct in respect of the number 1729?
PYP
2016 Elementary Mathematics
A shopkeeper increases the cost price of an item by 20% and offers a discount of 10% on this marked price. What is his percentage gain ?
PYP
2016 Elementary Mathematics
There are two numbers p and q such that their HCF is 1. Which of the following statements are correct ?
1. Both p and q may be prime.
2. One number may be prime and the other composite.
3. Both the numbers may be composite.
Select the correct answer using the code given below :
PYP
2016 Elementary Mathematics
What is
\( √{1+1/1²+1/2²} + √{1+1/2²+1/3²} + ... + √{1+1/2007²+1/2008²} \) equal to ?
PYP
2016 Elementary Mathematics
A person can row downstream 20 km in 2 hours and upstream 4 km in 2 hours. What is the speed of the current ?
PYP
2016 Elementary Mathematics
Consider the following statements in respect of positive odd integers x and y :
1. \( x² + y² \) is even integer.
2. \( x² + y² \) is divisible by 4.
Which of the above statements is/are correct ?
PYP
2016 Elementary Mathematics
What are the roots of the equation
\( 2^{x+2} \cdot 27^{x/x-1} = 9 \) ?
PYP
2016 Elementary Mathematics
There are twelve friends A, B, C, D, E, F, G, H, I, J, K and L who invested money in some business in the ratio of 1 : 2 : 3 : 4 : 5 : 6 : 7 : 8 : 9 : 10 : 11 : 12 and the duration for which they invested the money is in the ratio of 12 : 11 : 10 : 9 : 8 : 7 : 6 : 5 : 4 : 3 : 2 : 1 respectively. Who will get the maximum profit at the end of the year ?
PYP
2016 Elementary Mathematics
2¹22 + 4⁶2 + 8⁴2 + 4⁶4 + 2¹30 is divisible by which one of the following integers ?
PYP
2016 Elementary Mathematics
If 2p + 3q = 12 and 4p² + 4pq - 3q² = 126, then what is the value of p + 2q ?
PYP
2016 Elementary Mathematics
The number of digits in 3³0 is n and it is given that log₁0 3 = 0.4771. What is the value of n ?
PYP
2016 Elementary Mathematics
What is the unit digit of 7¹39 ?
PYP
2016 Elementary Mathematics
If 4x + 3a = 0, then what is the value of (x² + ax + a²) / (x³ - a³) - (x² - ax + a²) / (x³ + a³) ?
PYP
2016 Elementary Mathematics
Incomes of Mahesh and Kamal are in the ratio 1 : 2 and their expenses are in the ratio 1 : 3. Which one of the following statements is correct ?
PYP
2016 Elementary Mathematics
X and Y entered into partnership with Rs. 700 and Rs. 600 respectively. After 3 months X withdrew 2/7 of his stock but after 3 months, he puts back 3/5 of what he had withdrawn. The profit at the end of the year is Rs. 726. How much of this should X receive ?
PYP
2016 Elementary Mathematics
A tank can be filled by pipe X in 2 hours and pipe Y in 6 hours. At 10 a.m. pipe X was opened. At what time will the tank be filled if pipe Y is opened at 11 a.m. ?
PYP
2016 Elementary Mathematics
A train is travelling at 48 km/hour completely crosses another train having half its length and travelling in opposite direction at 42 km/hour in 12 s. It also passes a railway platform in 45 s. What is the length of the platform ?
PYP
2016 Elementary Mathematics
The speeds of three cars are in the ratio 2 : 3 : 4. What is the ratio between the times taken by these cars to travel the same distance ?
PYP
2016 Elementary Mathematics
If the mean age of combined group of boys and girls is 18 years and the mean of age of boys is 20 and that of girls is 16, then what is the percentage of boys in the group ?
PYP
2016 Elementary Mathematics
The area of four walls of a room is 120 m2. The length of the room is twice its breadth. If the height of the room is 4 m, what is area of the floor ?
PYP
2016 Elementary Mathematics
If a square of side x and an equilateral triangle of side y are inscribed in a circle, then what is the ratio of x to y ?
PYP
2016 Elementary Mathematics
The ratio of the curved surface area to the total surface area of a right circular cylinder is 1 : 2. If the total surface area is 616 cm2, what is the volume of the cylinder ?
PYP
2016 Elementary Mathematics
A cubic metre of copper weighing 9000 kg is rolled into a square bar 9 m long. An exact cube is cut off from the bar. How much does the cube weigh ?
PYP
2016 Elementary Mathematics
Into a conical tent of radius 8·4 m and vertical height 3·5 m, how many full bags of wheat can be emptied, if space required for the wheat in each bag is 1·96 m3?
PYP
2016 Elementary Mathematics
Let ABC be a right angled triangle with BC = 5 cm and AC = 12 cm. Let D be a point on the hypotenuse AB such that ∠BCD = 30°. What is length of CD?
PYP
2016 Elementary Mathematics
Two circles touch externally and sum of their areas is 130π cm2 and the distance between their centres is 14 cm. What is the difference in the radii of the circles?
PYP
2016 Elementary Mathematics
In a circle of radius 3 units, a diameter AB intersects a chord of length 2 units perpendicularly at P. If AP > BP, then what is the ratio of AP to BP?
PYP
2016 Elementary Mathematics
What is the number of rounds that a wheel of diameter 5/11 m will make in traversing 7 km?
PYP
2016 Elementary Mathematics
A building is in the form of a cylinder surmounted by a hemispherical dome on the diameter of the cylinder. The height of the building is three times the radius of the base of the cylinder. The building contains 67 1/21 m3 of air. What is the height of the building?
PYP
2016 Elementary Mathematics
The radius of the base and the height of a solid right circular cylinder are in the ratio 2 : 3 and its volume is 1617 cm3. What is the total surface area of the cylinder?
PYP
2016 Elementary Mathematics
The cost of painting a spherical vessel of diameter 14 cm is Rs. 8008. What is the cost of painting per square centimetre ?
PYP
2016 Elementary Mathematics
If a quadrilateral has an inscribed circle, then the sum of a pair of opposite sides equals
PYP
2016 Elementary Mathematics
A circle and a square have the same perimeter. Which one of the following is correct ?
PYP
2016 Elementary Mathematics
A drinking glass of height 24 cm is in the shape of frustum of a cone and diameters of its bottom and top circular ends are 4 cm and 18 cm respectively. If we take capacity of the glass as \( \pi x \) cm\(³\), then what is the value of x ?
PYP
2016 Elementary Mathematics
In an equilateral triangle another equilateral triangle is drawn inside joining the mid-points of the sides of given equilateral triangle and the process is continued up to 7 times. What is the ratio of area of fourth triangle to that of seventh triangle ?
PYP
2016 Elementary Mathematics
Rain water from a roof 22 m \( × \) 20 m drains into a cylindrical vessel having diameter of base 2 m and height 3.5 m. If the vessel is just full, what is the rainfall ?
PYP
2016 Elementary Mathematics
The height of a cone is 60 cm. A small cone is cut off at the top by a plane parallel to the base and its volume is \( 1/64 \) the volume of original cone. What is the height from the base at which the section is made ?
PYP
2016 Elementary Mathematics
If two tangents inclined at an angle 60° are drawn to a circle of radius 3 cm, then what is the length of each tangent ?
PYP
2016 Elementary Mathematics
What is the volume of a sphere of radius 3 cm ?
PYP
2016 Elementary Mathematics
The sides of a triangle are given by a + b, c + a and (b + c) where a, b, c are positive. What is the area of the triangle equal to ?
PYP
2016 Elementary Mathematics
What is area of largest triangle inscribed in a semi-circle of radius r units ?
PYP
2016 Elementary Mathematics
The diameter of the front wheel of an engine is 2x cm and that of rear wheel is 2y cm. To cover the same distance, what is the number of times the rear wheel revolves when the front wheel revolves n times ?
PYP
2016 Elementary Mathematics
For the next three (03) items that follow :
A tent of a circus is made of canvas and is in the form of right circular cylinder and right circular cone above it. The height and diameter of the cylindrical part of the tent are 5 m and 126 m respectively. The total height of the tent is 21 m.
What is the slant height of the cone ?
PYP
2016 Elementary Mathematics
What is the curved surface area of the cylinder ?
PYP
2016 Elementary Mathematics
How many square metres of canvas are used ?
PYP
2016 Elementary Mathematics
The wheels of a car are of diameter 80 cm each. The car is travelling at a speed of 66 km/hour. What is the number of complete revolutions each wheel makes in 10 minutes ?
PYP
2016 Elementary Mathematics
What is the area of a triangle with sides of length 12 cm, 13 cm and 5 cm ?
PYP
2016 Elementary Mathematics
If the perimeter of a circle is equal to that of a square, then what is the ratio of area of circle to that of square ?
PYP
2016 Elementary Mathematics
ABCDA is a con-cyclic quadrilateral of a circle ABCD with radius r and centre at O. If AB is the diameter and CD is parallel and half of AB and if the circle completes one rotation about the centre O, then the locus of the middle point of CD is a circle of radius
PYP
2016 Elementary Mathematics
If sinθ + cosθ = √7/2, then what is sinθ - cosθ equal to ?
PYP
2016 Elementary Mathematics
If sin x + sin2x = 1, then what is the value of cos8x + 2cos6x + cos4x ?
PYP
2016 Elementary Mathematics
A man from the top of a 100 m high tower sees a car moving towards the tower at an angle of depression 30°. After some time, the angle of depression becomes 60°. What is the distance travelled by the car during this time ?
PYP
2016 Elementary Mathematics
Two men on either side of a tower 75 m high observe the angle of elevation of the top of the tower to be 30° and 60°. What is the distance between the two men ?
PYP
2016 Elementary Mathematics
What is the value of cosec268° + sec256° - cot234° - tan222° ?
PYP
2016 Elementary Mathematics
If 2y cosθ = x sinθ and 2x secθ - y cosecθ = 3, then what is x2 + 4y2 equal to ?
PYP
2016 Elementary Mathematics
If sinθ + cosθ = (1 + √3)/2 where 0 < θ < π/2, then what is tanθ + cotθ equal to ?
PYP
2016 Elementary Mathematics
If A = sin2θ + cos4θ where 0 ≤ θ < π/2, then which one of the following is correct ?
PYP
2016 Elementary Mathematics
What is (cot A + cosec A - 1) / (cot A - cosec A + 1) equal to ?
PYP
2016 Elementary Mathematics
Consider the following :
1. sin 1° > sin 1°
2. cos 1° < cos 1°
3. tan 1° > tan 1°
Which of the above are not correct ?
PYP
2016 Elementary Mathematics
If tan² x + 1/tan² x = 2 and 0° < x < 90°, then what is the value of x?
PYP
2016 Elementary Mathematics
If the length of the shadow of a tower is equal to its height, then what is the Sun's altitude at that time?
PYP
2016 Elementary Mathematics
Consider the following :
1. (cos 75° / sin 15°) + (sin 12° / cos 78°) - (cos 18° / sin 72°) = 1
2. (cos 35° / sin 55°) - (sin 11° / cos 79°) + cos 28° cosec 62° = 1
3. (sin 80° / cos 10°) - sin 59° sec 31° = 0
Which of the above are correct?
PYP
2016 Elementary Mathematics
A pole stands vertically inside a triangular park ABC. If the angle of elevation of the top of the pole from each corner of the park is same, then in the triangle ABC, the foot of the pole is at the
PYP
2016 Elementary Mathematics
What is the value of tan 1° tan 2° tan 3° tan 4° ... tan 89° ?
PYP
2016 Elementary Mathematics
The average score of class X is 83.
The average score of class Y is 76.
The average score of class Z is 85.
The average score of class X and Y is 79 and average score of class Y and Z is 81.
What is the average score of X, Y and Z?
PYP
2016 Elementary Mathematics
For x > 0, if a variable takes discrete values x + 4, x - 3·5, x - 2·5, x - 3, x - 2, x + 0·5, x - 0·5, x + 5, then what is the median ?
PYP
2016 Elementary Mathematics
The median of set of 9 distinct observations is 20·5. If each of the largest 4 observations of the set is increased by 2, then the median of the new set
PYP
2016 Elementary Mathematics
A cricketer has a certain average of 10 innings. In the eleventh inning he scored 108 runs, thereby increasing his average by 6 runs. What is his new average ?
PYP
2016 Elementary Mathematics
The mean of 20 observations is 17. On checking it was found that the two observations were wrongly copied as 3 and 6. If wrong observations are replaced by correct values 8 and 9, then what is the correct mean ?
PYP
2016 Elementary Mathematics
Number of credit cards held by an individual can be treated as
PYP
2016 Elementary Mathematics
In a class of 100 students, there are 70 boys whose average marks in a subject are 75. If the average marks of the complete class is 72, then what is the average marks of the girls ?
PYP
2016 Elementary Mathematics
A pie chart depicts the classification of total funds of an organization according to different sources of funds. A particular sector of pie chart for corporate tax has 108° angle at the centre. What is the percentage of income from corporate tax to total funds ?
PYP
2016 Elementary Mathematics
Consider the following statements :
1. The classes of type 15-19, 20-24, 25-29 etc. are exclusive classes.
2. The classes of type 15-20, 20-25, 25-30 etc. are inclusive classes.
Which of the above statements is/are correct ?
PYP
2016 Elementary Mathematics
Suppose the class interval 10-15 has frequency 30, then what is the frequency density of this class interval ?
PYP
2016 Elementary Mathematics
Let S be a set of first ten natural numbers. What is the possible number of pairs (a, b) where a, b ∈ S and a ≠ b such that the product ab (>12) leaves remainder 4 when divided by 12 ?
PYP
2016 Elementary Mathematics
What is the remainder when 13⁵ + 14⁵ + 15⁵ + 16⁵ is divided by 29 ?
PYP
2016 Elementary Mathematics
What is the difference between the sum of the cubes and that of squares of first ten natural numbers ?
PYP
2016 Elementary Mathematics
A motorist travels to a place 150 km away at an average speed of 50 km/hour and returns at 30 km/hour. What is the average speed for the whole journey ?
PYP
2016 Elementary Mathematics
If x + (1 / (1 + (1 / (2 + 1/3)))) = 2, then what is x equal to ?
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