Q1
A cloth store is offering 'Buy 3, get 1 free'. What is the net percentage discount being offered by the store?
Elementary MathematicsArithmetic
UPSC CDS · Solved paper
All 100 questions, textbook-style — tap “Show answer” on any question to reveal the correct option and explanation.
A cloth store is offering 'Buy 3, get 1 free'. What is the net percentage discount being offered by the store?
X can do a piece of work in 25 days. Y is 25% more efficient than X. The number of days taken by Y is:
A train takes 10 s to cross a pole and 20 s to cross a platform of length 200 m. What is the length of the train?
A sum of money becomes 3 times in 5 years. In how many years will the same sum become 6 times at the same rate of simple interest?
In a certain school the ratio of boys to girls is 7 : 5. If there are 2400 students in the school, how many girls are there?
45 people take 18 days to dig a pond. If the pond would have to be dug in 15 days, then the number of people to be employed will be:
A merchant earns a profit of 20% by selling a basket containing 80 apples which cost Rs. 240. But he gives one-fourth of it to his friend at cost price and sells the remaining apples. In order to earn the same profit, at what price must he sell each apple?
The least number of four digits which is a perfect square is:
Consider the following statements:
Which of the above statements is/are correct?
The product of HCF and LCM of 18 and 15 is:
What is 3 x 0.3 x 0.03 x 0.003 x 0.0003 x 30 equal to?
What is 0.242424... (24 recurring) equal to?
A and B can do a piece of work in 10 hours. B and C can do it in 15 hours, while A and C take 12 hours to complete the work. B independently can complete the work in:
The sum of the squares of two numbers is 97 and the square of their difference is 25. The product of the two numbers is:
Age of X is six times that of Y. After 4 years, X is four times elder to Y. What is the present age of Y?
A milkman bought 15 kg of milk and mixed 3 kg of water in it. If the price per kg of the mixture becomes Rs. 22, what is cost price of the milk per kg?
What is 5% of 50% of 500?
Which one of the following has least number of divisors?
A man buys a television set which lists for Rs. 5,000 at 10% discount. He gets an additional 2% discount (after the first discount) for paying cash. What does he actually pay for the set?
Sex ratio is defined as the number of females per 1000 males. In a place the total inhabitants are 19,35,000 out of which 9,35,000 are females. What is the sex ratio for the place?
A car is traveling at a constant rate of 45 km per hour. The distance travelled by car from 10.40 am to 1.00 pm is:
A number consists of two digits whose sum is 8. If 18 is added to the number, the digits are reversed. The number is equal to:
If log10 a = p and log10 b = q, then what is log10 (a^p b^q) equal to?
If two factors of a^4 - 2a^3 - 9a^2 + 2a + 8 are (a + 1) and (a - 1), then what are the other two factors?
The price of an article is Rs. 25. After two successive cuts by the same percentage, the price becomes Rs. 20.25. If each time the cut was x%, then:
If 0.764 y = 1.236 x, then what is the value of (y - x)/(y + x)?
What is the value of [(2.247)^3 + (1.730)^3 + (1.023)^3 - 3*2.247*1.730*1.023] / [(2.247)^2 + (1.730)^2 + (1.023)^2 - 2.247*1.730 - 1.730*1.023 - 2.247*1.023]?
Three planets revolve round the sun once in 200, 250, 300 days respectively in their own orbits. When do they all come relatively to the same position as at a certain point of time in their orbits?
What is the greatest number that divides 13850 and 17030 and leaves a remainder 17?
If the sum of an integer and its reciprocal is 10/3, then the integer is equal to:
Let x in {2, 3, 4} and y in {4, 6, 9, 10}. Let A be the set of all ordered pairs (x, y) such that x is a factor of y. How many elements does the set A contain?
Which one of the following is a null set?
If (x - 6) is the HCF of x^2 - 2x - 24 and x^2 - kx - 6, then what is the value of k?
If the expression x^3 + 4x^2 + 4x + k has (x + 4) as a factor, then what is the value of k?
If sqrt(10 + cubert(x)) = 4, then what is x equal to?
Which one of the following is neither prime number nor composite number?
Consider the following table: x: 0 1 2 3 4; y: 100 90 70 40 0. How are x and y related?
If a/b - b/a = x/y and a/b + b/a = x - y, then what is x equal to?
The quadratic equation whose roots are 3 and -1 is:
Consider the following statements:
Which of the above statements is/are correct?
What is the value of k which will make the expression 4k^2 + 12k + k a perfect square?
If one root of the equation x^2/a + x/b + 1/c = 0 is reciprocal of the other, then which one of the following is correct?
If f(x) is a polynomial with constant term 10 having a factor (x - k) where k is an integer, then what is the possible value of k?
If a = 2 + sqrt(3), then what is the value of (a^2 + a^-2)?
If x + y = 9 and xy = 8, then what is one of the values of (x^4 - y^4)?
There are some benches in a class room having the number of rows 4 more than the number of columns. If each bench is seated with 5 students, there are two seats vacant in a class of 158 students. The number of rows is:
If tan theta = 3/4 and theta is acute, then what is sin theta equal to?
What is the value of sec(90 degrees - theta) * sin theta * sec 45 degrees?
On walking 120 m towards a chimney in a horizontal line through its base the angle of elevation of tip of the chimney changes from 30 degrees to 45 degrees. The height of the chimney is:
If an angle measures p degrees and q radians, then which one of the following is correct?
If the angle theta is in the first quadrant and tan theta = 3, then what is the value of (sin theta + cos theta)?
A wheel makes 12 revolutions per minute. The angle in radian described by a spoke of the wheel in 1 second is:
A ladder 20 m long is placed against a wall so that the foot of the ladder is 10 m from the wall. The angle of inclination of the ladder to the horizontal will be:
If 0 < theta < 90 degrees, then all the trigonometric ratios can be obtained when:
What is sin A cos A tan A + cos A sin A cot A equal to?
What is sin theta/(1+cos theta) + (1+cos theta)/sin theta equal to?
The angles of elevation of the top of a tower from two points which are at distances of 10 m and 5 m from the base of the tower and in the same straight line with it are complementary. The height of the tower is:
The angles of elevation of the top of an inaccessible tower from two points on the same straight line from the base of the tower are 30 degrees and 60 degrees respectively. If the points are separated at a distance of 100 m, then the height of the tower is close to:
If sin theta cos theta = sqrt(3)/4, then the value of sin^4 theta + cos^4 theta is:
The locus of a point in rhombus ABCD which is equidistant from A and C is:
In a triangle ABC, (1/2)angle A + (1/3)angle C + (1/2)angle B = 80 degrees, then what is angle C equal to?
In a triangle ABC, angle BCA = 60 degrees and AB^2 = BC^2 + CA^2 + X. What is X equal to?
Consider the following statements:
Which of the above statements is/are correct?
If the diagonals of a quadrilateral are equal and bisect each other at right angles, then the quadrilateral is a:
If two parallel lines are cut by two distinct transversals, then the quadrilateral formed by the four lines is always a:
ABCD is a parallelogram. If the bisectors of the angle A and angle C meet the diagonal BD at points P and Q respectively, then which one of the following is correct?
Let X be any point within a square ABCD. On AX a square AXYZ is described such that D is within it. Which one of the following is correct?
In a triangle ABC, XY is drawn parallel to BC, cutting sides at X and Y where AB = 4.8 cm, BC = 7.2 cm, BX = 2 cm. What is the length of XY?
Let ABC be a triangle with AB = 3 cm, AC = 5 cm. If AD is a median drawn from the vertex A to the side BC, then which one of the following is correct?
Consider the following statements:
Which of the above statements is/are correct?
In the figure, angles x degrees, a degrees, c degrees and (pi - b) degrees are indicated (D-C and E-B are drawn segments, A-B-C collinear, A-D-E collinear). Which one of the following is correct?
In the figure YZ is parallel to MN, XY is parallel to LM and XZ is parallel to LN (X on MN, Y on LN, Z on LM). Then MY is:
In the figure, AB is parallel to CD. angle ABC = 65 degrees, angle CDE = 15 degrees and AB = AE. What is angle AEF equal to? (F is on the extension of DE beyond E.)
In the figure ABC is a triangle. BC is parallel to AE. If BC = AC, then what is angle CAE equal to? (angle at B is 65 degrees.)
In the figure EC is parallel to AB, angle ECD = 70 degrees and angle BDO = 20 degrees. What is angle OBD equal to? (O is the intersection of AB and CD.)
In the figure, LOM is a straight line with angles (x+20) degrees, 50 degrees and (x-10) degrees at O. What is x equal to?
What is the volume of the largest sphere that can be carved out of a cube of edge 3 cm?
If the ratio of the diameters of two spheres is 3 : 5, then what is the ratio of their surface areas?
What is the height of a solid cylinder of radius 5 cm and total surface area 660 cm^2?
The diameter of base of a right circular cone is 7 cm and slant height is 10 cm, then what is its lateral surface area?
The perimeter of a rectangle is 82 m and its area is 400 m^2. What is the breadth of the rectangle?
The area enclosed between the circumferences of two concentric circles is 16*pi cm^2 and their radii are in the ratio 5:3. What is the area of the outer circle?
The volume of a cube is numerically equal to sum of its edges. What is the total surface area in square units?
Two poles of heights 6 m and 11 m stand on a plane ground. If the distance between their feet is 12 m, what is the distance between their tops?
A right circular metal cone (solid) is 8 cm high and the radius is 2 cm. It is melted and recast into a sphere. What is the radius of the sphere?
The sum of the perpendiculars drawn from an interior point of an equilateral triangle is 20 cm. What is the length of side of the triangle?
Let the largest possible right circular cone and largest possible sphere be fitted into two cubes of same length. Let C and S denote the volume of cone and volume of sphere respectively, then which one of the following is correct?
The radius of the base of a right circular cone is increased by 15% keeping the height fixed. The volume of the cone will be increased by:
If the circumference of a circle is equal to the perimeter of square, then which one of the following is correct?
10 circular plates each of thickness 3 cm each are placed one above the other and a hemisphere of radius 6 cm is placed on the top just to cover the cylindrical solid. What is the volume of the solid so formed?
The circumferences of two circles are in the ratio 2:3. What is the ratio of their areas?
The area of a circle inscribed in an equilateral triangle is 154 cm^2. What is the perimeter of the triangle?
The lengths of three line segments in cm are given in each of the four cases. Which one of the following cases is not suitable to be the three sides of a triangle?
In histogram the width of the bars is proportional to:
Which one of the following relations for the numbers 10, 7, 8, 5, 6, 8, 5, 8, 6 is correct?
What is the harmonic mean of 10, 20, 25, 40 and 50?
The mean weight of 150 students in a class is 60 kg. The mean weight of boys is 70 kg and that of girls is 55 kg. What is the number of boys in the class?
The mean of 100 values is 45. If 15 is added to each of the first forty values and 5 is subtracted from each of the remaining sixty values, the new mean becomes:
Which of the following is/are correctly matched?
Select the correct answer using the code given below:
Consider the following distribution: values 1 2 3 4 5 with frequencies 3 f 6 5 3. For what value of f, is the arithmetic mean of the above distribution 3.1?