Q1
What is the geometric means of the observations 125, 729, 1331?
Elementary MathematicsStatistics
UPSC CDS · Solved paper
All 99 questions, textbook-style — tap “Show answer” on any question to reveal the correct option and explanation.
What is the geometric means of the observations 125, 729, 1331?
Examples of data are given below:
Which one of the following in respect of the above is correct?
Which one of the following can be obtained from a historgam?
The median of three positive integers, no two of which are equal, is 5. What is the least possible value of arithmetic means of these integers?
Consider the following pairs of numbers: (8, 12) II. (9, 11) III. (6, 24) Which pairs of number have the same harmonic means?
If 27 × (81) 2n+3 – 3 m = 0, then what is m equal to?
There are four numbers forming a GP in which the third term is greater than the first by 9 and the second term is greater than the fourth by 18. What is the first term?
What is the value of [log 13 (10)]/[log 169 (10)]?
A boy travels a distance of 8 km at the rate of 4 km/h, 6 km at the rate of 3 km/h and 4 km at the rate of 2 km/h. What is the average speed for the entire journey?
Which one of the following is not correct in respect of the sets A and B?
If 0 < θ< Φ< 90°, then which one of the following is correct?
For what value of θ is (sin θ+ cosecθ ) = 2.5 where 0 <θ ≤ 90°?
The angles of a triangle are in AP and the greatest angle is double the least. What is the ratio of angles in the Indian measure?
The length of the shadow of a person s cm tall when the angle of elevation of the sun is α is p cm. It is q cm when the angle of elevation of the sun is β. Which one of the following is correct when β = 3α ?
If cot θ= 2xy/x 2 -y 2 ,then what is cosθ equal to?
The value of cosec 2 θ– 2 + sin 2 θis always
If tan θ=p/q ,then what is p sec θ-q cosec θ/p sec θ+q cosec θ equal to?
What is the value of sin 3 60° cot 30° – 2 sec 2 45° + 3 cos 60° tan 45° – tan2 60°?
If 0 < x < 45° and 45° < y < 90°, then which one of the following is correct?
The difference of the two angles in degree measure is 1 and their sum in circular measure is also I. What are the angles in circular measure?
(cos θ/(1 − sin θ) − cos θ/(1 + sin θ)) = 2 is satisfied by which one of the following values of θ?
Consider the following:
Which of the statements given above is/are correct?
What is the angle subtended at the centre of a circle of radius 8 m after traversing 4π m along its circumference?
If cot θ = 8/15, then what is the value of √[(1 − cos θ)/(1 + cos θ)], where θ is a positive acute angle?
In the figure given above, O is the centre of the circle ∠AOD = 106°. What is ∠BCD equal to?
The quadrilateral formed by joining the mid-points of the sides AB, BC, CD, DA of a quadrilateral ABCD is
In the figure given above, ABCD is a square in which AO = AX. What is ∠XOB?
In the figure AB is parallel to CD and BE is parallel to FH. What is ∠FHE equal to?
In the figure given above, ∠AOB = 46°; AC and OB intersect each other at right angles. What is the measure of ∠OBC? (O is the centre of the circle)
In the figure given above, O is the centre of the circle. The line UTV is a tangent to the circle at T, ∠VTR = 52° and triangle PTR is an isosceles traingle such that TP = TR. What is ∠x + ∠y + s equal to?
What is the number of points in the plane of a triangle ABC which are at equal distance from the vertices of the triangle?
The bisectors of the angles ABC and BCA of a triangle ABC meet in a point O. What is the angle at O facing the side BC?
ABC is a triangle in which AB = AC. Let BC be produced to D. From a point E on the line AC let EF be a straight line such that EF is parallel to AB. Consider the quadrilateral ECDF thus formed. If ∠ABC = 65° and ∠EFD = 80°, then what is ∠FDC equal to
ABC is a triangle and the perpendicular drawn from A meets BC in D. If AD 2 = BD.DC, then which one of the following is correct?
Consider the following statements:
Which of the statements given above is/are correct?
ABC is triangle. X is a point outside the triangle ABC such that CD = CX, where D is the point of intersection of BC and AX; and ∠BAX = ∠XACWhich one of the following is correct?
A point P moves such that its distance from two given points A and B are equal. Then what is the focus of the point P?
In the figure given above, PT is a tangent to a circle of radius 6 cm. If P is at a distance of 10 cm from the centre O and PB = 5 cm, then what is the length of the chord BC?
A solid cone of height 8 cm and base radius 6 cm is melted and recast into identical cones, each of height 2 cm and radius 1 cm. What is the number of cones formed?
In the triangle ABC, AB = 2 cm, BC = 3cm, and AC = 4 cm, D is the middle point of AC. If a square is constructed on the side BD, what is the area of the square?
From a cylindrical log whose height is equal to its diameter, the greatest possible sphere has been taken out. What is the fraction of the original log which is cut away?
If a sphere of radius 10 cm is intersected by a plane at a distance 8 cm from its centre, what is the radius of the curve of intersection of the plane of the plane and the sphere?
A cylindrical can of internal diameter 24 cm contains was. A solid sphere of radius 6 cm is completely immersed to water in the cylinder. The water level increases by
A person rides a bicycle round a circular path of radius SC. The radius of the wheel of the bicycle is 50 cm. The cycle comes to the starting point for the first time in 1 h. What the number of revolutions of the wheel in 15 min?
ABC is a straight right-angled at C. If p is the length of perpendicular from C to AB and a, b, c are the sides, the which one of the following is correct?
A bucket which is in the form of a frustum of a corner radii 3 and 5 unit and vertical height 6 unit. How may water can the bucket hold?
How many litres of water (approximately) hemispherical container of radius 21 cm hold?
PQRS is a diameter of a circle of radius 6 cm as shown in the figure above. The lengths PQ, QR and RS are equal. Semicircles are drawn on PQ and QS as diameters. What is the perimeter of the shaded region?
If the radius of the base and the height of a right circular cone are increased by 20% then what is the approximate percentage increase in volume?
Seven semi-circular areas are removed from the rectangle ABCD as shown in the figure above. In which AB = 2 cm and AD = 0.5 cm. The radius of each semi-circle r, s, t, u, v is half of that of semi-circle p or q. What is the area of the remaining portion?
A wire is in the form of a circle of radius 42 cm. If it is bent into a square, then what is the side of the square?
How many litres of water flow out of a pipe having an area of cross-section of 5 cm 2 in one minute. If the speed of water in the pipe is 30 cm/s?
A right triangle ABC with sides 5 cm, 12 cm and 13 cm is revolved about the side 12 cm. What is the volume of the solid so obtained?
The ratio of volumes of two cones is 4 : 5 and the ratio of the radii of their bases is 2 : 3. What is the ratio of their vertical heights?
The paint in certain container is sufficient to paint an area equal to 5.875 m2. How many bricks of dimensions 12.5 cm ×10 × 7.5 cm can be painted out of this container?
If p is an integer then every square integer is of the form
What least value must be given to Å so that the number 84705 Å 2 is divisible by 9?
If x = (a + √(a² + b²))^(1/3) + (a − √(a² + b²))^(1/3), then what is the value of x³ + 3bx − 2a?
If the roots of the equation (m + 1)x² + 2mx + (m − 1) = 0 are equal, then what is the value of m?
What is [(x − y)³ + (y − z)³ + (z − x)³]/[4(x − y)(y − z)(z − x)] equal to?
For two natural numbers m and n, let g(m,n) denote the greatest common divisor of m and n. Consider the following in respect of three natural numbers k, m and n:
Which of the above is/are correct?
What is the value of k for which the system of equations x + 2y – 3 = 0 and 5x + ky + 7 = 0 has no solution?
If x + y + z = 0 then what is the value of
The length of a line segement AB is 2 unit. It is divided into two parts at the point C such that AC 2 = AB × CB. What is the length of CB?
If pq + qr + rp = 0, then what is the value of
If a = 1+x/2-x, the what is 1/a+1+2a+1/a2-1equal to?
The following table shows the percentage of male and female coffee drinkers and non-coffee drinkers in two Towns A and B. Atributes Town A Town B Male Female Male Female Coffee drinkers 40% 5% 25% 15% Non-coffee drinkers 20% 35% 30% 30% If the total population of the Towns A and B are 10000 and 20000 respectively, then what is the total number of female coffee drinkers in both towns?
If (37) x = (0.037) y = 10000, then what is the value of 1/x-1/y?
If ax = by = cz and abc = 1, then what is xy + yz + zx equal
When a polynomial is divided by alinear polynomial, then what is the remainder?
What is the ratio of sum of squares of roots to the product of the roots of the equation 7x 2 + 12x + 18 = 0?
If x = 2 + √3, then what is (x 2 + x –2 ) equal to?
Which one of the following statements is correct?
When x 40 + 2 is divided by x 4 + 1, what is the remainder?
If the HCF of x 3 – 27 and x 3 + 4x 2 + 12x + k is quadratic polynomial, then what is the value of k?
A number consists of two digits, whose sum is 10. If 18 is subtracted from the number, digits of the number are reversed. What is the product?
What is the LCM of 3 (a 3 – b 3 ) and 11 (a 4 – b 4 )?
Students of a class are made to stand in rows. If one student is extra in a row, there would be two rows less. If one student is less is n a row, there would be three rows more. What is the number of students in the class?
A railway ticket for a child costs half the full fare but the reservation charge is the same on half ticket as much as on full ticket. One reserved first class ticket for a journey between two stations is Rs. 362; one full and one half reserved first class tickets cost Rs. 554. What is reservations charge?
Out of a group of swans 7/2 times the square root of the number are swimming in the pool while the two remaining are playing outside the pool. What is the total number of swans?
If the ratio of x to y is 25 times the ratio of y to x, then what is the ratio of x to y?
A milk vendor bought 28 L of milk at the cost of Rs. 8.50 per litre. After adding some water, he sold the mixture at the same price. If he gains 12.5%, how much water did he add?
If m and n are two integers such that m = n 2 -n, then (m 2 – 2m) is always divisible by
10% of the inhabitants of a certain city left that city. Later on 10% of the remaining inhabitants of that city again left the city. What is the remaining percentage of population of that city?
If the rate of interest is 10% per annum and is compounded half yearly, the principal of Rs. 400 in 3/2 yr will amount to
The number of workers in the employment guarantee scheme increased by 15 which resulted into an increase of 20%. What are the initial number of workers?
Two men P and Q start from a place walking at 5 km at 6.5 km/h respectively. What is the time they will take to ?? 92 km apart if they walk in opposite directions?
In an army camp ration is available for 100 soldier 10 days. After 2 days, 60 soldiers joined. Then for many more days will the remaining ration last?
Two trains travel in the same direction at 50 km/h and 32 km/h respectively. A man in the slower train observes that 15 s elapse before the faster train completely passes him. What is the length of the faster train?
A person walks a distance in 114 days, when he rests 9 h a day. How long will he take to walk twice the distance if he walks twice as fast and rests twice as long each day as before?
If x : y = 1 : 3, y : z = 5: k, z : t = 2 : 5 and t : x + 3 :4, then what is the value of k?
The number is √0.0001 is
A person P started a business with a capital of Rs. 2525 and another person Q joined P after some months with a capital of Rs. 1200. Out of the total annual profit of Rs. 1644, P’s share was Rs. 1212. When did Q join as partners?
The mess charges for 35 students for 24 days in Rs. 6300. In how many days will the mess charges be Rs. 3375 for 25 students?
If a + b = 2m 2 , b + c = 6m, a + c = 2, where m is a real number and a ≤ b ≤ c, then which one of the following is correct?
What is the least number which when divided by 42, 72 and 84 leaves the remainders 25, 55 and 67 respectively?
A trader sells two cycles at Rs. 1188 each and gains 10% on the first and loses 10% on the second. What is the profit or loss percent on the whole?
A person borrowed Rs. 7500 at 16% compound interest. How much does he have to pay at the end of 2 yr to clear the loan?
P and Q can do a job in 2 days: Q and R can do it in 4 days; and P and R in 12/5 days. What is the number of days required for P alone to do the job?