Q1
The HCF of two numbers is 98 and their LCM is 2352. The sum of the numbers may be
Elementary MathematicsNumber System
UPSC CDS · Solved paper
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The HCF of two numbers is 98 and their LCM is 2352. The sum of the numbers may be
Consider the following statements:
Which of the above statements is/are correct?
Which one is one of the factors of x² + 1/x² + 8(x + 1/x) + 14?
What is the HCF of a²b^4 + 2a²b² and (ab)^7 − 4a²b^9?
What is the LCM of x²+2x−8, x³−4x²+4x and x²+4x?
A can do a piece of work in 4 days and B can complete the same work in 12 days. What is the number of days required to do the same work together?
Consider the following statements:
Which of the statements given above is/are correct?
A person sold an article for Rs. 3,600 and got a profit of 20%. Had he sold the article for Rs. 3,150, how much profit would he have got?
What is [(x²+y²)(x−y) − (x−y)³]/(x²y−xy²) equal to?
If x+y−7=0 and 3x+y−13=0, then what is 4x²+y²+4xy equal to?
If the expression x³+3x²+4x+k has a factor x+5, then what is the value of k?
In a class of 110 students, x students take both Mathematics and Statistics, 2x+20 take Mathematics and 2x+30 take Statistics. There are no students who take neither. What is x equal to?
If x² = 6 + √(6+√(6+…)), then what is one of the values of x equal to?
The quantity which must be added to (1−x)(1+x²) to obtain x³ is
Consider the following statements:
Which of the statements given above is/are correct?
19^5 + 21^5 is divisible by
If 49² − 25² = 37x, then what is x equal to?
For what values of k will 4x^5+9x^4−7x³−5x²−4kx+3k² contain (x−1) as a factor?
x(y²−z²)+y(z²−x²)+z(x²−y²) is divisible by
If x/2+y/3=4 and 2/x+3/y=1, then what is x+y equal to?
A person's salary has increased from Rs. 7,200 to Rs. 8,100. What is the percentage increase in his salary?
X can do a work in 16 days. In how many days will the work be completed by Y if the efficiency of Y is 60% more than that of X?
Two lots of onions with equal quantity, one costing Rs. 10 per kg and the other Rs. 15 per kg, are mixed together and the whole lot is sold at Rs. 15 per kg. What is the profit or loss?
For integers a, b and c, if HCF(a,b)=1 and HCF(a,c)=1, then which one of the following is correct?
If b is the largest square divisor of c and a² divides c, then which one of the following is correct? (a,b,c integers)
If k is a positive integer, then every square integer is of the form
Every prime number of the form 3k+1 can be represented in the form 6m+1 (k,m integers) when
How many 200 mm lengths can be cut from 10 m of ribbon?
What is 26² + 97² equal to?
2 men and 1 woman can complete a piece of work in 14 days, while 4 women and 2 men can do the same work in 8 days. If a man gets Rs. 90 per day, what should be the wages per day of a woman?
Which is the smallest number among the following?
What is the last digit in 7^402 + 3^402?
A train running at 72 kmph goes past a pole in 15 seconds. What is the length of the train?
18 men can earn Rs. 360 in 5 days. How much money will 15 men earn in 9 days?
The pair of rational numbers that lie between 1/4 and 3/4 is
A bus starts with some passengers. At the first stop, one-fifth get down and 40 get in. At the second stop, half get down and 30 get in. The number now is 70. The number with which the bus started was
A can finish a work in 15 days, B in 20 days and C in 25 days. All three worked together and earned Rs. 4,700. The share of C is
If x is a positive even integer and y is a negative odd integer, then x×y is
Two cars A and B start simultaneously from a certain place at 30 km/hr and 45 km/hr respectively. Car B reaches the destination 2 hours earlier than A. What is the distance?
4 goats or 6 sheep can graze a field in 50 days. 2 goats and 9 sheep can graze the field in
A man cycles at 10 kmph and reaches office at 1 p.m. At 15 kmph he reaches at 11 a.m. At what speed should he cycle to reach at 12 noon?
20 workers working 5 hours a day complete a work in 10 days. If 25 workers work 10 hours a day, what is the time required?
If m and n are natural numbers, then the m-th root of n (m√n) is
Consider statements in respect of ax²+bx+b=0 (a≠0):
If α and β are roots of x²−x−1=0, then what is (α³+β³)/((α²+β²)(α−β)) equal to?
The perimeter of a rectangle having area 144 sq cm and sides in ratio 4:9 is
Let A be a pyramid on a square base and B be a cube. Let a,b,c denote edges, faces, corners. Then a=b+c is true for
What is the area between a square of side 10 cm and two inverted semicircular cross-sections each of radius 5 cm inscribed in the square?
One side of a parallelogram is 8.06 cm and its perpendicular distance from opposite side is 2.08 cm. What is the approximate area?
What is the volume of a cone having base radius 10 cm and height 21 cm?
What is the area of a circle whose area is equal to that of a triangle with sides 7 cm, 24 cm and 25 cm?
If the area of an equilateral triangle is x and its perimeter is y, then which one is correct?
A rectangular field 22 m by 10 m. Two hemispherical pits of radius 2 m are dug and mud spread over remaining field. The rise in level is
Diameter of circle with centre C is 50 cm. CP is radial segment. AB is chord perpendicular to CP through P. CP produced meets circle at D. If DP=18 cm, then length of AB?
A regular hexagon is inscribed in a circle of radius 5 cm. If x is the area inside circle but outside hexagon, then
If x is curved surface area and y is volume of a right circular cylinder, then which is correct?
Triangle DBF joins midpoints of ABC; triangle PQR joins midpoints of DBF. If PQR sides are 1,2,3, what is perimeter of ABC?
A tent is a cylinder (dia 24 m, height 11 m) surmounted by a cone; vertex 16 m above ground. Curved surface area of conical portion?
What is the whole surface area of a cone of base radius 7 cm and height 24 cm?
A conical cap has base diameter 24 cm and height 16 cm. Cost of painting at 70 paise per sq cm?
The area of isosceles triangle ABC with AB=AC and altitude AD=3 cm is 12 sq cm. What is its perimeter?
If total surface area of a cube is 6 sq units, then volume is
Diameter of moon is ~1/4 of earth's diameter. Ratio of volumes (approx)?
A hospital room for 56 patients; each gets 2.2 sq m floor and 8.8 cu m space. Length 14 m. Breadth and height respectively?
If diagonals of a rhombus are 4.8 cm and 1.4 cm, perimeter?
Consider statements re chords XY and ZT intersecting at P:
ABCD is a quadrilateral with BC=BA and CD>AD. Which is correct?
ABC and XYZ are similar triangles with ∠C=∠Z, areas 32 and 60.5 sq cm. If XY=7.7 cm, then AB=?
Quadrilateral ABCD inscribed in a circle. If AB∥CD and AC=BD, then it must be a
ABC is right-angled at A; AD perpendicular to hypotenuse BC. What is BC·AD equal to?
In triangle ABC, ∠B=90° and ∠C=2∠A, then AB² equals
Heights of two trees x and y (x>y); tops z apart; s = shortest distance between trees. Then s² equals
Side AC of triangle ABC produced to D with BC=CD. If ∠ACB=70°, then ∠ADB equals
Consider:
Consider:
E is midpoint of median AD of triangle ABC. BE produced meets AC at F. Then CF equals
PQR is equilateral; O is intersection of altitudes PL,QM,RN. If OP=8 cm, perimeter?
ABC is equilateral inscribed in a circle. D is any point on arc BC. ∠ADB equals
Consider:
If bisectors BI and CI of angles B and C meet at I, then ∠BIC equals
If sinθ+cosθ=√3, then tanθ+cotθ equals
What is the angle of elevation of the sun when the shadow of a pole of height x m is x/√3 m?
What is [cos²(45°+θ)+cos²(45°−θ)]/[tan(60°+θ)tan(30°−θ)] equal to?
If tanθ+secθ=m, then secθ equals
If 5sinθ+12cosθ=13, then 5cosθ−12sinθ equals
If 4tanθ=3, then (4sinθ−cosθ)/(4sinθ+9cosθ) equals
If sinθ−cosθ=0, then sin^4θ+cos^4θ equals
What is cosec(75°+θ)−sec(15°−θ) equal to?
If triangle ABC is right-angled at C, then cos(A+B)+sin(A+B) equals
If α,β,γ are acute with sinα=√3/2, cosβ=√3/2, tanγ=1, then α+β+γ equals
What is sin^6θ+cos^6θ+3sin²θcos²θ equal to?
Consider:
What is (sinθ+cosθ)(tanθ+cotθ)/(secθ+cosecθ) equal to?
What is [(1+secθ−tanθ)cosθ]/[(1+secθ+tanθ)(1−sinθ)] equal to?
A spherical balloon of radius r subtends 60° at the observer's eye. Angle of elevation of centre is 60°; h = height of centre. Which is correct?
Methods of presentation of data are
The average of u,v,w,x,y,z is 10. What is the average of u+10, v+20, w+30, x+40, y+50, z+60?
If m is the mean of p,q,r,s,t,u,v, then (p−m)+(q−m)+(r−m)+(s−m)+(t−m)+(u−m)+(v−m) equals
The median of the distribution is 14.4 and total frequency is 20. (Classes 0–6,6–12,12–18,18–24,24–30 with frequencies 4,x,5,y,1.) What is x equal to?
(Same distribution) What is the relation between x and y?