Previous Year Papers

Elementary Mathematics 2019 (II)

Set C

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100Questions

120Minutes

100Marks

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Q1What is the mean of frequency distribution of Series-I ?MeanModerate
Q2What is the mode of the frequency distribution of Series-II ?ModeModerate
Q3Number of scooters of company $Y$ sold by showroom $E$ is what per cent of the number of scooters of both companies sold by showroom $C$ ?TableModerate
Q4Number of scooters of both the companies sold by showroom $B$ is what per cent more than the number of scooters of company $X$ sold by showroom $A$ ?TableModerate
Q5What is the average number of scooters of company $Y$ sold by the showrooms $A$ , $C$ and $E$ ?TableModerate
Q6What is the difference between the number of scooters of both companies sold by showroom $A$ and total number of scooters of company $X$ sold by showrooms $B$ and $E$ together ?TableModerate
Q7What was the average number of pedestrians killed per day in the year $2017$ ?TableEasy
Q8What is the approximate percentage change in the pedestrians' fatalities during the period 2014-17 ?TableEasy
Q9What is the average number of bikers killed daily in road accidents in the year $2017$ ?TableEasy
Q10What is the average number of cyclists killed daily in road accidents in $2017$ ?TableEasy
Q11Let $a$ and $b$ be two positive real numbers such that $a a + b b = 32$ and $a b + b a = 31$ . What is the value of $\frac{5 ( a + b )}{7}$ ?SimplificationHard
Q12If $x = \frac{1 + 3}{2}$ and $y = x^{3}$ , then $y$ satisfies which one of the following equations ?Algebraic IdentitiesHard
Q13HCF of two numbers is $12$ . Which one of the following can never be their LCM ?LCM and HCFEasy
Q14Consider the following statements :DivisibilityHard
Q15The rate of interest on two different schemes is the same and it is $20%$ . But in one of the schemes, the interest is compounded half yearly and in the other the interest is compounded annually. Equal amounts are invested in the schemes. If the difference of the returns after $2$ years is Rs. $482$ , then what is the principal amount in each scheme ?Compound InterestModerate
Q16For what value of $k$ can the expression $x^{3} + k x^{2} - 7 x + 6$ be resolved into three linear factors ?FactorisationModerate
Q17 $X$ , $Y$ and $Z$ start at same point and same time in the same direction to run around a circular stadium. $X$ completes a round in $252$ seconds, $Y$ in $308$ seconds and $Z$ in $198$ seconds. After what time will they meet again at the starting point ?LCM and HCFModerate
Q18What is the LCM of $\frac{1}{3}, \frac{5}{6}, \frac{2}{9}, \frac{4}{27}$ ?LCM and HCFEasy
Q19If the equations $x^{2} + 5 x + 6 = 0$ and $x^{2} + k x + 1 = 0$ have a common root, then what is the value of $k$ ?RootsModerate
Q20 $A$ lent Rs. $25000$ to $B$ and at the same time lent some amount to $C$ at same $7%$ simple interest. After $4$ years $A$ received Rs. $11200$ as interest from $B$ and $C$ . How much did $A$ lend to $C$ ?Simple InterestEasy
Q21A trader sells two computers at the same price, making a profit of $30%$ on one and a loss of $30%$ on the other. What is the net loss or profit percentage on the transaction ?Profit and LossEasy
Q22The monthly incomes of $A$ and $B$ are in the ratio $4$ : $3$ . Each saves Rs. $600$ . If their expenditures are in the ratio $3$ : $2$ , then what is the monthly income of $A$ ?Ratio and ProportionEasy
Q23The train fare and bus fare between two stations is in the ratio $3$ : $4$ . If the train fare increases by $20%$ and bus fare increases by $30%$ , then what is the ratio between revised train fare and revised bus fare ?Ratio and ProportionEasy
Q24When $N$ is divided by $17$ , the quotient is equal to $182$ . The difference between the quotient and the remainder is $175$ . What is the value of $N$ ?DivisibilityEasy
Q25A stock of food grains is enough for $240$ men for $48$ days. How long will the same stock last for $160$ men ?Time and WorkEasy
Q26A hollow right circular cylindrical vessel of volume $V$ whose diameter is equal to its height, is completely filled with water. A heavy sphere of maximum possible volume is then completely immersed in the vessel. What volume of water remains in the vessel?Recasting and MeltingModerate
Q27Three parallel lines $x, y$ and $z$ are cut by two transversals $m$ and $n$ . Transversal $m$ cuts the lines $x, y, z$ at $P, Q, R$ respectively; and Transversal $n$ cuts the lines $x, y, z$ at $L, M, N$ respectively. If $P Q = 3 cm$ , $QR = 9 cm$ and $M N = 10.5 cm$ , then what is the length of $L M$ ?Parallel Lines and TransversalsModerate
Q28The area of a sector of a circle of radius $4 cm$ is $25.6 cm^{2}$ . What is the radian measure of the arc of the sector?CircleEasy
Q29Which one of the following is correct in respect of a right angled triangle?Pythagoras TheoremEasy
Q30Let the bisector of the angle $B A C$ of a triangle $A B C$ meet $B C$ in $X$ . Which one of the following is correct?Angle BisectorModerate
Q31What is the value of $lo g_{10} (cos θ) + lo g_{10} (sin θ) + lo g_{10} (tan θ) + lo g_{10} (cot θ) + lo g_{10} (sec θ) + lo g_{10} (cosec θ)$ ?Trigonometric IdentityEasy
Q32If $cos^{2} x + cos x = 1$ , then what is the value of $sin^{12} x + 3 sin^{10} x + 3 sin^{8} x + sin^{6} x$ ?Trigonometric IdentityHard
Q33If $0 < θ < 9 0^{\circ}$ , $sin θ = \frac{3}{5}$ and $x = cot θ$ , then what is the value of $1 + 3 x + 9 x^{2} + 27 x^{3} + 81 x^{4} + 243 x^{5}$ ?Trigonometric IdentityModerate
Q34The angles of elevation of the tops of two pillars of heights $h$ and $2 h$ from a point $P$ on the line joining the feet of the two pillars are complementary. If the distances of the foot of the pillars from the point $P$ are $x$ and $y$ respectively, then which one of the following is correct?Heights and DistancesModerate
Q35What is the value of $\frac{s i n 1 9 ^{\circ}}{c o s 7 1 ^{\circ}} + \frac{c o s 7 3 ^{\circ}}{s i n 1 7 ^{\circ}}$ ?Complementary AnglesEasy
Q36The perimeter of a triangle is $22 cm$ . Through each vertex of the triangle, a straight line parallel to the opposite side is drawn. What is the perimeter of triangle formed by these lines?SimilarityModerate
Q37The sides $A D, B C$ of a trapezium $A B C D$ are parallel and the diagonals $A C$ and $B D$ meet at $O$ . If the area of triangle $A O B$ is $3 cm^{2}$ and the area of triangle $B D C$ is $8 cm^{2}$ , then what is the area of triangle $A O D$ ?TrapeziumHard
Q38A line segment $A B$ is the diameter of a circle with centre at $O$ having radius $6.5 cm$ . Point $P$ is in the plane of the circle such that $A P = x$ and $B P = y$ . In which one of the following cases the point $P$ does not lie on the circle?LocusModerate
Q39The perimeters of two similar triangles $A B C$ and $P QR$ are $75 cm$ and $50 cm$ respectively. If the length of one side of the triangle $P QR$ is $20 cm$ , then what is the length of corresponding side of the triangle $A B C$ ?SimilarityEasy
Q40Let $P QR S$ be a parallelogram whose diagonals $P R$ and $QS$ intersect at $O$ . If triangle $QR S$ is an equilateral triangle having a side of length $10 cm$ , then what is the length of the diagonal $P R$ ?ParallelogramModerate
Q41The areas of three adjacent faces of a cuboid are $x, y$ and $z$ . If $V$ is the volume of the cuboid, then which one of the following is correct?CuboidEasy
Q42If $l$ is the length of the median of an equilateral triangle, then what is its area?TriangleEasy
Q43A piece of wire is in the form of a sector of a circle of radius $20 cm$ , subtending an angle $15 0^{\circ}$ at the centre. If it is bent in the form of a circle, then what will be its radius?CircleModerate
Q44Suppose $P, Q$ and $R$ are the mid-points of sides of a triangle of area $128 cm^{2}$ . If a triangle $A B C$ is drawn by joining the mid-points of sides of triangle $P QR$ , then what is the area of triangle $A B C$ ?TriangleEasy
Q45Let two lines $p$ and $q$ be parallel. Consider two points $B$ and $C$ on the line $p$ and two points $D$ and $E$ on the line $q$ . The line through $B$ and $E$ intersects the line through $C$ and $D$ at $A$ in between the two lines $p$ and $q$ . If $A C : A D = 4 : 9$ , then what is the ratio of area of triangle $A B C$ to that of triangle $A D E$ ?SimilarityModerate
Q46An equilateral triangle and a square are constructed using metallic wires of equal length. What is the ratio of area of triangle to that of square?Plane FiguresEasy
Q47All the four sides of a parallelogram are of equal length. The diagonals are in the ratio $1 : 2$ . If the sum of the lengths of the diagonals is $12 cm$ , then what is the area of the parallelogram?QuadrilateralEasy
Q48 $A B C$ is a triangle right angled at $B$ . If $A B = 5 cm$ and $B C = 10 cm$ , then what is the length of the perpendicular drawn from the vertex $B$ to the hypotenuse?Pythagoras TheoremEasy
Q49Two cylinders of equal volume have their heights in the ratio $2 : 3$ . What is the ratio of their radii?CylinderEasy
Q50The length and breadth of a rectangle are increased by $20%$ and $10%$ respectively. What is the percentage increase in the area of the rectangle?QuadrilateralVery easy
Q51If the length of the hypotenuse of a right angled triangle is $10$ cm, then what is the maximum area of such a right angled triangle?TriangleModerate
Q52A square is drawn such that its vertices are lying on a circle of radius $201$ mm. What is the ratio of area of circle to that of square?Composite and Shaded RegionsEasy
Q53A right circular cylinder has a diameter of $20$ cm and its curved surface area is $1000 cm^{2}$ . What is the volume of the cylinder?CylinderEasy
Q54A piece of wire of length $33$ cm is bent into an arc of a circle of radius $14$ cm. What is the angle subtended by the arc at the centre of the circle?CircleVery easy
Q55What is the ratio of the area of a square inscribed in a semicircle of radius $r$ to the area of square inscribed in a circle of radius $r$ ?Composite and Shaded RegionsModerate
Q56The quotient when $x^{4} - x^{2} + 7 x + 5$ is divided by $(x + 2)$ is $a x^{3} + b x^{2} + c x + d$ . What are the values of $a$ , $b$ , $c$ and $d$ respectively?Factor and Remainder TheoremModerate
Q57The sides of a triangle are $30$ cm, $28$ cm and $16$ cm respectively. In order to determine its area, the logarithm of which of the quantities are required?TriangleEasy
Q58If $lo g_{10} 1995 = 3.3000$ , then what is the value of $(0.001995)^{\frac{1}{8}}$ ?Characteristic and MantissaModerate
Q59What is $(x - a) (x - b) (x - c)$ equal to?Algebraic IdentitiesVery easy
Q60Let $X Y Z$ be an equilateral triangle in which $X Y = 7$ cm. If $A$ denotes the area of the triangle, then what is the value of $lo g_{10} A^{4}$ ? (Given that $lo g_{10} 1050 = 3.0212$ and $lo g_{10} 35 = 1.5441$ )Laws of LogarithmsHard
Q61A hollow sphere of external and internal diameters $6$ cm and $4$ cm respectively is melted into a cone of base diameter $8$ cm. What is the height of the cone?Recasting and MeltingModerate
Q62A solid metallic cylinder of height $10$ cm and radius $6$ cm is melted to make two cones in the ratio of volume $1 : 2$ and of same height as $10$ cm. What is the percentage increase in the flat surface area?Recasting and MeltingHard
Q63If one side of a right-angled triangle (with all sides integers) is $15$ cm, then what is the maximum perimeter of the triangle?Pythagoras TheoremHard
Q64A thin rod of length $24$ feet is cut into rods of equal size and joined so as to form a skeleton cube. What is the area of one of the faces of the largest cube thus constructed?CubeVery easy
Q65Consider a trapezium $A B C D$ , in which $A B$ is parallel to $C D$ and $A D$ is perpendicular to $A B$ . If the trapezium has an incircle which touches $A B$ at $E$ and $C D$ at $F$ , where $E B = 25$ cm and $F C = 16$ cm, then what is the diameter of the circle?TangentialHard
Q66Three copper spheres of radii $3$ cm, $4$ cm and $5$ cm are melted to form a large sphere. What is its radius?Recasting and MeltingEasy
Q67The volume of a hemisphere is $155232 cm^{3}$ . What is the radius of the hemisphere?SphereModerate
Q68A bucket is in the form of a truncated cone. The diameters of the base and top of the bucket are $6$ cm and $12$ cm respectively. If the height of the bucket is $7$ cm, what is the capacity of the bucket?FrustumEasy
Q69A right circular cone has height $8$ cm. If the radius of its base is $6$ cm, then what is its total surface area?ConeEasy
Q70Six cubes, each with $12$ cm edge are joined end to end. What is the surface area of resulting cuboid?Combination of SolidsEasy
Q71If the sum of a real number and its reciprocal is $\frac{26}{5}$ , then how many such numbers are possible?Word ProblemsEasy
Q72Consider the following statements:Prime NumbersModerate
Q73Radha and Rani are sisters. Five years back, the age of Radha was three times that of Rani, but one year back the age of Radha was two times that of Rani. What is the age difference between them?Age ProblemsEasy
Q74A person carries Rs. $500$ and wants to buy apples and oranges out of it. If the cost of one apple is Rs. $5$ and the cost of one orange is Rs. $7$ , then what is the number of ways in which a person can buy both apples and oranges using total amount?Linear EquationsModerate
Q75Given $y$ is inversely proportional to $x$ , and $x = 36$ when $y = 36$ . What is the value of $x$ when $y = 54$ ?Direct and Inverse VariationEasy
Q76What is the square root of $16 + 67$ ?SimplificationModerate
Q77What is the number of digits in $7^{25}$ , $8^{23}$ and $9^{20}$ respectively ? [Given $lo g_{10} 2 = 0.301$ , $lo g_{10} 3 = 0.477$ , $lo g_{10} 7 = 0.845$ ]Characteristic and MantissaModerate
Q78Let $x$ be the smallest positive integer such that when $14$ divides $x$ , the remainder is $7$ ; and when $15$ divides $x$ , the remainder is $5$ . Which one of the following is correct ?DivisibilityEasy
Q79Two taps $X$ and $Y$ are fixed to a water tank. If only $X$ is opened, it drains out the full tank of water in $20$ minutes. If both $X$ and $Y$ are opened, then they drain out the full tank of water in $15$ minutes. If only $Y$ is opened, how long does it take to drain out the full tank of water ?Pipes and CisternsEasy
Q80Consider the following statements :Rational NumbersHard
Q81A library has an average number of $510$ visitors on Sunday and $240$ on other days. What is the average number of visitors per day in a month of $30$ days beginning with Saturday ?MeanModerate
Q82If $\frac{36}{11} = 3 + \frac{1}{x + \frac{1}{y + \frac{1}{z}}}$ , where $x$ , $y$ and $z$ are natural numbers, then what is $(x + y + z)$ equal to ?Rational NumbersModerate
Q83A person sells two items each at Rs. $990$ , one at a profit of $10%$ and another at a loss of $10%$ . What is the combined percentage of profit or loss for the two items ?Profit and LossEasy
Q84It takes $11$ hours for a $600$ km journey if $120$ km is done by train and the rest by car. It takes $40$ minutes more if $200$ km are covered by train and the rest by car. What is the ratio of speed of the car to that of the train ?Time, Speed and DistanceHard
Q85A real number $x$ is such that $(x - x^{2})$ is maximum. What is $x$ equal to ?Maximum and Minimum ValuesEasy
Q86If $1 0^{n}$ divides $6^{23} \times 7 5^{9} \times 10 5^{2}$ , then what is the largest value of $n$ ?DivisibilityModerate
Q87What is the digit in the unit's place of the number represented by $3^{98} - 3^{89}$ ?Unit DigitEasy
Q88The sum of the squares of four consecutive natural numbers is $294$ . What is the sum of the numbers ?Word ProblemsEasy
Q89The equation $x^{2} + p x + q = 0$ has roots equal to $p$ and $q$ where $q \neq = 0$ . What are the values of $p$ and $q$ respectively ?RootsModerate
Q90How many pairs of natural numbers are there such that the difference of their squares is $35$ ?Number SystemModerate
Q91If $(b - 6)$ is one root of the quadratic equation $x^{2} - 6 x + b = 0$ , where $b$ is an integer, then what is the maximum value of $b^{2}$ ?RootsModerate
Q92If $a = 7 + 43$ , then what is the value of $a + \frac{1}{a}$ ?SimplificationModerate
Q93What is the maximum value of the expression $\frac{1}{x ^{2} + 5 x + 10}$ ?Maximum and Minimum ValuesEasy
Q94If the ratio of the work done by $(x + 2)$ workers in $(x - 3)$ days to the work done by $(x + 4)$ workers in $(x - 2)$ days is $3 : 4$ , then what is the value of $x$ ?Time and WorkModerate
Q95Which one of the following is not correct ?Number SystemEasy
Q96What is the sum of all integer values of $n$ for which $n^{2} + 19 n + 92$ is a perfect square ?Quadratic EquationsHard
Q97What is the LCM of the polynomials $x^{3} + 3 x^{2} + 3 x + 1$ , $x^{3} + 5 x^{2} + 5 x + 4$ and $x^{2} + 5 x + 4$ ?HCF and LCMModerate
Q98What is the value of $\frac{( x - y ) ^{3} + ( y - z ) ^{3} + ( z - x ) ^{3}}{9 ( x - y ) ( y - z ) ( z - x )}$ ?Algebraic IdentitiesEasy
Q99If $X = {a, {b}, c}$ , $Y = {{a}, b, c}$ and $Z = {a, b, {c}}$ , then $(X \cap Y) \cap Z$ equals toOperationsModerate
Q100Two numbers $p$ and $q$ are such that the quadratic equation $p x^{2} + 3 x + 2 q = 0$ has $- 6$ as the sum and the product of the roots. What is the value of $(p - q)$ ?RootsModerate

Topic mix

Arithmetic25
Mensuration24
Algebra23
Geometry12
Statistics11
Trigonometry5

Total questions100

Difficulty

P(a prepared candidate answers correctly in ~90 seconds)

Very easy4
Easy43
Moderate41
Hard12
Very hard0

Marking scheme

Correct answer+1
Wrong answer−1/3 × 1
Unattempted0

Options per question: 4Correct options per question: 1