Previous Year Papers

Elementary Mathematics 2018 (I)

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100Questions

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Q1 $5^{17} + 5^{18} + 5^{19} + 5^{20}$ is divisible byDivisibilityEasy
Q2If $a + b = 2 c$ , then what is the value of $\frac{a}{a - c} + \frac{c}{b - c}$ ?SimplificationModerate
Q3If $x = y^{1/ a}$ , $y = z^{1/ b}$ and $z = x^{1/ c}$ where $x \neq = 1$ , $y \neq = 1$ , $z \neq = 1$ , then what is the value of $ab c$ ?IndicesEasy
Q4If $2 b = a + c$ and $y^{2} = x z$ , then what is $x^{b - c} y^{c - a} z^{a - b}$ equal to ?IndicesModerate
Q5Which one of the following is correct ?Rational NumbersEasy
Q6If the roots of the equation $p x^{2} + x + r = 0$ are reciprocal to each other, then which one of the following is correct ?RootsEasy
Q7If $65 x - 33 y = 97$ and $33 x - 65 y = 1$ , then what is $x y$ equal to ?Linear EquationsModerate
Q8If $\frac{b}{y} + \frac{z}{c} = 1$ and $\frac{c}{z} + \frac{x}{a} = 1$ , then what is $\frac{ab + x y}{b x}$ equal to ?Linear EquationsModerate
Q9If $\frac{a ^{2} - 1}{a} = 5$ , then what is the value of $\frac{a ^{6} - 1}{a ^{3}}$ ?SimplificationModerate
Q10If $x + y + z = 0$ , then what is $(y + z - x)^{3} + (z + x - y)^{3} + (x + y - z)^{3}$ equal to ?SimplificationModerate
Q11If $(x + 3)$ is a factor of $x^{3} + 3 x^{2} + 4 x + k$ , then what is the value of $k$ ?Factor and Remainder TheoremVery easy
Q12The smallest integer with $4$ digits which is a perfect square isPerfect SquaresEasy
Q13Which one of the following is a zero of the polynomial $3 x^{3} + 4 x^{2} - 7$ ?Zeros and CoefficientsVery easy
Q14There are two numbers which are greater than $21$ and their LCM and HCF are $3003$ and $21$ respectively. What is the sum of these numbers ?LCM and HCFModerate
Q15If $α$ and $β$ are the roots of the equation $a x^{2} + b x + c = 0$ , then what is the value of the expression $(α + 1) (β + 1)$ ?RootsEasy
Q16The remainder when $3 x^{3} + k x^{2} + 5 x - 6$ is divided by $(x + 1)$ is $- 7$ . What is the value of $k$ ?Factor and Remainder TheoremEasy
Q17If $f (x)$ and $g (x)$ are polynomials of degree $p$ and $q$ respectively, then the degree of ${f (x) \pm g (x)}$ (if it is non-zero) isPolynomialEasy
Q18What is the value of $\frac{5 - 3}{5 + 3} - \frac{5 + 3}{5 - 3}$ ?SimplificationEasy
Q19What is the value of $\frac{1}{1 + x ^{b - a} + x ^{c - a}} + \frac{1}{1 + x ^{a - b} + x ^{c - b}} + \frac{1}{1 + x ^{a - c} + x ^{b - c}}$ where $x \neq = 0$ ?SimplificationModerate
Q20The sum of a number and its square is $20$ . Then the number isWord ProblemsEasy
Q21If the price of wheat rises by $25%$ , then by how much percent must a man reduce his consumption in order to keep his budget the same as before ?Price and ConsumptionEasy
Q22 $\frac{1}{25}$ of the students who registered did not appear for the examination, $\frac{11}{20}$ of those who appeared passed. If the number of registered students is $2000$ , the number who passed isRatio and ProportionEasy
Q23What is the difference between $0. 9$ and $0.9$ ?Rational NumbersModerate
Q24If $A : B = 1 : 2$ , $B : C = 3 : 4$ , $C : D = 2 : 3$ and $D : E = 3 : 4$ , then what is $B : E$ equal to ?ProportionEasy
Q25A work when done by $10$ women is completed in $12$ days. The same work can be completed in $8$ days when done by $5$ men. How many days will it take to complete when $6$ women and $3$ men are employed to perform the same job ?Time and WorkModerate
Q26A man undertakes to do a certain work in $150$ days. He employs $200$ men. He finds that only a quarter of the work is done in $50$ days. How many additional men should he employ so that the whole work is finished in time ?Time and WorkModerate
Q27A train moving with a speed of $60$ km per hour crosses an electric pole in $30$ seconds. What is the length of the train in metres ?TrainsEasy
Q28Rs. $120$ is distributed among A, B and C so that A's share is Rs. $20$ more than B's and Rs. $20$ less than C's. What is B's share ?Division into PartsEasy
Q29In the following table of inverse variation, what are the values of A, B and C respectively ?Direct and Inverse VariationEasy
Q30A person borrowed Rs. $5, 000$ at $5%$ rate of interest per annum and immediately lent it at $5.5%$ . After two years he collected the amount and settled his loan. What is the amount gained by him in this transaction ?Simple InterestEasy
Q31At present the average of the ages of a father and a son is $25$ years. After seven years the son will be $17$ years old. What will be the age of the father after $10$ years ?Age ProblemsEasy
Q32If $5$ tractors can plough $5$ hectares of land in $5$ days, then what is the number of tractors required to plough $100$ hectares in $50$ days ?Time and WorkEasy
Q33A merchant commences with a certain capital and gains annually at the rate of $25%$ . At the end of $3$ years he has Rs. $10, 000$ . What is the original amount that the merchant invested ?Compound InterestEasy
Q34Which one of the following decimal numbers is a rational number with denominator $37$ ?Rational NumbersModerate
Q35The annual income of a person decreases by Rs. $64$ if the annual rate of interest decreases from $4%$ to $3.75%$ . What is his original annual income ?Simple InterestModerate
Q36For $0 < m < 1$ , which one of the following is correct ?LogarithmEasy
Q37A gentleman left a sum of Rs. $39, 000$ to be distributed after his death among his widow, five sons and four daughters. If each son receives $3$ times as much as a daughter receives, and each daughter receives twice as much as their mother receives, then what is the widow's share ?Division into PartsEasy
Q38Three numbers which are co-prime to each other, are such that the product of the first two is $286$ and that of the last two is $770$ . What is the sum of the three numbers ?LCM and HCFModerate
Q39The age of a woman is a two-digit integer. On reversing this integer, the new integer is the age of her husband who is elder to her. The difference between their ages is one-eleventh of their sum. What is the difference between their ages ?Linear EquationsModerate
Q40A passenger train and a goods train are running in the same direction on parallel railway tracks. If the passenger train now takes three times as long to pass the goods train, as when they are running in opposite directions, then what is the ratio of the speed of the passenger train to that of the goods train ?TrainsModerate
Q41All odd prime numbers upto $110$ are multiplied together. What is the unit digit in this product ?Unit DigitEasy
Q42An alloy A contains two elements, copper and tin in the ratio $2 : 3$ , whereas an alloy B contains the same elements in the ratio $3 : 4$ . If $20$ kg of alloy A, $28$ kg of alloy B and some more pure copper are mixed to form a third alloy C which now contains copper and tin in the ratio $6 : 7$ , then what is the quantity of pure copper mixed in the alloy C ?Mixtures and AlligationEasy
Q43A quadratic polynomial $a x^{2} + b x + c$ is such that when it is divided by $x$ , $(x - 1)$ and $(x + 1)$ , the remainders are $3$ , $6$ and $4$ respectively. What is the value of $(a + b)$ ?Factor and Remainder TheoremEasy
Q44If the average of $9$ consecutive positive integers is $55$ , then what is the largest integer ?MeanVery easy
Q45The average of the ages of $15$ students in a class is $19$ years. When $5$ new students are admitted to the class, the average age of the class becomes $18.5$ years. What is the average age of the $5$ newly admitted students ?Weighted MeanEasy
Q46A man can row at a speed of $x$ km/hr in still water. If in a stream which is flowing at a speed of $y$ km/hr it takes him $z$ hours to row to a place and back, then what is the distance between the two places ?Boats and StreamsEasy
Q47A water tank has been fitted with two taps P and Q and a drain pipe R. Taps P and Q fill at the rate of $12$ litres per minute and $10$ litres per minute respectively.Pipes and CisternsModerate
Q48A car has an average speed of $60$ km per hour while going from Delhi to Agra and has an average speed of $y$ km per hour while returning to Delhi from Agra (by travelling the same distance). If the average speed of the car for the whole journey is $48$ km per hour, then what is the value of $y$ ?Average SpeedEasy
Q49An article is sold at a profit of $32%$ . If the cost price is increased by $20%$ and the sale price remains the same, then the profit percentage becomesProfit and LossEasy
Q50A, B, C, D and E start a partnership firm. Capital contributed by A is three times that contributed by D. E contributes half of A's contribution, B contributes one-third of E's contribution and C contributes two-third of A's contribution. If the difference between the combined shares of A, D and E and the combined shares of B and C in the total profit of the firm is Rs. $13, 500$ , what is the combined share of B, C and E ? (The shares are supposed to be proportional to the contributions)PartnershipModerate
Q51A Pie Chart is drawn for the following data :Pie ChartEasy
Q52The arithmetic mean of two numbers is $10$ and their geometric mean is $8$ . What are the two numbers ?MeanEasy
Q53The arithmetic mean of $11$ observations is $11$ . The arithmetic mean of the first $6$ observations is $10.5$ and the arithmetic mean of the last $6$ observations is $11.5$ . What is the sixth observation ?Weighted MeanEasy
Q54What is $sin^{4} θ - cos^{4} θ$ equal to for any real number $θ$ ?Trigonometric IdentityEasy
Q55What is $cot 1^{\circ} cot 2 3^{\circ} cot 4 5^{\circ} cot 6 7^{\circ} cot 8 9^{\circ}$ equal to ?Complementary AnglesEasy
Q56What angle does the hour hand of a clock describe in $10$ minutes of time ?Angle Between HandsVery easy
Q57Consider the following statements :Trigonometric IdentityModerate
Q58Each side of a square subtends an angle of $6 0^{\circ}$ at the tip of a tower of height $h$ metres standing at the centre of the square. If $l$ is the length of each side of the square, then what is $h^{2}$ equal to ?Heights and DistancesHard
Q59From a height of $h$ units, a man observes the angle of elevation as $α$ and angle of depression as $β$ of the top and the bottom respectively of a tower of height $H$ $(> 4 h)$ . To what further height should he climb so that the values of angle of elevation and angle of depression get interchanged for the top and bottom of the tower ?Heights and DistancesModerate
Q60If $sec x cosec x = 2$ , then what is $tan^{n} x + cot^{n} x$ equal to ?Trigonometric IdentityEasy
Q61If $cos x + cos^{2} x = 1$ , then what is $sin^{2} x + sin^{4} x$ equal to ?Trigonometric IdentityEasy
Q62If $sin A + cos A = p$ and $sin^{3} A + cos^{3} A = q$ , then which one of the following is correct ?Trigonometric IdentityModerate
Q63If $x = \frac{s e c ^{2} θ - t a n θ}{s e c ^{2} θ + t a n θ}$ , then which one of the following is correct ?Trigonometric IdentityHard
Q64ABC is a right angled triangle with base BC and height AB. The hypotenuse AC is four times the length of the perpendicular drawn to it from the opposite vertex. What is $tan C$ equal to ?TriangleHard
Q65ABC is a triangle right angled at C with BC $= a$ and AC $= b$ . If $p$ is the length of the perpendicular from C on AB, then which one of the following is correct ?TriangleEasy
Q66The radius and slant height of a right circular cone are $5$ cm and $13$ cm respectively. What is the volume of the cone ?ConeEasy
Q67Two equal circular regions of greatest possible area are cut off from a given circular sheet of area A. What is the remaining area of the sheet ?CircleEasy
Q68If the ratio of the radius of the base of a right circular cone to its slant height is $1 : 3$ , what is the ratio of the total surface area to the curved surface area ?ConeEasy
Q69A right circular cone is sliced into a smaller cone and a frustum of a cone by a plane perpendicular to its axis. The volume of the smaller cone and the frustum of the cone are in the ratio $64 : 61$ . Then their curved surface areas are in the ratioConeModerate
Q70In a room whose floor is a square of side $10$ m, an equilateral triangular table of side $2$ m is placed. Four book-shelves of size $4$ m $\times$ $1$ m $\times$ $9$ m are also placed in the room. If half of the rest of the area in the room is to be carpeted at the rate of Rs. $100$ per square metre, what is the cost of carpeting (approximately) ?Composite and Shaded RegionsModerate
Q71A region of area A bounded by a circle C is divided into $n$ regions, each of area $A / n$ , by drawing circles of radii $r_{1}$ , $r_{2}$ , $r_{3}$ , $\dots r_{n - 1}$ such that $r_{1} < r_{2} < r_{3} < \dots r_{n - 1}$ concentric with the circle C. If $p_{m} = \frac{r _{m + 1}}{r _{m}}$ where $m = 1, 2, 3, \dots (n - 2)$ , then which one of the following is correct ?CircleModerate
Q72What is the volume of a cone of maximum volume cut out from a cube of edge $2 a$ such that their bases are on the same plane ?ConeEasy
Q73The radii of two circles are $4.5$ cm and $3.5$ cm respectively. The distance between the centres of the circles is $10$ cm. What is the length of the transverse common tangent ?TangentsEasy
Q74There are as many square centimetres in the surface area of a sphere as there are cubic centimetres in its volume. What is the radius of the sphere ?SphereEasy
Q75The length of a line segment AB is $2$ cm. It is divided into two parts at a point C such that AC $^{2}$ = AB $\times$ CB. What is the length of CB ?LineModerate
Q76The locus of the mid-points of the radii of length $16$ cm of a circle isLocusVery easy
Q77The curved surface area of a right circular cone is $1.76$ m $^{2}$ and its base diameter is $140$ cm. What is the height of the cone ?ConeModerate
Q78Consider the following statements :Triangle CentresModerate
Q79The locus of a point equidistant from two intersecting lines isLineModerate
Q80Consider the following statements :CongruenceEasy
Q81Given that the angles of a polygon are all equal and each angle is a right angle.Interior and Exterior AnglesModerate
Q82If the length of a side of a square is increased by $8$ cm, its area increases by $120$ square cm. What is the length of a side of the square ?QuadrilateralEasy
Q83What is the largest power of $10$ that divides the product $1 \times 2 \times 3 \times 4 \dots \times 23 \times 24 \times 25$ ?DivisibilityModerate
Q84Walls (excluding their roofs and floors) of $5$ identical rooms having length, breadth and height $6$ m, $4$ m and $2.5$ m respectively are to be painted. Paints are available only in cans of $1$ L and one litre of paint can be used for painting $20$ square metres. What is the number of cans required for painting ?CuboidEasy
Q85A rectangular pathway having width $4.5$ m and length $10$ m will have to be tiled using square tiles of side $50$ cm. Each packet of such tiles contains $20$ pieces and costs Rs. $100$ . What will be the total cost of tiles for the pathway ?QuadrilateralEasy
Q86A cube of maximum volume (each corner touching the surface from inside) is cut from a sphere. What is the ratio of the volume of the cube to that of the sphere ?CubeModerate
Q87If the ratio of the circumference of the base of a right circular cone of radius $r$ to its height is $3 : 1$ , then what is the area of the curved surface of the cone ?ConeModerate
Q88A wire is in the form of a circle of radius $98$ cm. A square is formed out of the wire. What is the length of a side of the square ? (Use $π = 22/7$ )QuadrilateralEasy
Q89Which one of the following is correct ?Medians and CentroidHard
Q90Which one of the following is correct ?Medians and CentroidHard
Q91What is the area of the largest circular disc cut from a square of side $\frac{2}{π}$ units ?CircleEasy
Q92The product of the lengths of the diagonals of a square is $50$ square units. What is the length of a side of the square ?QuadrilateralEasy
Q93The surface area of a closed cylindrical box is $352$ square cm. If its height is $10$ cm, then what is its diameter ? (Use $π = \frac{22}{7}$ )CylinderModerate
Q94A square and an equilateral triangle have the same perimeter. If the diagonal of the square is $62$ cm, then what is the area of the triangle ?TriangleEasy
Q95What is the area of the region bounded internally by a square of side of length 'a' and externally by a circle passing through the four corners of the square ?CircleModerate
Q96In the figure given below, XA and XB are two tangents to a circle. If $∠ A X B = 5 0^{\circ}$ and AC is parallel to XB, then what is $∠ A C B$ equal to ?TangentsModerate
Q97In the figure given below, $p$ , $q$ , $r$ are parallel lines; $l$ and $m$ are two transversals.Parallel Lines and TransversalsModerate
Q98In the equilateral triangle ABC given below, AD = DB and AE = EC. If $l$ is the length of a side of the triangle, then what is the area of the shaded region ?TriangleEasy
Q99In the figure given below, SPT is a tangent to the circle at P and O is the centre of the circle. If $∠ QP T = α$ , then what is $∠ P O Q$ equal to ?TangentsModerate
Q100In the figure given below, two equal chords cut at point P. If AB = CD = $10$ cm, OC = $13$ cm (O is the centre of the circle) and PB = $3$ cm, then what is the length of OP ?ChordsModerate

Topic mix

Arithmetic31
Mensuration21
Algebra19
Geometry13
Trigonometry11
Statistics5

Total questions100

Difficulty

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

Very easy5
Easy52
Moderate38
Hard5
Very hard0

Marking scheme

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

Options per question: 4Correct options per question: 1