Previous Year Papers

Elementary Mathematics 2018 (II)

Set A

View solutions

100Questions

120Minutes

100Marks

Question index

Jump to any question in this paper.

Q1The highest four-digit number which is divisible by each of the numbers $16$ , $36$ , $45$ , $48$ isLCM and HCFEasy
Q2If $x = y^{a}$ , $y = z^{b}$ and $z = x^{c}$ , then the value of $ab c$ isIndicesEasy
Q3If $x = 2 + 2^{2/3} + 2^{1/3}$ , then the value of the expression $x^{3} - 6 x^{2} + 6 x$ will beSimplificationHard
Q4How many five-digit numbers of the form XXYXX is/are divisible by $33$ ?DivisibilityModerate
Q5A five-digit number XY235 is divisible by $3$ where X and Y are digits satisfying X $+$ Y $\leq 5$ . What is the number of possible pairs of values of (X, Y) ?DivisibilityModerate
Q6If $x^{2} - 6 x - 27 > 0$ , then which one of the following is correct ?Quadratic InequalitiesEasy
Q7The number of divisors of the number $38808$ , exclusive of the divisors $1$ and itself, isFactors and DivisorsModerate
Q8HCF and LCM of two polynomials are $(x + 3)$ and $(x^{3} - 9 x^{2} - x + 105)$ respectively. If one of the two polynomials is $x^{2} - 4 x - 21$ , then the other isHCF and LCMModerate
Q9If $α$ and $β$ are two real numbers such that $α + β = - \frac{q}{p}$ and $α β = \frac{r}{p}$ , where $1 < p < q < r$ , then which one of the following is the greatest ?RootsModerate
Q10Two workers 'A' and 'B' working together completed a job in $5$ days. Had 'A' worked twice as efficiently as he actually did and 'B' worked one-third as efficiently as he actually did, the work would have completed in $3$ days. In how many days could 'A' alone complete the job ?Time and WorkModerate
Q11If $x^{6} + \frac{1}{x ^{6}} = k (x^{2} + \frac{1}{x ^{2}})$ , then $k$ is equal toSimplificationModerate
Q12If the sum of the squares of three consecutive natural numbers is $110$ , then the sum of their cubes isAlgebraic IdentitiesEasy
Q13The product of two integers $p$ and $q$ , where $p > 60$ and $q > 60$ , is $7168$ and their HCF is $16$ . The sum of these two integers isLCM and HCFModerate
Q14If $lo g_{10} 2 = 0.3010$ and $lo g_{10} 3 = 0.4771$ , then the value of $lo g_{100} (0.72)$ is equal toLaws of LogarithmsHard
Q15If $a^{x} = b^{y} = c^{z}$ and $ab c = 1$ , then the value of $\frac{1}{x} + \frac{1}{y} + \frac{1}{z}$ will be equal toLogarithmModerate
Q16If $α$ and $β$ are the roots of the equation $a x^{2} + b x + c = 0$ , then the value of $\frac{1}{a α + b} + \frac{1}{a β + b}$ isRootsModerate
Q17Consider the following statements in respect of three 3-digit numbers XYZ, YZX and ZXY :DivisibilityEasy
Q18The number of all pairs (m, n), where m and n are positive integers, such that $\frac{1}{m} + \frac{1}{n} - \frac{1}{mn} = \frac{2}{5}$ isEquationsHard
Q19If $a = x y^{p - 1}$ , $b = y z^{q - 1}$ , $c = z x^{r - 1}$ , then $a^{q - r} b^{r - p} c^{p - q}$ is equal toIndicesHard
Q20The number of sides of two regular polygons are in the ratio $5 : 4$ . The difference between their interior angles is $9^{\circ}$ . Consider the following statements :Interior and Exterior AnglesHard
Q21The minimum value of the expression $2 x^{2} + 5 x + 5$ isMaximum and Minimum ValuesEasy
Q22If H is the harmonic mean of P and Q, then the value of $\frac{H}{P} + \frac{H}{Q}$ isMeanEasy
Q23The sum of all possible products taken two at a time out of the numbers $\pm 1$ , $\pm 2$ , $\pm 3$ , $\pm 4$ isAlgebraic IdentitiesModerate
Q24The remainder when $3 x^{3} - 2 x^{2} y - 13 x y^{2} + 10 y^{3}$ is divided by $(x - 2 y)$ is equal toFactor and Remainder TheoremEasy
Q25If $ab + b c + c a = 0$ , then the value of $\frac{( b ^{2} - c a ) ( c ^{2} - ab ) + ( a ^{2} - b c ) ( c ^{2} - ab ) + ( a ^{2} - b c ) ( b ^{2} - c a )}{( a ^{2} - b c ) ( b ^{2} - c a ) ( c ^{2} - ab )}$ isSimplificationHard
Q26What is the principal amount which earns Rs. $210$ as compound interest for the second year at $5%$ per annum ?Compound InterestEasy
Q27In an examination, $50%$ of the candidates failed in English, $40%$ failed in Hindi and $15%$ failed in both the subjects. The percentage of candidates who passed in both English and Hindi isOperationsEasy
Q28A train $100$ m long passes a platform $100$ m long in $10$ seconds. The speed of the train isTrainsEasy
Q29A cyclist covers his first $20$ km at an average speed of $40$ kmph, another $10$ km at an average speed of $10$ kmph and the last $30$ km at an average speed of $40$ kmph. Then the average speed of the entire journey isAverage SpeedModerate
Q30In a race of $1000$ m, A beats B by $150$ m, while in another race of $3000$ m, C beats D by $400$ m. Speed of B is equal to that of D. (Assume that A, B, C and D run with uniform speed in all the events). If A and C participate in a race of $6000$ m, then which one of the following is correct ?RacesHard
Q31The sum of ages of a father, a mother, a son Sonu and daughters Savita and Sonia is $96$ years. Sonu is the youngest member of the family. The year Sonu was born, the sum of the ages of all the members of the family was $66$ years. If the father's age now is $6$ times that of Sonu's present age, then $12$ years hence, the father's age will beAge ProblemsModerate
Q32'A' is thrice as good a workman as 'B' and takes $10$ days less to do a piece of work than 'B' takes. The number of days taken by 'B' alone to finish the work isTime and WorkEasy
Q33Out of $85$ children playing badminton or table tennis or both, the total number of girls in the group is $70%$ of the total number of boys in the group. The number of boys playing only badminton is $50%$ of the number of boys and the total number of boys playing badminton is $60%$ of the total number of boys. The number of children playing only table tennis is $40%$ of the total number of children and a total of $12$ children play badminton and table tennis both. The number of girls playing only badminton isOperationsHard
Q34A person bought two articles X and Y from a departmental store. The sum of prices before sales tax was Rs. $130$ . There was no sales tax on the article X and $9%$ sales tax on the article Y. The total amount the person paid, including the sales tax was Rs. $136.75$ . What was the price of the article Y before sales tax ?PercentageEasy
Q35According to Mr. Sharma's will, half of his property goes to his wife and the rest is equally divided between his two sons, Ravi and Raj. Some years later, Ravi dies and leaves half of his property to his widow and rest to his brother Raj. When Raj dies he leaves half of his property to his widow and remaining to his mother, who is still alive. The mother now owns Rs. $88, 000$ worth of the property. The total worth of the property of Mr. Sharma wasDivision into PartsModerate
Q36X bought $4$ bottles of lemon juice and Y bought one bottle of orange juice. Orange juice per bottle costs twice the cost of lemon juice per bottle. Z bought nothing but contributed Rs. $50$ for his share of the drink which they mixed together and shared the cost equally. If Z's Rs. $50$ is covered from his share, then what is the cost of one bottle of orange juice ?Ratio and ProportionHard
Q37Ten ( $10$ ) years before, the ages of a mother and her daughter were in the ratio $3 : 1$ . In another $10$ years from now, the ratio of their ages will be $13 : 7$ . What are their present ages ?Age ProblemsModerate
Q38In a class of $60$ boys, there are $45$ boys who play chess and $30$ boys who play carrom. If every boy of the class plays at least one of the two games, then how many boys play carrom only ?OperationsEasy
Q39Two equal amounts were borrowed at $5%$ and $4%$ simple interest. The total interest after $4$ years amounted to Rs. $405$ . What was the total amount borrowed ?Simple InterestEasy
Q40Twelve ( $12$ ) men work $8$ hours per day and require $10$ days to build a wall. If $8$ men are available, how many hours per day must they work to finish the work in $8$ days ?Time and WorkEasy
Q41A milk vendor bought $28$ litres of milk at the rate of Rs. $8.50$ per litre. After adding some water he sold the mixture at the same price. If his gain is $12.5%$ , how much water did he add ?Mixtures and AlligationModerate
Q42The minute hand of a clock overtakes the hour hand after every $72$ minutes of correct time. How much time does the clock lose or gain in a day of normal time ?Gaining and Losing ClocksHard
Q43A thief steals a car parked in a house and goes away with a speed of $40$ kmph. The theft was discovered after half an hour and immediately the owner sets off in another car with a speed of $60$ kmph. When will the owner meet the thief ?Relative SpeedModerate
Q44X and Y together can finish a job in $6$ days. X can alone do the same job in $12$ days. How long will Y alone take to do the same job ?Time and WorkVery easy
Q45Twelve ( $12$ ) persons can paint $10$ identical rooms in $16$ days. In how many days can $8$ persons paint $20$ such rooms ?Time and WorkEasy
Q46There are $n$ zeros appearing immediately after the decimal point in the value of $(0.2)^{25}$ . It is given that the value of $lo g_{10} 2 = 0.30103$ . The value of $n$ isCharacteristic and MantissaHard
Q47The ratio of the sum and difference of the ages of the father and the son is $11 : 3$ . Consider the following statements :Age ProblemsModerate
Q48The solution of linear inequalities $x + y \geq 5$ and $x - y \leq 3$ liesLinear EquationsModerate
Q49It is given that the equations $x^{2} - y^{2} = 0$ and $(x - a)^{2} + y^{2} = 1$ have single positive solution. For this, the value of 'a' isEquationsHard
Q50If $α$ , $β$ and $γ$ are the zeros of the polynomial $f (x) = a x^{3} + b x^{2} + c x + d$ , then $α^{2} + β^{2} + γ^{2}$ is equal toZeros and CoefficientsModerate
Q51What percentage of students passed in all the three subjects ?OperationsModerate
Q52What percentage of students passed in exactly one subject ?OperationsHard
Q53If the number of students is $360$ , then how many passed in at least two subjects ?OperationsModerate
Q54What is the ratio of number of students who passed in both Physics and Chemistry to number of students who passed in both Biology and Physics but not Chemistry ?OperationsModerate
Q55Data on ratings of hotels in a city is measured onData ClassificationModerate
Q56The average marks of section A are $65$ and that of section B are $70$ . If the average marks of both the sections combined are $67$ , then the ratio of number of students of section A to that of section B isWeighted MeanEasy
Q57The median of $19$ observations is $30$ . Two more observations are made and the values of these are $8$ and $32$ . What is the median of the $21$ observations ?MedianHard
Q58As the number of observations and classes increases, the shape of a frequency polygonFrequency DistributionEasy
Q59Let $x ˉ_{1}$ and $x ˉ_{2}$ (where $x ˉ_{2} > x ˉ_{1}$ ) be the means of two sets comprising $n_{1}$ and $n_{2}$ (where $n_{2} < n_{1}$ ) observations respectively. If $x ˉ$ is the mean when they are pooled, then which one of the following is correct ?Weighted MeanModerate
Q60Consider the following statements :MedianModerate
Q61If $cos θ = \frac{1}{5}$ , where $0 < θ < \frac{π}{2}$ , then $\frac{2 t a n θ}{1 - t a n ^{2} θ}$ is equal toTrigonometric IdentityEasy
Q62If $0 < θ < 9 0^{\circ}$ , $0 < ϕ < 9 0^{\circ}$ and $cos θ < cos ϕ$ , then which one of the following is correct ?Trigonometric IdentityEasy
Q63On the top of a hemispherical dome of radius $r$ , there stands a flag of height $h$ . From a point on the ground, the elevation of the top of the flag is $3 0^{\circ}$ . After moving a distance $d$ towards the dome, when the flag is just visible, the elevation is $4 5^{\circ}$ . The ratio of $h$ to $r$ is equal toHeights and DistancesVery hard
Q64Let $sin (A + B) = \frac{3}{2}$ and $cos B = \frac{3}{2}$ , where A, B are acute angles. What is $tan (2 A - B)$ equal to ?Trigonometric IdentityModerate
Q65Consider the following statements :Trigonometric EquationModerate
Q66Consider the following statements :Trigonometric IdentityHard
Q67Consider the following statements :Maximum and Minimum ValuesModerate
Q68If $sin^{2} x + sin x = 1$ , then what is the value of $cos^{12} x + 3 cos^{10} x + 3 cos^{8} x + cos^{6} x$ ?Trigonometric IdentityHard
Q69If $3 sin θ + 5 cos θ = 4$ , then what is the value of $(3 cos θ - 5 sin θ)^{2}$ ?Trigonometric IdentityEasy
Q70If $cot θ (1 + sin θ) = 4 m$ and $cot θ (1 - sin θ) = 4 n$ , then which one of the following is correct ?Elimination of the AngleModerate
Q71If base and hypotenuse of a right triangle are $(u^{2} - v^{2})$ and $(u^{2} + v^{2})$ respectively and the area of the triangle is $2016$ square units, then the perimeter of the triangle may beTriangleHard
Q72A circle is inscribed in an equilateral triangle of side of length $l$ . The area of any square inscribed in the circle isQuadrilateralModerate
Q73Walls (excluding 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. Out of five rooms, two rooms have one square window each having a side of $2.5$ m. Paints are available only in cans of $1$ litre; and $1$ litre of paint can be used for painting $20$ square metres. The number of cans required for painting isCuboidModerate
Q74Let S be the parallelogram obtained by joining the mid-points of the parallelogram T. Consider the following statements :ParallelogramModerate
Q75The sides of a triangle are $5$ cm, $6$ cm and $7$ cm. The area of the triangle is approximatelyTriangleEasy
Q76There is a path of width $5$ m around a circular plot of land whose area is $144 π$ m $^{2}$ . The total area of the circular plot including the path surrounding it isCircleEasy
Q77The lateral surface area of a cone is $462$ cm $^{2}$ . Its slant height is $35$ cm. The radius of the base of the cone isConeVery easy
Q78A semi-circular plate is rolled up to form a conical surface. The angle between the generator and the axis of the cone isConeModerate
Q79A solid right cylinder is of height $π$ cm. If its lateral surface area is half its total surface area, then the radius of its base isCylinderEasy
Q80A rectangular block of length $20$ cm, breadth $15$ cm and height $10$ cm is cut up into exact number of equal cubes. The least possible number of cubes will beCuboidEasy
Q81If the diagonal of a cube is of length $l$ , then the total surface area of the cube isCubeEasy
Q82An equilateral triangle, a square and a circle have equal perimeter. If T, S and C denote the area of the triangle, area of the square and area of the circle respectively, then which one of the following is correct ?Plane FiguresModerate
Q83The areas of two similar triangles are $(7 - 43)$ cm $^{2}$ and $(7 + 43)$ cm $^{2}$ respectively. The ratio of their corresponding sides isSimilarityModerate
Q84The chord of a circle is $3$ times its radius. The angle subtended by this chord at the minor arc is $k$ times the angle subtended at the major arc. What is the value of $k$ ?ChordsModerate
Q85In a triangle ABC, the sides AB, AC are produced and the bisectors of exterior angles of $∠ A B C$ and $∠ A C B$ intersect at D. If $∠ B A C = 5 0^{\circ}$ , then $∠ B D C$ is equal toAngle BisectorModerate
Q86Two cones have their heights in the ratio $1 : 3$ . If the radii of their bases are in the ratio $3 : 1$ , then the ratio of their volumes will beConeEasy
Q87If two lines AB and CD intersect at O such that $∠ A O C = 5∠ A O D$ , then the four angles at O areAngles at a PointVery easy
Q88If a point P moves such that the sum of the squares of its distances from two fixed points A and B is a constant, then the locus of the point P isLocusModerate
Q89If ABC is a right-angled triangle with AC as its hypotenuse, then which one of the following is correct ?Pythagoras TheoremModerate
Q90The area of the region bounded externally by a square of side $2 a$ cm and internally by the circle touching the four sides of the square isComposite and Shaded RegionsVery easy
Q91In the figure given below, ABC is a right-angled triangle where $∠ A = 9 0^{\circ}$ , AB $= p$ cm and AC $= q$ cm. On the three sides as diameters semicircles are drawn as shown in the figure. The area of the shaded portion, in square cm, isComposite and Shaded RegionsHard
Q92In the figure given below, the radius of the circle is $6$ cm and AT $= 4$ cm. The length of tangent PT isTangentsEasy
Q93In the figure given below, ABCD is the diameter of a circle of radius $9$ cm. The lengths AB, BC and CD are equal. Semicircles are drawn on AB and BD as diameters as shown in the figure. What is the area of the shaded region ?CircleModerate
Q94In the figure given below, what is $∠ B C D$ equal to ?ChordsModerate
Q95In the figure given below, AB is the diameter of the circle whose centre is at O. Given that $∠ E C D = ∠ E D C = 3 2^{\circ}$ , then $∠ C E F$ and $∠ C O F$ respectively areChordsHard
Q96In the figure given below, $Δ$ ABR $\sim$ $Δ$ PQR. If PQ $= 3$ cm, AB $= 6$ cm, BR $= 8.2$ cm and PR $= 5.2$ cm, then QR and AR are respectivelySimilarityEasy
Q97In the figure given below, ABC is a triangle with AB perpendicular to BC. Further BD is perpendicular to AC. If AD $= 9$ cm and DC $= 4$ cm, then what is the length of BD ?SimilarityEasy
Q98In the figure given below, the diameter of bigger semicircle is $108$ cm. What is the area of the shaded region ?CircleHard
Q99In the figure given below, ABC is an equilateral triangle with each side of length $30$ cm. XY is parallel to BC, XP is parallel to AC and YQ is parallel to AB. If XY $+$ XP $+$ YQ is $40$ cm, then the value of PQ isSimilarityModerate
Q100In the figure given below, ABCD is a square of side $4$ cm. Quadrants of a circle of diameter $2$ cm are removed from the four corners and a circle of diameter $2$ cm is also removed. What is the area of the shaded region ?Composite and Shaded RegionsEasy

Topic mix

Algebra27
Arithmetic25
Mensuration17
Geometry14
Trigonometry10
Statistics7

Total questions100

Difficulty

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

Very easy4
Easy32
Moderate43
Hard20
Very hard1

Marking scheme

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

Options per question: 4Correct options per question: 1