Previous Year Papers

Elementary Mathematics 2017 (II)

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100Questions

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Q1What is the value of $α$ ( $α \neq = 0$ ) for which $x^{2} - 5 x + α$ and $x^{2} - 7 x + 2 α$ have a common factor ?FactorisationModerate
Q2How many numbers from $1$ to $1000$ are divisible by $2, 3, 4$ and $5$ ?LCM and HCFVery easy
Q3What are the factors of $x^{3} + 4 x^{2} - 11 x - 30$ ?FactorisationEasy
Q4If $x = 111 \dots 1$ ( $20$ digits), $y = 333 \dots 3$ ( $10$ digits) and $z = 222 \dots 2$ ( $10$ digits), then what is $\frac{x - y ^{2}}{z}$ equal to ?SimplificationHard
Q5What is the positive value of $m$ for which the roots of the equation $12 x^{2} + m x + 5 = 0$ are in the ratio $3 : 2$ ?RootsModerate
Q6Let $f (x)$ and $g (x)$ be two polynomials (with real coefficients) having degrees $3$ and $4$ respectively. What is the degree of $f (x) g (x)$ ?PolynomialVery easy
Q7If $5 x^{3} + 5 x^{2} - 6 x + 9$ is divided by $(x + 3)$ , then the remainder isFactor and Remainder TheoremVery easy
Q8The product of two non-zero expressions is $(x + y + z) p^{3}$ . If their HCF is $p^{2}$ , then their LCM isLCM and HCFEasy
Q9If the points $P$ and $Q$ represent the real numbers $0.8 3$ and $0.6 2$ on the number line, then the distance between $P$ and $Q$ isRational NumbersModerate
Q10Sudhir purchased a chair with three consecutive discounts of $20%$ , $12.5%$ and $5%$ . The actual deduction will beDiscountEasy
Q11A fruit seller has a certain number of mangoes of which $5%$ are rotten. He sells $75%$ of the remainder and he is left with $95$ mangoes. How many mangoes did he have originally ?PercentageEasy
Q12If a train crosses a km-stone in 12 seconds, how long will it take to cross 91 km-stones completely if its speed is $60 km/hr$ ?TrainsHard
Q13In a 100 m race, A runs at $6 km/hr$ . If A gives B a start of $8 m$ and still beats him by 9 seconds, what is the speed of B ?RacesModerate
Q14The quotient of $8 x^{3} - y^{3}$ when divided by $2 x y + 4 x^{2} + y^{2}$ isFactorisationEasy
Q15If $(x + 2)$ is a common factor of $x^{2} + a x + b$ and $x^{2} + b x + a$ , then the ratio $a : b$ is equal toFactor and Remainder TheoremEasy
Q16Let $f (x) = a_{0} x^{n} + a_{1} x^{n - 1} + a_{2} x^{n - 2} + \dots + a_{n - 1} x + a_{n}$ , where $a_{0}, a_{1}, a_{2}, \dots, a_{n}$ are real numbers. If $f (x)$ is divided by $(a x - b)$ , then the remainder isFactor and Remainder TheoremVery easy
Q17Consider the following numbers :Perfect SquaresModerate
Q18The product of the polynomials $(x + 2)$ , $(x - 2)$ , $(x^{3} - 2 x^{2} + 4 x - 8)$ and $(x^{3} + 2 x^{2} + 4 x + 8)$ isSimplificationModerate
Q19The factors of $x (x + 2) (x + 3) (x + 5) - 72$ areFactorisationHard
Q20If the HCF of polynomials $f (x) = (x - 1) (x^{2} + 3 x + a)$ and $g (x) = (x + 2) (x^{2} + 2 x + b)$ is $(x^{2} + x - 2)$ , then what are the values of $a$ and $b$ respectively ?HCF and LCMModerate
Q21 $a, b, c, d$ are non-zero integers such that $(ab)$ divides $(c d)$ . If $a$ and $c$ are coprime, then which one of the following is correct ?DivisibilityModerate
Q22If the roots of the equation $a (b - c) x^{2} + b (c - a) x + c (a - b) = 0$ are equal, then which one of the following is correct ?RootsHard
Q23The non-zero solution of the equation $\frac{a - x ^{2}}{b x} - \frac{b - x}{c} = \frac{c - x}{b} - \frac{b - x ^{2}}{c x}$ , where $b \neq = 0, c \neq = 0$ isEquationsHard
Q24If $k$ is an integer, then $x^{2} + 7 x - 14 (k^{2} - \frac{7}{8}) = 0$ hasRootsHard
Q25How many numbers between $500$ and $1000$ are divisible by $13$ ?DivisibilityEasy
Q26To maintain $8$ cows for $60$ days, a milkman has to spend Rs. $6, 400$ . To maintain $5$ cows for $n$ days, he has to spend Rs. $4, 800$ . What is the value of $n$ ?Ratio and ProportionEasy
Q27A student has to secure $40%$ of marks to pass an examination. He gets only $45$ marks and fails by $5$ marks. The maximum marks arePercentageVery easy
Q28What is the value of $u$ in the system of equations $3 (2 u + v) = 7 uv, 3 (u + 3 v) = 11 uv$ ?Simultaneous EquationsModerate
Q29Five years ago, Ram was three times as old as Shyam. Four years from now, Ram will be only twice as old as Shyam. What is the present age of Ram ?Age ProblemsEasy
Q30Ram buys $4$ chairs and $9$ stools for Rs. $1, 340$ . If he sells chairs at $10%$ profit and stools at $20%$ profit, he earns a total profit of Rs. $188$ . How much money did he have to pay for the chairs ?Profit and LossEasy
Q31Which one of the following is a correct statement ?Types of SetsEasy
Q32If $ab + b c + c a = 0$ , then what is the value of $\frac{a ^{2}}{a ^{2} - b c} + \frac{b ^{2}}{b ^{2} - c a} + \frac{c ^{2}}{c ^{2} - ab}$ ?SimplificationModerate
Q33In an examination, $35%$ students failed in Hindi, $45%$ students failed in English and $20%$ students failed in both the subjects. What is the percentage of students passing in both the subjects ?OperationsEasy
Q34What is $\frac{( x - y ) ( y - z ) ( z - x )}{( x - y ) ^{3} + ( y - z ) ^{3} + ( z - x ) ^{3}}$ equal to ?SimplificationModerate
Q35The value of $1 + 1 + 1 + \dots$ Nested RadicalsModerate
Q36If $lo g_{10} 6 = 0 \cdot 7782$ and $lo g_{10} 8 = 0 \cdot 9031$ , then what is the value of $lo g_{10} 8000 + lo g_{10} 600$ ?Laws of LogarithmsEasy
Q37 $30$ men can complete a job in $40$ days. However, after $24$ days some men out of the assigned $30$ left the job. The remaining people took another $40$ days to complete the job. The number of men who left the job isTime and WorkEasy
Q38 $4$ goats or $6$ sheep can graze a field in $50$ days. $2$ goats and $3$ sheep will graze it inTime and WorkEasy
Q39A tap can fill a tub in $10$ hours. After opening the tap for $5$ hours it was found that a small outlet at the bottom of the tub was open and water was leaking through it. It was then immediately closed. It took $7$ hours to fill the tub after closing the outlet. What time will be taken by the outlet to empty the full tub of water ?Pipes and CisternsModerate
Q40A boy went to his school at a speed of $12$ km/hr and returned to his house at a speed of $8$ km/hr. If he has taken $50$ minutes for the whole journey, what was the total distance walked ?Average SpeedEasy
Q41If $78$ is divided into $3$ parts which are proportional to $1, \frac{1}{3}, \frac{1}{6}$ , then the middle part isDivision into PartsEasy
Q42There are $350$ boys in the first three standards. The ratio of the number of boys in first and second standards is $2 : 3$ , while that of boys in second and third standards is $4 : 5$ . What is the total number of boys in first and third standards ?Ratio and ProportionEasy
Q43The difference between the compound interest (compounded annually) and simple interest on a sum of money deposited for $2$ years at $5%$ per annum is Rs. $15$ . What is the sum of money deposited ?Difference of SI and CIEasy
Q44When prices rise by $12%$ , if the expenditure is to be the same, what is the percentage of consumption to be reduced ?Price and ConsumptionEasy
Q45A man rows down a river $18$ km in $4$ hours with the stream and returns in $10$ hours. Consider the following statements :Boats and StreamsModerate
Q46If a triangle has sides $5$ , $13$ and $12$ units and $θ$ is the acute angle of the triangle, then what is the value of $(sin θ + cos θ)$ ?TriangleEasy
Q47If $0 < x < \frac{π}{2}$ , then $(sin x + cosec x)$ isMaximum and Minimum ValuesModerate
Q48If $sin θ = \frac{m ^{2} - n ^{2}}{m ^{2} + n ^{2}}$ and $0 < θ < \frac{π}{2}$ , then what is the value of $cos θ$ ?Trigonometric IdentityEasy
Q49If angle A of triangle ABC is $3 0^{\circ}$ and the circum-radius of the triangle is $10$ cm, then what is the length of side BC ?TriangleEasy
Q50If $A = \frac{s i n 4 5 ^{\circ} - s i n 3 0 ^{\circ}}{c o s 4 5 ^{\circ} + c o s 6 0 ^{\circ}}$ and $B = \frac{s e c 4 5 ^{\circ} - t a n 4 5 ^{\circ}}{cosec 4 5 ^{\circ} + c o t 4 5 ^{\circ}}$ , then which one of the following is correct ?Trigonometric IdentityModerate
Q51If $θ$ measured in radians is the angle between the hour hand and the minute hand of a clock when the time is $4 : 36$ pm, then which one of the following is correct ?Angle Between HandsModerate
Q52Consider the following statements :Maximum and Minimum ValuesHard
Q53Let AB represent a building of height h metre with A being its top, B being its bottom. Let A'B' represent a tower of height (h + x) metre (x > 0) with A' being its top and B' being its bottom. Let BB' = d metre. Let the angle of elevation of A' as seen from A be $4 5^{\circ}$ .Heights and DistancesHard
Q54A man, standing at a point X on the bank XY of a river that cannot be crossed, observes a tower to be N $α^{\circ}$ E on the opposite parallel bank. He then walks $200$ m along the bank to the point Y towards East, and finds the tower to be N $β^{\circ}$ W. From these observations, the breadth of the river will beHeights and DistancesHard
Q55The value of $\frac{s i n 1 ^{\circ}}{s i n 1 ^{c}}$ where $1^{c}$ represents 1 radian isDegree and RadianModerate
Q56The diameters of two given circles are in the ratio $12 : 5$ and the sum of their areas is equal to the area of a circle of diameter $65$ cm. What are their radii ?CircleModerate
Q57A hollow cube is formed by joining six identical squares. A rectangular cello tape of length $4$ cm and breadth $0.5$ cm is used for joining each pair of edges. What is the total area of cello tape used ?CubeModerate
Q58Two straight lines AB and AC include an angle. A circle is drawn in this angle which touches both these lines. One more circle is drawn which touches both these lines as well as the previous circle. If the area of the bigger circle is $9$ times the area of the smaller circle, then what must be the angle A ?TangentsHard
Q59An isosceles triangle is drawn outside on one of the sides of a square as base in such a way that the perimeter of the complete figure is $\frac{7}{6}$ times the perimeter of the original square. What is the ratio of area of the triangle to the area of the original square ?TriangleModerate
Q60What is the area of the triangle whose sides are $51$ cm, $37$ cm and $20$ cm ?TriangleModerate
Q61Segment QR of length r is a tangent at Q to a circle of radius r with centre at P. What is the area of the part of the triangle PQR, which is outside the circular region ?CircleHard
Q62In a triangle ABC, AD is perpendicular on BC. If $∠ B A C = 9 0^{\circ}$ , AB = c, BC = a, CA = b and AD = p, then which one of the following is correct ?Pythagoras TheoremEasy
Q63AB and CD are parallel chords of a circle $3$ cm apart. If AB = $4$ cm, CD = $10$ cm, then what is the radius of the circle ?ChordsModerate
Q64The diagonals of a cyclic quadrilateral ABCD intersect at P and the area of the triangle APB is $24$ square cm. If AB = $8$ cm and CD = $5$ cm, then what is the area of the triangle CPD ?SimilarityModerate
Q65In an equilateral triangle ABC, BD is drawn perpendicular to AC. What is $BD^{2}$ equal to ?Pythagoras TheoremEasy
Q66The distance between the centres of two circles having radii $9$ cm and $4$ cm is $13$ cm. What is the length of the direct common tangent of these circles ?TangentsEasy
Q67If PL, QM and RN are the altitudes of triangle PQR whose orthocentre is O, then Q is the orthocentre of the triangleTriangle CentresModerate
Q68In triangle ABC, $∠ C = 9 0^{\circ}$ and CD is the perpendicular from C to AB.Pythagoras TheoremModerate
Q69If a point O in the interior of a rectangle ABCD is joined with each of the vertices A, B, C and D, then $OB^{2} + OD^{2}$ will be equal toParallelogramModerate
Q70A cylinder of height 2x is circumscribed by a sphere of radius 2x such that the circular ends of the cylinder are two small circles on the sphere. What is the ratio of the curved surface area of the cylinder to the surface area of the sphere ?CylinderModerate
Q71A cylindrical vessel $60$ cm in diameter is partially filled with water. A sphere $30$ cm in diameter is gently dropped into the vessel and is completely immersed. To what further height will the water in the cylinder rise ?Recasting and MeltingEasy
Q72The vertical angle of a right circular cone is $\frac{π}{2}$ and the slant height is $2 r$ cm. What is the volume of the cone in cubic cm ?ConeEasy
Q73The radii of the frustum of a right circular cone are in the ratio $2 : 1$ . What is the ratio of the volume of the frustum of the cone to that of the whole cone ?FrustumModerate
Q74From a solid cylinder whose height is $8$ cm and of base radius $6$ cm, a conical cavity of height $8$ cm and of base radius $6$ cm is formed by hollowing out. What is the inner surface area of the cavity ?ConeEasy
Q75A tent has been constructed which is in the form of a right circular cylinder surmounted by a right circular cone whose axis coincides with the axis of the cylinder. If the radius of the base of the cylinder is $50$ m, the height of the cylinder is $10$ m and the total height of the tent is $15$ m, then what is the capacity of the tent in cubic metres ?Combination of SolidsEasy
Q76Two rectangular sheets of sizes $2 π \times 4 π$ and $π \times 5 π$ are available. A hollow right circular cylinder can be formed by joining a pair of parallel sides of any sheet. What is the maximum possible volume of the circular cylinder that can be formed this way?CylinderModerate
Q77In a triangle ABC, the medians AD and BE intersect at G. A line DF is drawn parallel to BE such that F is on AC. If AC = $9$ cm, then what is CF equal to?SimilarityModerate
Q78In a triangle PQR, X is a point on PR and Y is a point on QR such that PR = $10$ cm, RX = $4$ cm, YR = $2$ cm, QR = $5$ cm. Which one of the following is correct?SimilarityEasy
Q79Consider the following statements in respect of three straight lines A, B and C on a plane:Parallel Lines and TransversalsModerate
Q80The diagonals of a rhombus are of length $20$ cm and $48$ cm. What is the length of a side of the rhombus?ParallelogramEasy
Q81An arc of a circle subtends an angle $π$ at the centre. If the length of the arc is $22$ cm, then what is the radius of the circle? (Take $π = \frac{22}{7}$ )CircleEasy
Q82One-fifth of the area of a triangle ABC is cut off by a line DE drawn parallel to BC such that D is on AB and E is on AC. If BC = $10$ cm, then what is DE equal to?SimilarityModerate
Q83There are $8$ lines in a plane, no two of which are parallel. What is the maximum number of points at which they can intersect?LineEasy
Q84A closed polygon has six sides and one of its angles is $3 0^{\circ}$ greater than each of the other five equal angles. What is the value of one of the equal angles?Interior and Exterior AnglesEasy
Q85Consider the following statements:Triangle CentresModerate
Q86What is the total number of boys studying Statistics and Physics?Data InterpretationEasy
Q87The number of girls studying Statistics is what percent (approximate) of the total number of students studying Chemistry?Data InterpretationEasy
Q88In which subjects is the difference between the number of boys and girls equal?Data InterpretationModerate
Q89What is the difference between the number of boys studying Mathematics and the number of girls studying Physics?Data InterpretationEasy
Q90What is the ratio of the total number of boys to the total number of girls?Data InterpretationModerate
Q91Frequency density of a class is computed by the ratioFrequency DensityVery easy
Q92A small company pays each of its $5$ category 'C' workers Rs. $20, 000$ , each of its $3$ category 'B' workers Rs. $25, 000$ and a category 'A' worker Rs. $65, 000$ . The number of workers earning less than the mean salary isMeanEasy
Q93A man travelled $12$ km at a speed of $4$ km/hr and further $10$ km at a speed of $5$ km/hr. What was his average speed?Average SpeedEasy
Q94The pie diagrams on the monthly expenditure of two families A and B are drawn with radii of two circles taken in the ratio $16 : 9$ to compare their expenditures. Which one of the following is the appropriate data used for the above mentioned pie diagrams?Pie ChartModerate
Q95Consider the following statements:ModeEasy
Q96Which one of the following is not correct? The proportion of various items in a pie diagram is proportional to thePie ChartModerate
Q97The geometric mean of x and y is $6$ and the geometric mean of x, y and z is also $6$ . Then the value of z isGeometric MeanEasy
Q98The total number of live births in a specific locality during different months of a specific year was obtained from the office of the Birth Registrar. This set of data may be calledData ClassificationVery easy
Q99The heights (in cm) of $5$ students are $150, 165, 161, 144$ and $155$ . What are the values of mean and median (in cm) respectively?MeanEasy
Q100The average height of $22$ students of a class is $140$ cm and the average height of $28$ students of another class is $152$ cm. What is the average height of students of both the classes?Weighted MeanEasy

Topic mix

Arithmetic25
Algebra22
Geometry17
Statistics14
Mensuration13
Trigonometry9

Total questions100

Difficulty

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

Very easy7
Easy44
Moderate38
Hard11
Very hard0

Marking scheme

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

Options per question: 4Correct options per question: 1