Previous Year Papers

Elementary Mathematics 2020 (I)

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100Questions

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Q1The number $2 \times 3 \times 5 \times 7 \times 11 + 1$ isPrime NumbersHard
Q2Two unequal pairs of numbers satisfy the following conditions :LCM and HCFModerate
Q3How many digits are there in $(54)^{10}$ ? (Given that $lo g_{10} 2 = 0.301$ and $lo g_{10} 3 = 0.477$ )Characteristic and MantissaEasy
Q4Which one of the following is a set of solutions of the equation $x^{x} = n x^{x}$ , if $n$ is a positive integer ?SurdsModerate
Q5In a competitive examination, $250$ students have registered. Out of these, $50$ students have registered for Physics, $75$ students for Mathematics and $35$ students for both Mathematics and Physics. What is the number of students who have registered neither for Physics nor for Mathematics ?OperationsVery easy
Q6If the sum of the digits of a number $1 0^{n} - 1$ , where $n$ is a natural number, is equal to $3798$ , then what is the value of $n$ ?Digit ProblemsEasy
Q7Which one of the following is the largest number among $222 2^{2}$ , $22 2^{22}$ , $2 2^{222}$ , $2^{2222}$ ?SurdsModerate
Q8If $m$ is the number of prime numbers between $0$ and $50$ ; and $n$ is the number of prime numbers between $50$ and $100$ , then what is $(m - n)$ equal to ?Prime NumbersModerate
Q9If $\frac{a}{b} = \frac{1}{3}$ , $\frac{b}{c} = 2$ , $\frac{c}{d} = \frac{1}{2}$ , $\frac{d}{e} = 3$ and $\frac{e}{f} = \frac{1}{4}$ , then what is the value of $\frac{ab c}{d e f}$ ?ProportionEasy
Q10Which one of the following is the largest divisor of $3^{x} + 3^{x + 1} + 3^{x + 2}$ , if $x$ is any natural number ?DivisibilityEasy
Q11A two-digit number is $9$ more than four times of the number obtained by interchanging its digits. If the product of digits in the two-digit number is $8$ , then what is the number ?Linear EquationsModerate
Q12If $α$ and $β$ are the roots of the quadratic equation $x^{2} + k x - 15 = 0$ such that $α - β = 8$ , then what is the positive value of $k$ ?RootsEasy
Q13What are the values of $p$ and $q$ respectively, if $(x - 1)$ and $(x + 2)$ divide the polynomial $x^{3} + 4 x^{2} + p x + q$ ?Factor and Remainder TheoremEasy
Q14If $(x + k)$ is the HCF of $x^{2} + 5 x + 6$ and $x^{2} + 8 x + 15$ , then what is the value of $k$ ?HCF and LCMVery easy
Q15If $5^{x + 1} - 5^{x - 1} = 600$ , then what is the value of $1 0^{2 x}$ ?Exponential EquationsEasy
Q16A number divides $12288$ , $28200$ and $44333$ so as to leave the same remainder in each case. What is that number ?LCM and HCFHard
Q17If $x^{2} + 9 y^{2} = 6 x y$ , then what is $y : x$ equal to ?Algebraic IdentitiesEasy
Q18If $m$ and $n$ are positive integers such that $m^{n} = 1331$ , then what is the value of $(m - 1)^{n - 1}$ ?Number SystemEasy
Q19What is $\frac{1}{a ^{m - n} - 1} + \frac{1}{a ^{n - m} - 1}$ equal to ?SimplificationModerate
Q20If $x = 2$ , $y = 33$ and $z = 66$ , then which one of the following is correct ?SimplificationEasy
Q21If $lo g x = 1.2500$ and $y = x^{l o g x}$ , then what is $lo g y$ equal to ?EquationsEasy
Q22If $f (x)$ is divided by $(x - α) (x - β)$ where $α \neq = β$ , then what is the remainder ?Factor and Remainder TheoremHard
Q23If the area of a square is $2401 x^{4} + 196 x^{2} + 4$ , then what is its side length ?FactorisationEasy
Q24If $x$ varies as $y z$ , then $y$ varies inversely asDirect and Inverse VariationModerate
Q25If the points $P$ and $Q$ represent real numbers $0.7 3$ and $0.5 6$ on the number line, then what is the distance between $P$ and $Q$ ?Rational NumbersEasy
Q26What is the point on the $x y$ -plane satisfying $5 x + 2 y = 7 x y$ and $10 x + 3 y = 8 x y$ ?Linear EquationsModerate
Q27The price of an article $X$ increases by $20%$ every year and price of article $Y$ increases by $10%$ every year. In the year $2010$ , the price of article $X$ was Rs. $5000$ and price of article $Y$ was Rs. $2000$ . In which year the difference in their prices exceeded Rs. $5000$ for the first time ?Successive Increase and DecreaseModerate
Q28The ratio of speeds of $X$ and $Y$ is $5 : 6$ . If $Y$ allows $X$ a start of $70$ m in a $1.2$ km race, then who will win the race and by what distance ?RacesModerate
Q29A train takes two hours less for a journey of $300$ km if its speed is increased by $5$ km/hr from its usual speed. What is its usual speed ?Time, Speed and DistanceEasy
Q30If $6$ men and $8$ women can do a piece of work in $10$ days; and $13$ men and $24$ women can do the same work in $4$ days, then what is the ratio of daily work done by a man to that of a woman ?Time and WorkEasy
Q31Students of a class are made to sit in rows of equal number of chairs. If number of students is increased by $2$ in each row, then the number of rows decreases by $3$ . If number of students is increased by $4$ in each row, then the number of rows decreases by $5$ . What is the number of students in the class ?Linear EquationsModerate
Q32A sum was put at simple interest at certain rate for $2$ years. Had it been put at $1%$ higher rate of interest, it would have fetched Rs. $24$ more. What is the sum ?Simple InterestEasy
Q33The population of two villages is $1525$ and $2600$ respectively. If the ratio of male to female population in the first village is $27 : 34$ and the ratio of male to female population in the second village is $6 : 7$ , then what is the ratio of male to female population of these two villages taken together ?Ratio and ProportionModerate
Q34In a class room the ratio of number of girls to that of boys is $3 : 4$ . The average height of students in the class is $4.6$ feet. If the average height of the boys in the class is $4.8$ feet, then what is the average height of the girls in the class ?Weighted MeanEasy
Q35What is the median of the data $3, 5, 9, 4, 6, 11, 18$ ?MedianVery easy
Q36In a pi-diagram there are three sectors. If the ratio of the angles of the sectors is $1 : 2 : 3$ , then what is the angle of the largest sector?Pie ChartVery easy
Q37The maximum marks in a Test are converted from $250$ to $50$ for the purpose of an Internal Assessment. The highest marks scored were $170$ and lowest marks were $70$ . What is the difference between the maximum and minimum marks scored in the Internal Assessment?Ratio and ProportionEasy
Q38Jails with highest and smallest percentage of trained convicts are respectivelyTableModerate
Q39Jail with highest placement rate of trained convicts isTableModerate
Q40Jails from which more than half of the trained convicts are offered jobs, areTableModerate
Q41The number of three digit numbers (all digits are different) which are divisible by $7$ and also divisible by $7$ on reversing the order of the digits, isDivisibilityHard
Q42How many integral values of $x$ and $y$ satisfy the equation $5 x + 9 y = 7$ , where $- 500 < x < 500$ and $- 500 < y < 500$ ?Linear EquationsHard
Q43Let $X Y Z$ be a $3$ -digit number. Let $S = X Y Z + Y Z X + Z X Y$ . Which of the following statements is/are correct?DivisibilityModerate
Q44In covering certain distance, the average speeds of $X$ and $Y$ are in the ratio $4 : 5$ . If $X$ takes $45$ minutes more than $Y$ to reach the destination, then what is the time taken by $Y$ to reach the destination?Time, Speed and DistanceEasy
Q45For two observations, the sum is $S$ and product is $P$ . What is the harmonic mean of these two observations?MeanEasy
Q46If the annual income of $X$ is $20%$ more than that of $Y$ , then the income of $Y$ is less than that of $X$ by $p %$ . What is the value of $p$ ?PercentageEasy
Q47What is the least perfect square which is divisible by $3$ , $4$ , $5$ , $6$ and $7$ ?LCM and HCFModerate
Q48In a water tank there are two outlets. It takes $20$ minutes to empty the tank if both the outlets are opened. If the first outlet is opened, the tank is emptied in $30$ minutes. What is the time taken to empty the tank by second outlet?Pipes and CisternsEasy
Q49If $(x^{2} - 1)$ is a factor of $a x^{4} + b x^{3} + c x^{2} + d x + e$ , then which one of the following is correct?Factor and Remainder TheoremModerate
Q50If $(x^{8} + \frac{1}{x ^{8}}) = 47$ , what is the value of $(x^{6} + \frac{1}{x ^{6}})$ ?Algebraic IdentitiesModerate
Q51A wheel makes $360$ revolutions in one minute. What is the number of radians it turns in one second?Degree and RadianEasy
Q52What is the least value of $(25 cosec^{2} x + sec^{2} x)$ ?Maximum and Minimum ValuesHard
Q53Let $0 < θ < 9 0^{\circ}$ and $100 θ = 9 0^{\circ}$ . If $α = \prod_{n = 1}^{99} cot n θ$ , then which one of the following is correct?Complementary AnglesHard
Q54If $tan 6 θ = cot 2 θ$ , where $0 < 6 θ < \frac{π}{2}$ , then what is the value of $sec 4 θ$ ?Trigonometric EquationEasy
Q55A tree of height $15$ m is broken by wind in such a way that its top touches the ground and makes an angle $3 0^{\circ}$ with the ground. What is the height from the ground to the point where tree is broken?Heights and DistancesEasy
Q56On a plane area there are two vertical towers separated by $100$ feet apart. The shorter tower is $40$ feet tall. A pole of length $6$ feet stands on the line joining the base of two towers so that the tip of the towers and tip of the pole are also on the same line. If the distance of the pole from the shorter tower is $75$ feet, then what is the height of the taller tower (approximately)?SimilarityHard
Q57The angles of elevation of the top of a tower from two points at distances $p$ and $q$ from the base and on the same straight line are $2 7^{\circ}$ and $6 3^{\circ}$ respectively. What is the height of the tower?Heights and DistancesEasy
Q58What is the value of $sin^{2} 6^{\circ} + sin^{2} 1 2^{\circ} + sin^{2} 1 8^{\circ} + \dots + sin^{2} 8 4^{\circ} + sin^{2} 9 0^{\circ}$ ?Complementary AnglesModerate
Q59What is $\frac{c o s θ}{1 + s i n θ} + \frac{1}{c o t θ}$ equal to?Trigonometric IdentityEasy
Q60What is $\frac{s i n θ - c o s θ + 1}{s i n θ + c o s θ - 1} - \frac{s i n θ + 1}{c o s θ}$ equal to ?Trigonometric IdentityModerate
Q61What is $(tan x + tan y) (1 - cot x cot y) + (cot x + cot y) (1 - tan x tan y)$ equal to ?Trigonometric IdentityEasy
Q62What is $\frac{s e c x - t a n x}{s e c x + t a n x}$ equal to ?Trigonometric IdentityEasy
Q63If $θ$ lies in the first quadrant and $cot θ = \frac{63}{16}$ , then what is the value of $(sin θ + cos θ)$ ?Trigonometric IdentityEasy
Q64What is the value of $\frac{1 - 2 s i n ^{2} θ c o s ^{2} θ}{s i n ^{4} θ + c o s ^{4} θ} + 4$ equal to ?Trigonometric IdentityEasy
Q65A rectangle is $48$ cm long and $14$ cm wide. If the diagonal makes an angle $θ$ with the longer side, then what is $(sec θ + cosec θ)$ equal to ?Trigonometric IdentityModerate
Q66What is the area of the triangle having side lengths $\frac{y}{z} + \frac{z}{x}$ , $\frac{z}{x} + \frac{x}{y}$ , $\frac{x}{y} + \frac{y}{z}$ ?TriangleHard
Q67If the angles of a triangle are $3 0^{\circ}$ and $4 5^{\circ}$ and the included side is $(3 + 1)$ cm, then what is the area of the triangle ?TriangleModerate
Q68 $A B C D$ is a plate in the shape of a parallelogram. $E F$ is the line parallel to $D A$ and passing through the point of intersection $O$ of the diagonals $A C$ and $B D$ . Further, $E$ lies on $D C$ and $F$ lies on $A B$ . The triangular portion $D O E$ is cut out from the plate $A B C D$ . What is the ratio of area of remaining portion of the plate to the whole ?ParallelogramHard
Q69Two circles of radii $20$ cm and $16$ cm intersect and the length of common chord is $24$ cm. If $d$ is the distance between their centres, then which one of the following is correct ?ChordsModerate
Q70In a circle of radius $5$ cm, $A B$ and $A C$ are two chords such that $A B = A C = 8$ cm. What is the length of chord $B C$ ?ChordsModerate
Q71Two circles touch internally. The sum of their areas is $136 π$ cm $^{2}$ and distance between their centres is $4$ cm. What are the radii of the circles ?Touching CirclesModerate
Q72If area of a circle and a square are same, then what is the ratio of their perimeters ?Plane FiguresModerate
Q73A circle of diameter $8$ cm is placed in such a manner that it touches two perpendicular lines. Then another smaller circle is placed in the gap such that it touches the lines and the circle. What is the diameter of the smaller circle ?TangentsHard
Q74The thickness of a cylinder is $1$ foot, the inner radius of the cylinder is $3$ feet and height is $7$ feet. To paint the inner surface it requires one litre of a particular colour. How much quantity of the same colour is required to paint all the surfaces of the cylinder ?CylinderModerate
Q75A square and a rectangle have equal areas. If one side of the rectangle is of length numerically equal to the square of the length of the side of the square then the other side of the rectangle isPlane FiguresEasy
Q76The length and breadth of a rectangle are in the ratio $4 : 3$ . Then what is the ratio of the area of the triangle formed by the parts of the diagonals with a long side to the area of the triangle formed by the parts of diagonals with a short side ?ParallelogramModerate
Q77Suppose a region is formed by removing a sector of $2 0^{\circ}$ from a circular region of radius $30$ feet. What is the area of this new region ?CircleEasy
Q78 $A B C D$ is a parallelogram where $A C$ and $B D$ are the diagonals. If $∠ B A D = 6 0^{\circ}$ , $∠ A D B = 9 0^{\circ}$ , then what is $B D^{2}$ equal to ?ParallelogramEasy
Q79A line through the vertex $A$ of a parallelogram $A B C D$ meets $D C$ in $P$ and $B C$ produced in $Q$ . If $P$ is the mid-point of $D C$ , then which of the following is/are correct ?ParallelogramHard
Q80How many cubic metre of earth is to be dug out to dig a well of radius $1.4$ m and depth $5$ m ?CylinderEasy
Q81If the diagonals of a rhombus are $x$ and $y$ , then what is its area ?QuadrilateralVery easy
Q82The lengths of sides of a triangle are $3 x, 4 y, 5 3 z$ , where $3 x < 4 y < 5 3 z$ . If one of the angles is $9 0^{\circ}$ , then what are the minimum integral values of $x, y, z$ respectively ?Pythagoras TheoremModerate
Q83What is the maximum number of circum-circles that a triangle can have ?Triangle CentresVery easy
Q84If an arc of a circle of radius $6$ cm subtends a central angle measuring $3 0^{\circ}$ , then which one of the following is an approximate length of the arc ?CircleEasy
Q85A ladder $5 m$ long is placed in a room so as to reach a point $4.8 m$ high on a wall and on turning the ladder over to the opposite side of the wall without moving the base, it reaches a point $1.4 m$ high. What is the breadth of the room?Pythagoras TheoremEasy
Q86What is the area of the largest square plate cut from a circular disk of radius one unit?Composite and Shaded RegionsEasy
Q87Out of $4$ identical balls of radius $r$ , $3$ balls are placed on a plane such that each ball touches the other two balls. The $4^{th}$ ball is placed on them such that this ball touches all the three balls. What is the distance of centre of $4^{th}$ ball from the plane?SphereVery hard
Q88A right circular cylinder just encloses a sphere. If $p$ is the surface area of the sphere and $q$ is the curved surface area of the cylinder, then which one of the following is correct?SolidsEasy
Q89 $A B C D$ is a quadrilateral such that $A D = D C = C A = 20 units$ , $B C = 12 units$ and $∠ A B C = 9 0^{\circ}$ . What is the approximate area of the quadrilateral $A B C D$ ?QuadrilateralModerate
Q90Let $P QR S$ be the diameter of a circle of radius $9 cm$ . The length $P Q$ , $QR$ and $R S$ are equal. Semi-circle is drawn with $QS$ as diameter (as shown in the given figure). What is the ratio of the shaded region to that of the unshaded region?CircleModerate
Q91What is the area of the shaded region in the given figure, if the radius of each of the circles is $2 cm$ ?CircleModerate
Q92In the given figure, what is the area of the shaded region?Composite and Shaded RegionsModerate
Q93In the given figure, if $\frac{y}{x} = 6$ and $\frac{z}{x} = 5$ , then what is the value of $x$ ?Angles at a PointEasy
Q94 $A B C D$ is a trapezium, where $A B$ is parallel to $D C$ . If $A B = 4 cm$ , $B C = 3 cm$ , $C D = 7 cm$ and $D A = 2 cm$ , then what is the area of the trapezium?QuadrilateralHard
Q95Angles are shown in the given figure. What is value of $∠1 + ∠2 + ∠3 + ∠4 + ∠5 + ∠6 + ∠7 + ∠8$ ?PolygonHard
Q96In the given figure $P Q$ is parallel to $R S$ , $∠ A E F = 9 5^{\circ}$ , $∠ B H S = 11 0^{\circ}$ , and $∠ A B C = x^{\circ}$ . Then what is the value of $x$ ?Parallel Lines and TransversalsModerate
Q97In the given figure $A B$ is parallel to $C D$ and $A C$ is parallel to $B D$ . If $∠ E A C = 4 0^{\circ}$ , $∠ F D G = 5 5^{\circ}$ , $∠ H A B = x^{\circ}$ , then what is the value of $x$ ?Parallel Lines and TransversalsModerate
Q98In the given figure, there are three semi circles $A B C$ , $A E F$ and $C D F$ . The distance between $A$ and $C$ is $28 units$ and $F$ is the mid-point of $A C$ . What is the total area of the three semi circles?CircleEasy
Q99What is the approximate area of the shaded region in the figure given?Composite and Shaded RegionsModerate
Q100Consider the following statements with reference to the given figure:ParallelogramHard

Topic mix

Arithmetic23
Algebra20
Mensuration19
Geometry17
Trigonometry14
Statistics7

Total questions100

Difficulty

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

Very easy6
Easy41
Moderate37
Hard15
Very hard1

Marking scheme

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

Options per question: 4Correct options per question: 1