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Elementary Mathematics 2017 (I)

Set A

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100Questions

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Q1What is $\frac{0.064 \times 6.25}{0.081 \times 4.84}$ equal to?SimplificationModerate
Q2 $(x + 4)$ is a factor of which one of the following expressions?Factor and Remainder TheoremEasy
Q3If $α$ and $β$ are the roots of the quadratic equation $2 x^{2} + 6 x + k = 0$ , where $k < 0$ , then what is the maximum value of $\frac{α}{β} + \frac{β}{α}$ ?RootsModerate
Q4Consider the following statements:LCM and HCFHard
Q5What is the square root of $\frac{( 0.35 ) ^{2} + 0.70 + 1}{2.25} + 0.19$ ?SimplificationEasy
Q6What is the number of digits in $2^{40}$ ? (Given that $lo g_{10} 2 = 0.301$ )Characteristic and MantissaEasy
Q7If one root of $(a^{2} - 5 a + 3) x^{2} + (3 a - 1) x + 2 = 0$ is twice the other, then what is the value of 'a'?RootsModerate
Q8What is the remainder when the number $(4444)^{4444}$ is divided by $9$ ?DivisibilityModerate
Q9If $x = \frac{a + b - a - b}{a + b + a - b}$ , then what is $b x^{2} - 2 a x + b$ equal to $(b \neq = 0)$ ?SimplificationModerate
Q10What is the value of $\frac{( 443 + 547 ) ^{2} + ( 443 - 547 ) ^{2}}{443 \times 443 + 547 \times 547}$ ?SimplificationEasy
Q11If $x = t^{\frac{1}{t - 1}}$ and $y = t^{\frac{t}{t - 1}}$ , $t > 0$ , $t \neq = 1$ , then what is the relation between $x$ and $y$ ?SimplificationModerate
Q12If $A : B = 3 : 4$ , then what is the value of the expression $(\frac{3 A ^{2} + 4 B}{3 A - 4 B ^{2}})$ ?Ratio and ProportionModerate
Q13If $A = {x : x$ is a multiple of $7}$ , $B = {x : x$ is a multiple of $5}$ and $C = {x : x$ is a multiple of $35}$ , then which one of the following is a null set?OperationsEasy
Q14If $x = 2 + 2^{2/3} + 2^{1/3}$ , then what is the value of $x^{3} - 6 x^{2} + 6 x$ ?SimplificationHard
Q15If $\frac{x}{y} = \frac{24}{5} + \frac{y}{x}$ and $x + y = 26$ , then what is the value of $x y$ ?EquationsModerate
Q16What is the solution of the equation $x lo g_{10} (\frac{10}{3}) + lo g_{10} 3 = lo g_{10} (2 + 3^{x}) + x$ ?EquationsHard
Q17If $α$ and $β$ are the roots of the equation $x^{2} + p x + q = 0$ , then what is $α^{2} + β^{2}$ equal to?RootsVery easy
Q18If $a^{3} = 335 + b^{3}$ and $a = 5 + b$ , then what is the value of $a + b$ (given that $a > 0$ and $b > 0$ )?SimplificationModerate
Q19If $9^{x} 3^{y} = 2187$ and $2^{3 x} 2^{2 y} - 4^{x y} = 0$ , then what can be the value of $(x + y)$ ?Exponential EquationsModerate
Q20The pair of linear equations $k x + 3 y + 1 = 0$ and $2 x + y + 3 = 0$ intersect each other, ifLinear EquationsEasy
Q21The number of prime numbers which are less than $100$ isPrime NumbersEasy
Q22The cost of a diamond varies directly as the square of its weight. A diamond broke into four pieces with their weights in the ratio of $1 : 2 : 3 : 4$ . If the loss in total value of the diamond was Rs. $70, 000$ , what was the price of the original diamond?Direct and Inverse VariationModerate
Q23In a $100$ m race, A runs at a speed of $\frac{5}{3}$ m/s. If A gives a start of $4$ m to B and still beats him by $12$ seconds, what is the speed of B?RacesModerate
Q24If $15$ men take $21$ days of $8$ hours each to do a piece of work, then what is the number of days of $6$ hours each that $21$ women would take, if $3$ women would do as much work as $2$ men?Time and WorkModerate
Q25What number must be subtracted from both the numerator and the denominator of the fraction $\frac{27}{35}$ so that it becomes $\frac{2}{3}$ ?Ratio and ProportionVery easy
Q26A sum of Rs. $8, 400$ was taken as a loan. This is to be paid in two equal instalments. If the rate of interest is $10%$ per annum, compounded annually, then the value of each instalment isCompound InterestHard
Q27Leela got married $6$ years ago. Today her age is $1 \frac{1}{4}$ times her age at the time of her marriage. Her son's age is $\frac{1}{10}$ times her age. What is the present age of her son?Age ProblemsEasy
Q28A and B working together can finish a piece of work in $12$ days while B alone can finish it in $30$ days. In how many days can A alone finish the work?Time and WorkVery easy
Q29The values of $x$ which satisfy the equation $5^{1 + x} + 5^{1 - x} = 26$ areExponential EquationsEasy
Q30If $5$ men can do a piece of work in $10$ days and $12$ women can do the same work in $15$ days, the number of days required to complete the work by $5$ men and $6$ women isTime and WorkEasy
Q31A passenger train departs from Delhi at 6 p.m. for Mumbai. At 9 p.m., an express train, whose average speed exceeds that of the passenger train by $15$ km/hour leaves Mumbai for Delhi. Two trains meet each other mid-route. At what time do they meet, given that the distance between the cities is $1080$ km?Relative SpeedModerate
Q32In a class of $49$ students, the ratio of girls to boys is $4 : 3$ . If $4$ girls leave the class, the ratio of girls to boys would beRatio and ProportionEasy
Q33If $a + b = 5$ and $ab = 6$ , then what is the value of $a^{3} + b^{3}$ ?SimplificationEasy
Q34Rajendra bought a mobile with $25%$ discount on the selling price. If the mobile cost him Rs. $4, 875$ , what is the original selling price of the mobile?DiscountEasy
Q35A $225$ m long train is running at a speed of $30$ km/hour. How much time does it take to cross a man running at $3$ km/hour in the same direction?TrainsEasy
Q36Which one among the following is the largest?Rational NumbersEasy
Q37The difference between the simple and the compound interest on a certain sum of money at $4%$ per annum in $2$ years is Rs. $10$ . What is the sum?Difference of SI and CIModerate
Q38If $a %$ of $a$ $+$ $b %$ of $b$ $=$ $2%$ of $ab$ , then what percent of $a$ is $b$ ?PercentageModerate
Q39 $\frac{5}{9}$ th part of the population in a village are males. If $30%$ of the males are married, the percentage of unmarried females in the total population isPercentageModerate
Q40Sunil wants to spend Rs. $200$ on two types of sweets, costing Rs. $7$ and Rs. $10$ respectively. What is the maximum number of sweets he can get so that no money is left over?Number SystemModerate
Q41What is the LCM of $x^{3} + 8$ , $x^{2} + 5 x + 6$ and $x^{3} + 4 x^{2} + 4 x$ ?HCF and LCMModerate
Q42The HCF of two expressions $p$ and $q$ is $1$ . What is the reciprocal of their LCM?LCM and HCFEasy
Q43What is the value of $3 4 \frac{12}{125}$ ?SimplificationEasy
Q44A thief is spotted by a policeman from a distance of $100$ m. When the policeman starts the chase, the thief also starts running. If the speed of the thief is $8$ km/hour and that of the policeman is $10$ km/hour, then how far will the thief have to run before he is overtaken?Relative SpeedEasy
Q45Aman and Alok attempted to solve a quadratic equation. Aman made a mistake in writing down the constant term and ended up in roots $(4, 3)$ . Alok made a mistake in writing down the coefficient of $x$ to get roots $(3, 2)$ . The correct roots of the equation areRootsModerate
Q46Consider the following statements:DivisibilityModerate
Q47The system of equations $2 x + 4 y = 6$ and $4 x + 8 y = 8$ isLinear EquationsEasy
Q48 $(N^{p - 1} - 1)$ is a multiple of $p$ , if $N$ is prime to $p$ and $p$ is aDivisibilityEasy
Q49The ratio of two numbers is $1 : 5$ and their product is $320$ . What is the difference between the squares of these two numbers?Ratio and ProportionEasy
Q50 $25$ kg of alloy X is mixed with $125$ kg of alloy Y. If the amount of lead and tin in the alloy X is in the ratio $1 : 2$ and the amount of lead and tin in the alloy Y is in the ratio $2 : 3$ , then what is the ratio of lead to tin in the mixture?Mixtures and AlligationModerate
Q51The mean of $5$ numbers is $15$ . If one more number is included, the mean of the $6$ numbers becomes $17$ . What is the included number?MeanVery easy
Q52The mean marks obtained by $300$ students in a subject are $60$ . The mean of top $100$ students was found to be $80$ and the mean of last $100$ students was found to be $50$ . The mean marks of the remaining $100$ students areWeighted MeanEasy
Q53Consider the following distribution:MeanModerate
Q54In a pie diagram, there are four slices with angles $15 0^{\circ}$ , $9 0^{\circ}$ , $6 0^{\circ}$ and $6 0^{\circ}$ . A new pie diagram is formed by deleting one of the slices having angle $6 0^{\circ}$ in the given pie diagram. In the new pie diagramPie ChartModerate
Q55In an asymmetrical distribution, if the mean and median of the distribution are $270$ and $220$ respectively, then the mode of the data isModeEasy
Q56Let $a$ , $b$ , $c$ , $d$ , $e$ , $f$ , $g$ be consecutive even numbers and $j$ , $k$ , $l$ , $m$ , $n$ be consecutive odd numbers. What is the average of all the numbers?MeanHard
Q57An individual purchases three qualities of pencils. The relevant data is given below:Weighted MeanModerate
Q58Consider the following frequency distribution:Frequency DistributionEasy
Q59If D is the number of degrees and R is the number of radians in an angle $θ$ , then which one of the following is correct?Degree and RadianEasy
Q60What is the minimum value of $9 tan^{2} θ + 4 cot^{2} θ$ ?Maximum and Minimum ValuesModerate
Q61If $x sin θ = y cos θ = \frac{2 z t a n θ}{1 - t a n ^{2} θ}$ , then what is $4 z^{2} (x^{2} + y^{2})$ equal to?Elimination of the AngleHard
Q62If $cos θ_{1} + cos θ_{2} + cos θ_{3} = 3$ , then what is $sin θ_{1} + sin θ_{2} + sin θ_{3}$ equal to?Trigonometric IdentityEasy
Q63What is the value of $θ$ which satisfies the equation $cos θ + tan θ = 1$ ?Trigonometric EquationVery easy
Q64What is the value of $sin x \frac{1}{1 + c o s x} + \frac{1}{1 - c o s x}$ ?Trigonometric IdentityModerate
Q65What is $\frac{c o s ^{4} A - s i n ^{4} A}{c o s ^{2} A - s i n ^{2} A}$ equal to?Trigonometric IdentityVery easy
Q66If $7 sin^{2} x + 3 cos^{2} x = 4$ , $0 < x < 9 0^{\circ}$ , then what is the value of $tan x$ ?Trigonometric EquationEasy
Q67An aeroplane flying at a height of $300$ m above the ground passes vertically above another plane at an instant when the angles of elevation of the two planes from the same point on the ground are $6 0^{\circ}$ and $4 5^{\circ}$ respectively. What is the height of the lower plane from the ground?Heights and DistancesEasy
Q68If $x = a cos θ + b sin θ$ and $y = a sin θ - b cos θ$ , then what is $x^{2} + y^{2}$ equal to?Elimination of the AngleEasy
Q69From the top of a building $90$ m high, the angles of depression of the top and the bottom of a tree are $3 0^{\circ}$ and $4 5^{\circ}$ respectively. What is the height of the tree?Heights and DistancesModerate
Q70Which one of the following triples does not represent the sides of a triangle?Triangle InequalityEasy
Q71If the perimeter of a rectangle is $10$ cm and the area is $4$ cm $^{2}$ , then its length isQuadrilateralEasy
Q72The angles of a triangle are in the ratio $2 : 4 : 3$ . The smallest angle of the triangle isAngles of a TriangleEasy
Q73A ball of radius $1$ cm is put into a cylindrical pipe so that it fits inside the pipe. If the length of the pipe is $14$ m, what is the surface area of the pipe?CylinderModerate
Q74The areas of two circular fields are in the ratio $16 : 49$ . If the radius of the bigger field is $14$ m, then what is the radius of the smaller field?CircleEasy
Q75Let ABCD be a rectangle. Let P, Q, R, S be the mid-points of sides AB, BC, CD, DA respectively. Then the quadrilateral PQRS is aParallelogramModerate
Q76Let P, Q, R be the mid-points of sides AB, BC, CA respectively of a triangle ABC. If the area of the triangle ABC is $5$ square units, then the area of the triangle PQR isSimilarityEasy
Q77If each of the dimensions of a rectangle is increased by $200%$ , the area is increased byQuadrilateralEasy
Q78Three circles each of radius $3.5$ cm touch one another. The area subtended between them isCircleHard
Q79The area of a regular hexagon of side 'a' is equal toPolygonEasy
Q80ABCDEF is a regular polygon. Two poles at C and D are standing vertically and subtend angles of elevation $3 0^{\circ}$ and $6 0^{\circ}$ at A respectively. What is the ratio of the height of the pole at C to that of the pole at D?Heights and DistancesHard
Q81Two parallel chords of a circle whose diameter is $13$ cm are respectively $5$ cm and $12$ cm in length. If both the chords are on the same side of the diameter, then the distance between these chords isChordsModerate
Q82If the radius of a right circular cone is increased by $p %$ without increasing its height, then what is the percentage increase in the volume of the cone?ConeModerate
Q83A copper wire when bent in the form of a square encloses an area of $121$ cm $^{2}$ . If the same wire is bent in the form of a circle, it encloses an area equal toCircleEasy
Q84ABC is a triangle and D is a point on the side BC. If BC $= 12$ cm, BD $= 9$ cm and $∠$ ADC $= ∠$ BAC, then the length of AC is equal toSimilarityModerate
Q85If the surface area of a sphere is reduced to one-ninth of the area, its radius reduces toSphereVery easy
Q86In a trapezium ABCD, AB is parallel to CD and the diagonals intersect each other at O. What is the ratio of OA to OC equal to?TrapeziumEasy
Q87Ice-cream, completely filled in a cylinder of diameter $35$ cm and height $32$ cm, is to be served by completely filling identical disposable cones of diameter $4$ cm and height $7$ cm. The maximum number of persons that can be served in this way isRecasting and MeltingModerate
Q88The radius of a circle is increased so that its circumference increases by $15%$ . The area of the circle will increase byCircleEasy
Q89ABCD is a rectangle. The diagonals AC and BD intersect at O. If AB $= 32$ cm and AD $= 24$ cm, then what is OD equal to?ParallelogramEasy
Q90A field is divided into four regions as shown in the given figure. What is the area of the field in square metres?Composite and Shaded RegionsVery hard
Q91In the figure given below, D is the diameter of each circle. What is the diameter of the shaded circle?Touching CirclesHard
Q92In the figure given below, AC is parallel to ED and AB $=$ DE $= 5$ cm and BC $= 7$ cm. What is the area ABDE : area BDE : area BCD equal to?SimilarityModerate
Q93In the figure given below, PQRS is a parallelogram. PA bisects angle P and SA bisects angle S. What is angle PAS equal to?ParallelogramEasy
Q94In the figure given below, $∠$ A $= 8 0^{\circ}$ and $∠$ ABC $= 6 0^{\circ}$ . BD and CD bisect angles B and C respectively. What are the values of $x$ and $y$ respectively?Angle BisectorEasy
Q95In the figure given below, PQR is a non-isosceles right-angled triangle, right angled at Q. If LM and QT are parallel and QT $=$ PT, then what is $∠$ RLM equal to?TriangleHard
Q96In the figure given below, PQ is parallel to RS and PR is parallel to QS. If $∠$ LPR $= 3 5^{\circ}$ and $∠$ UST $= 7 0^{\circ}$ , then what is $∠$ MPQ equal to?ParallelogramHard
Q97In the figure given below, ABC is a triangle with AB $=$ BC and D is an interior point of the triangle ABC such that $∠$ DAC $= ∠$ DCA.CongruenceModerate
Q98In the figure given below, M is the mid-point of AB and $∠$ DAB $= ∠$ CBA and $∠$ AMC $= ∠$ BMD. Then the triangle ADM is congruent to the triangle BCM byCongruenceEasy
Q99ABCD is a square. X is the mid-point of AB and Y is the mid-point of BC.CongruenceHard
Q100From an aeroplane vertically over a straight horizontal road, the angles of depression of two consecutive kilometre-stones on the opposite sides of the aeroplane are observed to be $α$ and $β$ . The height of the aeroplane above the road isHeights and DistancesModerate

Topic mix

Arithmetic27
Algebra23
Geometry17
Trigonometry13
Mensuration12
Statistics8

Total questions100

Difficulty

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

Very easy7
Easy43
Moderate37
Hard12
Very hard1

Marking scheme

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

Options per question: 4Correct options per question: 1