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Elementary Mathematics 2019 (I)

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100Questions

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Q1What is the remainder when $(1 7^{29} + 1 9^{29})$ is divided by $18$ ?DivisibilityEasy
Q2What is the largest value of n such that $1 0^{n}$ divides the product $2^{5} \times 3^{3} \times 4^{8} \times 5^{3} \times 6^{7} \times 7^{6} \times 8^{12} \times 9^{9} \times 1 0^{6} \times 1 5^{12} \times 2 0^{14} \times 2 2^{11} \times 2 5^{15}$ ?DivisibilityModerate
Q3How many pairs (A, B) are possible in the number $479865 A B$ if the number is divisible by $9$ and it is given that the last digit of the number is odd ?DivisibilityModerate
Q4Consider the multiplication $999 \times abc = def 132$ in decimal notation, where a, b, c, d, e and f are digits. What are the values of a, b, c, d, e and f respectively ?DivisibilityModerate
Q5Three cars A, B and C started from a point at $5$ p.m., $6$ p.m. and $7$ p.m. respectively and travelled at uniform speeds of $60$ km/hr, $80$ km/hr and $x$ km/hr respectively in the same direction. If all the three met at another point at the same instant during their journey, then what is the value of $x$ ?Relative SpeedModerate
Q6Priya's age was cube of an integral number (different from $1$ ) four years ago and square of an integral number after four years. How long should she wait so that her age becomes square of a number in the previous year and cube of a number in the next year ?Age ProblemsHard
Q7Which of the following statements is not true ?Number SystemModerate
Q8For $x > 0$ , what is the minimum value of $x + \frac{x + 2}{2 x}$ ?Maximum and Minimum ValuesEasy
Q9If $\frac{1 + p x}{1 - p x} \frac{1 - q x}{1 + q x} = 1$ , then what are the non-zero solutions of x ?SurdsHard
Q10In a hostel the rent per room is increased by $20%$ . If number of rooms in the hostel is also increased by $20%$ and the hostel is always full, then what is the percentage change in the total collection at the cash counter ?Successive Increase and DecreaseEasy
Q11Radha and Hema are neighbours and study in the same school. Both of them use bicycles to go to the school. Radha's speed is $8$ km/hr whereas Hema's speed is $10$ km/hr. Hema takes $9$ minutes less than Radha to reach the school. How far is the school from the locality of Radha and Hema ?Relative SpeedEasy
Q12Which of the following pair of numbers is the solution of the equation $3^{x + 2} + 3^{- x} = 10$ ?EquationsEasy
Q13It is given that $lo g_{10} 2 = 0.301$ and $lo g_{10} 3 = 0.477$ . How many digits are there in $(108)^{10}$ ?Characteristic and MantissaEasy
Q14The sum of three prime numbers is $100$ . If one of them exceeds another by $36$ , then one of the numbers isPrime NumbersModerate
Q15If a, b and c are positive integers such that $a + \frac{1}{b + \frac{1}{c + \frac{1}{2}}} = \frac{16}{23}$ , then what is the mean of a, b and c ?Rational NumbersModerate
Q16What is the number of people who read only one newspaper ?OperationsModerate
Q17What is the number of people who read at least two newspapers ?OperationsEasy
Q18What is the number of people who do not read any of these three newspapers ?OperationsEasy
Q19What is the unit place digit in the expansion of $7^{73}$ ?Unit DigitEasy
Q20Suppose n is a positive integer such that $(n^{2} + 48)$ is a perfect square. What is the number of such n ?Perfect SquaresModerate
Q21For $x = \frac{4 6}{2 + 3}$ , what is the value of $\frac{x + 2 2}{x - 2 2} + \frac{x + 2 3}{x - 2 3}$ ?SimplificationHard
Q22x, y and z are three numbers such that x is $30%$ of z and y is $40%$ of z. If x is $p %$ of y, then what is the value of p ?PercentageVery easy
Q23A plane is going in circles around an airport. The plane takes $3$ minutes to complete one round. The angle of elevation of the plane from a point P on the ground at time t seconds is equal to that at time (t + 30) seconds. At time (t + x) seconds, the plane flies vertically above the point P. What is x equal to ?Heights and DistancesHard
Q24Consider the following statements in respect of two integers p and q (both > $1$ ) which are relatively prime :Prime NumbersEasy
Q25In a class of $100$ students, the average weight is $30$ kg. If the average weight of the girls is $24$ kg and that of the boys is $32$ kg, then what is the number of girls in the class ?Weighted MeanEasy
Q26For any two real numbers a and b, $(a - b)^{2} + (b - a)^{2}$ isSurdsEasy
Q27If $a : b = c : d = 1 : 6$ , then what is the value of $\frac{a ^{2} + c ^{2}}{b ^{2} + d ^{2}}$ ?Ratio and ProportionEasy
Q28What is $0. 53 + 0.5 3$ equal to ?Rational NumbersModerate
Q29The inequality $3^{N} > N^{3}$ holds whenInequalitiesModerate
Q30Which one of the following is an irrational number?Rational NumbersEasy
Q31A race has three parts. The speed and time required to complete the individual parts for a runner is displayed on the following chart :Average SpeedModerate
Q32If $\frac{a}{b + c} = \frac{b}{c + a} = \frac{c}{a + b}$ , then which one of the following statements is correct?ProportionModerate
Q33The number $3^{521}$ is divided by $8$ . What is the remainder ?DivisibilityEasy
Q34A prime number contains the digit X at unit's place. How many such digits of X are possible ?Prime NumbersEasy
Q35If an article is sold at a gain of $6%$ instead of a loss of $6%$ , the seller gets Rs. $6$ more. What is the cost price of the article ?Profit and LossEasy
Q36A field can be reaped by $12$ men or $18$ women in $14$ days. In how many days can $8$ men and $16$ women reap it ?Time and WorkModerate
Q37If $3^{x} = 4^{y} = 1 2^{z}$ , then z is equal toEquationsEasy
Q38If $(4 a + 7 b) (4 c - 7 d) = (4 a - 7 b) (4 c + 7 d)$ , then which one of the following is correct ?ProportionEasy
Q39Given that the polynomial $(x^{2} + a x + b)$ leaves the same remainder when divided by $(x - 1)$ or $(x + 1)$ . What are the values of a and b respectively ?Factor and Remainder TheoremEasy
Q40Tushar takes $6$ hours to complete a piece of work, while Amar completes the same work in $10$ hours. If both of them work together, then what is the time required to complete the work ?Time and WorkVery easy
Q41What is the value of $2 + 2 + 2 + ........$ ?Nested RadicalsEasy
Q42In an examination, $52%$ candidates failed in English and $42%$ failed in Mathematics. If $17%$ failed in both the subjects, then what percent passed in both the subjects ?OperationsEasy
Q43A man who recently died left a sum of Rs. $3, 90, 000$ to be divided among his wife, five sons and four daughters. He directed that each son should receive $3$ times as much as each daughter receives and that each daughter should receive twice as much as their mother receives. What was the wife's share ?Division into PartsEasy
Q44What is the least number of complete years in which a sum of money put out at $40%$ annual compound interest will be more than trebled ?Compound InterestModerate
Q45A person divided a sum of Rs. $17, 200$ into three parts and invested at $5%$ , $6%$ and $9%$ per annum simple interest. At the end of two years, he got the same interest on each part of money. What is the money invested at $9%$ ?Simple InterestModerate
Q46What is $\frac{( x - y ) ^{3} + ( y - z ) ^{3} + ( z - x ) ^{3}}{3 ( x - y ) ( y - z ) ( z - x )}$ equal to ?Algebraic IdentitiesEasy
Q47If $a^{x} = b^{y} = c^{z}$ and $b^{2} = a c$ , then what is $\frac{1}{x} + \frac{1}{z}$ equal to ?EquationsModerate
Q48If p and q are the roots of the equation $x^{2} - 15 x + r = 0$ and $p - q = 1$ , then what is the value of r ?RootsEasy
Q49For the inequation $x^{2} - 7 x + 12 > 0$ , which one of the following is correct ?Quadratic InequalitiesEasy
Q50The expression $5^{2 n} - 2^{3 n}$ has a factorFactorisationModerate
Q51If $tan x = 1$ , $0 < x < 9 0^{\circ}$ , then what is the value of $2 sin x cos x$ ?Trigonometric IdentityEasy
Q52What is the value of $sin 4 6^{\circ} cos 4 4^{\circ} + cos 4 6^{\circ} sin 4 4^{\circ}$ ?Complementary AnglesEasy
Q53Suppose $0 < θ < 9 0^{\circ}$ , then for every $θ$ , $4 sin^{2} θ + 1$ is greater than or equal toMaximum and Minimum ValuesHard
Q54Consider a regular hexagon ABCDEF. Two towers are situated at B and C. The angle of elevation from A to the top of the tower at B is $3 0^{\circ}$ , and the angle of elevation to the top of the tower at C is $4 5^{\circ}$ . What is the ratio of the height of towers at B and C?Heights and DistancesHard
Q55What is the value of $tan 1^{\circ} tan 2^{\circ} tan 3^{\circ} \dots tan 8 9^{\circ}$ ?Complementary AnglesEasy
Q56There are two parallel streets each directed North to South. A person in the first street travelling from South to North wishes to take the second street which is on his right side. At some place, he makes a $15 0^{\circ}$ turn to the right and he travels for $15$ minutes at the speed of $20 km/hr$ . After that he takes a left turn of $6 0^{\circ}$ and travels for $20$ minutes at the speed of $30 km/hr$ in order to meet the second street. What is the distance between the two streets?TriangleHard
Q57If $3 tan θ = cot θ$ where $0 \leq θ \leq \frac{π}{2}$ , then what is the value of $θ$ ?Trigonometric EquationEasy
Q58What is the value of $sin^{2} 2 5^{\circ} + sin^{2} 6 5^{\circ}$ ?Complementary AnglesVery easy
Q59What is the value of $sin^{6} θ + cos^{6} θ + 3 sin^{2} θ cos^{2} θ - 1$ ?Trigonometric IdentityEasy
Q60Consider the following for real numbers $α$ , $β$ , $γ$ and $δ$ :Maximum and Minimum ValuesModerate
Q61Consider the following grouped frequency distribution:MeanModerate
Q62Consider the following frequency distribution:MedianModerate
Q63The average of $50$ consecutive natural numbers is $x$ . What will be the new average when the next four natural numbers are also included?MeanEasy
Q64Consider two-digit numbers which remain the same when the digits interchange their positions. What is the average of such two-digit numbers?MeanEasy
Q65Diagrammatic representation of data includes which of the following?Data ClassificationEasy
Q66The data collected from which one of the following methods is not a primary data?Data ClassificationEasy
Q67The monthly expenditure of a person is Rs. $6, 000$ . The distribution of expenditure on various items is as follows:Bar ChartModerate
Q68If the mean of $m$ observations out of $n$ observations is $n$ and the mean of remaining observations is $m$ , then what is the mean of all $n$ observations?Weighted MeanModerate
Q69Which one of the following pairs is correctly matched?MedianEasy
Q70The following pairs relate to frequency distribution of a discrete variable and its frequency polygon. Which one of the following pairs is not correctly matched?Frequency DistributionModerate
Q71In a rectangle, length is three times its breadth. If the length and the breadth of the rectangle are increased by $30%$ and $10%$ respectively, then its perimeter increases byQuadrilateralEasy
Q72What is the percentage decrease in the area of a triangle if its each side is halved?TriangleEasy
Q73The volume of a spherical balloon is increased by $700%$ . What is the percentage increase in its surface area?SphereEasy
Q74If the lengths of two parallel chords in a circle of radius $10 cm$ are $12 cm$ and $16 cm$ , then what is the distance between these two chords?ChordsEasy
Q75Considering two opposite vertices of a square of side ' $a$ ' as centres, two circular arcs are drawn within the square joining the other two vertices, thus forming two sectors. What is the common area in these two sectors?QuadrilateralHard
Q76The corners of a square of side 'a' are cut away so as to form a regular octagon. What is the side of the octagon?PolygonModerate
Q77Three consecutive integers form the lengths of a right-angled triangle. How many sets of such three consecutive integers is/are possible?Pythagoras TheoremModerate
Q78Two circles are drawn with the same centre. The circumference of the smaller circle is $44$ cm and that of the bigger circle is double the smaller one. What is the area between these two circles?CircleEasy
Q79A rectangular red carpet of size $6$ ft $\times$ $12$ ft has a dark red border $6$ inches wide. What is the area of the dark red border?QuadrilateralModerate
Q80The perimeter of a right-angled triangle is k times the shortest side. If the ratio of the other side to hypotenuse is $4$ : $5$ , then what is the value of k?TriangleEasy
Q81A $12$ m long wire is cut into two pieces, one of which is bent into a circle and the other into a square enclosing the circle. What is the radius of the circle?CircleModerate
Q82The angles of a triangle are in the ratio $1$ : $1$ : $4$ . If the perimeter of the triangle is k times its largest side, then what is the value of k?Angles of a TriangleModerate
Q83The hypotenuse of a right-angled triangle is $10$ cm and its area is $24$ cm $^{2}$ . If the shorter side is halved and the longer side is doubled, the new hypotenuse becomesTriangleModerate
Q84In a circle of radius $8$ cm, AB and AC are two chords such that AB = AC = 12 cm. What is the length of chord BC?ChordsHard
Q85Consider the following statements:Cyclic QuadrilateralModerate
Q86A ladder is resting against a vertical wall and its bottom is $2.5$ m away from the wall. If it slips $0.8$ m down the wall, then its bottom will move away from the wall by $1.4$ m. What is the length of the ladder?Pythagoras TheoremModerate
Q87Two equal circles intersect such that each passes through the centre of the other. If the length of the common chord of the circles is $103$ cm, then what is the diameter of the circle?ChordsModerate
Q88Consider the following statements:Arcs and AnglesModerate
Q89Consider the following inequalities in respect of any triangle ABC:Triangle InequalityEasy
Q90Consider the following statements:Medians and CentroidHard
Q91What is the ratio of the volume of the sphere to that of the cone?Combination of SolidsHard
Q92What is the ratio of the volume of the cube to that of the cylinder?Combination of SolidsModerate
Q93Consider the following statements:Combination of SolidsHard
Q94What is the area of triangle ADC?TriangleModerate
Q95What is the area of quadrilateral ABCD?QuadrilateralEasy
Q96What is the difference between perimeter of triangle ABC and perimeter of triangle ADC?TriangleEasy
Q97What is the length of the side of the triangle?Inscribed FiguresEasy
Q98The centroid of the triangle ABC is at a distance d from the vertex A. What is d equal to?Medians and CentroidEasy
Q99What is the surface area of the cuboid?CuboidModerate
Q100If S is the sum of the cubes of the dimensions of the cuboid and V is its volume, then what is (S - 3V) equal to?CuboidHard

Topic mix

Arithmetic29
Algebra19
Mensuration16
Geometry14
Trigonometry11
Statistics11

Total questions100

Difficulty

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

Very easy3
Easy47
Moderate37
Hard13
Very hard0

Marking scheme

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

Options per question: 4Correct options per question: 1