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Class 9 Maths Question Answers

Question Answer

Class 9

Maths

Master Class 9 Maths: Engaging...

Last updated date: 19th Sep 2024

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Class 9 Maths Question Answers

What is the algebraic expression for half of a number?

An equilateral triangle a square and a circle have equal parameters. If T denotes the area of the triangle S is the area of the square and C is the area of the circle then:A. $S T C$ B. $T C S$ C. $T S C$ D. $C S T$

Find the Highest Common Factor (HCF) of 16 and 28.

Draw a line segment AB of length 10 cm. Mark a point P on AB such that AP = 4 cm. Draw a line through P perpendicular to AB.

A rectangle has dimensions $40m\\times 25m$. If the length and breadth are increased by 15% find the percentage increases in its area.

A bus has wheels of diameter \\[1.4m\\]. Travelling from one town to another the wheels complete \\[20 000\\] rotations. Find the distance covered by the bus.(A) \\[88km\\](B) \\[44km\\](C) \\[8800m\\](D) \\[4400m\\]

According to the 2001 census the number of peoples who spoke the following languages was:Assamese: $13168484$ Hindi: $422048642$ Konkani: $2489015$ (a) Write the above numbers according to the Indian and International system of numeration.(b) Write the above numbers in words according to the Indian system of numeration.(c) Write the above numbers in words according to the International system of numeration.

A coin is tossed $ 100 $ times with the following frequencies: $ Head:20 $ . Find the probability for events having heads only.a) $ 0.2 $ b) $ 0.5 $ c) $ 0.65 $ d) $ 1.5 $

What is the area of the sector?\n \n \n \n \n A. $ 170\\ c{{m}^{2}} $ B. $ 100\\ c{{m}^{2}} $ C. $ 110\\ c{{m}^{2}} $ D. $ 130\\ c{{m}^{2}} $

A group of $50$ items has mean $70$ and standard deviation $8$. What will be the value of mean and standard deviation if each value is multiplied by $5$?

An A.P is 4 9 14 19... and so on. find its \\[{10^{th}}\\] term?

What annual installment will discharge a debt of $Rs.420$ due in $5$ years at $10\\% $ SI?$A)Rs.60$$B)Rs.70$$C)Rs.800$$D)Rs.900$

Classify the following numbers as rational or irrational:(i). \\[2 - \\sqrt 5 \\] (ii). \\[(3 + \\sqrt {23} ) - \\sqrt {23} \\] (iii). \\[\\dfrac{{2\\sqrt 7 }}{{7\\sqrt 7 }}\\] (iv). \\[\\dfrac{1}{{\\sqrt 2 }}\\] (v). \\[2\\pi \\]

Example of co-prime numbers from the below option is:(a) 25 14(b) 18 16(c) 9 18(d) 11 77

Find the area of the Quadrilateral ABCD whose vertices are A ( -3 -1) B (-2 -4) C (4 -1) and D (3 4)

Evaluate the following equation\\[\\log \\left( {x + 3} \\right) + \\log \\left( {x - 3} \\right) = \\log 16\\]

Factorize the equation given below:${x^3} + 3{x^2} - x - 3$

Are all natural numbers also whole numbers?

A motor boat whose speed is 15$\\dfrac{{{\\text{km}}}}{{{\\text{hr}}}}$ in still water goes 30km downstream and comes back in a total of 4hours 30minutes. Determine the speed of the stream.

A man buys a cycle for Rs 1400 and sells it at a loss of 15%. What is the selling price of the cycle?(a) Rs 1090(b) Rs 1160(c) Rs 1190(d) Rs 1202

All rhombuses are kites.(a) True(b) False

A number when divided by 143 leaves remainder 31. The remainder when the number is divided by 13 is [a] 0[b] 1[c] 3[d] 5

ABCD is a parallelogram with AB=8cm AD=4cm \\[\\angle B=120{}^\\circ \\](a) What is $\\angle $A?(b) What is the perpendicular distance from D to AB?(c) What is the area of ABCD?\n \n \n \n \n

Add the following rational numbers:-\\[\\dfrac{5}{8}\\] And \\[\\dfrac{-7}{12}\\]

A man earns Rs 600 per month more than his wife. One tenth of a man's salary and one sixth of a wife's salary amounts to Rs 1500 which is saved every month. Find their salaries.

A hollow cylindrical iron pipe of length 28cm has inner radius 6cm and outer radius 8cm. Find the volume of the pipe and the weight of the pipe if the weight of 1cu.cm of iron is 7gm.

Ajit Kaur bought a 50 kg sack of sugar for Rs. 1750 but as sugar prices fell he had to sell it at Rs. 32 per kg. How much loss did he incur?

A concave polygon has _____ interior angles more than \\[{{180}^{\\circ }}\\].(a) no(b) 3 angles(c) one or more(d) less than 5

A period of 4 hours 30 minutes makes up what percent of a day?

Alfred and Rani both picked different two digit numbers. If you multiply Alfred’s number by 5 and double Rani’s number the sum is 300. If you double Alfred’s number and multiply Rani’s number by 3 the sum of the two numbers is 252. What is the sum of their two numbers?(a) 96(b) 112(c) 128(d) 144

A General wishes to draw up his 7500 soldiers in the form of a largest square. After arranging he found out that some of them are left out. How many soldiers were left out?

A bell rings every 5 seconds. A second bell rings every 6 seconds and a third bell rings every 8 seconds. If all the three rings at the same time at 8:00 a.m. at what time will they all ring together next?(a) 1 minute past 8:00 a.m.(b) 2 minutes past 8:00 a.m.(c) 3 minutes past 8:00 a.m.(d) 4 minutes past 8:00 a.m.

A cylindrical tank has a capacity of 2156 m3 and diameter class 9 maths JEE_Main

A number consists of three digits the righthand digit class 9 maths JEE_Main

A box contains 5 times 102 paper clips Each paper clip class 9 maths JEE_Main

A field is in the shape of a trapezium whose parallel sides are 25 m and 10 m. The non-parallel sides are 14 m and 13 m. Find the area of the field.

Anuradha invests INR 500 every month in a recurring deposit scheme for 3 years. The interest earned is INR 2220. Find the rate of interest and the maturity values of the investment.

A cubic foot of water is poured into a rectangular aquarium with base 15 inch by 18 inch. To what height in inches does the water rise.(a) $ 6\\dfrac{2}{5} $ (b) 6(c) $ 5\\dfrac{3}{4} $ (d) $ 5\\dfrac{1}{2} $ (e) 5

ABCD is a quadrilateral in which all four sides are equal. Show that both pairs of opposite sides are equal.

Add p(p – q) q(q – r) and r(r – p).(a) \\[{{p}^{3}}+{{q}^{2}}+{{r}^{2}}-pq+qr-pr\\](b) \\[{{p}^{2}}+2{{q}^{2}}+{{r}^{2}}-pq-qr+pr\\](c) \\[{{p}^{2}}+{{q}^{2}}+{{r}^{2}}-pq-qr-pr\\](d) \\[{{p}^{3}}+{{q}^{2}}+{{r}^{2}}-pq-qr-pr\\]

A regular hexagon is inscribed in a circle of radius 6 cm. Find its area(in sq cm).a. \\[48\\sqrt 3 \\]b. \\[54\\sqrt 3 \\]c. \\[48\\sqrt 2 \\]d. \\[54\\sqrt 2 \\]

An emergency lamp costs Rs.1100. Every year its value depreciates by 10%. What is its value at the end of 3 years?A.Rs. 908.90B.Rs. 809.10C.Rs. 801.90D.Rs. 980.90

A cube edge \\[3\\]cm of iron weighs \\[12\\]g. What is the weight of the similar cube of iron whose edge is \\[12\\]cm?

A brass tray in the shape of a parallelogram was polished at a total cost of Rs. 2250 at the rate of Rs. 20 per \\[10c{{m}^{2}}\\].If the altitude of the parallelogram is 45 cm find the length of its base.

A box contains $12$ two rupee coins $7$ one rupee coins and $4$ half rupee coins. If $3$ are selected at random find the probability thatA) Sum of three coins is maximum.B) Each coin is of different value.C) Selection contains at least one-rupee coinD) All selected three coins have the same value.

ABC is a right-angled triangle and O is the midpoint of the side opposite to the right angle. Explain why O is equidistant from A B and C.(The dotted lines are drawn additionally to help you)\n \n \n \n \n

A man is \\[35\\] years old and his son \\[7\\]years now. In how many years will the son be half as old as his father?

\\[ABC\\] and \\[BDE\\] are two equilateral triangles such that \\[D\\] is the midpoint of \\[BC\\]. Ratio of the areas of triangles \\[\\Delta ABC\\] and $\\Delta BDE$ is:A) \\[2:1\\] B) \\[1:2\\]C) \\[4:1\\]D) \\[1:4\\]

A rectangular floor is fully covered with square tiles of identical size. The tiles on the edges are white and the tiles in the interior are red. The number of white tiles is the same as the number of red tiles. A possible value of the number of tiles along one of the edges is (a) 12(b) 10(c) 14(d) 16

A \\[5 \\times 5 \\times 5\\;\\] cube is formed by using \\[1 \\times 1 \\times 1\\;\\]cubes. If we add another layer of such \\[1 \\times 1 \\times 1\\;\\]cube around the \\[5 \\times 5 \\times 5\\;\\] cube. What will be the number of \\[1 \\times 1 \\times 1\\;\\]cubes in the newly formed cube?

A palindrome is a number that reads the same backward as forward (for example 101). What is the next greatest palindrome after 3443?

ABCD is a parallelogram M is the midpoint of DC. If AP=65 and PM=30 then the largest possible integer value of AB is\n \n \n \n \n (a) 124(b) 120(c) 119(d) 118

A line lies in the xy-plane and makes an angle of \\[{30^ \\circ }\\] with the positive x- axis. Find its direction cosines.

{a e} is the subset of {x: x is a vowel in the English alphabet}. Enter 1 if true or 0 otherwise.

A company declares a dividend of 12% on Rs.100 shares. A housewife buys such shares and gets 15% on her investment. At what price she bought the shares?A. Rs.80B. Rs.85C. Rs.125D. Rs.76

A dairy farmer uses a storage silo that is in the shape of the right circular cylinder above. If the volume of the silo is $ 72\\pi $ cubic yards what is the diameter of the base of the cylinder in yards?\n \n \n \n \n A. 5B. 6C. 7D. 4

A farmer travelled a distance of 61 km on foot at an average speed of 4km\/hr and partly on bicycle at an average speed of 9km\/hr and the total distance is travelled in 9 hours. Then find the distance travelled by him on foot?A. 14 kmB. 15 kmC. 16 kmD. 17 km

A man whose bowling average is 12.4 takes 5 wickets for 26 runs and thereby decreases his average by 0.4. The number of wickets taken by him before his last match is ______A. 85B. 78C. 72D. 64

An article is bought for Rs.2500 and Rs.175 is spent on its transportation. At what price must it be sold in order to gain Rs.350?a) 1025b) 2025c) 3025d) 4025

What are different types of tables?

A circle is inscribed in a regular hexagon of side \\[2\\sqrt 3 \\]cm. Find the circumference of the inscribed circle.

A dealer in Mumbai supplied an item at the following prices to a dealer in Delhi. Find the total amount of the bill.Rate per piece (in Rs.)Quantity (no. of pieces)Discount %SGST %18010Net92602020931030Net917520309

A pen stand is made of wood in the shape of cuboid with three conical depressions to hold the pens. The dimensions of the cuboid are 15cm by 10cm by 3.5cm. The radius of each depression is 0.5 cm and the depth is 1.4cm. Find the amount of the wood in the entire stand.

An object is thrown upwards with an initial velocity of 17 m\/sec from a building with 12 m height. It is at a height of $ S = 12 + 17t - 5{t^2} $ from the ground after a flight of 't' seconds. Find the time taken by the object to touch the ground.

Among the following which one is\/are correct?A.The slant height is the longest side of a pyramidB.The section between the base and a plane parallel to the base of a solid is known as frustum.C.All the surface of a cuboid are rectangularD.For a cylinder the top the bottom and the walls of the cylinder determine the total surface area.

A hollow square shaped tube open at both ends is made of iron. The side of the internal square is \\[5\\;cm\\] and the length of the tube is $ 8\\;cm $ . There is $ 192\\;c{m^3} $ of iron in this tube. Find its thickness.

A farmer connects a pipe of internal diameter $ 20\\ cm $ from a canal into a cylindrical tank in her field which is $ 10\\ m $ in diameter and $ 2\\ m $ deep. If water flows through the pipe at the rate of $ 4\\ \\dfrac{{km}}{h} $ in how much time will the tank be filled?

All rectangles are square.A. TrueB. False

All …. Triangles are similar.A. Right angledB. IsoscelesC. EquilateralD. Reflex

A B and C can reap a field in \\[15\\dfrac{3}{4}\\] days; B C and D in 14 days; C D and A in 18 days; D A and B in 21 days. In what time can A B C and D together reap it?

An isosceles triangle is to be cut from one edge of a square lamina (as shown in the figure) such that the remaining position when suspended from the apex $P$ of the cut will remain in equilibrium in any position. The value of $h$ is \n \n \n \n \n A. $\\dfrac{{\\left( {3 - \\sqrt 3 } \\right)l}}{2}$B. $\\dfrac{{\\left( {3 + \\sqrt 3 } \\right)l}}{2}$C. $\\dfrac{{\\left( {2 - \\sqrt 2 } \\right)l}}{2}$D. $\\dfrac{{\\left( {2 + \\sqrt 2 } \\right)l}}{2}$

A _____ has all four sides equal opposite sides are parallel with equal opposite angles.This question has multiple correct optionsA. RectangleB. RhombusC. SquareD. Kite.

A profit of 20% is made on the goods when a discount of 10% is given on the list price. If a discount of 20% is allowed on the list price the profit to be made will be$(A)\\ 6\\% \\\\(B)6\\dfrac{2}{3}\\% \\\\(C)3\\dfrac{1}{3}\\% \\\\(D)4\\dfrac{2}{3}\\% \\\\ $

An exterior angle of a regular polygon is 15 degrees. How many sides does the polygon have?

A garden measures \\[17\\] meters by \\[24\\] meters. What is the area of the garden and how much fencing is needed to enclose the garden?

A man is $66\\dfrac{5}{{12}}$ inches tall and his son is $58\\dfrac{8}{9}$ inches tall. How much taller is the man?

A rectangular park is \\[45{\\text{ m}}\\] long and \\[{\\text{30 m}}\\] wide. A path \\[{\\text{2}}{\\text{.5 m}}\\] wide is constructed outside the park. Find the area of the park. \n \n \n \n \n

What is 0.583333333……. (repeating 3) as a fraction?

A quadrilateral whose all opposite sides are parallel is called: (This question has multiple correct options)A. a rhombusB. a kiteC. a trapeziumD. a parallelogram

When a number \\[P\\] is divided by \\[4\\] it leaves the remainder \\[3\\] . If twice of the number \\[P\\] is divided by the same divisor \\[4\\] then will there be the remainder?\\[\\begin{align} A.0 \\\\ B.1 \\\\ C.2 \\\\ D.6 \\\\ \\end{align}\\]

A rectangular field is 16 m long and 10 m wide. There is a path of uniform width all around it having an area of \\[120\\ {m^2}\\]. Form the quadratic equation.

80 is $32\\%$ of a certain number find the number.

What is $ {a_4} $ when $ {a_1} = 2 $ $ r = - 3? $ A. $ 27 $ B. $ - 27 $ C. $ - 54 $ D. $ 54 $

What is \\[8\\] to the third power times \\[8\\] to the negative \\[10\\] power?

a+2b=10ab=15Find the value of $a^3+8b^3$.

What is 20% of 50% of 75% of 80?(a) 5.5(b) 6(c) 8(d) 6.5

When 6 boys were admitted and 6 girls left the percentage of boys increased from \\[60\\%\\] to \\[75\\%\\]. Find the original number of boys and girls in the class.

1. If the curved surface area of the solid sphere is \\[98.56c{{m}^{2}}\\] then find the radius of the sphere.2. Surface area of the solid hemisphere is 2772sq.cm then find its total surface area.

What is the ${{10}^{th}}$ prime number if they are listed in order?

Application of circles in real life.

\\[4 \\times \\left( {ABCD} \\right) = DCBA\\] what is \\[ABCD\\]?

An equilateral triangle has an altitude of \\[15\\]m. What is the perimeter of the triangle?

What should be added to the polynomial $4{x^2} + 8x$ so that it becomes a perfect square?

Degree of the polynomial of \\[4{x^4} + 0{x^3} + 0{x^5} + 5x + 7\\] is

Express each of the following as a product of prime factors only in exponential form.$270$

Fill in the blanks.…………………..INR 50 notes makes 300 rupees.${\\text{a}}{\\text{. 3}} \\\\{\\text{b}}{\\text{. 4}} \\\\{\\text{c}}{\\text{. 6}} \\\\{\\text{d}}{\\text{. 8}} \\\\ $

Classify the following as scalar and vector quantities(i)Time Period(ii) Distance(iii)Force(iv)Velocity(v)Work done

Divide 243 into three parts such that half of the first part one-third of the second part and one-fourth of the third part are all equal.

Expand each of the following using suitable identities:$(i) {\\left( {x + 2y + 4z} \\right)^2}$ $(ii) {\\left( {2x - y + z} \\right)^2}$ $(iii) {\\left( { - 2x + 3y + 2z} \\right)^2}$ $(iv) {\\left( {3a - 7b - c} \\right)^2}$ $(v) {\\left( { - 2x + 5y - 3z} \\right)^2}$ $(iv) {\\left( {\\dfrac{1}{4}a - \\dfrac{1}{2}b + 1} \\right)^2}$

Find the HCF of 1260 and 7344 using Euclid’s algorithm.