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Class 10

Maths

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Class 10 Maths Question Answers

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Vedantu’s Class 10 Maths Question Answers are expertly designed to help you excel in your board exams. These comprehensive solutions address all the important questions from the Maths syllabus, presenting every concept in a simple and easy-to-grasp manner.

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Class 10 Maths Question Answers

Construct LMN such that LM = 6.6 cm angle LMN = 60° and ND is the median and ND = 5 cm.

An empty tank was $\\dfrac{2}{5}$ full after 1.5 liters of water was poured into it. The base area of the tank was $250\\;c{m^2}$. What was the height of the tank?

Consider a polynomial as $f\\left( x \\right)={{x}^{4}}+a{{x}^{3}}+b{{x}^{2}}+cx+d$ such that $f\\left( 1 \\right)=10 f\\left( 2 \\right)=20 f\\left( 3 \\right)=30$ then the value of $\\dfrac{f\\left( 12 \\right)+f\\left( -8 \\right)}{10}$ is equal toA.2018B.1984C.60D.600

Angle inscribed in a minor segment is (A). acute(B). obtuse(C). right(D). straight

Consider the probability of an event E in which if $P\\left( E \\right)=0.42$ then what is the value of $P\\left( \\text{not E} \\right)$?

A mason has to fit a bathroom with square marble tiles of the largest possible size. The size of the bathroom is 10 ft by 8 ft. What should be the size in inches of the tile required that has to be cut and how many such tiles are required?

In a shelf there are 10 English and 8 Telugu books. The number of ways in which 6 books can be chosen if a particular English book is excluded and a particular Telugu book is excluded is:(a) \\[{}^{9}{{C}_{3}}\\cdot {}^{7}{{C}_{3}}\\](b) \\[{}^{16}{{C}_{6}}\\](c) \\[{}^{9}{{C}_{3}}\\cdot {}^{8}{{C}_{3}}\\](d) \\[{}^{18}{{C}_{8}}\\]

A pole is standing erect on the ground which is horizontal. The tip of the pole is tied right with a rope of $\\sqrt {12} m$ to a point on the ground. if the rope is making 30° angle with the horizontal then the height of the pole is A. 2$\\sqrt 3 $m B. 3$\\sqrt 2 $ m C. 3m D. $\\sqrt 3 $m

A pilot in an aeroplane observes that Vashi bridge is one side of a plane and Warli sea-link is on the opposite side. The angle of depression of Vashi bridge and Warli sea-link are \\[60^\\circ \\] and \\[30^\\circ \\] respectively. If the aeroplanes is at a height of 5500\\[\\sqrt 3 \\]m at that time. What is the distance between Vashi bridge and Warli sea-link?

A square is inscribed in a circle of radius 2 cm. Side of the square in cm is:$\\left( A \\right)\\sqrt 2 $$\\left( B \\right)2\\sqrt 2 $$\\left( C \\right)4\\sqrt 2 $$\\left( D \\right)2\\sqrt 3 $

A painter sets a ladder up to reach the bottom of a second storey window 16 feet above the ground. The base of the ladder is 12 feet from the house. While the painter mixes the paint a neighbor’s dog bumps the ladder which moves the base 2 feet farther away from the house. How far up the side of the house does the ladder reach?\n \n \n \n \n

There are 5 English 4 Sanskrit and 3 Telugu books. Two books from each group are to be arranged on a shelf. The number of possible arrangements is:$ \\begin{align} \\left( a \\right)\\left( 180 \\right)6! \\\\ \\left( b \\right)\\left( 12 \\right)7! \\\\ \\left( c \\right)7! \\\\ \\left( d \\right)180 \\\\ \\end{align} $

A rectangular tank of length \\[37\\dfrac{1}{3}\\] m internally 12 m in breadth and 8 m in depth is full of water. Find the weight of water in metric tons given that one cubic metre of water weighs 1000 kg.

Define the terms vertically opposite angles linear pair of angles and adjacent angles with suitable diagrams.

A man purchased sugar worth Rs. 400. He sold ${{\\dfrac{3}{4}}^{th}}$ at a loss of 10% and the remaining at a gain of 10%. On the whole he gets: (a) a loss of 5%(b) a gain of $5\\dfrac{1}{2}\\%$ (c) a loss of $5\\dfrac{1}{19}\\%$ (d) a gain of $5\\dfrac{1}{19}\\%$

Construct a $\\Delta ABC$ in which the base BC=5cm $\\angle BAC = {40^ \\circ }$and the median from A to BC is 6cm. Also measure the length of the altitude from A.

A door of width of 6m has an arc above it having a height of 2m as shown. Find the radius of the arc.\n \n \n \n \n

$A$ borrowed $Rs.5000$ from $B$ on simple interest after $8$ years receives $Rs.2000$ more than the amount given to $A$ on loan. Find the rate of interest.

A bus travels 120 km in 3 hours. How much distance can it travel in 9 hours?

4 tables and 3 chairs cost Rs.2250 and 3 tables and 4 chairs cost Rs.1950. Find the cost of 1 table and 2 chairs.

A bag contains 20 silver balls and x iron balls. If one ball is drawn from the bag what is the probability that it is silver?

A certain sum of money Q was deposited for 5 years and 4 months at 4.5% simple interest and amounted to Rs 248. Then the value of Q isA. Rs 200B. Rs 210C. Rs 220D. Rs 240

A boat covers 6 km in an hour in still water. It takes thrice as much time in covering the same distance against the current. What is the speed of the current?$(a){\\text{ 2km\/hr}} \\\\(b){\\text{ 3km\/hr}} \\\\(c){\\text{ 4km\/hr}} \\\\(d){\\text{ 5km\/hr}} \\\\ $

4 boys and 2 girls occupy seats in a row at random. Then the probability that the girls occupy seat side by side is[a] $\\dfrac{1}{2}$[b] $\\dfrac{1}{4}$[c] $\\dfrac{1}{3}$[d] $\\dfrac{1}{6}$

Anuj got marks 58 out of 75 in Physics and 97 marks out of 120 in Maths. In which of the two subjects did he perform better?

ABC is an isosceles triangle and $\\angle B = 90^\\circ $ then show that $A{C^2} = 2A{B^2}$.

10 students of class X took part in a mathematics quiz. If the number of girls is 4 more than the number of boys find the number of boys and girls who took part in the quiz.

How many 2 – digit numbers can be formed from the digits {1 2 3 4 5} without repetition and with repetition?

When 3 is added to the denominator and 2 is subtracted from the numerator a fraction becomes $\\dfrac{1}{4}$. And when 6 is added to the numerator and the denominator is multiplied by 3 it becomes $\\dfrac{2}{3}$. Find the fraction.

A boiler is in the form of a cylinder 2m long with hemispherical ends each of 2 metre diameter. Find the volume of the boiler.

2 cubes each of volume \\[64\\ c{{m}^{3}}\\] are joined end to end. Find the surface area of the resulting cuboid.(a) \\[128\\ c{{m}^{3}}\\](b) \\[130\\ c{{m}^{3}}\\](c) \\[160\\ c{{m}^{3}}\\](d) none of these

A bag contains one white and one red ball. A ball is drawn from the bag. If the ball drawn is white it is replaced in the bag and again a ball is drawn. Otherwise a die is tossed. Write the sample space for this experiment.

ABCD is a parallelogram AP and CQ are perpendicular drawn from vertices A and C on diagonal BD (see figure) show that AP = CQ.\n \n \n \n \n

A child makes a paper model in the shape of a cylinder surmounted by a right cone. The height of the cylindrical part is 7.5 cm. The base of the model has a diameter of 10 cm and the total height of the model is$19\\dfrac{1}{2}{\\text{ cm}}$. Find the area of the paper required by the child to make the tent.${\\text{A}}{\\text{. 440 c}}{{\\text{m}}^2} \\\\{\\text{B}}{\\text{. 775}}\\dfrac{1}{2}{\\text{ c}}{{\\text{m}}^2} \\\\{\\text{C}}{\\text{. 880 c}}{{\\text{m}}^2} \\\\{\\text{D}}{\\text{. 1028}}\\dfrac{1}{2}{\\text{ c}}{{\\text{m}}^2} \\\\ $

A boy is cycling such that the wheels of the cycle are making 140 revolutions per minute. If the diameter of the wheel is 60cm calculate the speed per hour with which the boy is cycling.

A child draws the figure of an aeroplane as given. Here the wings EDCF and AGHB are parallelograms the tail ADK is an isosceles triangle the cockpit BLC is a semicircle and the portion ABCD is a square. Let $FP\\bot CD$ and $HQ\\bot AB$. $AB=6\\ cm$ $KD=5\\ cm$ $FP=HQ=2\\ cm$. The area of the figure is \n \n \n \n \n (a) $98.14\\ c{{m}^{2}}$(b) $87.25\\ c{{m}^{2}}$(c) $86.14\\ c{{m}^{2}}$(d) $91.56\\ c{{m}^{2}}$

A car travels 360 km in 4 hrs. Find the distance it covers in 6 hours and 30 minutes at the same speed.

A charitable associate sold an average of 66 raffle tickets per member. Among the female members the average was 70 raffle tickets. The male to female ratio of the association is 1:2. What was the average number of tickets sold by the male members of the association?(a) 55(b) 58(c) 60(d) 50

ACEG is a square. AB is \\[\\dfrac{1}{2}\\] of AC. What is the perimeter of square?\n \n \n \n \n \\[\\begin{align} \\text{(A) 48 cm} \\\\ \\text{(B) 40 cm} \\\\ \\text{(C) 36 cm} \\\\ \\text{(D) 24 cm} \\\\ \\end{align}\\]

A circle and a square have the same perimeter. ThenA) Their areas are equal.B) The area of the circle is greater.C) The area of the square is greater.D) None of the above.

A bucket is in the shape of a frustum with the top and bottom circles of radii \\[15\\] cm and \\[10\\] cm. its depth is \\[12\\] cm. Find its curved surface area and total surface area. (Express the answer in terms of \\[\\pi \\])

A 25m long ladder is placed against a vertical wall such that the foot of the ladder is 7m from the feet of the wall. If the top of the ladder slides down by 4m by how much distance will the foot of the ladder slide ?

ABCD is a square in which a circle is inscribed touching all the sides of the square. In the four corners of the square 4 similar circles of equal radii are drawn containing maximum possible area. What is the ratio of the area of the larger circle to that of the sum of the areas of four smaller circles?\n \n \n \n \n

ABC and DBC are two isosceles triangles on the same side of BC. Then DA (or AD ) produced bisects the BC at the right angle. If the statement is true mention 1 otherwise 0.

(1): The price of a computer is\\[Rs.27000\\]. The GST charged is $12\\%$. Find the amount to be paid.(2): Uma purchased a hair dryer for \\[Rs.5400\\]including $8\\%$GST. Find the price before GST was added.

A circle has only a finite number of chords. True or false.

A amount of Rs. 3270 is made up with the notes of denominations Rs. 100 Rs. 50 Rs. 20 and Rs. 10. The number of Rs. 10 notes is 5 times the number of Rs. 20 notes. The number of Rs. 20 notes are 4 times the number of Rs. 50 notes. The number of Rs. 50 notes is 3 times the number of Rs. 100 notes. How many total notes of denomination Rs. 20 are there?

A clock was set correct at 12 o’clock. It loses 10 minutes per hour. What will be the angle between the hour and the minute hand of the clock after one hour?A. ${{60}^{\\circ }}$ B. ${{90}^{\\circ }}$ C. ${{105}^{\\circ }}$ D. ${{75}^{\\circ }}$

A boat goes 30 km upstream and 44 km downstream in 13 hours it can go 14 km upstream and 55 km downstream. Determine the speed of the stream and that of the boat in still water.

ABCD is quadrilateral in which $AD=BC$. If P Q R S be the mid-points of AB AC CD and BD respectively show that PQRS is a rhombus.

How many $ 3 $ digit numbers can be formed with the digits $ 1 2 3 4 5 $ where digits may not be repeated?$ A.\\ \\ 60 \\\\B.\\ \\ 125 \\\\C.\\ \\ 216 \\\\D.\\ \\ none\\ \\ of\\ \\ these \\\\ $

A boat has to cross a river. It crosses the river by making an angle of \\[60^\\circ \\] with the bank of the river due to the stream of the river and travels a distance of 600 m to reach the other side of the river. What is the width of the river?

A certain shade of green is made from six parts yellow mixed with four parts blue. If seventy cans of paint was used in all how many cans of blue were used?

10 cylindrical pillars of the building have to be painted. The diameter of each pillar is $70$ cm and the height is 4 m. What is the cost of painting at the rate of 5 per square meter?A. Rs. 400B. Rs. 440C. Rs. 480D. Rs. 500

A box contains cards bearing numbers 6 to 70. If one card is drawn at random from the box find the probability that it bears a composite number between 50 and 70.\t

A canal is $300\\ cm$ wide and $120\\ cm$ deep. The water in the canal is flowing with a speed of $20\\ km\/hr$ . How much area will it irrigate in $20$ minutes if $8\\ cm$ of standing water is required?

AB = BC = 6Km. Junior students follow a similar path but they only walk 4Km North from A then 4Km on a bearing \\[{110^ \\circ }\\]before returning to A.Senior students walk to a total of 18.9KmCalculate the distance walked by junior students.\n \n \n \n \n

A cheque was written for M rupees and N paisa both M and N being-two digit numbers but was mistakenly cashed for N rupees and M paisa. The incorrect amount exceeded the correct amount by Rs.1782 ThenA. M cannot be more than 70B. N can be equal to 2MC. The amount of the cheque cannot be multiple of 5. D. The incorrect amount can be twice the correct amount.

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

A 5m wide cloth is used to make a conical tent of base diameter $14m$ and height $24m$. Find the cost of cloth used at the rate of $Rs.25$ per meter. (Use $\\pi = \\dfrac{{22}}{7}$ )

All the black face cards are removed from a pack of 52 cards. The remaining cards are well shuffled and then a card is drawn at random. Find the probability of getting a(i) face card(ii) red card(iii) black card(iv) king

Arun bought a car for Rs. 350 000. The next year the price went up to Rs. 370 000. What was the percentage of price increased?

D and E are the points on the sides AB and AC respectively of a triangle ABC such that AD=8 cm DB=12 cm AE=6 cm and CE=9 cm. Prove that ${\\text{BC}} = \\dfrac{{5\\left( {{\\text{DE}}} \\right)}}{2}$ .\n \n \n \n \n

As observed from the top of a 75m high lighthouse from the sea-level the angles of depression of two ships are 30 degree and 45 degree. If one ship is exactly behind the other on the same side of the lighthouse find the distance between the two ships.

A right triangle ABC with sides 5cm 12cm and 13cm is revolved about the side 5cm. Find the volume of the solid so obtained. Also find the ratio of volume of two solids obtained.

An observer 1.5 m tall is 28.5 m away from a tower. The angle of elevation of the top of the tower from his\/her eyes has measure 45 degrees. What is the height of the tower?A. 28.5 mB. 30 mC. 27 mD. 1.5 m

An unbiased die is thrown. What is the probability of getting:(1) an even number and (2) a multiple of 3.

Determine whether or not the operation * defined on ${{Z}^{+}}$ defined by a*b = a-b gives a binary operation. If the event * is not a binary operation give justification of this.

A dice is thrown twice. What is the probability that1) 3 will not come up either time? 2) 6 will come up at least once?A. \\[\\begin{gathered}(i)\\dfrac{{12}}{{25}} \\\\(ii)\\dfrac{{16}}{{25}} \\\\ \\end{gathered} \\]B.\\[\\begin{gathered}(i)\\dfrac{{18}}{{25}} \\\\(ii)\\dfrac{9}{{25}} \\\\ \\end{gathered} \\]C.\\[\\begin{gathered}(i)\\dfrac{{25}}{{36}} \\\\(ii)\\dfrac{{11}}{{36}} \\\\ \\end{gathered} \\]D.\\[\\begin{gathered}(i)\\dfrac{{23}}{{36}} \\\\(ii)\\dfrac{{17}}{{36}} \\\\ \\end{gathered} \\]

Calculate the simple interest on 18000 for 4 years at $12\\dfrac{1}{2}$ % p.a.

A veranda of width 2.25 m is constructed all along outside a room which is 5.5 m long and 4 m wide. Find: (i) The area of the veranda.(ii) The cost of cementing the floor of the veranda at the cost of Rs. 200 per sq. m.

A copper rod of diameter 1 cm and length 8 cm is drawn into a wire of length 18 m of uniform thickness. Find the thickness of the wire.

A farmer moves along the boundary of a square field of side 10m in 40s. What will be the magnitude of displacement of the farmer at the end of 2 minutes 20 seconds from his initial position?

As we observed from the top of a 75 m lighthouse from the sea level the angle of depression of 2 ships \\[{{30}^{\\circ }}\\] and \\[{{45}^{\\circ }}\\]. If one ship is exactly behind the other on the same side of the lighthouse find the distance between two ships.

A conical vessel of radius 6cm and height 8 cm is completely filled with water. A sphere is lowered into the water and its size is such that when it touches the sides it is just immersed. What fraction of water overflows?

An urn contains 3 white 4 red and 5 black balls. Two balls are drawn one by one without replacement. What is the probability that at least one ball is black?

Diagonals of a rhombus are 12cm and 16cm respectively then find the side of the rhombus and its perimeter.

$\\Delta ABC$ is a right triangle right-angled at C. If A = 30${}^\\circ $ and AB = 40 units find the remaining two sides and $\\angle B$ in $\\Delta ABC$.

A pole 5m high is fixed on the top of a tower. The angle of elevation of the top of the poles observed from a point A on the ground is $60{}^\\circ $ and the angle of depression of point A from the tower is $45{}^\\circ $. Find the height of the tower. Take $\\sqrt{3}=1.732$ .

All the vertices of a rhombus lie on a circle. Find the area of the rhombus if the area of the circle is 1256$c{m^2}$.\n \n \n \n \n

A student gets an aggregate of 60% marks in five subjects in the ratio $10:9:8:7:6$. If the passing marks are 50% of the maximum marks and each subject has the same maximum marks in how many subjects did he pass the exam?(a) 2(b) 3(c) 4(d) 5

A merchant purchases a wristwatch for Rs. 450 and fixes the list price in such a way after allowing a discount of 10 % he earns a profit of 20 %. What is the list price of the watch?(a). Rs. 500(b). Rs. 600(c). Rs. 700(d). Rs. 750

What is a four-sided polygon called?(a). triangle(b). quadrilateral(c). circle(d). diagonal

A manufacturer has 600 litres of a 12% solution of acid. How many litres of 30% acid solution must be added to it so that acid content in the resulting mixture is more than 15% but less than 18%.

What are the co – ordinates of origin?(a). (0 1)(b). (1 0)(c). (1 1)(d). (0 0)

A four digit number ( numbered from 0000 to 9999) is said to be lucky if the sum of its first two digits is equal to the sum of its last two digits. If a four digit number is picked at random; then find the probability that it is a lucky number.(a) Required probability \\[=0.067\\](b) Required probability \\[=0.077\\](c) Required probability \\[=0.167\\](d) Required probability \\[=0.177\\]

At what rate percent per annum will a sum of Rs. 2000 amount to Rs. 2205 in 2 years compounded annually ?

Check the commutativity and associativity of the following binary operation:$' \\odot '$ on Q defined by $a \\odot b = {a^2} + {b^2}$ for all $a b \\in Q$.

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

A path of width 3.5m runs around a semi-circular grassy plot whose perimeter is 72m. Find the area of the path. \\[\\left( {{\\text{Use }}\\pi = \\dfrac{{22}}{7}} \\right)\\]

An army contingent of 616 members is to march behind an army band of 32 members in a parade. The two groups are to march in the same number of columns. What is the maximum number of columns in which they can march?

Calculate the area and the height of an equilateral triangle whose perimeter is 60 cm.A. $173.2c{{m}^{2}};11.32$B. $173.2c{{m}^{2}};19.32$ C. $173.2c{{m}^{2}};17.32$ D. $173.2c{{m}^{2}};14.32$

What annual installment will discharge a debt of INR 1092 due in 3 years at 12 % simple interest?(a). INR 250(b). INR 275(c). INR 300(d). INR 325

A wooden article was made by scooping out a hemisphere from each end of a solid cylinder as shown in figure. If the height of the cylinder is 10cm and its base is of radius 3.5cm. Find the total surface area of the article.\n \n \n \n \n

Out of 100 students 15 passed in English 12 passed in Mathematics 8 in Science 6 in English and Mathematics 7 in Mathematics and Science 4 in English and Science 4 in all the three. Find how many passed in English and mathematics but not in science?

: A quadratic polynomial the sum of whose zeros is 0 and one zero is 3 isA.${{x}^{2}}-9$ B.${{x}^{2}}+9$ C.${{x}^{2}}+3$ D.${{x}^{2}}-3$

All points lying inside the triangle formed by the points (1 3) (5 0) and (-1 2) satisfy the equationa)$3x+2y\\ge 0$b)$2x+y-13\\ge 0$c)$2x-3y-12\\le 0$d)$-2x+y\\ge 0$

A pizza is cut into 8 pieces. Annu ate one piece. What part of pizza was eaten by Annu?a) \\[\\dfrac{1}{4}\\] b) \\[\\dfrac{1}{8}\\]c) \\[\\dfrac{2}{4}\\]d) \\[\\dfrac{3}{4}\\]

Differentiate ${{\\left( \\log x \\right)}^{x}}$ with respect to $\\log x$ and obtain the answer.

A man bought a number of clips at 3 for a rupee and an equal number at 2 for a rupee. At what price per dozen should he sell them to make a profit of 20%?(a) 4(b) 5(c) 6(d) 7

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Boost your preparation with Vedantu’s Class 10 Maths Question Answers. Covering every syllabus topic with clear and concise explanations, these solutions make learning easier and more effective.

Crafted by experts, Vedantu’s step-by-step answers ensure a strong grasp of concepts, empowering you to approach your board exams with confidence. Rely on these trusted resources for stress-free studying and success in Maths. Let Vedantu guide you towards achieving your academic goals and excelling in your exams!