Surface Areas and Volumes,Probability - Mathematics - Assignment

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Surface Areas and Volumes,Probability

1462 minutes

Feb 27, 2:38 PM

100.0 marks

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55 questions

Surface Areas and Volumes,Probability

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Assignment of Class9th, Mathematics & Science & English Surface Areas and Volumes,Probability - Study Material

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Question 1 : A coin is tossed. What is the probability of getting a head and a tail?

Question 2 : In a box containing only purple and green marshmallows, $6$ marshmallows are purple. If the probability of choosing a purple marshmallow from the box is $\dfrac {1}{3}$, calculate the number of green marshmallows in the box.

Question 3 : When $2$ dice are thrown simultaneously what is the probability that there is exactly one $5$?

Question 4 : A card is drawn from a well shuffled deck of $52$ cards. Find the probability of getting a club card?

Question 5 : If a coin is tossed, then the probability that a head turns up is ______.

Question 6 : $400$ students of class $X$ of a school appeared in a test of $100$ marks in the subject of social studies and the data about the marks secured is as below : <table class="wysiwyg-table"><tbody><tr><td>            Marks           secured</td><td>Number of Students</td></tr><tr><td>            $0-25$</td><td>     $50$</td></tr><tr><td>          $26-50$</td><td>    $220$</td></tr><tr><td>          $51-75$</td><td>    $100$</td></tr><tr><td>        Above $75$</td><td>      $30$</td></tr><tr><td>Total number of students</td><td>    $400$</td></tr></tbody></table>If the result card of a student he picked up at random, what is the probability that the student has secured more than $50$ marks.

Question 7 : A survey was conducted by car manufacturing company in a metropolitan city on $1000$ persons having monthly income from Rs. $30,001$ to Rs. $50,000$. The data about the number of persons in various categories is as under: <table class="wysiwyg-table"><tbody><tr><td> Monthly income </td><td colspan="3"> Number of Cars </td></tr><tr><td> (in rupees) </td><td> $1$ </td><td> $2$ </td><td> More than $2$ </td></tr><tr><td> $30,001-40,000$ </td><td> $400$ </td><td> $50$ </td><td> $25$ </td></tr><tr><td> $40,001-50,000$ </td><td> $100$ </td><td> $300$ </td><td> $125$ </td></tr></tbody></table> Find the probability that a person selected at random in the income slab $40,001-50,000$ have more than $2$ cars.

Question 8 : If $3$ coins are tossed simultaneously, the probability of $2$ heads and $1$ tail is:

Question 9 : In a non-leap year the probability of getting $53$ Sundays or $53$ Tuesdays or $53$ Thursdays is.

Question 10 : Observe the table given.<table class="wysiwyg-table"><tbody><tr><td>Club</td><td>English</td><td>Maths</td><td>Science</td></tr><tr><td>Number of students</td><td>$99$</td><td>$121$</td><td>$154$</td></tr></tbody></table>A student is chosen randomly from the group as the co-ordinator of all the clubs. What is the probability that the student is from the science club?

Question 11 : There are only two women among $20$ persons taking part in a pleasure trip. The $20$ persons are divided into two groups, each group consisting of $10$ persons. Then the probability that the two women will be in the same group is:

Question 12 : Two dice are thrown. The number of sample points in the sample space when six does not appear on any one side is

Question 13 : From a normal pack of cards, a card is drawn at random. Find the probability of getting a jack or a king.

Question 14 : A box contains $40$ red and blue marbles. If a marble is drawn at random, the probability of picking a blue marble is $\dfrac {3}{8}$. Ansh takes out one red and nine blue marbles and then draws a marble at random. Find the probability of drawing a blue marble

Question 15 : Two coins are tossed $1000$ times and the outcomes are recorded as below: <table class="wysiwyg-table"><tbody><tr><td>No of heads </td><td>$2$ </td><td>$1$ </td><td>$0$ </td></tr><tr><td>Frequency </td><td>$200$ </td><td>$550$ </td><td>$250$ </td></tr></tbody></table>Based on this information, the probability for at most one head is $\dfrac{a}{b}$. Where $(a,b)=1$, then

Question 16 : A card is drawn from a well-shuffled deck of playing cards. Find the probability of drawing a face card.

Question 17 : When two dice are thrown simultaneously, the probability that the sum of the two numbers that turn up is less than $11$ is:

Question 18 : A ball is drawn at random from a box containing 10 red, 30 white, 20 blue and 15 orange marbles. The probability of a ball drawn is red, white or blue .......

Question 19 : A box contains $25$ tickets number $1,2,....25$. If two tickets are drawn at random then the probability that the product of their numbers is even, is

Question 20 : A bag contains a number of marbles of which $80$ are red, $24$ are white and the rest are blue. If the probability of randomly selecting a blue marble from this bag is $\dfrac {1}{5}$, how many blue marbles are there in the bag?

Question 21 : In a school, $\displaystyle \frac{5}{8}$ of the total students are girls. If the number of girls is $120$ more than that of the boys. What is the strength of the school? how many boys are there?

Question 22 : Archaeological survey indicates that the odd of occurring earthquake in Greater Himalayan region due to Tehri Dam are $5$ to $7$. What is the probability of earthquake in Greater Himalayan region?

Question 23 : A dies is thrown three times and the sum of three numbers obtained is $15$. The probability of first throw being $5$ is:

Question 24 : A die is thrown three times and the sum of three numbers obtained is $15$. The probability of first throw being $6$ is:

Question 25 : A box contains coupons labeled 1, 2, 3, ... , n. A coupon is picked at random and the number x is noted. The coupon is put back into box and a new coupon is picked at random. The new number is y. Then the probability that one of the numbers x, y divides the other is : (in the options below [r] denotes the largest integer less than or equal to r)

Question 26 : If volume and surface area of a sphere are numerically equal then it's radius is

Question 27 : If the height and radius of a cone are doubled then the volume of the cone becomes

Question 28 : A right circular cone an and circular and a right cylinder have the same radius and the same volume. The ratio of the height of the cone to that of the cylinder is

Question 29 : Area of canvas needed to erect a right conical tent of height 12 m and a circular base having circumference$\displaystyle 10\pi $ m is

Question 30 : Find the volume and surface area of a sphere of radius $4.2$ cm. $\displaystyle \left [ \pi =\frac{22}{7} \right ]$

Question 31 : A cone of height $24$ cm and radius of base $6$ cm is made up of modelling clay. A child reshapes it in the form of a sphere. The radius of sphere is

Question 32 : Two cones have their heights in the ratio 1:3 and their radii in the ratio 3:1 Find the ratio of their volumes

Question 33 : Three solid spheres of a lead are melted into a single solid sphere If the radii of the three spheres be 1 cm, 6 cm and 8 cm respectively Then radius of the new sphere is :

Question 34 : If the surface area of a sphere is $324\pi cm^2$ then its volume is

Question 35 : There is water to a height of $16cm$ in a cylindrical glass jar of radius $12.5cm$. Inside the water, there is a sphere of diameter $15cm$, completely immersed. By what height will water go down, when the sphere is removed?

Question 36 : The radius of a sphere is $2r$, then its volume will be:

Question 37 : The diameter of a sphere is decreased by $25\%$. By what percent does its curved surface area decrease

Question 38 : The volume of a right circular cylinder whose height is $40 cm$ and the circumference of its base is $66 cm$ is

Question 39 : The volume of a cone is $462$ m$^3$. Its base radius is $7$ m. Find its height.

Question 40 : If a solid sphere and a solid hemisphere have the same volume then the ratio of their total surface areas is

Question 41 : Find the radius of a sphere whose surface area is $154{cm}^{2}.$

Question 42 : A right circular cone of vertical height $24 cm$ has volume $\displaystyle 1232cm^{3}$. Its curved surface area is

Question 43 : A cubical of wood was cut into 8 equal cubes of sides 4 cm. What is the volume of the block of wood?

Question 44 : A rectangular piece of paper $11$ cm $\times$ $4$ cm is folded without overlapping to make a cylinder of height $4$ cm. What will be volume of the cylinder ?

Question 45 : Volume and total surface area of a solid hemisphere are equal. Find the radius of hemisphere

Question 46 : If the diameter of the base of a cylinder is $14$ cm and its height is $12$ cm then the volume of the cylinder in $m^3$ is 

Question 47 : A right circular metallic cone of height $20$ cm and radius of base $5$ cm is melted and recast into a sphere. Find the radius of the sphere.

Question 48 : Radius and height of a right circular cone and that of a right circular cylinder are respectively, equal. If the volume of the cylinder is $120{cm}^{3}$, then the volume of the cone is equal to

Question 49 : The radii of the bases of two cylinder are in the ratio of $3 : 4$ respectively and their heights are in the ratio $2 : 3$ respectively. Find the ratio of their volumes.

Question 50 : A sphere of diameter $12.6$ cm is melted and cast into a right circular cone of height $25.2$ cm. The diameter of the base of  the cone is ?

Question 51 : The volume of sphere is$\displaystyle 904.77{ cm }^{ 3 }$. Find its radius. (Round off your answer to the nearest whole number).

Question 53 : The ratio of the radii of two cylinders is $\displaystyle 1:\sqrt{3}$ and their heights are in the ratio $2 : 3$. The ratio of their volumes is

Question 54 : A sphere of radius $4$ cm has the same volume as that of a cone with a circular base of  radius $4$ cm.The height of the  cone is

Question 55 : A hemispherical tank of radius $1\frac {3}{4}$m is full of water. Itis connected with a pipe which empties It at the rate of 7 liters per second. How much time will it take to empty the tank completely?

Himanshu

Teacher

Class Details:- Class9th | Mathematics Science English

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