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All Questions and Answers

NTSE Maths Volume II Chapter 17 to 22

Illustrative Examples

19 Qs

Find the volume of a right circular cylinder of height 7 cm and radius of the base 2 cm.

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How many cubic meters of earth must be dug out to make a well of dimeter 5 m and depth 14 m?

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Find the lateral surface area and the total surface area of a cylinder with base radius 7 m and height 9 m

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Find the total surface area of a hollow cylinder of internal radius 3 cm thickness 1 cm and height 14 cm

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The sum of the radius and the height of a solid cylinder is 37 cm If the total surface area of the solid is 1628 cm $^{2}$ find the circumference of the base and the volume of the solid

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A roll of newspaper of length 7000 m and thickness 0.022 cm is rolled into a solid cylinder Find its radius

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The radius and height of a cylinder are in the ratio 5:7 and its volume is 550 cm $^{3}$ Find its radius

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The curved surface area of a cone is 670 cm $^{2}$ and its radius is 15cm Find its slant height and total surface area

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A conical cup has a height of 21 cm and the diameter of its base is 18 cm Find the amount of water it can hold

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A conical cup $18$ cm high has a circular base of diameter $14$ cm The cup is full of water which is now poured into a cylindrical vessel of circular base whose diameter is $10$ cm What will be the height of water in the vessel

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What is the total surface area of a cone with slant height $9$ m and radius of base $6$ m?

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The circumference of the base of a $24$ m high conical tent is $44$ m. Calculate the length of canvas used in making the tent, if the width of the canvas is $2$ m.

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The radius of the base and the height of a right circular cone are $7$ cm and $24$ cm respectively Find the total surface area of the cone

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The radius of a sphere is 9 cm It is melted and drawn into a wire of diameter 2 mm Find the lenght of the wire in meters

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A metallic sphere of radius $10.5$ cm is melted and then recast into small cones each of radius $3.5$ cm and height $3$ cm Find the number of cones thus formed

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Find the volume of the sphere whose diameter is 30 cm

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Find the surface area of the sphere whose radius is $35 c m$ .

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The inner radius of a hemispherical steel bowl is $5$ cm If the thickness of the bowl is $0.25$ m find the volume of steel used in making the bowl

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The diameter of acopper sphere is $18$ cm The sphere is melted and is drawn into a long wire of uniform circular cross-section If the length of the wire is $108$ m find its diameter

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Multiple choice questions

30 Qs

The height of a right circular cylinder is 10 cm and the radius of the base is 7 cm Then the difference between the total base area and the curved surface area is

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The circumference of the base of the of a cylinder is 12 m and its height is $π$ meters. The volume of the cylinder is

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Two cylinders have their radii in the ratio 4:5 and their heights in the ratio 5:6. Then, the ratio of their volumes is

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A well 2 m in radius and 14 m deep is to be dug. What is the cost of digging the well at Rs. 1.20 per cubic meter?

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Earth dug out on making a circular tank of radius 7 m is spread all round the tank uniformly to a width of 1 m to form an embankment of height 3.5 m. Calculate the depth of the tank.

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The sum of the radius and the height of a solid cylinder is 37 cm If the total surface area of the solid is $1628 c m^{2}$ find the circumference of the base

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An iron pipe is $42$ cm long and its experior radius is $4$ cm If the thickness of the pipe is $1$ cm and iron weights $100 g / c m^{3}$ the weight of the pipe is

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The diameters of two cylinders are in the ratio 2:3 Find the ratio of their heights if their volume is the same

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The radius of a roller is 0.7 m and it is 2 m long How much area will it cover in 10 revolutions?

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A cube of copper of edge 11 cm is melted and formed into a cylindrical wire of diameter 0.5 cm What length of wire will be obtained from the cube?

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A right circular cone is 84 cm high The radius of the base is 350 m Find the curved surface area

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Given that the volume of a cone is $2355 c m^{3}$ and the area of its base is $314 c m^{2}$ Its height is

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The total surface area of a cone is $770 c m^{2}$ . If its slant height is four times the radius of the cone, the diameter of the cone is:

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The radius and the slant height of a cone are in the ratio $7 : 13$ and the curved surface area is $286 c m^{2}$ . Find its radius.

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From a solid cylinder whose height is 8 cm and radius is 6 cm a conical cavity of height 8 cm and base radius 6 cm is hollowed out Find the volume of the remaining solid

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A right circular cone of vertical height $24 c m$ has volume $1232 c m^{3}$ . Its curved surface area is:

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A right triangle with sides 5 cm 12 cm and 13 cm is revolved about the side 12 cm Find the volume of the cone thus formed

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The radius of a conical tent is $12 m$ and the slant height is $5.6 m$ . Find the length of canvas required to make the tent it the width of canvas is $4 m$ .

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

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The ratio of the volumes of a cylinder and a cone having equal radii and equal heights is

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The surface area of a sphere is $5544 c m^{2}$ . Its volume is

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The volume of a solid hemisphere of radius 2 cm is

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The radii of two spheres are in the ratio 3:5 The ratio of their volumes is

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If the radius of a sphere is doubled what is the ratio of the volume of the first sphere to that of the second?

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If the numerical value of surface area of a sphere is equal to its volume, then the radius of the sphere is:

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If the sum of the radii of two spheres is 2 km and their volumes are in the ratio 64:27 then the ratio of their radii is

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How many spherical bullets can be made out of a solid cube of lead whose edge measures 44 cm if each bullet has radius 2 cm?

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200 wooden balls each of diameter 70 mm are to be painted Find the cost of painting these balls at 10 paise/ $c m^{2}$

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The largest sphere is carved out of a cube of edge 14 cm Find the volume of the sphere

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A solid metal sphere is cut through the center into two equal parts. Find the total surface area of each part if the radius of the sphere is $3.5 c m$ .

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Multiple choice questions

28 Qs

In any continuous class interval table (a-b)

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Consider the class intervals 1-10, 11-20, 21-30, etc Here what is the class boundary of class interval 11-20?

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The mean of $x_{1}, x_{2}, . . ., x_{50}$ is M. If every $x_{i}, i = 1$ , 2,....,50, is replaced by $x_{i}$ /50 the mean will be

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Find the mode of 0,0,2,2,3,3,3,4,5,5,5,5,6,6,7,8

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The midvalue of the class interval (a-b) is

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The mode of the series 2,3,1,2,5,3,2,2,3,5 is

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The mean of $x_{1} + x_{2} + . . . + x_{n}$ is M. When $x_{i}, i$ =1,2,....,10, is replaced by $x_{i} + 10$ , the mean is $M_{1}$ . Then $M_{1}$ =

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The median of 9, 5, 7, 11, 13, 3 is

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Which of the following is true?

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In a bar chart:

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In any pie chart the sum of the central angles is

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If the number of boys and the number of girls in a class are 45% and 55% respectively and it is represented in a pie chart what will be the central angles of the portions representing boys and girls respectively?

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The mean of the data $16, 20, 26, 40, 50, 60, 70, 30$ is:

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Find the mean of the following frequency distribution.

x 10 15 30 25 42 21 11
f 5 2 6 4 3 8 2

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The weights in kilogram of $9$ members in a school boxing team are $54, 59, x, 53, 73, 49, 50, 58, 45$ . If the average is $56$ , then $x$ is:

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The mode of some observations is 4 and the median is 3 Then mean is

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The median of 1, 3, 6, 8, 4, 2, 7, 10 is

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The geometric mean of 4,5,6,7,4 is

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A letter is chosen at random from the letters of the English alphabet The probability that it is not a vowel is

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A box has tokens numbered 3 to 100. If a token is taken out at random the chance that the number is divisible by 7 is

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A pair of dice is thrown once The probability that the sum of the outcomes is less than 11 is

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A bag contains six red four green and eight white balls If a ball is picked at random the probability that it is not white is

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There are 50 marbles of 3 colors: blue yellow and black The probability of picking up a blue marble is 3/10 and that of picking up a yellow marble is 1/2 The probability of picking up a black ball is

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A box has 20 balls of which x are red When 4 more red balls are added and then a ball is picked up the probability is 1/2 The value of x is

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A bag contains some green white and pink beads The probability of taking out one green bead is 1/3 and that of picking up one pink bead is 1/4 If it is known that the box has 10 white beads how many beads were in the box initially?

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Out of 132 screws in a pack 12 screws are known to be defective If one screw is picked up at random the probability that it is a good screw is

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A bag contains five yellow balls and some white balls If the probability of picking a white ball is twice that of picking a yellow ball how many white balls are there?

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A coin is tossed three times If all the outcomes are identical then I win What is the chance that I lose?

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Illustrative examples

3 Qs

Following are the ages of 10 teachers in a school : 32, 41, 28, 54, 35, 26, 23, 33, 38 and 40
(i) The range of their ages is

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The man of six observation was found to be 40 Later on it was detected that in one observation 82 was misread as 28 Find the correct mean

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The mean temperature of a town in a certain week was $2 5^{\circ}$ C If the mean temperature of Monday, Tuesday,Wednesday, and Thursday was $2 3^{\circ}$ C and that of Thursday, Friday. Saturday and Sunday was $2 8^{\circ}$ C Fing the temperature on Thursday

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Multiple choice questions

70 Qs

The reflection of (5,2) on the x-axis has coordinates

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The reflection of (-6,-3) on the y-axis has coordinates

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Two adjacent vertices of a rhombus are (-1,0) and (-3,4) The other two vertices are

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A point P(4,3) is reflected on the x-axis Its image Q is reflected on the y-axis to get R and R is again reflected on the x-axis If S is the image of R then the length of the diagonal of rectangle PQRS is

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The vertices of a triangle AOD are (4,0) (0,0) (0,3) If the triangle is rotated clockwise about its circumcenter till AD returns to its original position then the vertices of the triangle in its new positions are

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The reflection of a point P(-3,4) on the y-axis is Q and the reflection of Q on the x-axis is R Then PR=

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A point P(-3,2) reflected about the line l shown in the diagram goes over to Q If Q is reflected again about the x-axis and it goes over to R then the coordinates of R are

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The points (4,0), (0,4), (-4,0), and (0, -4) form

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The points $(- 3, - 4), (3, - 4), (3, 4)$ and $(- 3, 4)$ are the vertices of:

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The points (-2,10), (-2,2), and (6,2) are the vertices of

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The distance between (a,-b) and (-a, -b) is given by

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If the distance between the origin and (x,3)is 5 then x=

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The triangle formed by the points (3,5), (6,9), and (2,6) is

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The triangle formed by the points (2,4), (2,1) and (6,1) is:

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The points (3,7), (6,5), and (15,-1)

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The radius of the circle with center (0,0) and which passes through (-6,8) is

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The diameter of the circle with center (1,2) and which passes through (-4,6) is

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The points (-2,0), (3,0), (3,5) and (-2,5) are the vertices of a:

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The center of a circle is at the origin and the radius is 10 units The point (6,8) lies

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If the point (x,y) is equidistant from (a,0) and (2a,a) then

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The vertices of a rhombus are (-5,0), (0,8), (5,0), and (0,-8) The product of the lengths of its diagonals is

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An isosceles triangle has vertices at (4,0), (-4,0), and (0,8) The length of the equal sides is

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The vertices P, Q, R, and S of a parallelogram are at (3,-5), (-5,-4), (7,10) and (15,9) respectively The length of the diagonal PR is

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If the point (P,0) is equidistant from (3,2) and (5,3) then P=

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The center A of a circle is (3,8) and its radius is 5 The length of the tangent from B(-6,8) is

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The circumcenter of the triangle with vertices (9,3),(7,-1) and (-1,3) is (4,3) Circumradius is

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If A(x,0), B(-4,6), and C(14, -2) form an isosceles triangle with AB=AC, then x=

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If P(1,4), Q(9,-2), and R(5,1) are collinear then

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If the points (1,1) (2,3) and (5,-1) form a right triangle, then the hypotenuse is of length

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The length of the diagonal of rectangle ABCD formed by A(2,-2), B(8,4), C(5,7) and D(-1,1) is

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The midpoint of the line segment with endpoints $(- 6, 4)$ and $(8, 2)$ is

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The line segment with endpoints (-9,7) and (6,4) is trisected at P and Q The coordinates of Q are

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If the midpoint of PQ is (7,10) and Q is (5,8) then the coordinates of P are

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A(4,0) and B(5,0) are two points If AB is produced to C such that AB=BC then the coordinates of C are

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The ratio in which the line joining of (-2,5) and (1,-9) is divided by the x-axis is

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The ratio in which the joining of (-3,2) and (5,6) is divided by the y-axis is

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The centroid of the triangle with vertices (2,6), (-5,6) and (9,3) is

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A(2,6) and B(1,7) are two vertices of a triangle ABC and the centroid is (5,7) The coordinates of C are

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In the diagram M(2,3) is the midpoint of AB The coordinates of A and B are respectively

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In the diagram P(-4,-2) divides AB in the ratio 2:1 The coordinates of A and B are respectively

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The circumcenter of the triangle with vertices at (0,0), (8,0) and (0,-6) is at

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A triangle has vertices A(1,-1) B(2,4) and C(6,0) The length of the median from A is

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The opposite vertices of a rectangle ABCD are A(-5,4) and C(5,-4) The area of the rectangle is

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The opposite vertices of a rectangle OABC are $O (0, 0)$ and $B (6, 4)$ If $P (1, \frac{1 0}{3})$ is a point on the other diagonal AC then the ratio in which P divides AC is

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A line segement AB is divided into four equal parts at P, Q, R in that order If A is (8,12) and B is (12,16) then R has coordinates

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A line segment AB is produced to C such that AC=2AB. If the coordinates of A and B are (6,8) and (8,6) respectively then the coordinates of C are

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In a triangle ABC, vertex A is (6,8) and the midpoint of BC is (3,2) Then the coordinates of the centroid G are

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A and B are the centres of two circles that just touch each other at P If A is (4,1), B is (2,2) and the radii of the circles are 2 and 3 respectively then P has coordinates

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A(2,4), B(6,-2), and C(0,6) are the vertices of a triangle ABC. If L and M are, respectively, the midpoints of AB and AC, then LM=

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P(4,-5) and Q(5,8) are the endpoints of a line segment PQ. The ratio in which PQ is divided by the y-axis is

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The area of the triangle whose vertices are (2,-3), (3,2) and (-2,5) is

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AD is the median of triangle ABC with vertices A(-3,2), B(5,-2) and C(1,3) The area of triangle ABD is

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L,M, and N are the midpoints of the sides BC CA and AB respectively of triangle ABC If the vertices are A(3,-4), B(5,-2), and C(1,3) the area of $△ L M N$ is

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In the diagram the coordinates of P,Q, and R are (3,6),(-1,3) and (2,-1) respectively The area of $△ S Q R$ is

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If the area of the triangle formed by (-2,5), (x,-3) and (3,2) is 14 square units then x=

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If the area of the triangle formed by the points (-2,3), (4,-5), and (-3,y) is 10 square units then y=

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If the points (1,3), (x,2) and (4,6) are collinear then x=

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If the points (4,y) (6,4), and (-1,-3) are collinear then y=

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If the points (2,1), (3,-2) and (a,b) are collinear then

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The condition for the points (x,y), (-2,2) and (3,1) to be collinear is

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If (a,b) (c,d) and (a-c, b-d) are collinear then

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The midpoints of the sides of triangle ABC are (-1,-2),(6,1), and (3,5) The area of $△ A B C$ is

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The area of the quadrilateral with vertices (0,0), (4,0), (4,2), and (0,2) is

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The area of the quadrilateral formed by the points (0,0), (1,0), (1,4) and (0,2) is

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If G is the centroid of the triangle with vertices A(-1,6), B(7,1) and C(3,5) then the area of triangle GAB is

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The area of the triangle formed by the points (a,b+c), (b,c+a) and (c,a+b) is

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The point (x,y) lies on the line joining (3,4) and (-5,-6) if

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If the points (a,0), (0,b), and (1,1) are collinear then

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The area of the parallelogram with vertices (0,0), (2,3), (-2,3) and (-4,0) is

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The area of the rhombus formed by the points (3,0),(0,4),(-3,0) and (0,-4) is

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Multiple choice questions

13 Qs

The angle of elevation at the top of a tower from a point 10 m from the foot of the tower is $3 0^{\circ}$ The height of the tower is

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the angle of depression of a boat from the top of a cliff 300 m high is $6 0^{\circ}$ The distance of the boat from the foot of the cliff is

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The length of the shadow of a pole is $3$ times its height The elevation of the sum must be

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the shadow cast by a tower is 30 m long when the elevation of sum is $3 0^{\circ}$ If the elevation of sum is $6 0^{\circ}$ then the length of the shadow is

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The elevation at the top of a building under construction at a point 120 m from the base is $4 5^{\circ}$ How much higher should the building be raised so that the elevation becomes $6 0^{\circ}$ ?

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The angles of depression at the top and foot of a tower as seen from a hill 45 m high are $3 0^{\circ}$ and $6 0^{\circ}$ respectivelyThe height of the tower is

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The angles of elevation at the top of a lamp-post 4m tall from a point on the ground is $3 0^{\circ}$ How far should the observer walk so that the elevation gets doubled?

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A kite is flying with the string inclined at $4 5^{\circ}$ to the horizontal If the string is straight and 50 m long the height at which the kite is flying is

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A flagstaff stands on the top of a building From a point on the ground 15 away the elevations at the top of the building and the flagstaff are $4 5^{\circ}$ and $6 0^{\circ}$ respectively the length of the flagstaff is

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A man in a boat rowed away from a cliff $50$ m high It takes $2$ minutes to change the elevation at the top of the cliff from $6 0^{\circ}$ to $4 5^{\circ}$ The speed of the boat is

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The angles of elevation of a church from two points at distance $d_{1}$ and $d_{2}$ from the floor of the church on the side are complementary The height of the church is

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From the top of a tower 60 m tall the elevation at the top of a hill is found to be equal to the depression at the foot of the hill The height of the hill is

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There are two poles on a horizontal plane From the midpoint of the line joining their feet the tops of the poles appear at angles of elevation of $6 0^{\circ}$ and $3 0^{\circ}$ If the height of the first pole is 100 m then the height of the second is

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Multiple choice questions

40 Qs

$sin θ sec θ c o s e c θ cos θ =$

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$tan θ + cot θ =$

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$\frac{c o s e c θ}{cot θ + tan θ}$

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$\frac{c o s e c A}{cot A} =$

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$(1 - cos^{2} θ) (1 + cot^{2} θ) =$

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$sin θ 1 + tan^{2} θ =$

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$cos θ 1 + cot^{2} θ =$

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$(sin A + cos A)^{2} + (sin A - cos A)^{2}$

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$1 + tan^{2} θ 1 + cot^{2} θ 1 - cos^{2} θ 1 - sin^{2} θ =$

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$sin θ cos θ tan θ + cos θ cot θ sin θ =$

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If $θ$ is acute and $sin θ = 3 / 5$ then $cot θ =$

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If $θ$ is acute and $cot θ = 12 / 5,$ then $sin θ + cos θ =$

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If $θ$ is acute and $sec θ = 5 / 3$ then $tan θ + cot θ =$

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If $cos θ = 1 / 2$ and $θ$ is acute then $\frac{sin θ + cos θ}{sin θ - cos θ} =$

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If $sin θ = \frac{m ^{2} - n ^{2}}{m ^{2} + n ^{2}}$ where $θ$ is an acute angle then $m n (sec θ + tan θ) =$

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If $x = 8 cos^{3} θ$ and $y = 8 sin^{3} θ,$ then $x^{2 / 3} + y^{2 / 3} =$

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If $x = 5 cos θ$ and $y = 5 sin θ,$ then $x^{2} + y^{2} =$

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If $x = a sec θ$ and $y = a tan θ,$ then $x^{2} - y^{2} =$

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If $tan θ + sin θ = m$ and $tan θ - sin θ = n$ then $4 m n =$

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If $x = a cos θ$ and $y = b sin θ$ then $\frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} =$

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If $3 sin θ + 5 cos θ = 5$ then $5 sin θ - 3 cos θ =$

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If $sin θ, cos θ$ and $tan θ$ are in GP then $cot^{6} θ - cot^{2} θ =$

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If $cos θ + sin θ = 2$ then $cos θ - sin θ =$

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If $cos x + cos^{2} x = 1$ then $sin^{2} x + sin^{4} x =$

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If $sin^{2} A + sin^{2} B + sin^{2} C = 9 / 4,$ then

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The value of $3 sin^{2} 4 5^{\circ} + 2 cos^{2} 6 0^{\circ}$ is

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The value of $sin^{2} 6 0^{\circ} + cos^{2} 4 5^{\circ}$ is

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The value of $4 sin^{2} 6 0^{\circ} + 3 tan^{2} 3 0^{\circ}$ is

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The value of $cos 6 0^{\circ} cos 3 0^{\circ} - sin 6 0^{\circ} sin 3 0^{\circ}$

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A pole 15 m long rests against a vertical wall at an angle of $3 0^{\circ}$ with the ground How high up the wall does the pole reach?

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If $x = 3 0^{\circ},$ then $\frac{2 tan x}{1 - tan ^{2} x} =$

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If $θ$ is acute and $4 sin^{2} θ - 1 = 0$ then $θ =$

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A kite flying at a height of 75 m from the ground is attached to a straight string Which is inclined at an angle of $6 0^{\circ}$ to the ground The length of the string is

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In the diagram, $A D ⊥ B C$ and AC = 8 cm If $∠ A B C = 4 5^{\circ}$ and $∠ A C B = 3 0^{\circ}$ then BC =

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In the diagram PQRS is a square of side 3 cm and $∠ P T S = 6 0^{\circ}$ Then the length of TR is approximately

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In the diagram, $F P$ represents a flag pole on top of a building. From the information given in the figure, the approximate length of the flag pole is

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$sin 4 8^{\circ} sec 4 2^{\circ} - cos 4 8^{\circ} c o s e c 4 2^{\circ} =$

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$cos^{2} 5^{\circ} + cos^{2} 1 0^{\circ} + cos^{2} 1 5^{\circ} + . . . + cos^{2} 8 5^{\circ} =$

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The value of $tan 1^{\circ} tan 2^{\circ} . . . tan 8 9^{\circ} =$

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If $x sin 4 5^{\circ} cos 4 5^{\circ} + tan^{2} 6 0^{\circ} = sec^{2} 3 0^{\circ} c o s e c^{2} 3 0^{\circ}$ then x =

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Multiple choice questions

15 Qs

If $∣ ∣ ∣ ∣ ∣ ∣ x 1 y 6 ∣ ∣ ∣ ∣ ∣ ∣$ = $∣ ∣ ∣ ∣ ∣ ∣ 1186 ∣ ∣ ∣ ∣ ∣ ∣$ then x+2y=

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If A= $∣ ∣ ∣ ∣ ∣ ∣ 23 - 3 2 ∣ ∣ ∣ ∣ ∣ ∣$ and B= $∣ ∣ ∣ ∣ ∣ ∣ 32 - 2 3 ∣ ∣ ∣ ∣ ∣ ∣$ then 2A-B=

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If A= $∣ ∣ ∣ ∣ ∣ ∣ 0214 ∣ ∣ ∣ ∣ ∣ ∣$ , B= $∣ ∣ ∣ ∣ ∣ ∣ - 1 2 12 ∣ ∣ ∣ ∣ ∣ ∣$ ,
C= $∣ ∣ ∣ ∣ ∣ ∣ 1100 ∣ ∣ ∣ ∣ ∣ ∣$ , then 2A+3B-C=

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If $∣ ∣ ∣ ∣ ∣ ∣ 2434 ∣ ∣ ∣ ∣ ∣ ∣$ + $∣ ∣ ∣ ∣ ∣ ∣ x y 31 ∣ ∣ ∣ ∣ ∣ ∣$ = $∣ ∣ ∣ ∣ ∣ ∣ 10865 ∣ ∣ ∣ ∣ ∣ ∣$ ,then (x,y)=

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If A+ $∣ ∣ ∣ ∣ ∣ ∣ 4123 ∣ ∣ ∣ ∣ ∣ ∣$ = $∣ ∣ ∣ ∣ ∣ ∣ 6194 ∣ ∣ ∣ ∣ ∣ ∣$ then A=

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If $∣ ∣ ∣ ∣ ∣ ∣ x y 12 ∣ ∣ ∣ ∣ ∣ ∣$ - $∣ ∣ ∣ ∣ ∣ ∣ y 8 10 ∣ ∣ ∣ ∣ ∣ ∣$ = $∣ ∣ ∣ ∣ ∣ ∣ 2 - x 02 ∣ ∣ ∣ ∣ ∣ ∣$ then the values of x and y respectively are

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If A+B= $∣ ∣ ∣ ∣ ∣ ∣ 10884 ∣ ∣ ∣ ∣ ∣ ∣$ and A-B= $∣ ∣ ∣ ∣ ∣ ∣ 20 - 4 6 ∣ ∣ ∣ ∣ ∣ ∣$ then A is

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If A= $∣ ∣ ∣ ∣ ∣ ∣ 13 ∣ ∣ ∣ ∣ ∣ ∣$ B= $∣ ∣ ∣ ∣ ∣ ∣ - 1 4 ∣ ∣ ∣ ∣ ∣ ∣$ then 2A+B =

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If P= $[432]$ and Q= $[- 1 23]$ then P-Q=

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IF A= $∣ ∣ ∣ ∣ ∣ ∣ 1100 ∣ ∣ ∣ ∣ ∣ ∣$ And B= $∣ ∣ ∣ ∣ ∣ ∣ 1001 ∣ ∣ ∣ ∣ ∣ ∣$ then A+B=

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IF A= $∣ ∣ ∣ ∣ ∣ ∣ 5 y x 6 ∣ ∣ ∣ ∣ ∣ ∣$ B= $∣ ∣ ∣ ∣ ∣ ∣ - 4 - 4 y - 5 ∣ ∣ ∣ ∣ ∣ ∣$ and A+B=I then the values of x and y respectively are

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If $A + 2 B =$ $∣ ∣ ∣ ∣ ∣ ∣ 5450 ∣ ∣ ∣ ∣ ∣ ∣$ and $2 A - B = ∣ ∣ ∣ ∣ ∣ ∣ 03 - 5 5 ∣ ∣ ∣ ∣ ∣ ∣$ , then A+B=

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If $[x 5 4 y]$ + $[- 2 1 12]$ = $[0650]$ , then $x - y =$

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The values of x satisfying the equation
$∣ ∣ ∣ ∣ ∣ ∣ 1 x^{2} 64 ∣ ∣ ∣ ∣ ∣ ∣$ - $∣ ∣ ∣ ∣ ∣ ∣ 1 2 x 10 ∣ ∣ ∣ ∣ ∣ ∣$ = $∣ ∣ ∣ ∣ ∣ ∣ 0054 ∣ ∣ ∣ ∣ ∣ ∣$ are

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The value of x satisfying the equation 2 $∣ ∣ ∣ ∣ ∣ ∣ 3112 ∣ ∣ ∣ ∣ ∣ ∣$ + $∣ ∣ ∣ ∣ ∣ ∣ x^{2} - 1 90 ∣ ∣ ∣ ∣ ∣ ∣$ = $∣ ∣ ∣ ∣ ∣ ∣ 5 x 0 61 ∣ ∣ ∣ ∣ ∣ ∣$ + $∣ ∣ ∣ ∣ ∣ ∣ 0153 ∣ ∣ ∣ ∣ ∣ ∣$ are

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NTSE Maths Volume II Chapter 17 to 22

Illustrative Examples

Related questions

Find the volume of a right circular cylinder of height 7 cm and radius of the base 2 cm.

How many cubic meters of earth must be dug out to make a well of dimeter 5 m and depth 14 m?

Find the lateral surface area and the total surface area of a cylinder with base radius 7 m and height 9 m

Find the total surface area of a hollow cylinder of internal radius 3 cm thickness 1 cm and height 14 cm

The sum of the radius and the height of a solid cylinder is 37 cm If the total surface area of the solid is 1628 cm2 find the circumference of the base and the volume of the solid

A roll of newspaper of length 7000 m and thickness 0.022 cm is rolled into a solid cylinder Find its radius

The radius and height of a cylinder are in the ratio 5:7 and its volume is 550 cm3 Find its radius

The curved surface area of a cone is 670 cm2 and its radius is 15cm Find its slant height and total surface area

A conical cup has a height of 21 cm and the diameter of its base is 18 cm Find the amount of water it can hold

A conical cup 18 cm high has a circular base of diameter 14 cm The cup is full of water which is now poured into a cylindrical vessel of circular base whose diameter is 10 cm What will be the height of water in the vessel

What is the total surface area of a cone with slant height 9 m and radius of base 6 m?

The circumference of the base of a 24 m high conical tent is 44 m. Calculate the length of canvas used in making the tent, if the width of the canvas is 2 m.

The radius of the base and the height of a right circular cone are 7 cm and 24 cm respectively Find the total surface area of the cone

The radius of a sphere is 9 cm It is melted and drawn into a wire of diameter 2 mm Find the lenght of the wire in meters

A metallic sphere of radius 10.5 cm is melted and then recast into small cones each of radius 3.5 cm and height 3 cm Find the number of cones thus formed

Find the volume of the sphere whose diameter is 30 cm

Find the surface area of the sphere whose radius is 35cm.

The inner radius of a hemispherical steel bowl is 5 cm If the thickness of the bowl is 0.25 m find the volume of steel used in making the bowl

The diameter of acopper sphere is 18 cm The sphere is melted and is drawn into a long wire of uniform circular cross-section If the length of the wire is 108 m find its diameter

Multiple choice questions

Related questions

The height of a right circular cylinder is 10 cm and the radius of the base is 7 cm Then the difference between the total base area and the curved surface area is

The circumference of the base of the of a cylinder is 12 m and its height is π meters. The volume of the cylinder is

Two cylinders have their radii in the ratio 4:5 and their heights in the ratio 5:6. Then, the ratio of their volumes is

A well 2 m in radius and 14 m deep is to be dug. What is the cost of digging the well at Rs. 1.20 per cubic meter?

Earth dug out on making a circular tank of radius 7 m is spread all round the tank uniformly to a width of 1 m to form an embankment of height 3.5 m. Calculate the depth of the tank.

The sum of the radius and the height of a solid cylinder is 37 cm If the total surface area of the solid is 1628cm2 find the circumference of the base

An iron pipe is 42 cm long and its experior radius is 4 cm If the thickness of the pipe is 1 cm and iron weights 100g/cm3 the weight of the pipe is

The diameters of two cylinders are in the ratio 2:3 Find the ratio of their heights if their volume is the same

The radius of a roller is 0.7 m and it is 2 m long How much area will it cover in 10 revolutions?

A cube of copper of edge 11 cm is melted and formed into a cylindrical wire of diameter 0.5 cm What length of wire will be obtained from the cube?

A right circular cone is 84 cm high The radius of the base is 350 m Find the curved surface area

Given that the volume of a cone is 2355cm3 and the area of its base is 314cm2 Its height is

The total surface area of a cone is 770cm2. If its slant height is four times the radius of the cone, the diameter of the cone is:

The radius and the slant height of a cone are in the ratio 7:13 and the curved surface area is 286cm2. Find its radius.

From a solid cylinder whose height is 8 cm and radius is 6 cm a conical cavity of height 8 cm and base radius 6 cm is hollowed out Find the volume of the remaining solid

A right circular cone of vertical height 24cm has volume 1232cm3. Its curved surface area is:

A right triangle with sides 5 cm 12 cm and 13 cm is revolved about the side 12 cm Find the volume of the cone thus formed

The radius of a conical tent is 12m and the slant height is 5.6m. Find the length of canvas required to make the tent it the width of canvas is 4m.

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

The ratio of the volumes of a cylinder and a cone having equal radii and equal heights is

The surface area of a sphere is 5544cm2. Its volume is

The volume of a solid hemisphere of radius 2 cm is

The radii of two spheres are in the ratio 3:5 The ratio of their volumes is

If the radius of a sphere is doubled what is the ratio of the volume of the first sphere to that of the second?

If the numerical value of surface area of a sphere is equal to its volume, then the radius of the sphere is:

If the sum of the radii of two spheres is 2 km and their volumes are in the ratio 64:27 then the ratio of their radii is

How many spherical bullets can be made out of a solid cube of lead whose edge measures 44 cm if each bullet has radius 2 cm?

200 wooden balls each of diameter 70 mm are to be painted Find the cost of painting these balls at 10 paise/cm2

The largest sphere is carved out of a cube of edge 14 cm Find the volume of the sphere

A solid metal sphere is cut through the center into two equal parts. Find the total surface area of each part if the radius of the sphere is 3.5cm.

Multiple choice questions

Related questions

In any continuous class interval table (a-b)

Consider the class intervals 1-10, 11-20, 21-30, etc Here what is the class boundary of class interval 11-20?

The mean of x1​,x2​,...,x50​ is M. If every xi​,i=1, 2,....,50, is replaced by xi​/50 the mean will be

Find the mode of 0,0,2,2,3,3,3,4,5,5,5,5,6,6,7,8

The midvalue of the class interval (a-b) is

The mode of the series 2,3,1,2,5,3,2,2,3,5 is

The mean of x1​+x2​+...+xn​ is M. When xi​,i=1,2,....,10, is replaced by xi​+10, the mean is M1​. Then M1​=

The median of 9, 5, 7, 11, 13, 3 is

Which of the following is true?

In a bar chart:

In any pie chart the sum of the central angles is

If the number of boys and the number of girls in a class are 45% and 55% respectively and it is represented in a pie chart what will be the central angles of the portions representing boys and girls respectively?

The mean of the data 16,20,26,40,50,60,70,30 is:

Find the mean of the following frequency distribution. x10153025422111f5264382

The weights in kilogram of 9 members in a school boxing team are 54,59,x,53,73,49,50,58,45. If the average is 56, then x is:

The mode of some observations is 4 and the median is 3 Then mean is

The median of 1, 3, 6, 8, 4, 2, 7, 10 is

The geometric mean of 4,5,6,7,4 is

A letter is chosen at random from the letters of the English alphabet The probability that it is not a vowel is

A box has tokens numbered 3 to 100. If a token is taken out at random the chance that the number is divisible by 7 is

A pair of dice is thrown once The probability that the sum of the outcomes is less than 11 is

A bag contains six red four green and eight white balls If a ball is picked at random the probability that it is not white is

There are 50 marbles of 3 colors: blue yellow and black The probability of picking up a blue marble is 3/10 and that of picking up a yellow marble is 1/2 The probability of picking up a black ball is

A box has 20 balls of which x are red When 4 more red balls are added and then a ball is picked up the probability is 1/2 The value of x is

The sum of the radius and the height of a solid cylinder is 37 cm If the total surface area of the solid is 1628 cm $^{2}$ find the circumference of the base and the volume of the solid

The radius and height of a cylinder are in the ratio 5:7 and its volume is 550 cm $^{3}$ Find its radius

The curved surface area of a cone is 670 cm $^{2}$ and its radius is 15cm Find its slant height and total surface area

A conical cup $18$ cm high has a circular base of diameter $14$ cm The cup is full of water which is now poured into a cylindrical vessel of circular base whose diameter is $10$ cm What will be the height of water in the vessel

What is the total surface area of a cone with slant height $9$ m and radius of base $6$ m?

The circumference of the base of a $24$ m high conical tent is $44$ m. Calculate the length of canvas used in making the tent, if the width of the canvas is $2$ m.

The radius of the base and the height of a right circular cone are $7$ cm and $24$ cm respectively Find the total surface area of the cone

A metallic sphere of radius $10.5$ cm is melted and then recast into small cones each of radius $3.5$ cm and height $3$ cm Find the number of cones thus formed

Find the surface area of the sphere whose radius is $35 c m$ .

The inner radius of a hemispherical steel bowl is $5$ cm If the thickness of the bowl is $0.25$ m find the volume of steel used in making the bowl

The diameter of acopper sphere is $18$ cm The sphere is melted and is drawn into a long wire of uniform circular cross-section If the length of the wire is $108$ m find its diameter

The circumference of the base of the of a cylinder is 12 m and its height is $π$ meters. The volume of the cylinder is

The sum of the radius and the height of a solid cylinder is 37 cm If the total surface area of the solid is $1628 c m^{2}$ find the circumference of the base

An iron pipe is $42$ cm long and its experior radius is $4$ cm If the thickness of the pipe is $1$ cm and iron weights $100 g / c m^{3}$ the weight of the pipe is

Given that the volume of a cone is $2355 c m^{3}$ and the area of its base is $314 c m^{2}$ Its height is

The total surface area of a cone is $770 c m^{2}$ . If its slant height is four times the radius of the cone, the diameter of the cone is:

The radius and the slant height of a cone are in the ratio $7 : 13$ and the curved surface area is $286 c m^{2}$ . Find its radius.

A right circular cone of vertical height $24 c m$ has volume $1232 c m^{3}$ . Its curved surface area is:

The radius of a conical tent is $12 m$ and the slant height is $5.6 m$ . Find the length of canvas required to make the tent it the width of canvas is $4 m$ .

The surface area of a sphere is $5544 c m^{2}$ . Its volume is

200 wooden balls each of diameter 70 mm are to be painted Find the cost of painting these balls at 10 paise/ $c m^{2}$

A solid metal sphere is cut through the center into two equal parts. Find the total surface area of each part if the radius of the sphere is $3.5 c m$ .

The mean of $x_{1}, x_{2}, . . ., x_{50}$ is M. If every $x_{i}, i = 1$ , 2,....,50, is replaced by $x_{i}$ /50 the mean will be

The mean of $x_{1} + x_{2} + . . . + x_{n}$ is M. When $x_{i}, i$ =1,2,....,10, is replaced by $x_{i} + 10$ , the mean is $M_{1}$ . Then $M_{1}$ =

The mean of the data $16, 20, 26, 40, 50, 60, 70, 30$ is:

Find the mean of the following frequency distribution.

x 10 15 30 25 42 21 11
f 5 2 6 4 3 8 2

The weights in kilogram of $9$ members in a school boxing team are $54, 59, x, 53, 73, 49, 50, 58, 45$ . If the average is $56$ , then $x$ is:

Following are the ages of 10 teachers in a school : 32, 41, 28, 54, 35, 26, 23, 33, 38 and 40
(i) The range of their ages is

The mean temperature of a town in a certain week was $2 5^{\circ}$ C If the mean temperature of Monday, Tuesday,Wednesday, and Thursday was $2 3^{\circ}$ C and that of Thursday, Friday. Saturday and Sunday was $2 8^{\circ}$ C Fing the temperature on Thursday

The points $(- 3, - 4), (3, - 4), (3, 4)$ and $(- 3, 4)$ are the vertices of:

The midpoint of the line segment with endpoints $(- 6, 4)$ and $(8, 2)$ is

The opposite vertices of a rectangle OABC are $O (0, 0)$ and $B (6, 4)$ If $P (1, \frac{1 0}{3})$ is a point on the other diagonal AC then the ratio in which P divides AC is

L,M, and N are the midpoints of the sides BC CA and AB respectively of triangle ABC If the vertices are A(3,-4), B(5,-2), and C(1,3) the area of $△ L M N$ is

In the diagram the coordinates of P,Q, and R are (3,6),(-1,3) and (2,-1) respectively The area of $△ S Q R$ is