Question 1 :
Two poless of equal heights are standing opposite to each ofher on either side of the road, which is 80 m wide. From a point between them on the road, the Angles of elevation of the top of the poless are 60° and 30°, respectively. Find the height of the poless.
Question 2 :
The angle of elevation of the top of a building from the foof of the tower is 30° and the angle of elevation of the top of the tower from the foof of building is 60°. If the tower is 50 m high, then find the height of the building.
Question 3 :
As observed from the top of a 75 m high lighthouse from the sea level, the Angles of depression of two ships are 30° and 45°. If one ship is exactly behind the ofher on the same side of the lighthouse, then find the distance between the two ships.
Question 4 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19a62273b230584979933.jpeg' />
In the above image, a 1.2 m tall girl spofs a balloon moving with the wind in a horizontal line at a height of 88.2 m from the ground. The angle of elevation of the balloon from the eyes of the girl at any instant is 60°. After sometime, the angle of elevation reduces to 30°. Find the distance travelled by the balloon during the interval.
Question 5 :
A tree breaks due to storm and the broken part bends, so that the top of the tree touches the ground making an angle 30° with it. The distance between the foof of the tree to the point, where the top touches the ground is 8 m. Find the height of the tree.
Question 6 :
The angle of elevation of the top of a tower from a point on the ground, which is 30 m away from the foof of the tower, is 30°. Find the height of the tower.
Question 7 :
A contractor plans to install two slides for the children to play in a park. For the children below the age of 5 yr, she prefers to have a slide whose top is at a height of 1.5 m and is inclined at an angle of 30° to the ground, whereas for elder children, she wants to have a steep slide at a height of 3 m and inclined at an angle of 60° to the ground. What should be the length of the slides in each case?
Question 8 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19a61273b230584979932.jpeg' />
In the above image, a TV tower stands vertically on a bank of a canal. From a point on the ofher bank directly opposite the tower, the angle of elevation of the top of the tower is 60°. From another point 20 m away from this point on the line joining this point to the foof of the tower, the angle of elevation of the top of the tower is 30°. Find the height of the tower and the width of the canal.
Question 9 :
Two poless of equal heights are standing opposite to each ofher on either side of the road, which is 80 m wide. From a point between them on the road, the Angles of elevation of the top of the poless are 60° and 30°, respectively. Find the distances of the point from the poless.
Question 10 :
A straight highway leads to the foof of a tower. A man standing at the top of the tower observes a car at an angle of depression of 30°, which is approaching the foof of the tower with a uniform speed. Six seconds later, the angle of depression of the car is found to be 60°. Find the time taken by the car to reach the foof of the tower from this point.
Question 11 :
From a point on the ground, the angles of elevation of the bottom and the top of a transmission tower fixed at the top of a 20 m high building are $45^\circ and 60^\circ$, respectively. Find the height of the tower.
Question 12 :
A statue, 1.6 m tall, stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60° and from the same point, the angle of elevation of the top of the pedestal is 45°. Find the height of the pedestal.
Question 13 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19a60273b230584979931.jpeg' />
In the above image, a circus artist is climbing a 20 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole, if the angle made by the rope with ground level is 30°.
Question 14 :
A kite is flying at a height of 60 m above the ground. The string attached to the kite is temporarily tied to a point on the ground. The inclination of the string with the ground is 60°. Find the length of the string, assuming that there is no slack in the string.
Question 15 :
From the top of a 7 m high building, the angle of elevation of the top of a cable tower is 60° and the angle of depression of its foof is 45°. Determine the height of the tower.
Question 16 :
A 1.5 m tall boy is standing at some distance from a 30 m tall building. The angle of elevation from his eye to the top of the building increases from 30° to 60° as he walks tonwards the building. Find the distance he walked tonwards the building.
Question 17 :
The Angles of elevation of the top of a tower from two points at a distance of 4 m and 9 m from the base of the tower and in the same straight line with it are complementary. Find the height of the tower.
Question 18 :
If $\sin A = \frac{3}{4}$, calculate cos A and tan A respectively.
Question 19 :
In $\Delta PQR$, right-angled at Q, PR + QR = 25 cm and PQ = 5 cm. Determine the values of $\sin P, \cos P, \tan P$ respectively.
Question 20 :
In triangle ABC, right-angled at B, if $\tan A = \frac{1}{\sqrt3}$, then find the value of $\sin A \cos C +\cos A\sin C$
Question 21 :
In triangle ABC, right-angled at B, if $\tan A = \frac{1}{\sqrt3}$, then find the value of $\cos A \cos C -\sin A\sin C$
Question 22 :
Given $\sec \theta = \frac{13}{12}$ calculate $cosec\ \theta$ and $\cot \theta$ respectively.
Question 23 :
Given $15 \cot A = 8$, find $\sin A$ and $\sec A$ respectively.
Question 24 :
If $\tan \begin{pmatrix}A + B\end{pmatrix} = \sqrt3$, $\tan \begin{pmatrix}A - B\end{pmatrix} =\frac{1}{\sqrt3}$, $0^{\circ}< A + B ≤ 90^{\circ}$, $A > B$, find A and B respectively.
Question 28 :
The value of $\sin \theta$ increases as $\theta$ increases. True or False?
Question 29 :
$\sin \theta=\cos \theta$ for all values of $\theta$. True or False?
Question 33 :
The value of $\cos \theta$ increases as $\theta$ increases. True or False?
Question 36 :
$\sin 2A = 2 \sin A$ is true when A is equal to
Question 40 :
If $\sec 4A = cosec\ \begin{pmatrix}A – 20^{\circ}\end{pmatrix}$, where 4A is an acute angle, find the value of A.
Question 42 :
$\tan 48^{\circ} \tan 23^{\circ} \tan 42^{\circ} \tan 67^{\circ} = 1$. TRUE or FALSE?
Question 44 :
Express $\sin 67^{\circ} + \cos 75^{\circ}$ in terms of trigonometric ratios of angles between $0^{\circ}$ and $45^{\circ}$.
Question 46 :
If $\tan 2A = \cot \begin{pmatrix}A – 18^{\circ}\end{pmatrix}$, where 2A is an acute angle, find the value of A.
Question 48 :
If A, B and C are interior angles of a triangle ABC, then $\sin\begin{pmatrix}\frac{B+C}{2}\end{pmatrix}\ne\cos\begin{pmatrix}\frac{A}{2}\end{pmatrix}$. TRUE or FALSE ?
Question 49 :
$\cos 38^{\circ} \cos 52^{\circ} – \sin 38^{\circ} \sin 52^{\circ} \ne 0$. TRUE or FALSE?
Question 51 :
Evaluate : $sin 25° cos 65° + cos 25° sin 65°$
Question 52 :
(1 + tan θ + sec θ) (1 + cot θ – cosec θ) = ____
Question 53 :
Can the trigonometric ratios sin A, sec A and tan A be expressed in terms of cot A?
Question 54 :
Is $\frac{cos A – sin A + 1}{cos A + sin A - 1}= cosecA + cotA$?
Question 57 :
(sec A + tan A) (1 – sin A) = ______
Question 58 :
Is this equality correct ? $\frac{tan A}{1- cotA} + \frac{cotA}{1-tanA}= 1+ secAcosecA$
Question 59 :
Is this equality correct ?$(cosec A – sin A) (sec A – cos A)= \frac{1}{tan A +cot A}$
Question 61 :
Is $(sin A + cosec A)^2 + (cos A + sec A)^2 = 7 + tan^2 A + cot^2 A$?
Question 67 :
Can all the other trigonometric ratios of ∠ A be written in terms of sec A?
Question 69 :
A solid consisting of a right circular cone of height 120 cm and radius 60 cm standing on a hemisphere of radius 60 cm is placed upright in a right circular cylinder full of water such that it touches the bottom. Find the volume of water left in the cylinder, if the radius of the cylinder is 60 cm and its height is 180 cm.
Question 70 :
Water in a canal, 6 m wide and 1.5 m deep is flowing at a speed of 10 km/hr. How much area will it irrigate in 30 minutes, if 8 cm of standing water is needed?
Question 71 :
A toy is in the form of a cone of radius 3.5 cm surmounted on a hemisphere of same radius. The total height of the toy is 15.5 cm. Find the total surface area of the toy.
Question 72 :
How many silver coins, 1.75 cm in diameter and of thickness 2 mm, must be melted to form a cuboid of dimensions $5.5 cm\times 10 cm\times 3.5 cm$?
Question 73 :
What is the formulae for volume of a spherical shell?(where $r_1$ and $r_2$ are respectively its external and internal radii)
Question 74 :
A copper wire, 3 mm in diameter, is wound about a cylinder whose length is 12 cm, and diameter 10 cm, so as to cover the curved surface of the cylinder. Find the mass of the wire, assuming the density of copper to be 8.88 g per $cm^3$.
Question 75 :
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. Find the radius of the sphere.
Question 76 :
How many shots each having diameter 3 cm can be made from a cuboidal lead solid of dimensions 9cm × 11cm × 12cm?
Question 77 :
Metallic spheres of radii 6 cm, 8 cm and 10 cm, respectively, are melted to form a single solid sphere. Find the radius of the resulting sphere.
Question 78 :
Two identical solid hemispheres of equal base radius r cm are stuck together along their bases. The total surface area of the combination is $6\pi r^2$.
Question 79 :
A hemispherical tank full of water is emptied by a pipe at the rate of $3\frac{4}{7}$ litres per second. How much time will it take to empty half the tank, if it is 3m in diameter? (Take $\pi$ = $\frac{22}{7}$ )
Question 80 :
A container shaped like a right circular cylinder having diameter 12 cm and height 15 cm is full of ice-cream. The ice-cream is to be filled into cones of height 12 cm and diameter 6 cm, having a hemispherical shape on the top. Find the number of such cones which can be filled with ice-cream.
Question 81 :
A tent is in the shape of a cylinder surmounted by a conical top. If the height and diameter of the cylindrical part are 2.1 m and 4 m respectively, and the slant height of the top is 2.8 m, find the area of the canvas used for making the tent. (Note that the base of the tent will not be covered with canvas.)
Question 82 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b97273b2305849799d5.PNG ' />
A funnel'(see the above figure) is the combination of
Question 83 :
What is the formulae for curved surface area of solid hemisphere?
Question 84 :
An open metallic bucket is in the shape of a frustum of a cone, mounted on a hollow cylindrical base made of the same metallic sheet. The surface area of the metallic sheet used is equal to curved surface area of frustum of a cone + area of circular base + curved surface area of cylinder.
Question 85 :
A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the hemisphere is 14 cm and the total height of the vessel is 13 cm. Find the inner surface area of the vessel.
Question 86 :
Two identical cubes each of volume 64 $cm^3$ are joined together end to end. What is the surface area of the resulting cuboid?
Question 87 :
A cubical block of side 7 cm is surmounted by a hemisphere.Find the surface area of the solid.
Question 88 :
A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the hemisphere is 14 cm and the total height of the vessel is 13 cm. Find the inner surface area of the vessel.
Question 89 :
A metallic sphere of radius 4.2 cm is melted and recast into the shape of a cylinder of radius 6 cm. Find the height of the cylinder.
Question 90 :
A mason constructs a wall of dimensions 270cm× 300cm × 350cm with the bricks each of size 22.5cm × 11.25cm × 8.75cm and it is assumed that $\frac{1}{8}$ space is covered by the mortar. Then the number of bricks used to construct the wall is
Question 91 :
A cubical block of side 7 cm is surmounted by a hemisphere. What is the greatest diameter the hemisphere can have?
Question 92 :
From a solid cylinder whose height is 2.4 cm and diameter 1.4 cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid to the nearest $cm^2$ .
Question 93 :
The rain water from a roof of dimensions 22 m × 20 m drains into a cylindrical vessel having diameter of base 2 m and height 3.5 m. If the rain water collected from the roof just fill the cylindrical vessel, then find the rainfall in cm.
Question 94 :
A cistern, internally measuring $150 cm\times 120 cm\times 110 cm$, has 129600 $cm^3$ of water in it. Porous bricks are placed in the water until the cistern is full to the brim. Each brick absorbs one-seventeenth of its own volume of water. How many bricks can be put in without overflowing the water, each brick being $22.5 cm\times 7.5 cm\times 6.5 cm$.
Question 95 :
The barrel of a fountain pen, cylindrical in shape, is 7 cm long and 5 mm in diameter.A full barrel of ink in the pen is used up on writing 3300 words on an average.How many words can be written in a bottle of ink containing one fifth of a litre?
Question 96 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c39273b230584979a99.JPG' />
In the above image, a pen stand made of wood is in the shape of a cuboid with four conical depressions to hold pens. The dimensions of the cuboid are 15 cm by 10 cm by 3.5 cm. The radius of each of the depressions is 0.5 cm and the depth is 1.4 cm. Find the volume of wood in the entire stand.
Question 97 :
A drinking glass is in the shape of a frustum of a cone of height 14 cm. The diameters of its two circular ends are 4 cm and 2 cm. Find the capacity of the glass.
Question 98 : <img style='object-fit:contain' src='61b19b28273b23058497994c' />
As shown in the above figure, a medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends. The length of the entire capsule is 14 mm and its diameter is 5 mm. Find its surface area.
Question 99 :
What is the formulae for total surface area of solid hemisphere?
Question 100 :
Two identical solid cubes of side a are joined end to end. Then the total surface area of the resulting cuboid is $12a^2$.
Question 101 :
Metallic spheres of radii 6 cm, 8 cm and 10 cm, respectively are melted to form a single solid sphere. Find the radius of the resulting sphere.
Question 102 :
Water in a canal, 6 m wide and 1.5 m deep, is flowing with a speed of 10 km /h. How much area will it irrigate in 30 minutes, if 8 cm of standing water is needed?
Question 103 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c3b273b230584979a9c.JPG' />
In the above image, an oil funnel made of tin sheet consists of a 10 cm long cylindrical portion attached to a frustum of a cone. If the total height is 22 cm, diameter of the cylindrical portion is 8 cm and the diameter of the top of the funnel is 18 cm, find the area of the tin sheet required to make the funnel.
Question 104 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c31273b230584979a8f.jpg' />
In the above image, a solid toy is in the form of a hemisphere surmounted by a right circular cone. The height of the cone is 2 cm and the diameter of the base is 4 cm. Determine the volume of the toy. (Take $\pi$ = 3.14)
Question 105 :
A container, opened from the top and made up of a metal sheet, is in the form of a frustum of a cone of height 16 cm with radii of its lower and upper ends as 8 cm and 20 cm, respectively. Find the cost of metal sheet used to make the container, if it costs Rs 8 per 100 $cm^2$ .
Question 106 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b90273b2305849799cb.jpg' />
In the above figure, plumbline (sahul) is the combination of
Question 107 :
A container, opened from the top and made up of a metal sheet, is in the form of a frustum of a cone of height 16 cm with radii of its lower and upper ends as 8 cm and 20 cm, respectively. Find the cost of the milk which can completely fill the container, at the rate of Rs 20 per litre.
Question 108 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b93273b2305849799cf.jpg' />
The capacity of a cylindrical vessel with a hemispherical portion raised upward at the bottom as shown in the above figure is $\frac{1}{3}\pi r^2\left[3h-2r\right]$.
Question 109 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b32273b230584979950.jpeg' />
In the above image, a Fez, the cap used by the Turks, is shaped like the frustum of a cone. If its radius on the open side is 10 cm, radius at the upper base is 4 cm and its slant height is 15 cm, then find the area of material used for making it.
Question 110 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c2d273b230584979a8b.JPG' />
In the above image, a juice seller was serving his customers using glasses as shown. The inner diameter of the cylindrical glass was 5 cm, but the bottom of the glass had a hemispherical raised portion which reduced the capacity of the glass. If the height of a glass was 10 cm, find the actual capacity of the glass . (Use $\pi$ = 3.14.)
Question 112 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c2b273b230584979a88.JPG' />
In the above image, a wooden toy rocket is in the shape of a cone mounted on a cylinder, as shown. The height of the entire rocket is 26 cm, while the height of the conical part is 6 cm. The base of the conical portion has a diameter of 5 cm, while the base diameter of the cylindrical portion is 3 cm. If the conical portion is to be painted orange and the cylindrical portion yellow, find the area of the rocket painted with each of these colours . (Take $\pi$ = 3.14)
Question 113 :
A bucket is in the form of a frustum of a cone and holds 28.490 litres of water.The radii of the top and bottom are 28 cm and 21 cm, respectively. Find the height of the bucket
Question 114 :
A farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank in his field, which is 10 m in diameter and 2 m deep. If water flows through the pipe at the rate of 3 km/hr, in how much time will the tank be filled?
Question 115 :
Three metallic solid cubes whose edges are 3 cm, 4 cm and 5 cm are melted and formed into a single cube. Find the edge of the cube so formed.
Question 116 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c36273b230584979a95.JPG' />
The radii of the ends of a frustum of a cone 45 cm high are 28 cm and 7 cm (see the above image). Find its total surface area(Take $\pi$ = $\frac{22}{7}$ ).
Question 117 :
Find the number of metallic circular disc with 1.5 cm base diameter and of height 0.2 cm to be melted to form a right circular cylinder of height 10 cm and diameter 4.5 cm.
Question 118 :
For what value of n, are the nth terms of two APs: 63, 65, 67, . . . and 3, 10, 17, . . . equal?
Question 119 :
If the sum of first 7 terms of an AP is 49 and that of 17 terms is 289, find the sum offirst n terms.
Question 120 :
In an AP, given a = 5, d = 3, $a_n$= 50, find n and $S_n$.
Question 121 :
In an AP, given $a = 2, d = 8, S_n = 90$, find n and $a_n$.
Question 122 :
The first and the last terms of an AP are 17 and 350 respectively. If the common difference is 9, how many terms are there in the AP?
Question 123 :
Subba Rao started work in 1995 at an annual salary of Rs. 5000 and received an increment of Rs. 200 each year. In which year did his income reach Rs. 7000?
Question 124 :
Find the sum of the following AP: 34 + 32 + 30 + . . . + 10
Question 125 :
How many terms of the AP : 9, 17, 25, . . . must be taken to give a sum of 636?
Question 126 :
Which term of the AP : 3, 15, 27, 39, . . . will be 132 more than its 54th term?
Question 127 :
Find the 31st term of an AP whose 11th term is 38 and the 16th term is 73.
Question 128 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bc4273b230584979a10.JPG' />
In the above fig, find the missing value corresponding to (i)
Question 129 :
The first term of an AP is 5, the last term is 45 and the sum is 400. Find the number of terms and the common difference.
Question 130 :
The 17th term of an AP exceeds its 10th term by 7. Find the common difference.
Question 131 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bc3273b230584979a0e.JPG' />
In the above fig, find the missing value corresponding to (iii)
Question 132 :
Determine the AP whose third term is 16 and the 7th term exceeds the 5th term by 12.
Question 134 :
In an AP, given $a_{12} = 37, d = 3$, find a and $S_{12}$.
Question 135 :
The first and the last terms of an AP are 17 and 350 respectively. If the common difference is 9, what is the sum of the AP?
Question 136 :
In an AP, given $d = 5, S_9 = 75$, find a and $a_9$.
Question 137 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bc9273b230584979a17.JPG' />
A small terrace at a football ground comprises of 15 steps each of which is 50 m long and built of solid concrete. Each step has a rise of 0.25 m and a tread of 0.5 m. Calculate the total volume of concrete required to build the terrace.
Question 138 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bc9273b230584979a16.JPG' />
In the above fig. A ladder has rungs 25 cm apart. The rungs decrease uniformly in length from 45 cm at the bottom to 25 cm at the top. If the top and the bottom rungs are $2\frac{1}{2}$ m apart, what is the length of the wood required for the rungs?
Question 139 :
Does $a_1, a_2, . . ., a_n, . . $ form an AP where $a_n = 3 + 4n$?
Question 140 :
Find the sum of the following AP: –5 + (–8) + (–11) + . . . + (–230)
Question 141 :
A contract on construction job specifies a penalty for delay of completion beyond a certain date as follows: Rs 200 for the first day, Rs 250 for the second day, Rs 300 for the third day, etc., the penalty for each succeeding day being Rs 50 more than for the preceding day. How much money the contractor has to pay as penalty, if he has delayed the work by 30 days?
Question 142 :
Find the sum of the first 15 terms in $a_n = 3 + 4n$.
Question 143 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bc7273b230584979a14.JPG' />
In the above fig. 200 logs are stacked in the following manner: 20 logs in the bottom row, 19 in the next row, 18 in the row next to it and so on. In how many rows are the 200 logs placed and how many logs are in the top row?
Question 144 :
Find the sum of the following AP: 2, 7, 12, . . ., to 10 terms.
Question 145 :
In the following AP, find the missing term: 2, __ ,26
Question 146 :
Does $a_1, a_2, . . ., a_n, . . $ form an AP where $a_n = 9 – 5n$?
Question 147 :
Check whether – 150 is a term of the AP : 11, 8, 5, 2 . . .
Question 148 :
In an AP, given l = 28, S = 144, and there are total 9 terms. Find a.
Question 149 :
Find the sum of the first 40 positive integers divisible by 6.
Question 150 :
If the sum of the first n terms of an AP is $4n – n^2$, what is the first term (that is $S_1$)?
Question 151 :
Find the sum of the following AP: 7 + 10.5 + 14 + . . . + 84
Question 152 :
If the sum of the first n terms of an AP is $4n – n^2$, What is the 2nd term ?
Question 153 :
Two APs have the same common difference. The difference between their 100th terms is 100, what is the difference between their 1000th terms?
Question 154 :
Ramkali saved Rs. 5 in the first week of a year and then increased her weekly savings by Rs. 1.75. If in the nth week, her weekly savings become Rs. 20.75, find n.
Question 155 :
Find the sum of the odd numbers between 0 and 50.
Question 156 :
Which term of the AP : 121, 117, 113, . . ., is its first negative term?
Question 157 :
Find the number of terms in the following AP :18, 15.5, 13, . . . , – 47
Question 158 :
The sum of the 4th and 8th terms of an AP is 24 and the sum of the 6th and 10th terms is 44. Find the first three terms of the AP.
Question 159 :
If the sum of the first n terms of an AP is $4n – n^2$, What is the 3rd term ?
Question 160 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bc6273b230584979a13.JPG' />
In the above fig. A spiral is made up of successive semicircles, with centres alternately at A and B, starting with centre at A, of radii 0.5 cm, 1.0 cm, 1.5 cm, 2.0 cm, . . . as shown in above figure. What is the total length of such a spiral made up of thirteen consecutive semicircles?
Question 161 :
11th term of the AP: – 3, -0.5, 2, . . ., is
Question 162 :
Find the sum of the first 15 terms in $a_n = 9 – 5n$
Question 163 :
In a school, students thought of planting trees in and around the school to reduce air pollution. It was decided that the number of trees, that each section of each class will plant, will be the same as the class, in which they are studying, e.g., a section of Class I will plant 1 tree, a section of Class II will plant 2 trees and so on till Class XII. There are three sections of each class. How many trees will be planted by the students?
Question 164 :
If the 3rd and the 9th terms of an AP are 4 and – 8 respectively, which term of this AP is zero?
Question 165 :
Find the 20th term from the last term of the AP : 3, 8, 13, . . ., 253.
Question 166 :
In an AP, given $a = 7, a_{13} = 35$, find d and $S_{13}$.
Question 167 :
If the sum of the first n terms of an AP is $4n – n^2$, What is the nth term ?
Question 168 :
The radii of the top and bottom of a bucket of slant height 45 cm are 28 cm and 7 cm, respectively. The curved surface area of the bucket is
Question 169 :
A container, opened from the top and made up of a metal sheet, is in the form of a frustum of a cone of height 16 cm with radii of its lower and upper ends as 8 cm and 20 cm, respectively. Find the cost of metal sheet used to make the container, if it costs Rs 8 per 100 $cm^2$ .
Question 170 :
A milk container of height 16 cm is made of metal sheet in the form of a frustum of a cone with radii of its lower and upper ends as 8 cm and 20 cm respectively. Find the cost of milk at the rate of Rs. 22 per litre which the container can hold.
Question 171 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c2e273b230584979a8c.JPG' />
In the above image, shanta runs an industry in a shed which is in the shape of a cuboid surmounted by a half cylinder. The base of the shed is of dimension 7 m × 15 m, and the height of the cuboidal portion is 8 m. Further, suppose the machinery in the shed occupies a total space of 300 $m^3$, and there are 20 workers , each of whom occupy about 0.08 $m^3$ space on an average. Then, how much air is in the shed? (Take $\pi$ = $\frac{22}{7}$ )
Question 172 :
What is the formulae for volume of a spherical shell?(where $r_1$ and $r_2$ are respectively its external and internal radii)
Question 173 :
Two identical solid cubes of side a are joined end to end. Then the total surface area of the resulting cuboid is $12a^2$.
Question 174 :
A 20 m deep well with diameter 7 m is dug and the Earth from digging is evenly spread out to form a platform $22 m\times 14 m$. Find the height of the platform.
Question 175 :
A vessel is in the form of an inverted cone. Its height is 8 cm and the radius of its top, which is open is 5 cm. It is filled with water upto brim. When lead shots each in the shape of a sphere with radius 0.5 cm are dropped into the vessel, the one-fourth of the water flows out. Find the number of lead shots dropped in the vessel.
Question 176 :
Find the number of metallic circular disc with 1.5 cm base diameter and of height 0.2 cm to be melted to form a right circular cylinder of height 10 cm and diameter 4.5 cm.
Question 177 : <img style='object-fit:contain' src='61b19b28273b23058497994c' />
As shown in the above figure, a medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends. The length of the entire capsule is 14 mm and its diameter is 5 mm. Find its surface area.
Question 178 :
A solid consisting of a right circular cone of height 120 cm and radius 60 cm standing on a hemisphere of radius 60 cm is placed upright in a right circular cylinder full of water such that it touches the bottom. Find the volume of water left in the cylinder, if the radius of the cylinder is 60 cm and its height is 180 cm.
Question 179 :
A solid consisting of a right circular cone of height 120 cm and radius 60 cm standing on a hemisphere of radius 60 cm is placed upright in a right circular cylinder full of water such that it touches the bottom. Find the volume of water left in the cylinder, if the radius of the cylinder is 60 cm and its height is 180 cm.
Question 180 :
A canal is 300 cm wide and 120 cm deep. The water in the canal is flowing with a speed of 20 km/h. How much area will it irrigate in 20 minutes if 8 cm of standing water is desired?
Question 181 :
A spherical steel ball is melted to make eight new identical balls.Then, the radius of each new ball be $\frac{1}{8}$th the radius of the original ball.
Question 182 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c2c273b230584979a8a.JPG' />
In the above image, mayank made a bird-bath for his garden in the shape of a cylinder with a hemispherical depression at one end . The height of the cylinder is 1.45 m and its radius is 30 cm. Find the total surface area of the bird-bath. (Take $\pi$ = $\frac{22}{ 7}$ )
Question 183 :
A solid iron pole consists of a cylinder of height 220 cm and base diameter 24 cm, which is surmounted by Another cylinder of height 60 cm and radius 8 cm. Find the mass of the pole, given that 1 $cm^3$ of iron has approximately 8 g mass.
Question 184 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b30273b23058497994d.jpeg' />
As shown in the above figure, a wooden article was made by scooping out a hemisphere from each end of a solid cylinder. If the height of the cylinder is 10 cm and its base is of radius 3.5 cm, then find the total surface area of the article.
Question 185 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c2b273b230584979a88.JPG' />
In the above image, a wooden toy rocket is in the shape of a cone mounted on a cylinder, as shown. The height of the entire rocket is 26 cm, while the height of the conical part is 6 cm. The base of the conical portion has a diameter of 5 cm, while the base diameter of the cylindrical portion is 3 cm. If the conical portion is to be painted orange and the cylindrical portion yellow, find the area of the rocket painted with each of these colours . (Take $\pi$ = 3.14)
Question 186 :
Metallic spheres of radii 6 cm, 8 cm and 10 cm, respectively are melted to form a single solid sphere. Find the radius of the resulting sphere.
Question 187 :
A rocket is in the form of a right circular cylinder closed at the lower end and surmounted by a cone with the same radius as that of the cylinder. The diameter and height of the cylinder are 6 cm and 12 cm, respectively. If the the slant height of the conical portion is 5 cm, find the volume and total surface area of the rocket.
Question 188 :
Water in a canal, 6 m wide and 1.5 m deep is flowing at a speed of 10 km/hr. How much area will it irrigate in 30 minutes, if 8 cm of standing water is needed?
Question 189 :
A solid iron cuboidal block of dimensions 4.4 m × 2.6 m × 1m is recast into a hollow cylindrical pipe of internal radius 30 cm and thickness 5 cm. Find the length of the pipe.
Question 190 :
A metallic sphere of radius 4.2 cm is melted and recast into the shape of a cylinder of radius 6 cm. Find the height of the cylinder.
Question 191 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b37273b230584979956.jpg' />
In the above figure, AB is the diameter of the circle, AC = 6 cm and BC = 8 cm. Find the area of the shaded region (Use $\pi=3.14$).
Question 192 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bb7273b2305849799ff.png' />
(As shown in the above image)From each corner of a square of side 4 cm a quadrant of a circle of radius 1 cm is cut and also a circle of diameter 2 cm is cut . Find the area of the remaining portion of the square.
Question 193 :
Find the difference of the areas of two segments of a circle formed by a chord of length 5 cm subtending an angle of $90^{\circ}$ at the centre.
Question 194 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bbd273b230584979a06.png' />
The area of an equilateral triangle ABC is 17320.5 $cm^{2}$ . With each vertex of the triangle as centre, a circle is drawn with radius equal to half the length of the side of the triangle (see the above image). Find the area of the shaded region. (Use $\pi$= 3.14 and $\sqrt{3}$ = 1.73205)
Question 195 :
The numerical value of the area of a circle is greater than the numerical value of its circumference. Is it true or false?
Question 196 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b38273b230584979958.jpg' />
In the above figure, dimensions are given. Find the area of the shaded region.
Question 197 :
Find the area of a sector of a circle with radius 6 cm if angle of the sector is $60^{\circ}$.
Question 198 :
Is the area of the largest circle that can be drawn inside a rectangle of length $a\ cm$ and breadth $b\ cm$ $\left(a>b\right)$ is $\pi\ b^2\ cm^2$ ?
Question 199 :
Find the area of the sector of a circle of radius 5 cm, if the corresponding arc length is 3.5 cm.
Question 200 :
In covering a distance s metres, a circular wheel of radius r metres makes $\frac{s}{2\pi r}$ revolutions. Is it true or false?
Question 201 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19baf273b2305849799f4.png' />
The above image depicts an archery target marked with its five scoring regions from the centre outwards as Gold, Red, Blue, Black and White. The diameter of the region representing Gold score is 21 cm and each of the other bands is 10.5 cm wide. Find the area of the black scoring region.
Question 202 :
The area of the square that can be inscribed in a circle of radius 8 cm is
Question 203 :
It is proposed to build a single circular park equal in area to the sum of areas of two circular parks of diameters 16 m and 12 m in a locality. The radius of the new park would be
Question 204 :
Find the difference of tha areas of a sector of an angle $120^{\circ}$ and its corresponding major sector of a circle of radius 21 cm.
Question 205 :
If the length of an arc of a circle of radius r is equal to that of an arc of a circle of radius 2r, then the angle of the corresponding sector of the first circle is double the angle of the corresponding sector of the other circle. Is it true or false?
Question 206 :
The wheel of a motor cycle is of radius 35 cm. How many revolutions per minute must the wheel make so as to keep a speed of 66 km/h ?
Question 207 :
Find the number of revolutions made by a circular wheel of area $1.54\ m^2$ in rolling a distance of 176 m.
Question 208 :
If $\theta$ is the angle (in degrees) of a sector of a circle of radius $r$, then area of the sector is
Question 209 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bba273b230584979a03.png' />
The above figure depicts a racing track whose left and right ends are semicircular.The distance between the two inner parallel line segments is 60 m and they are each 106 m long. If the track is 10 m wide, find the distance around the track along its inner edge.
Question 210 :
In a circle of radius 21 cm , an arc subtends an angle of $60^{\circ}$ at the centre. Find area of the sector formed by the arc.
Question 211 :
The radii of two circless are 8 cm and 6 cm, respectively. Find the radius of the circle having area equal to the sum of the areas of the two circless.
Question 212 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19a48273b230584979913.jpeg' />
The above figure depicts an archery target marked with its five scoring regions from centre outwards as gold, red, blue, black and white. The diameter of the region representing gold score is 21 cm and each of the ofher bands is 10.5 cm wide. Find the area of white scoring region.
Question 213 :
A chord of a circle of radius 10 cm subtends a right angle at the centre. Find the area of the corresponding major sector.(Use $\pi$=3.14)
Question 214 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b35273b230584979954.jpg' />
In the above figure, a square of diagonal 8 cm is inscribed in a circle. Find the area of the shaded region.
Question 215 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bae273b2305849799f3.png' />
The above image depicts an archery target marked with its five scoring regions from the centre outwards as Gold, Red, Blue, Black and White. The diameter of the region representing Gold score is 21 cm and each of the other bands is 10.5 cm wide. Find the area of the blue scoring region.
Question 216 :
The wheels of a car are of diameter 80 cm each. How many complete revolutions does each wheel make in 10 minutes when the car is travelling at a speed of 66 km per hour?
Question 217 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b3b273b23058497995c.jpg' />
In the above figure, arcs have been drawn of radius 21 cm each with vertices A, B, C and D of quadrilateral ABCD as centres. Find the area of the shaded region.
Question 218 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b3e273b230584979960.jpg' />
In the above figure, dimensions are given. Find the area of the shaded region.
Question 219 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19ba9273b2305849799ed.png' />
Find the area of the segment AYB shown in the above image, if radius of the circle is 21 cm and $\angle AOB$ = $120 ^{\circ}$. (Use $\pi$= $\frac{22}{7}$ )
Question 220 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b3a273b23058497995a.jpg' />
In the above figure, arcs are drawn by taking vertices A, B and C of an equilateral triangle of side 10 cm to intersect the sides BC, CA and AB at their respective mid-points D, E and F. Find the area of the shaded region (Use $\pi=3.14$).
Question 221 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bc0273b230584979a0b.png' />
In the above figure , AB and CD are respectively arcs of two concentric circles of radii 21 cm and 7 cm and centre O . If $\angle AOB$=$30^{\circ}$ , find the area of the shaded region.
Question 222 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b3d273b23058497995f.jpg' />
In the above figure, an archery target formed by 3 concentric circles is shown which has three regions. If the diameters of the concentric circles are in the ratio 1: 2: 3, then find the ratio of the areas of three regions.
Question 223 :
Find the area of the minor segment of a circle of radius 14 cm, when the angle of the corresponding sector is $60^{\circ}$ .
Question 224 :
If the perimeter and the area of a circle are numerically equal, then the radius of the circle is
Question 225 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19a48273b230584979912.jpeg' />
The above figure depicts an archery target marked with its five scoring regions from centre outwards as gold, red, blue, black and white. The diameter of the region representing gold score is 21 cm and each of the ofher bands is 10.5 cm wide. Find the area of black scoring region.
Question 226 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b3d273b23058497995e.jpg' />
In the above figure, a floor of a room of dimensions $5\ m\times4\ m$ covered with circular tiles of diameters 50 cm each is shown. Find the area of the floor that remains uncovered with tiles.
Question 227 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bbf273b230584979a09.png' />
In the above figure , OACB is a quadrant of a circle with centre O and radius 3.5 cm . If OD = 2 cm , find the area of the shaded region.
Question 228 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bbe273b230584979a08.png' />
In the above figure , OACB is a quadrant of a circle with centre O and radius 3.5 cm . If OD = 2 cm , find the area of the quadrant OACB.
Question 229 :
A chord of a circle of radius 15 cm subtends an angle of $60^{\circ}$ at the centre. Find the area of the corresponding major segment of the circle. (Use $\pi$= 3.14 and $\sqrt{3}$ = 1.73)
Question 230 :
A car has two wipers which do not overlap. Each wiper has a blade of length 25 cm sweeping through an angle of $115^{\circ}$ . Find the total area cleaned at each sweep of the blades.
Question 231 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bad273b2305849799f2.png' />
The above image depicts an archery target marked with its five scoring regions from the centre outwards as Gold, Red, Blue, Black and White. The diameter of the region representing Gold score is 21 cm and each of the other bands is 10.5 cm wide. Find the area of the red scoring region.
Question 232 :
Find the area of the segment of a circle of radius 12 cm whose corresponding sector has a central angle of $60^{\circ}$ (Use $\pi=3.14$).
Question 233 :
Find the area of the major sector of a circle with radius 4 cm and of angle $30^{\circ}$.
Question 234 :
The perimeter of a square circumscribing a circle of radius a cm is 8a cm . Is it true or false?
Question 235 :
A chord of a circle of radius 12 cm subtends an angle of $120^{\circ}$ at the centre. Find the area of the corresponding segment of the circle.(Use $\pi$= 3.14 and $\sqrt{3}$ = 1.73)
Question 236 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bad273b2305849799f1.png' />
The above image depicts an archery target marked with its five scoring regions from the centre outwards as Gold, Red, Blue, Black and White. The diameter of the region representing Gold score is 21 cm and each of the other bands is 10.5 cm wide. Find the area of the gold scoring region.
Question 237 :
Area of a sector of central angle $200^{\circ}$ of a circle is $770\ cm^2$. Find the length of the corresponding arc of this sector.
Question 238 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bc1273b230584979a0c.png' />
In the above figure , ABC is a quadrant of a circle of radius 14 cm and a semicircle is drawn with BC as diameter . Find the area of the shaded region.
Question 239 :
The radii of two circless are 19 cm and 9 cm, respectively. Find the radius of the circle which has circumference equal to the sum of the circumferences of the two circless.
Question 240 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19baf273b2305849799f5.png' />
The above image depicts an archery target marked with its five scoring regions from the centre outwards as Gold, Red, Blue, Black and White. The diameter of the region representing Gold score is 21 cm and each of the other bands is 10.5 cm wide. Find the area of the white scoring region.
Question 241 :
Other than algebraical methods, how can the pair of linear equations be solved?
Question 242 :
Solve the following pair of linear equations by the elimination method and the substitution method : $3x – 5y – 4 = 0 ~and ~9x = 2y + 7$
Question 243 :
Solve the following pair of linear equations by the elimination method and the substitution method : $\frac{x}{2}+\frac{2y}{3}=-1 ~and~ x-\frac{y}{3}=3$
Question 244 :
Aftab tells his daughter, “Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be.” Which of these represent this situation algebraically?
Question 245 :
Solve the following pair of equations by substitution method: $7x – 15y =2 ; x + 2y =3$
Question 246 :
Romila went to a stationery shop and purchased 2 pencils and 3 erasers for Rs. 9. Her friend Sonali saw the new variety of pencils and erasers with Romila, and she also bought 4 pencils and 6 erasers of the same kind for Rs. 18. Which of these represent this situation algebraically ?
Question 247 :
Given the linear equation 2x + 3y – 8 = 0, write another linear equation in two variables such that the geometrical representation of the pair so formed are intersecting lines.
Question 248 :
On comparing the ratios $\frac{a_1}{a_2]$, $\frac{b_1}{b_2}$ and $\frac{c_1}{c_2}$, find out whether the lines representing a pair of linear equations intersect at a point, are parallel or coincident: $6x – 3y + 10 = 0 ; 2x – y + 9 = 0$
Question 249 :
Solve the pair of equations: $\frac{2}{x} + \frac{3}{y} = 13 ; \frac{5}{x} - \frac{4}{y} = -2$
Question 250 :
In case of infinitely many solutions, the pair of linear equations is said to be __________.
Question 251 :
The sum of the digits of a two-digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the number.
Question 252 :
Given the linear equation 2x + 3y – 8 = 0, write another linear equation in two variables such that the geometrical representation of the pair so formed are parallel lines.
Question 253 :
Find out whether the lines representing a pair of linear equations are consistent or inconsistent: $x – y = 8 , 3x – 3y = 16$
Question 254 :
Draw the graphs of the equations x – y + 1 = 0 and 3x + 2y – 12 = 0. Determine the coordinates of the vertices of the triangle formed by these lines and the x-axis.
Question 255 :
The sum of the digits of a two-digit number is 9. If 27 is added to it, the digits of the number get reversed. The number is ___________.
Question 257 :
Solve the following pair of linear equations by the substitution method : $x + y = 14 ; x - y = 4$
Question 258 :
Half the perimeter of a rectangular garden, whose length is 4 m more than its width, is 36 m. Find the dimensions of the garden.
Question 259 :
On comparing the ratios $\frac{a_1}{a_2]$, $\frac{b_1}{b_2}$ and $\frac{c_1}{c_2}$, find out whether the lines representing a pair of linear equations are consistent or inconsistent: $\frac{4}{3}x + 2y = 8 ; 2x + 3y = 12$
Question 260 :
Solve the following pair of equations by reducing them to a pair of linear equations : $6x + 3y = 6xy ; 2x + 4y = 5xy$.
Question 261 :
Do the equations 4x + 3y – 1 = 5 and 12x + 9y = 15 represent a pair of coincident lines?
Question 262 :
In the following pair of equations: 2x + y = 6 and 2x – y + 2 = 1, find the ratio of the areas of the two triangles formed by the lines representing these equations with the x-axis and the lines with the y-axis.
Question 263 :
A fraction becomes $\frac{1}{3}$ when 1 is subtracted from the numerator and it becomes $\frac{1}{4}$ when 8 is added to its denominator. Find the fraction.
Question 264 :
A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Saritha paid Rs. 27 for a book kept for seven days, while Susy paid Rs. 21 for the book she kept for five days. Find the fixed charge and the charge for each extra day.
Question 265 :
For which values of p does the pair of equations given below has unique solution?$4x + py + 8 =0 ; 2x + 2y + 2 =0$
Question 266 :
Let a pair of linear equations in two variables be $a_{1}x+b_{1}y+c_{1}=0$ and $a_{2}x+b_{2}y+c_{2}=0$. If $\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne\frac{c_1}{c_2}$, then the pair of linear equations is _______.
Question 267 :
If the lines are represented by the equation $a_1x + b_1y + c_1 =0$ and $a_2x + b_2y + c_2 =0$, then the lines are parallel when _____________.
Question 268 :
Solve the following pair of equations by reducing them to a pair of linear equations : $\frac{7x-2y}{xy} = 5 ; \frac{8x+7y}{xy} = 15$.
Question 269 :
Solve the following pair of linear equations by the substitution method : $0.2x + 0.3y = 1.3 ; 0.4x + 0.5y = 2.3$
Question 270 :
On comparing the ratios $\frac{a_1}{a_2]$, $\frac{b_1}{b_2}$ and $\frac{c_1}{c_2}$, find out whether the lines representing a pair of linear equations are consistent or inconsistent: $2x – 3y = 8 ; 4x – 6y = 9$
Question 272 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b5c273b230584979988.png' />
In the above given graph of the pair of linear equations x – y + 2 = 0 and 4x – y – 4 = 0, calculate the area of the triangle formed by the lines so drawn and the x-axis.
Question 273 :
If we add 1 to the numerator and subtract 1 from the denominator, a fraction reduces to 1. It becomes $\frac{1}{2}$ if we only add 1 to the denominator. What is the fraction?
Question 274 :
Every solution of the equation is a _________ on the line representing it.
Question 275 :
The pair of equations 5x – 15y = 8 and $3x-9y=\frac{24}{5}$ has __________.
Question 276 :
Solve the following pair of equations by reducing them to a pair of linear equations : $\frac{2}{\sqrt{x}} + \frac{3}{\sqrt{y}} = 2 ; \frac{4}{\sqrt{x}} - \frac{9}{\sqrt{y}} = -1$.
Question 277 :
5 pencils and 7 pens together cost Rs. 50, whereas 7 pencils and 5 pens together cost Rs. 46. Find the cost of one pencil and that of one pen, graphically.
Question 278 :
A person, rowing at the rate of 5 km/h in still water, takes thrice as much time in going 40 km upstream as in going 40 km downstream. Find the speed of the stream.
Question 279 :
For what values of k will the following pair of linear equations have infinitely many solutions? $kx + 3y – (k – 3) =0 ; 12x + ky – k =0$
Question 280 :
Solve the following pair of linear equations by the substitution method : $s - t = 3 ; \frac{s}{3} + \frac{t}{2} = 6$
Question 281 :
Solve the following pair of linear equations by the elimination method and the substitution method : $x + y = 5 ~and ~2x – 3y = 4$
Question 282 :
Five years ago, Nuri was thrice as old as Sonu. Ten years later, Nuri will be twice as old as Sonu. How old are Nuri and Sonu?
Question 283 :
The cost of 2 pencils and 3 erasers is Rs. 9 and the cost of 4 pencils and 6 erasers is Rs. 18. Find the cost of each pencil and each eraser.
Question 284 :
Let a pair of linear equations in two variables be $a_{1}x+b_{1}y+c_{1}=0$ and $a_{2}x+b_{2}y+c_{2}=0$. If $\frac{a_1}{a_2}\ne\frac{b_1}{b_2}$, then the pair of linear equations is _______.
Question 285 :
Is x = 1, y = 7 a solution of $2x + 3y = 5$?
Question 286 :
On comparing the ratios $\frac{a_1}{a_2]$, $\frac{b_1}{b_2}$ and $\frac{c_1}{c_2}$, find out whether the lines representing a pair of linear equations are consistent or inconsistent: $3x + 2y = 5 ; 2x – 3y = 7$
Question 287 :
Solve the following pair of linear equations: 21x + 47y = 110 and 47x + 21y = 162.
Question 289 :
State whether the following pair of linear equations has unique solution, no solution, or infinitely many solutions : $x – 3y – 3 = 0 ; 3x – 9y – 2 = 0$
Question 290 :
Solve the following pair of equations by substitution method: $s-7t+42=0 ; s-3t=6$
