Question 1 :
At any point on a circle there can be one and only one tangent .
TRUE OR FALSE?
Question 2 :
Two tangents PQ and PR are drawn from an external point to a circle with centre O. Is QORP is a cyclic quadrilateral?
Question 3 :
Is it TRUE or FALSE, that AB is a diameter of a circle and AC is its chord such that $\angle BAC = 30^{\circ}$. If the tangent at C intersects AB extended at D, then BC = BD?
Question 4 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b44273b230584979968.PNG' />
In the above figure, if O is the centre of a circle, PQ is a chord and the tangent PR at P makes an angle of $50^{\circ}$ with PQ, then $\angle POQ$ is equal to
Question 5 :
If a circle touches the side BC of a triangle ABC at P and extended sides AB and AC at Q and R, respectively, Is it TRUE or FALSE that $AQ = \frac { 1 } { 2 } ( BC + CA + AB )$.
Question 6 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bb3273b2305849799fa.png' />
In the above figure , an umbrella has 8 ribs which are equally spaced . Assuming umbrella to be a flat circle of radius 45 cm , find the area between the two consecutive ribs of the umbrella.
Question 7 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bb6273b2305849799fd.png' />
Find the area of the shaded region in the above figure , if radii of the two concentric circles with centre O are 7 cm and 14 cm respectively and $\angle AOC$=$40^{\circ}$.
Question 8 : <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 9 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19a45273b23058497990f.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 each of the gold scoring region.
Question 10 :
If the circumferences of two circles are equal, then their areas are also equal. Is it true or false?
Question 11 :
State True / False, by geometrical construction, it is possible to divide a line segment in the ratio $\begin{array}{l}2+\sqrt{3}:2-\sqrt{3}\end{array}$.
Question 12 :
To divide a line segment AB in the ratio 4:7, a ray AX is drawn first such that ∠BAX is an acute angle and then points $A_1,A_2,A_3,.........$ are located at equal distances on the ray AX and the point B is joined to
Question 13 :
Scale factor means the ratio of the sides of the triangle to be constructed with the corresponding sides of the given triangle . State whether the above statement is TRUE or FALSE ?
Question 14 :
To construct a triangle similar to a given ∆ABC with its sides $\frac{8}{5}$ of the corresponding sides of ∆ABC draw a ray BX such that ∠CBX is an acute angle and X is on the opposite side of A with respect to BC. The minimum number of points to be located at equal distances on ray BX is
Question 15 :
If an isosceles triangle ABC, in which AB = AC = 6 cm, is inscribed in a circle of radius 9 cm, what is the area of the triangle?
Question 16 :
The area of a triangle with vertices A (3, 0), B (7, 0) and C (8, 4) is :
Question 17 :
If Q $\left(0, 1\right)$ is equidistant from P $\left(5, –3\right)$ and R $\left(x, 6\right)$, find the values of x.
Question 18 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bd5273b230584979a26.JPG' />
To conduct Sports Day activities, in your rectangular shaped school ground ABCD, lines have been drawn with chalk powder at a distance of 1 m each. 100 flower pots have been placed at a distance of 1 m from each other along AD, as shown in the above image. Niharika runs $\frac{1}{4}$ th the distance AD on the 2nd line and posts a green flag. Preet runs $\frac{1}{5}$ th the distance AD on the eighth line and posts a red flag. If Rashmi has to post a blue flag exactly halfway between the line segment joining the two flags, where should she post her flag?
Question 19 :
A line intersects the y-axis and x-axis at the points P and Q, respectively. If (2, –5) is the mid-point of PQ, then the coordinates of P and Q are, respectively :
Question 20 :
The point P (–2, 4) lies on a circle of radius 6 and centre C (3, 5). State true or false.
Question 22 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19be4273b230584979a3a.png' />
Look at the graph given above. The graph of $y=p\left(x\right)$, where $p\left(x\right)$ is a polynomial. Here, find the number of zeroes of $p\left(x\right)$.
Question 23 :
Find a quadratic polynomial, the sum and product of whose zeroes are 1 and 1, respectively.
Question 24 :
Given that the zeroes of the cubic polynomial $x^3-6x^2+3x+10$ are of the form a, a+b, a+2b for some real numbers a and b, find the value of b.
Question 25 :
Find a quadratic polynomial, the sum and product of whose zeroes are $\frac{1}{4}$ and -1, respectively.
Question 26 :
What is the probability of an event which is sure (or certain) to occur?
Question 27 :
If two coins are tossed simultaneously there are three possible outcomes—two heads, two tails or one of each. Therefore, for each of these outcomes, the probability is $\frac{1}{3}$⋅ Check whether the argument is correct or incorrect.
Question 28 :
Fill in the blanks: The probability of an event is greater than or equal to _____ and lesss than or equal to _____.
Question 29 :
A lof consists of 144 ball pens of which 20 are defective and the ofhers are good. Nuri will buy a pen if it is good, but will not buy if it is defective. The shopkeeper draws one pen at random and gives it to her. What is the probability that she will buy it ?
Question 30 :
A die is thrown twice. What is the probability that 5 will come up at least once?
Question 31 :
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 32 :
A fraction becomes $\frac{9}{11}$, if 2 is added to both the numerator and the denominator.If, 3 is added to both the numerator and the denominator it becomes $\frac{5}{6}$. Find the fraction.
Question 33 :
Is it true to say that the pair of equations – x + 2y + 2 = 0 and $\frac{1}{2}x-\frac{1}{4}y-1=0$ has a unique solution?
Question 34 :
Solve the following pair of equations by substitution method: $s-7t+42=0 ; s-3t=6$
Question 35 :
A pair of linear equations which has no solution, is called an __________________ pair of linear equations.
Question 38 :
Is $(sin A + cosec A)^2 + (cos A + sec A)^2 = 7 + tan^2 A + cot^2 A$?
Question 39 :
Is this equality correct ?$(cosec A – sin A) (sec A – cos A)= \frac{1}{tan A +cot A}$
Question 40 :
Is this equality correct ? $\frac{tan A}{1- cotA} + \frac{cotA}{1-tanA}= 1+ secAcosecA$
Question 41 :
Find the roots of the quadratic equations, if they exist, by the method of completing the square: $2x^2 + x + 4 = 0$
Question 42 :
Find the nature of the roots of the equation $3x^2 – 2x +\frac{1}{3} = 0$.
Question 44 :
If $b=0$, $c<0$, is it true that the roots of $x^2+bx+c=0$ are numerically equal and opposite in sign?
Question 45 :
Is it possible to design a rectangular mango grove whose length is twice its breadth,and the area is $800 m^2$ ? If so, find its length and breadth.
Question 46 :
How is 7429 expressed as a product of its prime factors?
Question 47 :
Using Euclid’s division lemma can we show that the cube of any positive integer is of the form 9m, 9m + 1 or 9m + 8 ?
Question 48 :
Without actually performing the long division, state whether $\frac{35}{50}$ will have a terminating decimal expansion or a non-terminating repeating decimal expansion.
Question 49 :
The rational number $\frac{257}{5000}$ in the form $2^m × 5^n$ , where m, n are non-negative integers, write its decimal expansion, without actual division.
Question 50 :
Can two numbers have 18 as their HCF and 380 as their LCM?
Question 51 :
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 52 :
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 53 :
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 54 : <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 55 :
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 56 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c18273b230584979a74.PNG' />
The distribution below gives the weights of 30 students of a class. Find the median weight of the students.
Question 57 : <img style='object-fit:contain' src='61b19b06273b230584979948' />
The distribution given above gives the weights of 30 students of a class. Find the median weights of the students.
Question 58 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bfd273b230584979a55.PNG' />
The table above gives the percentage distribution of female teachers in the primary schools of rural areas of various states and union territories (U.T.) of India. Find the mean percentage of female teachers.
Question 59 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c0e273b230584979a68.PNG' />
The above data gives the information on the observed lifetimes (in hours) of 225 electrical components. Determine the modal lifetimes of the components.
Question 60 :
If number of observations(n) is odd, then median equals _______ observation?
Question 61 :
What is the formulae for curved surface area of solid hemisphere?
Question 62 : <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 63 :
What is the formulae for volume of a spherical shell?(where $r_1$ and $r_2$ are respectively its external and internal radii)
Question 64 :
During conversion of a solid from one shape to another, the volume of the new shape will
Question 65 :
A hollow cube of internal edge 22 cm is filled with spherical marbles of diameter 0.5 cm and it is assumed that $\frac{1}{8}$ space of the cube remains unfilled. Then the number of marbles that the cube can accomodate is
Question 66 :
The area of a segment of a circle is less than the area of its corresponding sector. Is it true or false?
Question 67 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b34273b230584979953.jpg' />
In the above figure, a square is inscribed in a circle of diameter d and another square is circumscribing the circle. Is the area of outer square 4 times the area of inner square ?
Question 68 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bb3273b2305849799f9.png' />
In the above figure a brooch is made with silver wire in the form of a circle with diameter 35 mm . The wire is also used in making 5 diameters which divide the circle into 10 equal sectors . Find the area of each sector of the brooch.
Question 69 :
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 70 :
The area of the circle that can be inscribed in a square of side 6 cm is
Question 71 :
E is a point on the side AD produced of a parallelogram ABCD and BE intersects CD at F. Is ∆ ABE ~ ∆ CFB ?
Question 72 :
E and F are points on the sides PQ and PR respectively of a ∆ PQR. State whether EF || QR if PQ = 1.28 cm, PR = 2.56 cm, PE = 0.18 cm and PF = 0.36 cm
Question 73 :
Two poles of heights 6 m and 11 m stand on a plane ground. If the distance between the feet of the poles is 12 m, find the distance between their tops.
Question 74 :
State true or false:
If in two triangles, sides of one triangle are proportional to (i.e., in the same ratio of ) the sides of the other triangle, then their corresponding angles are equal and hence the two triangles are similiar.
Question 75 :
If in two triangles DEF and PQR, $\angle$D = $\angle$Q and $\angle$R = $\angle$E, then which of the following is not true?
Question 77 :
If the 3rd and the 9th terms of an AP are 4 and – 8 respectively, which term of this AP is zero?
Question 78 :
Find the sum of the following AP: 2, 7, 12, . . ., to 10 terms.
Question 79 :
Find the sum of the following AP: –5 + (–8) + (–11) + . . . + (–230)
Question 80 :
If the sum of the first n terms of an AP is $4n – n^2$, What is the nth term ?
Question 81 :
(sec A + tan A) (1 – sin A) = ______
Question 82 :
$\sin \theta=\cos \theta$ for all values of $\theta$. True or False?
Question 83 :
If $\sec 4A = cosec\ \begin{pmatrix}A – 20^{\circ}\end{pmatrix}$, where 4A is an acute angle, find the value of A.
Question 84 :
Is this equality correct ? $\frac{tan A}{1- cotA} + \frac{cotA}{1-tanA}= 1+ secAcosecA$
Question 86 : <img style='object-fit:contain' src='61b19bcf273b230584979a1e' />
In the above figure , a triangle ABC is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC into which BC is divided by the point of contact D are of lengths 8 cm and 6 cm respectively . Find the side AB .
Question 87 :
State true or false. Lengths of tangents from an external point to a circle are equal.
Question 88 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b44273b230584979968.PNG' />
In the above figure, if O is the centre of a circle, PQ is a chord and the tangent PR at P makes an angle of $50^{\circ}$ with PQ, then $\angle POQ$ is equal to
Question 89 :
Two concentric circles are of radii 5 cm and 3 cm . Find the length of the chord of the larger circle which touches the smaller circle .
Question 90 : <img style='object-fit:contain' src='61b19b49273b23058497996f' />
In the above figure, tangents PQ and PR are drawn to a circle such that $\angle RPQ = 30^{\circ}$. A chord RS is drawn parallel to the tangent PQ. What is the value of $\angle RQS$?
Question 91 :
A bag contains 40 balls out of which some are red, some are blue and remaining are black. If the probability of drawing a red ball is $\frac{11}{20}$ and that of blue ball is $\frac{1}{5}$ then the number of black balls is
Question 92 :
If $\frac{6}{5}$, a, 4 are in AP, the value of a is
Question 93 :
If sinθ = $\frac{1}{3}$,then the value of ($9 cot^{2}θ + 9$) is
Question 94 : If in the following figure, ∆ ABC ~ ∆ QPR, then the measure of ∠Q is
<img style='object-fit:contain' src='61b19b62273b230584979990' />
Question 95 : The number of zeroes lying between –2 to 2 of the polynomial f (x), whose graph is given below, is
<img style='object-fit:contain' src='61b19b61273b23058497998f' />
Question 96 :
The number of zeroes, the polynomial p (x) = $(x – 2)^2 + 4$ can have, is
Question 97 : 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 as shown in figure. The area of the remaining (shaded) portion is <img style='object-fit:contain' src='61b19b67273b230584979997' />
Question 98 : <img style='object-fit:contain' src='61b19b68273b230584979998' />
In the adjoining figure, PA and PB are tangents from a point P to a circle with centre O. Then the quadrilateral OAPB must be a
Question 99 :
Euclid’s division lemma states that for two positive integers a and b, there exist unique integers q and r such that a = bq + r, where
Question 100 :
The coordinates of the points P and Q are (4, –3) and (–1, 7). Then the abscissa of a point R on the line segment PQ such that $\frac{PR}{PQ}$ = $\frac{3}{5}$ is
Question 102 :
In case of infinitely many solutions, the pair of linear equations is said to be __________.
Question 103 : <img style='object-fit:contain' src='61b19bdd273b230584979a31' />
In the above fig, ABCD is a cyclic quadrilateral. Find the angles of the cyclic quadilateral?
Question 104 :
Five years hence, the age of Jacob will be three times that of his son. Five years ago, Jacob’s age was seven times that of his son. What are their present ages?
Question 105 :
An equation which can be put in the form ax + by + c = 0,where a, b and c are real numbers, and a and b are not both zero, is called a linear equation in two variables x and y. TRUE or FALSE?
Question 106 :
A card is selected from a deck of 52 cards. The probability of its being a red face card is
Question 107 :
Which of the following cannot be the probability of an event?
Question 108 :
One ticket is drawn at random from a bag containing tickets numbered 1 to 40. The probability that the selected ticket has a number which is a multiple of 5 is
Question 109 :
Someone is asked to take a number from 1 to 100. The probability that it is a prime is
Question 110 : The times, in seconds, taken by 150 atheletes to run a 110 m hurdle race are tabulated below :
<img style='object-fit:contain' src='61b19b71273b2305849799a4' />
The number of atheletes who completed the race in less then 14.6 seconds is :
Question 111 :
If two solid hemispheres of same radius r are joined together along their bases, then curved surface area of this new solid is
Question 112 : <img style='object-fit:contain' src='61b19b94273b2305849799d0' />
Two solid cones A and B are placed in a cylinderical tube as shown in the above figure.The ratio of their capacities are 2:1 and 6 cm is the diameter of cylinder. Find the heights cones.
Question 113 :
From a solid cube of side 7 cm, a conical cavity of height 7 cm and radius 3 cm is hollowed out. Find the volume of the remaining solid.
Question 114 :
A rectangular water tank of base 11 m × 6 m contains water upto a height of 5 m. If the water in the tank is transferred to a cylindrical tank of radius 3.5 m, find the height of the water level in the tank.
Question 115 : <img style='object-fit:contain' src='61b19c32273b230584979a91' />
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 curved surface area(Take $\pi$ = $\frac{22}{7}$ ).
Question 116 :
30th term of the AP: 10, 7, 4, . . . , is
Question 117 :
Find the number of terms in the following AP :18, 15.5, 13, . . . , – 47
Question 118 :
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 119 : <img style='object-fit:contain' src='61b19bc9273b230584979a16' />
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 120 :
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 121 :
Two poles of equal heights are standing opposite each other 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 poles are $60^{\circ}$ and $30^{\circ}$, respectively. Find the height of the poles and the distances of the point from the poles respectively.
Question 122 :
A contractor plans to install two slides for the children to play in a park. For the children below the age of 5 years, she prefers to have a slide whose top is at a height of 1.5 m, and is inclined at an angle of $30^{\circ}$ 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 $60^{\circ}$ to the ground. What should be the length of the slide in each case respectively?
Question 123 :
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 $60^{\circ}$. Find the length of the string, assuming that there is no slack in the string.
Question 124 :
A tower stands vertically on the ground. From a point on the ground, which is 15 m away from the foot of the tower, the angle of elevation of the top of the tower is found to be $60^{\circ}$. Find the height of the tower.
Question 125 :
From a point on a bridge across a river, the angles of depression of the banks on opposite sides of the river are $30^{\circ}$ and $45^{\circ}$, respectively. If the bridge is at a height of 3 m from the banks, find the width of the river.
Question 126 : <img style='object-fit:contain' src='61b19c2b273b230584979a88' />
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 127 :
The diameters of the two circular ends of the bucket are 44 cm and 24 cm. The height of the bucket is 35 cm. The capacity of the bucket is
Question 128 : <img style='object-fit:contain' src='61b19c37273b230584979a97' />
In the above image, 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 the diameter of the capsule is 5 mm. Find its surface area.
Question 129 :
2 cubes each of volume 64 $cm^3$ are joined end to end. Find the surface area of the resulting cuboid.
Question 130 :
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.
