Question 1 :
A circle has only finite number of equal chords. TRUE or FALSE?
Question 2 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d1aaf59b460d7261f49e.png' />
In the above fig, A, B, C and D are four points on a circle. AC and BD intersect at a point E such that ∠ BEC = 130° and ∠ ECD = 20°. Find ∠ BAC.
Question 3 :
State Yes or No: AB and AC are two chords of a circle of radius r such that AB = 2AC. If p and q are the distances of AB and AC from the centre, then $4q^2=p^2+3r^2$ .
Question 4 :
State Yes or No: that two circles cannot intersect at more than two points.
Question 5 :
State True or False: Among all the chords of a circle passing through a given point inside the circle that one is smallest which is perpendicular to the diameter passing through the point.
Question 6 :
Bisectors of angles A, B and C of a triangle ABC intersect its circumcircle at D, E and F respectively. The angles of the triangle DEF are 90°– mA, 90°– mB and 90°– mC. What is the value of m?
Question 7 :
State Yes or No: If ABC is an equilateral triangle inscribed in a circle and P be any point on the minor arc BC which does not coincide with B or C, then PA is angle bisector of $\angle BPC$.
Question 8 :
If a line segment joining two points subtends equal angles at two other points lying on the same side of the line containing the line segment, the four points lie on a circle. TRUE or FALSE?
Question 9 :
The angle subtended by an arc at the centre is __________ the angle subtended by it at any point on the remaining part of the circle.
Question 10 :
State true or false: If two equal chords of a circle intersect, prove that the parts of one chord are separately equal to the parts of the other chord.
Question 11 :
An arc is a _________________ when its ends are the ends of a diameter.
Question 12 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d112f59b460d7261f3c2.PNG' />
In the above figure, if OA = 5 cm, AB = 8 cm and OD is perpendicular to AB, then CD is equal to
Question 13 :
A chord of a circle is equal to its radius. Find the angle subtended by this chord at a point in major segment.
Question 14 :
A circular park of radius 20m is situated in a colony. Three boys Ankur, Syed and David are sitting at equal distance on its boundary each having a toy telephone in his hands to talk each other. Find the length of the string of each phone.
Question 15 :
The distance of a line from a given point is found out by calculting the length of the perpendicular from the point to the line. TRUE or FALSE?
Question 17 :
State true or false: $(x+y)^2 = x^2 + 2xy + y^2$.
Question 18 :
If x – 1 is a factor of $p(x) = kx^2– 3x + k$ , k is-
Question 20 :
The remainder when $x^3 + 3x^2 + 3x + 1$ is divided by $x+\pi$ is-
Question 22 :
What is the value of p(1) for the polynomial $p(y)=y^2-y+1$ ?
Question 25 :
Does $x^4 + x^3 + x^2 + x + 1$ has x+1 as a factor -
Question 28 :
What is the value of p(2) for the polynomial $p(y)=y^2-y+1$ ?
Question 30 :
State true or false: $(x + y)^3 = x^3 + y^3 + 3xy (x + y)$.
Question 31 :
State true or false: A triangle is unique if two sides and the included angle is given.
Question 32 :
State true or false: A triangle is unique if three sides are given.
Question 33 :
State true or false: An angle of 67.5° can be constructed.
Question 34 :
State true or false: We can construct a triangle when its base, a base angle and the sum of other two sides is given.
Question 35 :
State true or false: We can construct a triangle given its perimeter and the two base angles.
Question 36 :
With the help of a ruler and a compass it is not possible to construct an angle of
Question 37 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d1acf59b460d7261f4a0.png' />
State true or false: The above image shows the construction of an equilateral triangle where its two sides and two angles are given.
Question 38 :
The construction of a triangle ABC, given that BC = 3 cm, ∠C = 60° is possible when difference of AB and AC is equal to
Question 39 :
State true/false, a triangle ABC can be constructed in which BC = 6 cm, ∠C = 30° and AC – AB = 4 cm.
Question 40 :
State true or false: We can construct a triangle when its base, a base angle and the difference of other two sides is given.
Question 41 :
State true/false, a triangle ABC can be constructed in which ∠ B = 60°, ∠C = 45° and AB + BC + AC = 12 cm
Question 42 :
State true/false, a triangle ABC can be constructed in which ∠ B = 105°, ∠C = 90° and AB + BC + AC = 10 cm.
Question 43 :
State true/false, a triangle ABC can be constructed in which AB = 5 cm, ∠A = 45° and BC + AC = 5 cm.
Question 46 :
The paint in a certain container is sufficient to paint an area equal to 9.375 $m^2$ . How many bricks of dimensions $22.5cm\times10cm\times7.5cm$ can be painted out of this container?
Question 47 :
The height and the slant height of a cone are 21 cm and 28 cm respectively. Find the volume of the cone.
Question 48 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d234f59b460d7261f564.jpeg' />
In the above image, Mary wants to decorate her Christmas tree. She wants to place the tree on a wooden box covered with coloured paper with picture of Santa Claus on it. She must know the exact quantity of paper to buy for this purpose. If the box has length, breadth and height as 80 cm, 40 cm and 20 cm respectively how many square sheets of paper of side 40 cm would she require?
Question 49 :
Find the volume of a sphere whose surface area is 154 $cm^2$ .
Question 50 :
Find the total surface area of a cone whose radius is $\frac{r}{2}$ and slant height 2l.
Question 51 :
Find the volume of a sphere whose radius is 7 cm.
Question 52 :
If the triangle ABC with sides 5 cm,12 cm and 13 cm is revolved about the side 5 cm, then find the volume of the solid so obtained.
Question 53 :
Find the cost of digging a cuboidal pit 8 m long, 6 m broad and 3 m deep at the rate of Rs 30 per $m^3$.
Question 54 :
A small indoor greenhouse (herbarium) is made entirely of glass panes (including base) held together with tape. It is 30 cm long, 25 cm wide and 25 cm high.What is the area of the glass?
Question 55 :
State true or false: Cylinder whose radius = r, height = h, it's total surface area should be $2\pi rh$.
Question 56 :
The inner diameter of a cylindrical wooden pipe is 24 cm and its outer diameter is 28 cm. The length of the pipe is 35 cm. Find the mass of the pipe, if 1 $cm^3$ of wood has a mass of 0.6 g.
Question 57 :
The capacity of a closed cylindrical vessel of height 1 m is 15.4 litres. How many square metres of metal sheet would be needed to make it?
Question 58 :
A solid cube of side 12 cm is cut into eight cubes of equal volume.Find the ratio between their surface areas.
Question 59 :
State true or false: Cone having height = h, radius = r and slant height = l, should have the curved surface area of $\pi rl$.
Question 60 :
Find the total surface area of a hemisphere of radius 21 cm.
Question 61 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d1f7f59b460d7261f50c.JPG' />
From the above image, find the probability that a student obtained less than 20% in the mathematics test.
Question 62 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d1ecf59b460d7261f4fc.JPG' />
Refer to the above image. An insurance company selected 2000 drivers at random (i.e., without any preference of one driver over another) in a particular city to find a relationship between age and accidents. The data obtained are given in the above image. Find the probabillity of the event for a driver chosen at random from the city being 18-29 years of age and having exactly 3 accidents in one year.
Question 63 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d1f3f59b460d7261f507.JPG' />
Refer to the above image. An organisation selected 2400 families at random and surveyed them to determine a relationship between income level and the number of vehicles in a family. The information gathered is in the above image. Suppose a family is chosen. Find the probability that the family chosen is earning Rs 10000 – 13000 per month and owning exactly 2 vehicles.
Question 64 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d1fbf59b460d7261f512.JPG' />
Refer to the above image. What is the empirical probability that an engineer lives less than 7 km from her place of work?
Question 65 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d1e8f59b460d7261f4f7.JPG' />
From above the image Consider the frequency distribution table which gives the weights of 38 students of a class. Find the probability that the weight of a student in the class lies in the interval 46-50 kg.
Question 66 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d1e6f59b460d7261f4f3.JPG' />
On one page of a telephone directory, there were 200 telephone numbers. The frequency distribution of their unit place digit (for example, in the number 25828573, the unit place digit is 3) is given in the above image. Without looking at the page, the pencil is placed on one of these numbers, i.e., the number is chosen at random. What is the probability that the digit in its unit place is 6?
Question 67 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d1f2f59b460d7261f505.JPG' />
From the above image the data is recorded of 1500 families with 2 children that were selected randomly. Compute the probability of a family, chosen at random, having 2 girls.
Question 68 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d1e5f59b460d7261f4f2.JPG' />
Refer to the above image. A die is thrown 1000 times with the frequencies for the outcomes 1, 2, 3,4, 5 and 6 as given in the above image. Find the probabilty of getting outcome 4
Question 69 :
In a cricket match, a batswoman hits a boundary 6 times out of 30 balls she plays. Find the probability that she did not hit a boundary.
Question 70 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d1e8f59b460d7261f4f6.JPG' />
Refer to the above image. A die is thrown 1000 times with the frequencies for the outcomes 1, 2, 3,4, 5 and 6 as given in the above image. Find the probabilty of getting outcome 2
Question 71 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d1fdf59b460d7261f516.JPG' />
From the above image, you were asked to prepare a frequency distribution table regarding the blood groups of 30 students of a class. Use this table to determine the probability that a student of this class, selected at random, has blood group AB.
Question 72 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d1f2f59b460d7261f506.JPG' />
From the above image the data is recorded of 1500 families with 2 children that were selected randomly. Compute the probability of a family, chosen at random, having No girl.
Question 73 :
Two coins are tossed simultaneously 500 times, and we get Two heads : 105 times, One head : 275 times, No head : 120 times. Find the probability of getting one head.
Question 74 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d1eaf59b460d7261f4f9.JPG' />
Refer to the above image. A tyre manufacturing company kept a record of the distance covered before a tyre needed to be replaced. The above image shows the results of 1000 cases. If you buy a tyre of this company, what is the probability that it will last more than 9000 km?
Question 75 :
True or false. The uncertainty of ‘probably’ can be measured numerically by means of ‘probability’.
Question 76 :
State true or false: A rectangle or a rhombus is not a square.
Question 77 :
Diagonals AC and BD of a parallelogram ABCD intersect each other at O. If OA = 3 cm and OD = 2 cm, determine the length of AC.
Question 78 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d209f59b460d7261f526.PNG' />
In the above fig, two parallel lines l and m that are intersected by a transversal p are shown. The quadrilateral formed by the bisectors of interior angles is a ____________.
Question 79 :
ABCD is a rhombus in which altitude from D to side AB bisects AB. Find the $\angle BCD$ of the rhombus.
Question 80 :
State true or false: Figure formed by joining four points in an order is called a quadrilateral.
Question 81 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d208f59b460d7261f525.PNG' />
In the above fig, ABC is an isosceles triangle in which AB = AC. AD bisects exterior angle PAC and CD || AB . ABCD is a ____________.
Question 82 :
Diagonals AC and BD of a quadrilateral ABCD intersect each other at O such that OA : OC = 3 : 2. Is ABCD a parallelogram?
Question 83 :
A diagonal of a rectangle is inclined to one side of the rectangle at $25^{\circ}$. The acute angle between the diagonals is
Question 84 :
If ABCD is a quadrilateral in which $AB\parallel DC$ and AD = BC, then which of the following statement is true?
Question 85 :
If the diagonals of a quadrilateral are equal and bisect each other at right angles, then it is a __________.
Question 86 :
The figure formed by joining the mid-points of the sides of a quadrilateral ABCD, taken in order, is a square only if,
Question 87 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d219f59b460d7261f53d.PNG' />
In ∆ ABC and ∆ DEF in the above fig, AB = DE, AB || DE, BC = EF and BC || EF. Vertices A, B and C are joined to vertices D, E and F respectively. Is ∆ ABC ≅ ∆ DEF ?
Question 88 :
A diagonal of a parallelogram divides it into two ____________ triangles.
Question 90 :
If APB and CQD are two parallel lines, then the bisectors of the angles APQ, BPQ, CQP and PQD form
