Question 1 :
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 2 :
State true or false: A right triangle is unique if the hypotenuse and one side is given.
Question 3 : <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 4 :
With the help of a ruler and a compass, it is possible to construct an angle of
Question 6 :
State true/false, a triangle ABC can be constructed in which β B = 105Β°, β C = 90Β° and AB + BC + AC = 10 cm.
Question 8 :
State true or false: An angle of 67.5Β° can be constructed.
Question 9 :
The construction of a triangle ABC, given that BC = 6 cm, β B = 45Β° is not possible when difference of AB and AC is equal to
Question 10 :
State true or false: A triangle is unique if two angles and the included side is given.
Question 13 :
What is the value of p(2) for the polynomial $p(t)=2+t+2t^2-t^3$ ?
Question 15 :
State true or false: 7 + 3x is a factor of $3x^3 + 7x$.
Question 17 :
What is $ x^3 + y^3 + z^3 β 3xyz$ equal to?
Question 18 :
State true or false: $(x - y)^3 = x^3 - y^3 - 3xy (x - y)$.
Question 21 :
State true or false : Cuboid whose length = l, breadth = b and height = h ; Volume of cuboid = lbh
Question 22 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d23cf59b460d7261f56f.jpeg' />
In the above image, you see the frame of a lampshade. It is to be covered with a decorative cloth. The frame has a base diameter of 20 cm and height of 30 cm. A margin of 2.5 cm is to be given for folding it over the top and bottom of the frame. Find how much cloth is required for covering the lampshade.Assume $\pi$ =$\frac{22}{7}$.
Question 23 :
How many litres of milk can a hemispherical bowl of diameter 10.5 cm hold?
Question 24 :
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. How much of tape is needed for all the 12 edges?
Question 25 :
A school provides milk to the students daily in a cylindrical glasses of diameter 7 cm. If the glass is filled with milk upto an height of 12 cm, find how many litres of milk is needed to serve 1600 students
Question 26 :
A conical tent is 10 m high and the radius of its base is 24 m. Find the cost of the canvas required to make the tent, if the cost of 1 $m^2$ canvas is Rs 70.
Question 27 :
The diameter of the moon is approximately one-fourth of the diameter of the earth. What fraction of the volume of the earth is the volume of the moon?
Question 28 :
A solid cube of side 12 cm is cut into eight cubes of equal volume. What will be the side of the new cube?
Question 29 :
State true or false: If the edge of the cube is a, then Total surface area of cube = $6a^{2}$
Question 30 :
A sphere and a right circular cylinder of the same radius have equal volumes. By what percentage does the diameter of the cylinder exceed its height ?
Question 31 :
State true or false: If no three points out of four are collinear, we obtain a closed figure with four sides.
Question 32 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d154f59b460d7261f421.jpg' />
In the above figure, ABCD and AEFG are two parallelograms. If $\angle C = 55^{\circ}$, determine $\angle F$.
Question 33 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d20cf59b460d7261f52b.PNG' />
In β ABC shown in the above fig, D, E and F are respectively the mid-points of sides AB, BC and CA. β ABC is divided into four triangles by joining D, E and F. How many of these triangles are congruent ?
Question 34 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d217f59b460d7261f53b.PNG' />
In β ABC and β 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 AC = DF ?
Question 36 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d201f59b460d7261f51c.PNG' />
In the fig shown above, (iv) is a ___________ ?
Question 37 :
ABCD is a parallelogram. If its diagonals are equal, then find the value of $\angle ABC$.
Question 38 :
If APB and CQD are two parallel lines, then the bisectors of the angles APQ, BPQ, CQP and PQD form
Question 39 :
The figure formed by joining the mid-points of the sides of a quadrilateral ABCD, taken in order, is a square only if,
Question 40 :
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 BD.
Question 41 :
ABCD is a cyclic quadrilateral such that AB is a diameter of the circle circumscribing it and $\angle ADC=140^{\circ}$, then $\angle BAC$ is equal to
Question 42 :
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 43 :
Equal chords of a circle (or of congruent circles) are not necessarily equidistant from the centre (or centres). TRUE or FALSE?
Question 44 :
The collection of all the points in a plane, which are at a fixed distance from a fixed point in the plane, is called a circle. TRUE or FALSE?
Question 45 :
State whether the given statement is true or false:- Two chords AB and CD of a circle are each at distances 4 cm from the centre, then AB = CD.
Question 46 :
State whether the given statement is true or false:- If A, B, C and D are four points such that $\angle BAC=45^{\circ}$ and $\angle BDC=45^{\circ}$, then A, B, C, D are concyclic.
Question 47 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d11cf59b460d7261f3d0.PNG' />
State Yes or No: In the above figure, if two chords AB and CD of a circle AYDZBWCX intersect at right angles, Then arc CXA + arc DZB = arc AYD + arc BWC = semicircle.
Question 48 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d114f59b460d7261f3c5.PNG' />
In the above figure, if $\angle ABC = 20^{\circ}$, then $\angle AOC$ is equal to
Question 49 :
ABCD is a parallelogram. The circle through A, B and C intersect CD (produced if necessary) at E. Is AE = AD?
Question 50 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d1a0f59b460d7261f490.png' />
In the above fig, segment AB is the _____________ of the circle.
Question 51 : <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 52 :
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 NO head.
Question 53 :
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 54 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d1f5f59b460d7261f50a.JPG' />
Refer to the above image. In a particular section of Class IX, 40 students were asked about the months of their birth Find the probability that a student of the class was born in August.
Question 55 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d1fbf59b460d7261f513.JPG' />
Refer to the above image. What is the empirical probability that an engineer lives more than or equal to 7 km from her place of work?
Question 56 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d1f5f59b460d7261f509.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 Rs16000 or more per month and owning exactly 1 vehicle.
Question 57 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d1fdf59b460d7261f515.JPG' />
Refer to the above image. What is the empirical probability that an engineer lives within $\frac{1}{2}$ km from her place of work?
Question 58 :
Eleven bags of wheat flour, each marked 5 kg, actually contained the following weights of flour (in kg): 4.97, 5.05, 5.08, 5.03, 5.00, 5.06, 5.08, 4.98, 5.04, 5.07, 5.00. Find the probability that any of these bags chosen at random contains more than 5 kg of flour.
Question 59 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d1faf59b460d7261f511.JPG' />
Refer to the above image. To know the opinion of the students about the subject statistics, a survey of 200 students was conducted. The data is recorded in the above image. Find the probability that a student chosen at random does not like it.
Question 60 :
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.
