Question 1 :
State true or false: A triangle is unique if two angles and the included side is given.
Question 2 :
With the help of a ruler and a compass it is not possible to construct an angle of
Question 3 :
A point, whose distance from the centre of a circle is greater than its radius lies in _______________ of the circle.
Question 4 :
State true or false: If ABCD is a parallelogram. A circle through A, B is so drawn that it intersects AD at P and BC at Q then P, Q, C and D are concyclic
Question 5 :
State True or False: If two chords of a circle are equal, then their corresponding arcs are congruent and conversely, if two arcs are congruent, then their corresponding chords are equal.
Question 6 :
If two circles intersect at two points, their centres lie on the perpendicular bisector of the common chord. TRUE or FALSE?
Question 7 :
Two circles of radii 5 cm and 3 cm intersect at two points and the distance between their centres is 4 cm. Find the length of the common chord.
Question 8 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d10ff59b460d7261f3be.jpg' />
In the above figure, $BD\ \parallel\ CA$. E is the mid pointof CA and $BD=\frac{1}{2}CA$. Is ar (ABC) = 2ar (DBC)?
Question 9 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d103f59b460d7261f3ac.jpg' />
In the above figure, PSDA is a parellelogram. Points Q and R are taken on PS such that PQ = QR = RS and $PA\ \parallel\ QB\ \parallel\ RC$. Is ar (PQE) = ar (CFD)?
Question 11 :
State whether the statement is TRUE or FALSE: If medians of a triangle ABC intersects at G, then $ar\left(AGB\right)=ar\left(AGC\right)=ar\left(BGC\right)=\frac{1}{3}ar\left(ABC\right)$.
Question 12 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d10bf59b460d7261f3b8.png' />
In the above figure, ABCDE is any pentagon. BP drawn parallel to AC meets DC produced at P and EQ drawn parallel to AD meets CD produced at Q. Is ar (ABCDE) = ar (APQ)?
Question 13 :
State whether the statement is TRUE or FALSE: If ∆ ABC ≅ ∆ PQR, then ar (∆ ABC) = ar (∆ PQR).
Question 14 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d10ef59b460d7261f3bc.jpg' />
In the above figure, ABCD is a parallelogram. Points P and Q on BC trisects BC in three equal parts. Is $ar\left(APQ\right)$ = $ar\left(DPQ\right)$ = $\frac{1}{6}ar\left(ABCD\right)$?
Question 15 :
State whether the statement is TRUE or FALSE: A diagonal of a parallelogram divides the parallelogram in two triangles of equal area.
Question 16 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d10af59b460d7261f3b6.jpg' />
In the above figure, if the mid-points of the sides of a quadrilateral are joined in order, then will the area of the parallelogram so formed be half of the area of the given quadrilateral?
Question 17 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d10ff59b460d7261f3bd.jpg' />
In the above figure, $l$, $m$, $n$ are straight lines such that and $n$ intersects $l$ at P and $m$ at Q. ABCD is a quadrilateral such that its vertex A is on $l$. The vertices C and D are on $m$ and $AD\ \parallel\ n$. Is ar (ABCQ) = ar (ABCDP)?
Question 18 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d1bcf59b460d7261f4b7.JPG' />
Refer to the above image. Students of a school staged a rally for cleanliness campaign. They walked through the lanes in two groups. One group walked through the lanes AB, BC and CA; while the other through AC, CD and DA. Then they cleaned the area enclosed within their lanes. If AB = 9 m, BC = 40 m, CD = 15 m, DA = 28 m and $\angle B = 90^{\circ}$, Find the total area cleaned by the students.
Question 19 :
The sides of a triangle are 56 cm, 60 cm and 52 cm long. Find the area of the triangle.
Question 20 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d137f59b460d7261f3f9.JPG' />
From the above image, a design is made on a rectangular tile of dimensions 50 cm × 70 cm. The design shows 8 triangles, each of sides 26 cm, 17 cm and 25 cm. Find the remaining area of the tile.
Question 21 :
Write True or False. In a triangle, the sides are given as 11 cm, 12 cm and 13 cm. The length of the altitude is 10.25 cm corresponding to the side having length 12 cm.
Question 22 :
Write True or False. The cost of levelling the ground in the form of a triangle having the sides 51 m, 37 m and 20 m at the rate of Rs 3 per $m^2$ is Rs 918.
Question 23 :
Which of the following is the solution of the equation a - 15=25 ?
Question 24 :
State true or false: In Vedic period, squares and circular shaped altars were used for household rituals, while altars whose shapes were combination of rectangles, triangles and trapeziums were used for public worship.
Question 25 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d13bf59b460d7261f3fe.png' />
In the above figure, $\angle 1=\angle 3,\ \angle 2=\angle 4\ and\ \angle 3=\angle 4$, Is $\angle 1\ = \ \angle2 $ ?
Question 26 :
Given two distinct points, there is a _____ line passing through them.
Question 27 :
It is known that if $x+y=10$ then $x+y+z=10+z$. The Euclid’s axiom that illustrates this statement is :
Question 29 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d12df59b460d7261f3ea.PNG' />
In the above figure, LM is a line parallel to the y-axis at a distance of 3 units. What are the coordinates of the point Q?
Question 30 :
If P (– 1, 1), Q (3, – 4), R(1, –1), S(–2, –3) and T (– 4, 4) are plotted on the graph paper, then the point(s) in the fourth quadrant are
Question 31 :
What are the coordinates of a point whose abscissa is 5 and which lies on x-axis?
Question 32 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d1aef59b460d7261f4a3.png' />
According to the fig above -The x-coordinate and the y-coordinate of the point M are _ _ _ and _ _ _, respectively.
Question 33 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d147f59b460d7261f40f.PNG' />
In the above figure, a table is shown. The coordinates of points given in the table represent some of the solutions of the equation 2x + 2 = y. State true or false.
Question 34 :
If the temperature of a liquid can be measured in Kelvin units as x°K or in Fahrenheit units as y°F, the relation between the two systems of measurement of temperature is given by the linear equation $y = \frac {9}{5}$ (x - 273) + 32 . Find the temperature of the liquid in Fahrenheit if the temperature of the liquid is 313°K.
Question 35 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d143f59b460d7261f40a.PNG' />
In the above figure, a graph is shown. This graph represents the linear equation x + y = 0. True or false ?
Question 36 :
If (2, 0) is a solution of the linear equation 2x + 3y = k, then the value of k is :
Question 39 :
If one of the angles of a triangle is $130^{\circ}$, then the angle between the bisectors of the other two angles can be __________.
Question 40 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d14ff59b460d7261f41a.png' />
In the above figure, $∠$1 = $60^{\circ}$ and ∠6 = $120^{\circ}$. Thus, the lines 'm' and 'n' are ____________.
Question 41 :
A transversal intersects two lines in such a way that the two interior angles on the same side of the transversal are equal. Will the two lines always be parallel?
Question 42 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d14bf59b460d7261f415.png' />
In the above given figure, if OP||RS, $∠$OPQ = $110^{\circ}$ and $∠$QRS = $130^{\circ}$, then $∠$PQR is equal to _________.
Question 48 :
ABCD is a trapezium in which $AB\parallel DC$ and $\angle A = \angle B = 45^{\circ}$. Find angles C and D of the trapezium
Question 49 :
D and E are the mid-points of the sides AB and AC respectively of $\triangle ABC$. DE is produced to F. To prove that CF is equal and parallel to DA, we need an additional information which is
Question 50 :
ABCD is a rhombus in which altitude from D to side AB bisects AB. Find the $\angle BCD$ of the rhombus.
Question 51 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d155f59b460d7261f423.jpg' />
In the above figure, through A, B and C, lines RQ, PR and QP have been drawn, respectively parallel to sides BC, CA and AB of a ∆ ABC. What would the value of BC?
Question 52 :
ABCD is a parallelogram. If its diagonals are equal, then find the value of $\angle ABC$.
Question 53 :
A class consists of 50 students out of which 30 are girls. The mean of marks scored by girls in a test is 73 (out of 100) and that of boys is 71. Determine the mean score of the whole class.
Question 54 :
In the class intervals 10-20, 20-30, the number 20 is included in :
Question 59 :
State true or false: $(x + y)^3 = x^3 + y^3 + 3xy (x + y)$.
Question 60 :
A right triangle with sides 6 cm, 8 cm and 10 cm is revolved about the side 8 cm. Find the volume of the solid so formed.
Question 61 :
In a cylinder, if radius is halved and height is doubled, the volume will be:
Question 62 :
The students of a Vidyalaya were asked to participate in a competition for making and decorating penholders in the shape of a cylinder with a base, using cardboard. Each penholder was to be of radius 3 cm and height 10.5 cm. The Vidyalaya was to supply the competitors with cardboard. If there were 35 competitors, how much cardboard was required to be bought for the competition?Assume $\pi$ =$\frac{22}{7}$.
Question 63 :
Find the capacity in litres of a conical vessel with radius 7 cm, slant height 25 cm .
Question 64 :
The water for a factory is stored in a hemispherical tank whose internal diameter is 14 m. The tank contains 50 kilolitres of water. Water is pumped into the tank to fill to its capacity. Calculate the volume of water pumped into the tank.
Question 65 :
In triangles ABC and DEF, AB = FD and $∠$A = $∠$D. The two triangles will be congruent by SAS axiom if
Question 66 :
State true or false: ABCD is a quadrilateral such that AB = AD and CB = CD. Also, AC is the perpendicular bisector of BD.
Question 67 :
If AB = QR, BC = PR and CA = PQ, then
Question 68 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d246f59b460d7261f57e.PNG' />
In the above fig, AB is a line segment and line $l$ is its perpendicular bisector. If a point P lies on $l$, is the point P equidistant from A and B?
Question 69 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d249f59b460d7261f582.PNG' />
In the above fig, line-segment AB is parallel to another line-segment CD. O is the mid-point of AD. Is O the mid point of BC?
Question 70 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d195f59b460d7261f47f.PNG' />
In the above fig, D and E are two points on BC such that BD = DE = EC. Is $ar\left(ABD\right)=ar\left(ADE\right)=ar\left(AEC\right)$?
Question 71 :
Diagonals AC and BD of a trapezium ABCD with $AB\parallel DC$ intersect each other at O. Is $ar\left(AOD\right)=ar\left(BOC\right)$?
Question 72 :
Yamini and Fatima, two students of Class IX of a school, together contributed Rs 100 towards the Prime Minister’s Relief Fund to help the earthquake victims. Write a linear equation which satisfies this data.
Question 73 :
If the work done by a body on application of a constant force is directly proportional to the distance travelled by the body. What is the work done when the distance travelled by the body is 0 unit? Take the constant force as 5 units.
Question 74 :
State true or false: Theorems are statements which are proved, using definitions, axioms, previously proved statements and deductive reasoning.
Question 75 :
State true or false: Every line segment has one and only one mid-point.
Question 76 :
If the sum of two adjacent angles is 180°, then the non-common arms of the angles form a line. Is it true?
Question 77 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61cc1ad978c526e972caf08d.PNG' />
In the above fig, if $PQ \parallel ST$, $\angle PQR = 110^{\circ}$ and $\angle RST = 130^{\circ}$, find $\angle QRS$.
Question 79 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d1f1f59b460d7261f503.JPG' />
Refer to the above image. Fifty seeds were selected at random from each of 5 bags of seeds, and were kept under standardised conditions favourable to germination. After 20 days, the number of seeds which had germinated in each collection were counted and recorded in the above image. What is the probability of germination of more that 35 seeds in a bag?
Question 80 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d1eaf59b460d7261f4fa.JPG' />
From above the image Consider the frequency distribution table which gives the weights of 38 students of a class. Find the probability of a student weighing more than 30 kg.
