Question 1 :
The points (0, 5), (0, –9) and (3, 6) are collinear. State true or false.
Question 2 :
Find the coordinates of the points of trisection of the line segment joining $\left(4, -1\right)$ and $\left(-2, -3\right)$.
Question 3 :
The tangent at any point of a circle is perpendicular to the radius through the point of contact . TRUE or FALSE ?
Question 5 :
A tangent to a circle is a line that intersects the circle at only one point . TRUE or FALSE ?
Question 6 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19a49273b230584979914.PNG' />
In the above figure, if TP and TQ are the two tangents to a circle with centre O so that ∠ POQ = 110°, then ∠ PTQ is equal to
Question 7 :
The tangents drawn at the ends of a diameter of a circle are ______.
Question 8 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19a56273b230584979924.png' />
In the image 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 9 :
What are the LCM and HCF (by prime factorisation method) of 96 and 404?
Question 10 :
Choose the correct answer from the given four options in the question: The product of a non-zero rational and an irrational number is _______ .
Question 11 :
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 12 :
State true or false: The sum or difference of a rational and an irrational number is irrational.
Question 14 : <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 15 :
A cubical block of side 7 cm is surmounted by a hemisphere.Find the surface area of the solid.
Question 17 :
Volumes of two spheres are in the ratio 64:27. The ratio of their surface areas is
Question 18 :
2 cubes each of volume 64 $cm^3$ are joined end to end. Find the surface area of the resulting cuboid.
Question 19 :
A chord of a circle of radius 10 cm subtends a right angle at the centre. Find the area of the corresponding minor segment.(Use $\pi$ =3.14)
Question 20 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bb7273b2305849799fe.png' />
In the above figure , find the area of the shaded region if ABCD is a square of side 14 cm and APD and BPC are semicircles.
Question 21 :
If the circumferences of two circles are equal, then their areas are also equal. Is it true or false?
Question 22 :
A circular park is surrounded by a road 21 m wide. If the radius of the park is 105 m, find the area of the road.
Question 23 :
The area of the square that can be inscribed in a circle of radius 8 cm is
Question 25 :
Let ∆ ABC ~ ∆ DEF and their areas be, respectively, 64 $cm^2$ and 121 $cm^2$ . If EF = 15.4 cm, find BC.
Question 26 :
Find the sum of the following AP: 34 + 32 + 30 + . . . + 10
Question 27 :
Find the sum of the first 40 positive integers divisible by 6.
Question 29 :
In an AP, given $a_{12} = 37, d = 3$, find a and $S_{12}$.
Question 30 :
30th term of the AP: 10, 7, 4, . . . , is
Question 31 :
The line drawn from the eye of an observer to the point in the object viewed by the observer , is known as ________
Question 32 :
The shadow of a tower standing on a level ground is found to be 40 m longer when the Sun’s altitude is $30^{\circ}$ than when it is $60^{\circ}$. Find the height of the tower.
Question 33 :
The angles of depression of the top and the bottom of an 8 m tall building from the top of a multi-storeyed building are $30^{\circ}$ and $45^{\circ}$, respectively. Find the height of the multi-storeyed building and the distance between the two buildings respectively.
Question 34 :
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 35 :
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 36 :
An AP consists of 50 terms of which 3rd term is 12 and the last term is 106. Find the 29th term.
Question 37 :
If the sum of the first n terms of an AP is $4n – n^2$, What is the 3rd term ?
Question 38 :
In an AP, given $a = 3, n = 8, S = 192$, find d.
Question 39 :
In an AP, given $a = 7, a_{13} = 35$, find d and $S_{13}$.
Question 40 :
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.
