Question 1 :
Can we divide a line segment in a ratio m : n, where both m and n are positive integers ?
Question 2 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b53273b23058497997c.PNG' />
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 3 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b55273b23058497997f.PNG' />
In the above figure, The tangent at a point C of a circle and a diameter AB when extended intersect at P. If $\angle PCA=110^{\circ}$ , what is the value of $\angle CBA$?
Question 4 :
Two tangents PQ and PR are drawn from an external point to a circle with centre O. Is QORP is a cyclic quadrilateral?
Question 5 :
Draw an equilateral triangle ABC of each side 4 cm. Construct a triangle similar to it and of scale factor $\frac{3}{5}$ . Is the new triangle also an equilateral?
Question 6 :
Solve the following pair of linear equations by the substitution method : $0.2x + 0.3y = 1.3 ; 0.4x + 0.5y = 2.3$
Question 7 :
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 are consistent or inconsistent: $3x + 2y = 5 ; 2x – 3y = 7$
Question 8 :
A part of monthly hostel charges is fixed and the remaining depends on the number of days one has taken food in the mess. When a student A takes food for 20 days she has to pay Rs. 1000 as hostel charges whereas a student B, who takes food for 26 days, pays Rs. 1180 as hostel charges. Find the fixed charges and the cost of food per day.
Question 9 :
If we add 1 to the numerator and subtract 1 from the denominator, a fraction reduces to 1. It becomes $\frac{1}{2}$ if we only add 1 to the denominator. What is the fraction?
Question 10 :
For which values of a and b does the following pair of linear equations have an infinite number of solutions? $2x + 3y = 7 ; (a – b) x + (a + b) y = 3a + b – 2$
Question 13 :
$\cos 38^{\circ} \cos 52^{\circ} – \sin 38^{\circ} \sin 52^{\circ} \ne 0$. TRUE or FALSE?
Question 16 :
State true or false: The sum or difference of a rational and an irrational number is irrational.
Question 17 :
Use Euclid's division algorithm to find the HCF of : 135 and 225
Question 19 :
What are the LCM and HCF of 8, 9 and 25?
Question 21 :
The area of a triangle with vertices A (3, 0), B (7, 0) and C (8, 4) is :
Question 22 :
If (– 4, 3) and (4, 3) are two vertices of an equilateral triangle, find the coordinates of the third vertex, given that the origin lies in the interior of the triangle.
Question 23 :
The fourth vertex D of a parallelogram ABCD whose three vertices are A (–2, 3), B (6, 7) and C (8, 3) is :
Question 24 :
Find the value of ‘k’, for which the points $\left(7, -2\right)$, $\left(5, 1\right)$ and $\left(3, k\right)$ are collinear
Question 25 :
A circle drawn with origin as the centre passes through ($\frac {13}{2}$,0). The point which does not lie in the interior of the circle is :
Question 26 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b36273b230584979955.jpg' />
In the above figure, dimensions are given. Find the area of the flower bed (with semi-circular ends).
Question 27 :
Area of a sector of a circle of radius 36 cm is 54 $\pi\ cm^2$ . Find the length of the corresponding arc of the sector.
Question 28 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b38273b230584979957.jpg' />
In the above figure, dimensions are given. Find the area of the shaded field.
Question 29 :
State True or False: Area of segment of a circle = area of the corresponding sector - area of the corresponding triangle.
Question 30 :
Sides of a triangular field are 15 m, 16 m and 17 m. With the three corners of the field a cow, a buffalo and a horse are tied separately with ropes of length 7 m each to graze in the field. Find the area of the field which cannot be grazed by the three animals.
Question 31 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bfc273b230584979a54.PNG' />
The marks obtained by 30 students of Class X of a certain school in a Mathematics paper consisting of 100 marks are presented in table above. Find the mean of the marks obtained by the students
Question 32 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c15273b230584979a71.PNG' />
The above given frequency distribution gives the monthly consumption of electricity of 68 consumers of a locality. Find the median.
Question 33 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c14273b230584979a6f.PNG' />
The above given frequency distribution gives the monthly consumption of electricity of 68 consumers of a locality. Find the mean.
Question 34 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c11273b230584979a6c.PNG' />
The above data gives the distribution of total monthly household expenditure of 200 families of a village. Find the mean monthly expenditure.
Question 35 : <img style='object-fit:contain' src='61b19aa7273b23058497993c' />
The above table gives the literacy rate (in percentage) of 35 cities. Find the mean literacy rate.
Question 36 :
The volume of the largest right circular cone that can be cut out from a cube of edge 4.2 cm is
Question 37 :
A bucket is in the form of a frustum of a cone and holds 28.490 litres of water.The radii of the top and bottom are 28 cm and 21 cm, respectively. Find the height of the bucket
Question 38 :
A copper wire, 3 mm in diameter, is wound about a cylinder whose length is 12 cm, and diameter 10 cm, so as to cover the curved surface of the cylinder. Find the mass of the wire, assuming the density of copper to be 8.88 g per $cm^3$.
Question 39 :
A container shaped like a right circular cylinder having diameter 12 cm and height 15 cm is full of ice cream. The ice cream is to be filled into cones of height 12 cm and diameter 6 cm, having a hemispherical shape on the top. Find the number of such cones which can be filled with ice cream.
Question 40 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c32273b230584979a91.JPG' />
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 41 :
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 42 : <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 43 :
A contractor plans to install two slides for the children to play in a park. For the children below the age of 5 yr, she prefers to have a slide whose top is at a height of 1.5 m and is inclined at an angle of 30° 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° to the ground. What should be the length of the slides in each case?
Question 44 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19a60273b230584979931.jpeg' />
In the above image, a circus artist is climbing a 20 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole, if the angle made by the rope with ground level is 30°.
Question 45 :
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 46 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19ba5273b2305849799e7.png' />
If in the figure, PA, QB, RC and SD are all perpendiculars to a line l, AB = 6 cm, BC = 9 cm, CD = 12 cm and SP = 36 cm. Find RS.
Question 48 :
An aeroplane leaves an airport and flies due north at a speed of 1000 km per hour. At the same time, another aeroplane leaves the same airport and flies due west at a speed of 1200 km per hour. How far apart will be the two planes after 1.5 hours?
Question 49 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c6b273b230584979ad5.PNG' />
In the above fig, O is a point in the interior of a triangle ABC, OD ⊥ BC, OE ⊥AC and OF ⊥AB. Is $OA^2 + OB^2 + OC^2 – OD^2 – OE^2 – OF^2$ = $AF^2 + BD^2 + CE^2$ ?
Question 50 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c72273b230584979add.PNG' />
In the above fig, AD is a median of a triangle ABC and AM ⊥ BC. Is $AC^2 + AB^2$ = $2AD^2 + \frac{1}{2} BC^{2}$?
Question 51 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19baf273b2305849799f4.png' />
The above image depicts an archery target marked with its five scoring regions from the centre outwards as Gold, Red, Blue, Black and White. The diameter of the region representing Gold score is 21 cm and each of the other bands is 10.5 cm wide. Find the area of the black scoring region.
Question 52 :
In covering a distance s metres, a circular wheel of radius r metres makes $\frac{s}{2\pi r}$ revolutions. Is it true or false?
Question 53 :
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 54 :
A circular pond is 17.5 m of diameter. It is surrounded by a 2 m wide path. Find the cost of constructing the path at the rate of Rs. 25 per $m^2$.
Question 55 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19a48273b230584979913.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 white scoring region.
