Question 1 :
State True / False, by geometrical construction, it is possible to divide a line segment in the ratio $\begin{array}{l}2+\sqrt{3}:2-\sqrt{3}\end{array}$.
Question 2 :
Can we construct as many concentric circles as we want to a given circle?
Question 3 :
If an isosceles triangle ABC, in which AB = AC = 6 cm, is inscribed in a circle of radius 9 cm, what is the area of the triangle?
Question 4 :
State true or false. Construction of a triangle similar to a given triangle as per given scale factor which may be less than 1 or greater than 1 is possible.
Question 5 :
To construct a triangle similar to a given ∆ABC with its sides $\frac{3}{7}$ of the corresponding sides of ∆ABC, first draw a ray BX such that ∠CBX is an acute angle and X lies on the opposite side of A with respect to BC. Then locate points $B_1,B_2,B_3,.........$ on BX at equal distances and next step is to join
Question 6 :
On a square cardboard sheet of area 784 $cm^2$, four congruent circular plates of maximum size are placed such that each circular plate touches the other two plates and each side of the square sheet is tangent to two circular plates. Find the area of the square sheet not covered by the circular plates.
Question 7 :
The wheels of a car are of diameter 80 cm. How many complete revolutions does each wheel make in 10 minutes when the car is travelling at a speed of 66 km per h?
Question 8 :
If the perimeter of a circle is equal to that of a square, then the ratio of their areas is
Question 9 :
All the vertices of a rhombus lie on a circle. Find the area of the rhombus, if area of the circle is $1256\ cm^2$ (Use $\pi=3.14$).
Question 10 :
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 11 :
If $\sec 4A = cosec\ \begin{pmatrix}A – 20^{\circ}\end{pmatrix}$, where 4A is an acute angle, find the value of A.
Question 15 :
$\sin 2A = 2 \sin A$ is true when A is equal to
Question 16 :
Solve the following pair of equations by reducing them to a pair of linear equations : $\frac{2}{\sqrt{x}} + \frac{3}{\sqrt{y}} = 2 ; \frac{4}{\sqrt{x}} - \frac{9}{\sqrt{y}} = -1$.
Question 17 :
Akhila goes to a fair with Rs. 20 and wants to have rides on the Giant Wheel and play Hoopla. The number of times she played hoopla is half the number of times she went on giant wheel. Which of these represent this situation algebraically ?
Question 18 :
The difference between two numbers is 26 and one number is three times the other. Find them.
Question 19 :
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 intersect at a point, are parallel or coincident: $9x + 3y + 12 = 0 ; 18x + 6y + 24 = 0$
Question 20 :
10 students of Class X took part in a Mathematics quiz. If the number of girls is 4 more than the number of boys, find the number of boys and girls who took part in the quiz. Find the solution graphically.
Question 21 : <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 22 :
A 1.5 m tall boy is standing at some distance from a 30 m tall building. The angle of elevation from his eye to the top of the building increases from 30° to 60° as he walks tonwards the building. Find the distance he walked tonwards the building.
Question 23 :
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 24 :
The angle of elevation of the top of a building from the foof of the tower is 30° and the angle of elevation of the top of the tower from the foof of building is 60°. If the tower is 50 m high, then find the height of the building.
Question 25 :
Two poless of equal heights are standing opposite to each ofher on either side of the road, which is 80 m wide. From a point between them on the road, the Angles of elevation of the top of the poless are 60° and 30°, respectively. Find the distances of the point from the poless.
Question 27 :
(7 × 11 × 13 + 13) and (7 × 6 × 5 × 4 × 3 × 2 × 1 + 5) are composite numbers. TRUE or FALSE ?
Question 28 :
Find the LCM and HCF of the following integer by applying the prime factorisation method: 12, 15 and 21
Question 29 :
Without actually performing the long division, state whether $\frac{77}{210}$ will have a terminating decimal expansion or a non-terminating repeating decimal expansion.
Question 30 :
A positive integer is of the form 3q + 1, q being a natural number. Can you write its square in any form other than 3m + 1, i.e., 3m or 3m + 2 for some integer m?
Question 31 :
If number of observations(n) is odd, then median equals _______ observation?
Question 32 : <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 33 : <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 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='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c21273b230584979a7e.PNG' />
During the medical check-up of 35 students of a class, their weights were recorded as given above. Draw a less than type ogive for the given data and choose the median weight using the graph.
Question 36 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c55273b230584979abb.PNG' />
In the above fig, DE || AC and DF || AE. Is $\frac{BF}{FE}$ = $\frac{BE}{EC}$ ?
Question 37 :
Diagonals of a trapezium PQRS intersect each other at the point O, PQ is parallel to RS and PQ = 3 RS. Find the ratio of the areas of triangles POQ and ROS.
Question 38 : <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 39 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c6f273b230584979ada.PNG' />
In the above fig, ABC is a triangle in which ∠ABC > 90° and AD ⊥ CB produced. Is $AC^2$ = $AB^2 + BC^2 + 2 BC . BD$ ?
Question 41 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b34273b230584979953.jpg' />
In the above figure, a square is inscribed in a circle of diameter d and another square is circumscribing the circle. Is the area of outer square 4 times the area of inner square ?
Question 42 :
State True or False: Area of segment of a circle = area of the corresponding sector - area of the corresponding triangle.
Question 43 :
A chord of a circle of radius 15 cm subtends an angle of $60^{\circ}$ at the centre. Find the area of the corresponding major segment of the circle. (Use $\pi$= 3.14 and $\sqrt{3}$ = 1.73)
Question 44 :
In a circle of radius 21 cm , an arc subtends an angle of $60^{\circ}$ at the centre. Find area of the sector formed by the arc.
Question 45 :
The diameters of front and rear wheels of a tractor are 80 cm and 2 m respectively. Find the number of revolutions that rear wheel will make in covering a distance in which the front wheel makes 1400 revolutions.
Question 46 :
In a right circular cone, the cross-section made by a plane parallel to the base is a
Question 47 :
In one fortnight of a given month, there was a rainfall of 10 cm in a river valley. If the area of the valley is 7280 $km^2$, check whether the total rainfall is approximately equivalent to the addition to the the normal water of three rivers each 1072 km long, 75 m wide and 3 m deep .
Question 48 :
The diameters of the two circular ends of the bucket are 44 cm and 24 cm. The height of the bucket is 35 cm. The capacity of the bucket is
Question 49 :
A metallic right circular cone 20 cm high and whose vertical angle is $60^{\circ}$, is cut into two parts at the middle of its height by a plane parallel to its base. If the frustum so obtained be drawn into a wire of diameter $\frac{1}{16}$ cm, then find the length of the wire.
Question 50 :
A cubical ice cream brick of edge 22 cm is to be distributed among some children by filling ice cream cones of radius 2 cm and height 7 cm upto its brim. How many children will get the ice cream cones?
Question 51 :
The distance of a point from the y-axis is called its x-coordinate, or abscissa. TRUE or FALSE ?
Question 52 :
Name the type of quadrilateral formed, if any, by the following points (4,5) , (7,6) , (4,3) , (1,2).
Question 53 :
Name the type of triangle formed by the points $\left(5, – 2\right)$, $\left(6, 4\right)$ and $\left(7, – 2\right)$.
Question 54 :
Find the point on the x-axis which is equidistant from $\left(2, –5\right)$ and $\left(–2, 9\right)$.
Question 55 :
Point P (0, –7) is the point of intersection of y-axis and perpendicular bisector of line segment joining the points A (–1, 0) and B (7, –6). State true or false.
