Question 1 :
To construct a triangle similar to a given ∆ABC with its sides $\frac{8}{5}$ of the corresponding sides of ∆ABC draw a ray BX such that ∠CBX is an acute angle and X is on the opposite side of A with respect to BC. The minimum number of points to be located at equal distances on ray BX is
Question 2 :
A chord PQ of a circle is parallel to the tangent drawn at a point R of the circle. Does R bisects the arc PRQ?
Question 3 :
If a circle touches the side BC of a triangle ABC at P and extended sides AB and AC at Q and R, respectively, Is it TRUE or FALSE that $AQ = \frac { 1 } { 2 } ( BC + CA + AB )$.
Question 4 :
State True / False, to construct a triangle similar to a given ∆ABC with its sides $\frac{7}{3}$ of the corresponding sides of ∆ABC, draw a ray BX making acute angle with BC and X lies on the opposite side of A with respect to BC. The points $B_1 , B_2 , ...., B_7$ are located at equal distances on $BX, B_3$ is joined to C and then a line segment $B_6C'$ is drawn parallel to $B_3C$ where C' lies on BC produced. Finally, line segment A'C' is drawn parallel to AC.
Question 5 :
Draw a line segment of length 7.6 cm and divide it in the ratio 5:8. Measure the two parts.
Question 6 :
State True or False: Area of segment of a circle = area of the corresponding sector - area of the corresponding triangle.
Question 7 :
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 8 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bbd273b230584979a06.png' />
The area of an equilateral triangle ABC is 17320.5 $cm^{2}$ . With each vertex of the triangle as centre, a circle is drawn with radius equal to half the length of the side of the triangle (see the above image). Find the area of the shaded region. (Use $\pi$= 3.14 and $\sqrt{3}$ = 1.73205)
Question 9 :
Tick the correct answer in the following and justify your choice. If the perimeter and the area of a circle are numerically equal, then the radius of the circle is
Question 10 :
If the sum of the areas of two circles with radii $R_1$ and $R_2$ is equal to the area of a circle of radius $R$, then
Question 11 :
Find the coordinates of a point A, where AB is the diameter of a circle whose centre is $\left(2, – 3\right)$ and B is $\left(1, 4\right)$.
Question 12 :
Find the ratio in which the y-axis divides the line segment joining the points $\left(5, – 6\right)$ and $\left(–1, – 4\right)$.
Question 13 :
The points A (2, 9), B (a, 5) and C (5, 5) are the vertices of a triangle ABC right angled at B. Find the values of a and hence the area of ∆ABC.
Question 14 :
What is the distance between two points P ($x_1,y_1$) and Q ($x_2,y_2$) ?
Question 15 :
Find the coordinates of the points of trisection of the line segment joining $\left(4, -1\right)$ and $\left(-2, -3\right)$.
Question 16 :
The cost of 4 pens and 4 pencil boxes is Rs 100. Three times the cost of a pen is Rs 15 more than the cost of a pencil box. Form the pair of linear equations for the above situation. Find the cost of a pencil box.
Question 17 :
If the lines are represented by the equation $a_1x + b_1y + c_1 =0$ and $a_2x + b_2y + c_2 =0$, then the lines are coinciding when _____________.
Question 18 :
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: $6x – 3y + 10 = 0 ; 2x – y + 9 = 0$
Question 19 :
Draw the graphs of the equations 5x – y = 5 and 3x – y = 3. Determine the co-ordinates ofthe vertices of the triangle formed by these lines and the y axis.
Question 20 :
Solve the following pair of linear equations by the elimination method and the substitution method : $\frac{x}{2}+\frac{2y}{3}=-1 ~and~ x-\frac{y}{3}=3$
Question 22 :
(sec A + tan A) (1 – sin A) = ______
Question 24 :
The value of $\cos \theta$ increases as $\theta$ increases. True or False?
Question 25 :
Is this equality correct ? $\frac{tan A}{1- cotA} + \frac{cotA}{1-tanA}= 1+ secAcosecA$
Question 26 :
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 27 :
The Angles of elevation of the top of a tower from two points at a distance of 4 m and 9 m from the base of the tower and in the same straight line with it are complementary. Find the height of the tower.
Question 28 : <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 29 :
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 30 :
From a point on the ground, the angles of elevation of the bottom and the top of a transmission tower fixed at the top of a 20 m high building are $45^\circ and 60^\circ$, respectively. Find the height of the tower.
Question 31 :
State true or false: From the fundamental theorem of arithmetic, we can say that every composite number can be expressed as a product of primes.
Question 32 :
Without actually performing the long division, state whether $\frac{129}{2^25^77^5}$ will have a terminating decimal expansion or a non-terminating repeating decimal expansion.
Question 33 :
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 34 :
There is a circular path around a sports field. Sonia takes 18 minutes to drive one round of the field, while Ravi takes 12 minutes for the same. Suppose they both start at the same point and at the same time, and go in the same direction. After how many minutes will they meet again at the starting point?
Question 35 :
The least number that is divisible by all the numbers from 1 to 10 (both inclusive) is _____ .
Question 36 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c17273b230584979a73.PNG' />
100 surnames were randomly picked up from a local telephone directory and the frequency distribution of the number of letters in the English alphabets in the surnames was obtained as given above. Determine the median number of letters in the surnames.
Question 38 :
The wickets taken by a bowler in 10 cricket matches are as follows: 2, 6 ,4 ,5, 0, 2, 1, 3, 2, 3. Find the mode of the data.
Question 39 : <img style='object-fit:contain' src='61b19a74273b230584979936' />
The table above shows the daily expenditure on food of 25 households in a locality. Find the mean daily expenditure on food by a suitable method.
Question 40 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c09273b230584979a63.PNG' />
The above distribution shows the daily pocket allowance of children of a locality. The mean pocket allowance is Rs 18. Find the missing frequency $f$.
Question 41 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c41273b230584979aa2.PNG' />
Are the two figures shown above similar ?
Question 42 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c53273b230584979ab8.PNG' />
In the above fig, (i) and (ii), DE || BC. Find EC in (i).
Question 43 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c41273b230584979aa3.PNG' />
Are the two figures shown above similar ?
Question 44 :
A ladder 10 m long reaches a window 8 m above the ground. Find the distance of the foot of the ladder from base of the wall.
Question 45 :
I - All congruent figures are similar.
II - All similar figures are congruent.
Which of these is correct ?
Question 46 :
A medicine-capsule is in the shape of a cylinder of diameter 0.5 cm with two hemispheres stuck to each of its ends. The length of entire capsule is 2 cm. The capacity of the capsule is
Question 47 :
How many spherical lead shots of diameter 4 cm can be made out of a solid cube of lead whose edge measures 44 cm.
Question 48 :
A heap of rice is in the form of a cone of diameter 9 m and height 3.5 m. How much canvas cloth is required to just cover the heap?
Question 49 :
What is the formulae for total surface area of the frustum of the solid cone? (where l=slant height of frustum, $r_1$ and $r_2$ are radii of the two bases (ends) of the frustum)
Question 50 :
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 51 :
A piece of wire 20 cm long is bent into the form of an arc of a circle subtending an angle of $60^{\circ}$ at its centre. Find the radius of the circle.
Question 52 :
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 53 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b3b273b23058497995c.jpg' />
In the above figure, arcs have been drawn of radius 21 cm each with vertices A, B, C and D of quadrilateral ABCD as centres. Find the area of the shaded region.
Question 54 :
The radius of a circle whose circumference is equal to the sum of the circumferences of the two circles of diameters 36 cm and 20 cm is
Question 55 :
Is the area of the largest circle that can be drawn inside a rectangle of length $a\ cm$ and breadth $b\ cm$ $\left(a>b\right)$ is $\pi\ b^2\ cm^2$ ?
