Question 1 :
Draw two concentric circles of radii 3 cm and 5 cm. Taking a point on outer circle construct the pair of tangents to the other. Measure the length of a tangent and verify it by actual calculation.
Question 2 :
Scale factor means the ratio of the sides of the triangle to be constructed with the corresponding sides of the given triangle . State whether the above statement is TRUE or FALSE ?
Question 3 :
To draw a pair of tangents to a circle which are inclined to each other at an angle of 35$^{\circ}$, it is required to draw tangents at the end points of those two radii of the circle, the angle between which is ( in degrees)?
Question 4 :
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 5 :
If a point lies inside a circle, there can be a tangent to the circle through this point . State whether the above statement is TRUE or FALSE ?
Question 6 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bd4273b230584979a25.JPG' />
To conduct Sports Day activities, in your rectangular shaped school ground ABCD, lines have been drawn with chalk powder at a distance of 1 m each. 100 flower pots have been placed at a distance of 1 m from each other along AD, as shown in the above image. Niharika runs $\frac{1}{4}$ th the distance AD on the 2nd line and posts a green flag. Preet runs $\frac{1}{5}$ th the distance AD on the eighth line and posts a red flag. What is the distance between both the flags?
Question 7 :
The line segment joining the points A (3, 2) and B (5,1) is divided at the point P in the ratio 1: 2 and it lies on the line 3x – 18y + k = 0. Find the value of k.
Question 8 :
AOBC is a rectangle whose three vertices are vertices A (0, 3), O (0, 0) and B (5, 0). The length of its diagonal is :
Question 9 :
If Q $\left(0, 1\right)$ is equidistant from P $\left(5, –3\right)$ and R $\left(4, 6\right)$. Find the distance PR.
Question 10 :
Find the coordinates of the points of trisection of the line segment joining $\left(4, -1\right)$ and $\left(-2, -3\right)$.
Question 11 :
(1 + tan θ + sec θ) (1 + cot θ – cosec θ) = ____
Question 12 :
If A, B and C are interior angles of a triangle ABC, then $\sin\begin{pmatrix}\frac{B+C}{2}\end{pmatrix}\ne\cos\begin{pmatrix}\frac{A}{2}\end{pmatrix}$. TRUE or FALSE ?
Question 15 :
$\cos 38^{\circ} \cos 52^{\circ} – \sin 38^{\circ} \sin 52^{\circ} \ne 0$. TRUE or FALSE?
Question 16 :
Find the nature of the roots of the quadratic equation $2x^2 – 4x + 3 = 0$.
Question 17 :
Justify why the following quadratic equation has no two distinct real roots: $x\left(1-x\right)-2=0$
Question 18 :
Find the roots of the quadratic equations, if they exist, by applying quadratic formula: $2x^2 + x – 4 = 0$
Question 19 :
State True or False: Every quadratic equation has at least one real root.
Question 20 :
State True or False whether the following quadratic equation has two distinct real roots: $3x^2-4x+1=0$
Question 21 :
Use Euclid's division algorithm to find the HCF of : 196 and 38220
Question 26 :
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 27 :
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 height of the poless.
Question 28 :
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 29 :
From the top of a 7 m high building, the angle of elevation of the top of a cable tower is 60° and the angle of depression of its foof is 45°. Determine the height of the tower.
Question 30 : <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 31 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c18273b230584979a74.PNG' />
The distribution below gives the weights of 30 students of a class. Find the median weight of the students.
Question 32 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c04273b230584979a5d.PNG' />
Consider the above distribution of daily wages of 50 workers of a factory. Find the mean daily wages of the workers of the factory by using an appropriate method.
Question 33 : <img style='object-fit:contain' src='61b19a62273b230584979934' />
A class teacher has the above absentee record of 40 students of a class for the whole term. Find the mean number of days a student was absent.
Question 34 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bfd273b230584979a55.PNG' />
The table above gives the percentage distribution of female teachers in the primary schools of rural areas of various states and union territories (U.T.) of India. Find the mean percentage of female teachers.
Question 35 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c1a273b230584979a77.PNG' />
A life insurance agent found the above data for distribution of ages of 100 policy holders. Calculate the median age, if policies are given only to persons having age 18 years onwards but less than 60 year.
Question 36 :
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 37 :
Solve the following pair of linear equations: $\frac{x}{a} - \frac{y}{b} = 0 ; ax + by = a^2 + b^2$
Question 38 :
Solve the following pair of equations by reducing them to a pair of linear equations : $\frac{4}{x} + 3y = 14 ; \frac{3}{x} - 4y =23 $.
Question 39 :
Five years ago, Nuri was thrice as old as Sonu. Ten years later, Nuri will be twice as old as Sonu. How old are Nuri and Sonu?
Question 40 :
The area of a rectangle gets reduced by 9 square units, if its length is reduced by 5 units and breadth is increased by 3 units. If we increase the length by 3 units and the breadth by 2 units, the area increases by 67 square units. Find the dimensions of the rectangle.
Question 41 :
A cone of radius 4 cm is divided into two parts by drawing a plane through the mid point of its axis and parallel to its base. Compare the volumes of the two parts.
Question 42 :
A cubical block of side 7 cm is surmounted by a hemisphere.Find the surface area of the solid.
Question 43 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c36273b230584979a96.JPG' />
In the above image, an open metal bucket is in the shape of a frustum of a cone, mounted on a hollow cylindrical base made of the same metallic sheet (see the above image). The diameters of the two circular ends of the bucket are 45 cm and 25 cm, the total vertical height of the bucket is 40 cm and that of the cylindrical base is 6 cm. Find the volume of water bucket can hold.Take $\pi$ = $\frac{22}{7}$ .
Question 44 :
A right circular cylinder of radius r cm and height h cm (h>2r) just encloses a sphere of diameter
Question 45 :
Three metallic solid cubes whose edges are 3 cm, 4 cm and 5 cm are melted and formed into a single cube. Find the edge of the cube so formed.
Question 46 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b35273b230584979954.jpg' />
In the above figure, a square of diagonal 8 cm is inscribed in a circle. Find the area of the shaded region.
Question 47 : <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 48 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b37273b230584979956.jpg' />
In the above figure, AB is the diameter of the circle, AC = 6 cm and BC = 8 cm. Find the area of the shaded region (Use $\pi=3.14$).
Question 49 :
In a circle of radius 21 cm , an arc subtends an angle of $60^{\circ}$ at the centre. Find the length of the arc.
Question 50 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bb3273b2305849799fa.png' />
In the above figure , an umbrella has 8 ribs which are equally spaced . Assuming umbrella to be a flat circle of radius 45 cm , find the area between the two consecutive ribs of the umbrella.
Question 51 :
A guy wire attached to a vertical pole of height 18 m is 24 m long and has a stake attached to the other end. How far from the base of the pole should the stake be driven so that the wire will be taut?
Question 52 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c55273b230584979aba.PNG' />
In the above fig, if LM || CB and LN || CD, Is $\frac{AM}{AB}$ = $\frac{AN}{AD}$ ?
Question 53 :
If AD and PM are medians of triangles ABC and PQR, respectively where ∆ ABC ~ ∆ PQR, Is $\frac{AB}{PQ}$ = $\frac{AD}{PM}$ ?
Question 54 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c66273b230584979acf.PNG' />
In the above fig, sides AB and BC and median AD of a triangle ABC are respectively proportional to sides PQ and QR and median PM of ∆ PQR. Is ∆ABC ~ ∆PQR ?
Question 55 :
Hypotenuse of a right triangle is 25 cm and out of the remaining two sides, one is longer than the other by 5 cm. Find the lengths of the other two sides.
