Question 1 :
Find the area of a triangle whose vertices are $\left(1, –1\right)$, $\left(– 4, 6\right)$ and $\left(–3, –5\right)$.
Question 2 :
Find the value of m if the points (5, 1), (–2, –3) and (8, 2m) are collinear.
Question 3 :
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.
Question 4 :
What are the coordinates of the point P which divides the line segment joining the points A ($x_1, y_1$) and B ($x_2, y_2$) internally in the ratio $m_1 : m_2$ ?
Question 5 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19a4c273b230584979918.PNG' />
Look at the above image. In a classroom, 4 friends are seated at the points A, B, C and D as shown in figure. Champa and Chameli walk into the class and after observing for a few minutes, Champa asks Chameli, 'Don't you think ABCD is a square?', Chameli disagrees. Using distance formula, find which of them is correct.
Question 6 :
Two line segments AB and AC include an angle of 60$^{\circ}$ where AB = 5 cm and AC = 7 cm. Locate points P and Q on AB and AC, respectively such that AP = $\frac{3}{4}$ AB and AQ = $\frac{1}{4}$ AC. Join P and Q and measure the length PQ.
Question 7 :
In a right triangle ABC in which $\angle B = 90^{\circ}$, a circle is drawn with AB as diameter intersecting the hypotenuse AC and P. Does the tangent to the circle at P bisects BC?
Question 8 :
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 9 :
Draw a line segment of length 7.6 cm and divide it in the ratio 5:8. Measure the two parts.
Question 10 :
Do the tangents drawn at the ends of a chord of a circle make equal angles with the chord?
Question 11 :
A calf is tied with a rope of length 6 m at the corner of a square grassy lawn of side 20 m. If the length of the rope is increased by 5.5 m, find the increase in area of the grassy lawn in which the calf can graze.
Question 12 :
Is the area of the circle inscribed in a square of side $a\ cm$, $\pi a^2\ cm^2$ ?
Question 13 :
The area of a segment of a circle is less than the area of its corresponding sector. Is it true or false?
Question 14 :
Find the diameter of the circle whose area is equal to the sum of the areas of the two circles of diameters 20 cm and 48 cm.
Question 15 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bac273b2305849799f0.png' />
Find the area of the shaded design in the above figure, where ABCD is a square of side 10 cm and semicircles are drawn with each side of the square as diameter. (Use $\pi$= 3.14)
Question 17 :
If $\sec 4A = cosec\ \begin{pmatrix}A – 20^{\circ}\end{pmatrix}$, where 4A is an acute angle, find the value of A.
Question 20 :
Is $(sin A + cosec A)^2 + (cos A + sec A)^2 = 7 + tan^2 A + cot^2 A$?
Question 21 :
Solve the following pair of equations by reducing them to a pair of linear equations : $\frac{7x-2y}{xy} = 5 ; \frac{8x+7y}{xy} = 15$.
Question 22 :
Given the linear equation 2x + 3y – 8 = 0, write another linear equation in two variables such that the geometrical representation of the pair so formed are coincident lines.
Question 23 :
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 24 :
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 25 :
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 27 :
The cube of any positive integer is of the form 4m, 4m + 1 or 4m + 3, for some integer m. Is it true?
Question 29 :
A/An ________ is a proven statement used for proving another statement.
Question 30 :
Given that HCF (306, 657) = 9, find LCM (306, 657).
Question 31 :
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 32 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19a62273b230584979933.jpeg' />
In the above image, a 1.2 m tall girl spofs a balloon moving with the wind in a horizontal line at a height of 88.2 m from the ground. The angle of elevation of the balloon from the eyes of the girl at any instant is 60°. After sometime, the angle of elevation reduces to 30°. Find the distance travelled by the balloon during the interval.
Question 33 :
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 34 : <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 35 : <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 36 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c1b273b230584979a78.PNG' />
The lengths of 40 leaves of a plant are measured correct to the nearest millimetre, and the data obtained is represented in the above table. Find the median length of the leaves
Question 37 : <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 38 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c0a273b230584979a64.PNG' />
Thirty women were examined in a hospital by a doctor and the number of heartbeats per minute were recorded and summarised as given above. Find the mean heartbeats per minute for these women, choosing a suitable method.
Question 39 : <img style='object-fit:contain' src='61b19a9e273b23058497993b' />
The above table shows the daily pocket allowance of children of a locality. The mean pocket allowance is Rs.18. Find the missing frequency.
Question 40 : <img style='object-fit:contain' src='61b19a96273b23058497993a' />
To find out the concentration of $SO_2$ in the air (in parts per million, i.e. ppm), the data was collected for 30 localities in a certain city and is presented above. Find the mean concentration of $SO_2$ in the air.
Question 41 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c2c273b230584979a8a.JPG' />
In the above image, mayank made a bird-bath for his garden in the shape of a cylinder with a hemispherical depression at one end . The height of the cylinder is 1.45 m and its radius is 30 cm. Find the total surface area of the bird-bath. (Take $\pi$ = $\frac{22}{ 7}$ )
Question 42 :
A copper rod of diameter 1 cm and length 8 cm is drawn into a wire of length 18 m of uniform thickness. Find the thickness of the wire.
Question 43 :
A right circular cylinder of radius r cm and height h cm (h>2r) just encloses a sphere of diameter
Question 44 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c36273b230584979a95.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 total surface area(Take $\pi$ = $\frac{22}{7}$ ).
Question 45 :
How many silver coins, 1.75 cm in diameter and of thickness 2 mm, must be melted to form a cuboid of dimensions $5.5 cm\times 10 cm\times 3.5 cm$?
Question 46 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c4c273b230584979ab0.PNG' />
In the above fig, CM and RN are respectively the medians of ∆ ABC and ∆ PQR. If ∆ ABC ~ ∆ PQR, Is $\frac{CM}{RN}$ = $\frac{AB}{PQ}$ ?
Question 47 :
Two poles of heights 6 m and 11 m stand on a plane ground. If the distance between the feet of the poles is 12 m, find the distance between their tops.
Question 48 :
Two polygons of the same number of sides are similar, if (a) their corresponding angles are ___________ and (b) their corresponding sides are ___________.
Question 49 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c6e273b230584979ad8.PNG' />
In the above fig, PS is the bisector of ∠ QPR of ∆ PQR. Is $\frac{QS}{SR}$ = $\frac{PQ}{PR}$ ?
Question 50 :
It is given that $\Delta$ ABC ~ $\Delta$ EDF such that AB = 5 cm,AC = 7 cm, DF= 15 cm and DE = 12 cm. Find the lengths of the remaining sides of the triangles.
Question 51 :
Express $\sin 67^{\circ} + \cos 75^{\circ}$ in terms of trigonometric ratios of angles between $0^{\circ}$ and $45^{\circ}$.
Question 53 :
Can all the other trigonometric ratios of ∠ A be written in terms of sec A?
Question 54 :
$\cos 38^{\circ} \cos 52^{\circ} – \sin 38^{\circ} \sin 52^{\circ} \ne 0$. TRUE or FALSE?
Question 55 :
The value of $\cos \theta$ increases as $\theta$ increases. True or False?
