Question 1 :
A is a point at a distance 13 cm from the centre O of a circle of radius 5 cm. AP and AQ are the tangents to the circle at P and Q. If a tangent BC is drawn at a point R lying on the minor arc PQ to intersect AP at B and AQ at C, what is the perimeter of the $\triangle ABC$?
Question 2 :
If a point lies on the circle , then there is only one tangent to the circle at this point and it is perpendicular to the radius through this point . State whether the above statement is TRUE or FALSE ?
Question 3 :
Two circles with centres O and $O ^ { \prime }$ of radii 3 cm and 4 cm, respectively intersect at two points P and Q such that OP and $O ^ { \prime }P$ are tangents to the two circles. What is the length of the common chord PQ?
Question 4 :
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 5 :
Do the tangents drawn at the ends of a chord of a circle make equal angles with the chord?
Question 6 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bad273b2305849799f1.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 gold scoring region.
Question 7 : <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 8 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bae273b2305849799f3.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 blue scoring region.
Question 9 :
The wheel of a motor cycle is of radius 35 cm. How many revolutions per minute must the wheel make so as to keep a speed of 66 km/h ?
Question 10 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bab273b2305849799ef.png' />
Find the area of the shaded region in the above figure, where ABCD is a square of side 14 cm.
Question 11 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b57273b230584979982.PNG' />
In the above figure, students of a school standing in rows and columns in their playground for a drill practice are shown. A, B, C and D are the positions of four students as shown in figure. Is it possible to place Jaspal in the drill in such a way that he is equidistant from each of the four students A, B, C and D? If so, what should be his position?
Question 12 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bd7273b230584979a29.png ' />
The Class X students of a secondary school in Krishinagar have been allotted a rectangular plot of land for their gardening activity. Sapling of Gulmohar are planted on the boundary at a distance of 1m from each other. There is a triangular grassy lawn in the plot as shown in the above image. The students are to sow seeds of flowering plants on the remaining area of the plot.What will be the area of ∆PQR if C is the Origin?
Question 13 : <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 14 :
Find the area of the triangle whose vertices are $\left(-5, -1\right)$, $\left(3, -5\right)$, $\left(5, 2\right)$
Question 15 :
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 16 :
The taxi charges in a city consist of a fixed charge together with the charge for the distance covered. For a distance of 10 km, the charge paid is Rs. 105 and for a journey of 15 km, the charge paid is Rs. 155. What are the fixed charges and the charge per km?
Question 17 :
Let a pair of linear equations in two variables be $a_{1}x+b_{1}y+c_{1}=0$ and $a_{2}x+b_{2}y+c_{2}=0$. If $\frac{a_1}{a_2}\ne\frac{b_1}{b_2}$, then the pair of linear equations is _______.
Question 18 :
State whether the following pair of linear equations has unique solution, no solution, or infinitely many solutions : $3x – 5y = 20 ; 6x – 10y = 40$
Question 19 :
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 20 :
Solve the following pair of equations by reducing them to a pair of linear equations : $\frac{6}{x-1} - \frac{3}{y-2} = 1 ; \frac{5}{x-1} + \frac{1}{y-2} = 2$
Question 21 :
$\cos 38^{\circ} \cos 52^{\circ} – \sin 38^{\circ} \sin 52^{\circ} \ne 0$. TRUE or FALSE?
Question 24 :
Evaluate : $sin 25° cos 65° + cos 25° sin 65°$
Question 25 :
If $\sec 4A = cosec\ \begin{pmatrix}A – 20^{\circ}\end{pmatrix}$, where 4A is an acute angle, find the value of A.
Question 26 :
State True or False whether the following quadratic equation has two distinct real roots: $\left(x+4\right)^2-8x=0$
Question 27 :
Find the roots of the quadratic equation (by using the quadratic formula): $x^2+2\sqrt{2}x-6=0$
Question 28 :
State True or False: Every quadratic equation has exactly one root.
Question 29 :
Justify why the following quadratic equation has no two distinct real roots: $x\left(1-x\right)-2=0$
Question 31 :
Choose the correct answer from the given four options in the question: The product of a non-zero rational and an irrational number is _______ .
Question 33 :
What are the LCM and HCF of 26 and 91 ?
Question 34 :
State true or false: The sum or difference of a rational and an irrational number is irrational.
Question 36 :
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 37 :
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 38 :
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 39 :
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 40 :
As observed from the top of a 75 m high lighthouse from the sea level, the Angles of depression of two ships are 30° and 45°. If one ship is exactly behind the ofher on the same side of the lighthouse, then find the distance between the two ships.
Question 41 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c08273b230584979a61.PNG' />
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 42 :
For finding the median of ungrouped data, we first arrange the data values of the observations in ascending order. TRUE OR FALSE?
Question 43 : <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 44 : <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 45 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19ab8273b23058497993e.PNG' />
The above given distribution shows the number of runs scored by some top batsmen of the world in one-day inetrnational cricket matches. Find the mode.
Question 46 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b9d273b2305849799dd.png' />
If DE is parallel to BC, find the ratio of the area ADE and area DECB.
Question 47 : <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 48 :
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 49 :
In triangles ABC and DEF, $\angle$B = $\angle$E, $\angle$F = $\angle$C and AB = 3 DE. Then, the two triangles are
Question 50 :
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.
Question 51 :
What is the formulae for curved surface area of solid hemisphere?
Question 52 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b32273b23058497994f.jpeg' />
As shown in the above figure, a pen stand made of wood, is in the shape of a cuboid with four conical depressions to hold pens. The dimensions of the cuboid are $15 cm\times10 cm \times 3.5 cm$. The radius of each of the depressions is 0.5 cm and the depth is 1.4 cm. Find the volume of wood in the entire stand.
Question 53 :
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 54 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c39273b230584979a99.JPG' />
In the above image, a pen stand made of wood is in the shape of a cuboid with four conical depressions to hold pens. The dimensions of the cuboid are 15 cm by 10 cm by 3.5 cm. The radius of each of the depressions is 0.5 cm and the depth is 1.4 cm. Find the volume of wood in the entire stand.
Question 55 :
Water in a canal, 6 m wide and 1.5 m deep, is flowing with a speed of 10 km /h. How much area will it irrigate in 30 minutes, if 8 cm of standing water is needed?
