Question 1 :
Find the distance between the points $\left(0, 0\right)$ and $\left(36, 15\right)$.
Question 2 : <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 3 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bd6273b230584979a28.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 co-ordinates of the vertices of ∆PQR if C is the Origin?
Question 4 :
Find the area of a triangle whose vertices are $\left(1, –1\right)$, $\left(– 4, 6\right)$ and $\left(–3, –5\right)$.
Question 5 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19a45273b23058497990f.jpeg' />
The above figure depicts an archery target marked with its five scoring regions from centre outwards as gold, red, blue, black and white. The diameter of the region representing gold score is 21 cm and each of the ofher bands is 10.5 cm wide. Find the area of each of the gold scoring region.
Question 6 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b38273b230584979958.jpg' />
In the above figure, dimensions are given. Find the area of the shaded region.
Question 7 :
The radii of two circles are 8 cm and 6 cm respectively. Find the radius of the circle having area equal to the sum of the areas of the two circles.
Question 8 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bb0273b2305849799f6.png' />
(As shown in the above figure)A horse is tied to a peg at one corner of a square shaped grass field of side 15 m by means of a 5 m long rope . Find the area of that part of the field in which the horse can graze.
Question 9 :
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 10 :
A line and a circle in the same plane can co-exist in _______ different ways.
Question 11 :
Let s denote the semi-perimeter of a triangle ABC in which BC = a, CA = b, AB = c. If a circle touches the sides BC, CA, AB at D, E, F, respectively, Is it TRUE or FALSE that BD = s – b?
Question 12 :
The opposite sides of a quadrilateral circumscribing a circle subtend ________ angles at the centre of the circle.
Question 14 :
Can the trigonometric ratios sin A, sec A and tan A be expressed in terms of cot A?
Question 15 :
If $\sec 4A = cosec\ \begin{pmatrix}A – 20^{\circ}\end{pmatrix}$, where 4A is an acute angle, find the value of A.
Question 17 :
The pair of equations 5x – 15y = 8 and $3x-9y=\frac{24}{5}$ has __________.
Question 18 :
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 19 :
The sum of the digits of a two-digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the number.
Question 20 :
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: $5x – 4y + 8 = 0 ; 7x + 6y – 9 = 0$
Question 22 :
If the zeroes of the quadratic polynomial $x^2+\left(a+1\right)x+b$ are 2 and -3, then:
Question 23 :
Are the numbers given alongside of the cubic polynomials their zeroes? $2x^3+x^2-5x+2$; $\frac{1}{2}$, 1, -2 .
Question 24 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19a58273b230584979926.png' />
In the image above, the graph of $y=p\left(x\right)$, where $p\left(x\right)$ is a polynomial. Here, find the number of zeroes of $p\left(x\right)$
Question 25 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19be8273b230584979a3f.PNG' />
In the above imafe, a missing helicopter is reported to have crashed somewhere in the rectangular region. What is the probability that it crashed inside the lake?
Question 26 :
Probability of an event E + Probability of the event ‘not E’ =
Question 27 :
It is given that in a group of 3 students, the probability of 2 students not having the same birthday is 0.992. What is the probability that the 2 students have the same birthday?
Question 28 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bed273b230584979a44.PNG' />
A game of chance consists of spinning an arrow which comes to rest pointing at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8, and these are equally likely outcomes. What is the probability that it will point at a number less than 9?
Question 29 :
Find the roots of the following quadratic equation (by the factorisation method): $3x^2+5\sqrt{5}x-10=0$
Question 32 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c0e273b230584979a68.PNG' />
The above data gives the information on the observed lifetimes (in hours) of 225 electrical components. Determine the modal lifetimes of the components.
Question 33 :
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 34 : <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 36 :
A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the hemisphere is 14 cm and the total height of the vessel is 13 cm. Find the inner surface area of the vessel.
Question 37 :
A hollow cube of internal edge 22 cm is filled with spherical marbles of diameter 0.5 cm and it is assumed that $\frac{1}{8}$ space of the cube remains unfilled. Then the number of marbles that the cube can accomodate is
Question 38 :
If two solid hemispheres of same radius r are joined together along their bases, then curved surface area of this new solid is
Question 39 :
A cone of height 24 cm and radius of base 6 cm is made up of modelling clay. A child reshapes it in the form of a sphere. Find the radius of the sphere.
Question 40 :
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 41 :
State True or False:In two triangles, an angle of one triangle is equal to an angle of another triangle and two sides of one triangle are proportional to the two sides of the other triangle, then the triangles are similar.
Question 42 :
Determine which of them are right triangles:
(i) 7 cm, 24 cm, 25 cm
(ii) 3 cm, 8 cm, 6 cm
(iii) 50 cm, 80 cm, 100 cm
(iv) 13 cm, 12 cm, 5 cm
Question 43 :
A hollow cube of internal edge 22 cm is filled with spherical marbles of diameter 0.5 cm and it is assumed that $\frac{1}{8}$ space of the cube remains unfilled. Then the number of marbles that the cube can accomodate is
Question 44 :
A vessel is in the form of an inverted cone. Its height is 8 cm and the radius of its top, which is open is 5 cm. It is filled with water upto brim. When lead shots each in the shape of a sphere with radius 0.5 cm are dropped into the vessel, the one-fourth of the water flows out. Find the number of lead shots dropped in the vessel.
Question 45 :
A tent is in the shape of a cylinder surmounted by a conical top. If the height and diameter of the cylindrical part are 2.1 m and 4 m respectively, and the slant height of the top is 2.8 m, find the area of the canvas used for making the tent. (Note that the base of the tent will not be covered with canvas.)
Question 46 :
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 47 :
Find the sum of the odd numbers between 0 and 50.
Question 48 :
Does $a_1, a_2, . . ., a_n, . . $ form an AP where $a_n = 3 + 4n$?
Question 49 :
The houses of a row are numbered consecutively from 1 to 49. Show that there is a value of x such that the sum of the numbers of the houses preceding the house numbered x is equal to the sum of the numbers of the houses following it. Find this value of x.
Question 50 :
Determine the AP whose third term is 16 and the 7th term exceeds the 5th term by 12.
