Question 1 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b41273b230584979963.jpg' />
In the above figure, A Triangle ABC with vertices A, B and C as centres, arcs are drawn with radii 5 cm each. If AB = 14 cm, BC = 48 cm and CA = 50 cm, then find the area of the shaded region.
Question 2 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bb9273b230584979a01.png' />
(As shown in the above image) In a circular table cover of radius 32 cm , a design is formed leaving an equilateral triangle ABC in the middle . Find the area of the design .
Question 3 :
In a circle of radius 21 cm , an arc subtends an angle of $60^{\circ}$ at the centre. Find area of the sector formed by the arc.
Question 4 :
Can we construct a triangle similar to a given triangle as per the given scale factor ?
Question 5 :
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 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 :
From an external point P, two tangents, PA and PB are drawn to a circle with centre O. At one point E on the circle tangent is drawn which intersects PA and PB at C and D, respectively. If PA = 10 cm, what is the perimeter of the triangle PCD?
Question 8 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b4b273b230584979971.PNG' />
In the above figure, O is the centre of a circle of radius 5 cm, T is a point such that OT = 13 cm and OT intersects the circle at E. If AB is the tangent to the circle at E, what is the length of AB?
Question 9 :
If tangents PA and PB from a point P to a circle with centre O are inclined to each ofher at angle of 80°, then ∠ POA is equal to
Question 10 :
Find the area of the triangle whose vertices are $\left(2, 3\right)$, $\left(–1, 0\right)$, $\left(2, – 4\right)$
Question 11 :
Name the type of quadrilateral formed, if any, by the following points (-1,-2) , (1,0) , (-1,2) , (-3,0).
Question 12 :
Name the type of quadrilateral formed, if any, by the following points (4,5) , (7,6) , (4,3) , (1,2).
Question 14 :
$\sin \theta=\cos \theta$ for all values of $\theta$. True or False?
Question 15 :
Is $(sin A + cosec A)^2 + (cos A + sec A)^2 = 7 + tan^2 A + cot^2 A$?
Question 16 :
The sum of the digits of a two-digit number is 9. If 27 is added to it, the digits of the number get reversed. The number is ___________.
Question 17 :
State whether the following pair of linear equations has unique solution, no solution, or infinitely many solutions : $x – 3y – 7 = 0 ; 3x – 3y – 15 = 0$
Question 18 :
Solve the following pair of linear equations by the substitution method : $s - t = 3 ; \frac{s}{3} + \frac{t}{2} = 6$
Question 19 :
Divide the polynomial $p\left(x\right)$ by the polynomial $g\left(x\right)$ and find the quotient and remainder in the following : $p\left(x\right)$ = $x^3–3x^2+5x–3$, $g\left(x\right)$ = $x^2–2$
Question 20 :
Find a quadratic polynomial, the sum and product of whose zeroes are 1 and 1, respectively.
Question 21 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19a51273b23058497991f.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 22 :
A bag contains lemon flavoured candies only. Malini takes out one candy without looking into the bag. What is the probability that she takes out a lemon flavoured candy?
Question 23 :
A box contains 3 blue, 2 white, and 4 red marbles. If a marble is drawn at random from the box, what is the probability that it will be white?
Question 24 :
Five cards—the ten, jack, queen, king and ace of diamonds, are well-shuffled with their face downwards. One card is then picked up at random. What is the probability that the card is the queen?
Question 25 :
Justify why the following quadratic equation has no two distinct real roots: $x\left(1-x\right)-2=0$
Question 26 :
Justify why the following quadratic equation has no two distinct real roots: $2x^2-6x+\frac{9}{2}=0$
Question 27 :
Find the values of k for each of the following quadratic equations, so that they have two equal roots: $kx (x – 2) + 6 = 0$
Question 32 : <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 33 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c14273b230584979a6f.PNG' />
The above given frequency distribution gives the monthly consumption of electricity of 68 consumers of a locality. Find the mean.
Question 34 :
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 35 :
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 36 :
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 37 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b99273b2305849799d7.png' />
In the given figure, two line segments AC and BD intersect each other at the point P such that PA = 6 cm, PB = 3 cm, PC = 2.5 cm, PD = 5 cm, $\angle$ APB = 50° and $\angle$ CDP = 30°. Then, $\angle$ PBA is equal to
Question 38 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c43273b230584979aa5.PNG' />
In the above fig, If a line intersects sides AB and AC of a ∆ ABC at D and E respectively and is parallel to BC. Is $\frac{AD}{AB}$= $\frac{AE}{AC}$ ?
Question 39 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c6d273b230584979ad7.PNG' />
In the above fig, the perpendicular from A on side BC of a ∆ ABC intersects BC at D such that DB = 3 CD. Is $2AB^2$ = $2AC^2 + BC^2$ ?
Question 40 :
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 41 :
Metallic spheres of radii 6 cm, 8 cm and 10 cm, respectively, are melted to form a single solid sphere. Find the radius of the resulting sphere.
Question 42 :
A pen stand made of wood is in the shape of a cuboid with four conical depressions and a cubical depression to hold the pens and pins, respectively. The dimension of the cuboid are 10 cm, 5 cm and 4 cm. The radius of each the conical depressions is 0.5 cm and the depth is 2.1 cm. The edge of the cubical depression is 3 cm. Find the volume of the wood in the entire stand.
Question 43 :
Area of the largest triangle that can be inscribed in a semi-circle of radius $r$ units is
Question 44 :
If the perimeter of a circle is equal to that of a square, then the ratio of their areas is
Question 45 : <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 46 :
The first and the last terms of an AP are 17 and 350 respectively. If the common difference is 9, how many terms are there in the AP?
Question 47 :
The 17th term of an AP exceeds its 10th term by 7. Find the common difference.
Question 48 :
An AP consists of 50 terms of which 3rd term is 12 and the last term is 106. Find the 29th term.
Question 49 :
Does a diameter AB of a circle bisects all those chords which are parallel to the tangent at the point A?
Question 50 :
At any point on a circle there can be one and only one tangent .
TRUE OR FALSE?
Question 51 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19a49273b230584979914.PNG' />
In the above figure, if TP and TQ are the two tangents to a circle with centre O so that ∠ POQ = 110°, then ∠ PTQ is equal to
Question 55 :
Two coins are tossed simultaneously. The probability of getting at most one head is
Question 56 : In the adjoining figure, ∆ ABC is circumscribing a circle. Then, the length of BC is <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b63273b230584979991.PNG' />
Question 57 :
The radii of the ends of a frustum of a cone 40 cm high are 20 cm and 11 cm. Its slant height is
Question 58 :
Solve the following pair of linear equations by the elimination method and the substitution method : $x + y = 5 ~and ~2x – 3y = 4$
Question 59 :
Solve the following pair of equations by substitution method: $7x – 15y =2 ; x + 2y =3$
Question 60 :
State whether the following pair of linear equations has unique solution, no solution, or infinitely many solutions : $x – 3y – 3 = 0 ; 3x – 9y – 2 = 0$
Question 61 : Consider the following frequency distribution of the heights of 60 students of a class :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b8e273b2305849799c9.PNG' />
The sum of the lower limit of the modal class and upper limit of the median class is?
Question 62 :
A card is selected at random from a well shuffled deck of 52 playing cards. The probability of its being a face card is
Question 63 :
In any situation that has only two possible outcomes, each outcome will have probability $\frac{1}{2}$.
Question 64 :
Selvi’s house has an overhead tank in the shape of a cylinder. This is filled by pumping water from a sump (an underground tank) which is in the shape of a cuboid. The sump has dimensions 1.57 m × 1.44 m × 95cm. The overhead tank has its radius 60 cm and height 95 cm. Compare the capacity of the tank with that of the sump. (Use $\pi$ = 3.14)
Question 65 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b31273b23058497994e.jpeg' />
As shown in the above figure, a gulabjamun contains sugar syrup upto about 30% of its volume. Find approximately how much syrup would be found in 45 gulabjamuns, each shaped like a cylinder with two hemispherical ends with length 5 cm and diameter 2.8 cm.
Question 66 :
If two solid hemispheres of same radius r are joined together along their bases, then curved surface area of this new solid is
Question 67 :
Two poles of equal heights are standing opposite each other 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 poles are $60^{\circ}$ and $30^{\circ}$, respectively. Find the height of the poles and the distances of the point from the poles respectively.
Question 68 :
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 69 :
A 1.5 m tall boy is standing at some distance from a 30 m tall building. The angle of elevation from his eyes to the top of the building increases from $30^{\circ}$ to $60^{\circ}$ as he walks towards the building. Find the distance he walked towards the building.
Question 70 :
In an AP, given l = 28, S = 144, and there are total 9 terms. Find a.
Question 71 :
If the sum of the first n terms of an AP is $4n – n^2$, what is the first term (that is $S_1$)?
Question 72 :
For what value of n, are the nth terms of two APs: 63, 65, 67, . . . and 3, 10, 17, . . . equal?
Question 73 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c2e273b230584979a8c.JPG' />
In the above image, shanta runs an industry in a shed which is in the shape of a cuboid surmounted by a half cylinder. The base of the shed is of dimension 7 m × 15 m, and the height of the cuboidal portion is 8 m. Further, suppose the machinery in the shed occupies a total space of 300 $m^3$, and there are 20 workers , each of whom occupy about 0.08 $m^3$ space on an average. Then, how much air is in the shed? (Take $\pi$ = $\frac{22}{7}$ )
Question 74 :
A solid iron cuboidal block of dimensions 4.4 m × 2.6 m × 1m is recast into a hollow cylindrical pipe of internal radius 30 cm and thickness 5 cm. Find the length of the pipe.
Question 75 :
A cylindrical bucket, 32 cm high and with radius of base 18 cm, is filled with sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is 24 cm, find the slant height of the heap.
