32581 + Interview Questions in Mathematics Page 223 InterviewSolution

11101.	If ABCD is a cyclic quadrilateral with AB as the diameter of the circle and ∠ACD=50∘, then ∠BAD = ___ degrees.40
Answer» If ABCD is a cyclic quadrilateral with AB as the diameter of the circle and $∠ A C D = 50^{\circ},$ then $∠ B A D$ = ___ degrees. 40

Discussion

11102.

From the following Trial Balance extracted from the books of A, prepare Trading and Profit & Loss Account for the year ending 31st March, 2019 and a Balance Sheet as at that date:- Dr. (₹) Cr. (₹) Furniture 640 Loose Tools 6,250 Buildings 7,500 Capital Account 12,500 Bad-debts 125 Provision for Bad-debts 200 Sundry Debtors and Creditors 3,800 2,500 Stock on 1st April, 2018 3,460 Purchases and Sales 5,475 15,450 Bank Overdraft 2,850 Sales Return and Purchases Return 200 125 Stationery 450 Interest Account 118 Commission 375 Cash in hand 650 Taxes and Insurance 1,250 General Expenses 782 Salaries 3,300 34,000 34,000 The following adjustments are to be made:(i) Stock in hand on 31st March, 2019 was ₹ 3,250.(ii) Depreciate Building at 5% and Furniture at 10%. Loose Tools are revalued at ₹ 5,000 at the end of the year.(iii) Salaries ₹ 300 and taxes ₹ 120 are outstanding.(iv) Insurance amounting to ₹ 100 is prepaid.(v) Write off a further ₹ 100 as Bad-Debts and provision for Doubtful Debts is to be made equal to 5% on Sundry Debtors.(vi) Half of the stationery was used by the proprietor for his personal purposes.

Answer» From the following Trial Balance extracted from the books of A, prepare Trading and Profit & Loss Account for the year ending 31st March, 2019 and a Balance Sheet as at that date:-

	Dr. (₹)	Cr. (₹)
Furniture	640
Loose Tools	6,250
Buildings	7,500
Capital Account		12,500
Bad-debts	125
Provision for Bad-debts		200
Sundry Debtors and Creditors	3,800	2,500
Stock on 1st April, 2018	3,460
Purchases and Sales	5,475	15,450
Bank Overdraft		2,850
Sales Return and Purchases Return	200	125
Stationery	450
Interest Account	118
Commission		375
Cash in hand	650
Taxes and Insurance	1,250
General Expenses	782
Salaries	3,300
	34,000	34,000

The following adjustments are to be made:

(i) Stock in hand on 31st March, 2019 was ₹ 3,250.

(ii) Depreciate Building at 5% and Furniture at 10%. Loose Tools are revalued at ₹ 5,000 at the end of the year.

(iii) Salaries ₹ 300 and taxes ₹ 120 are outstanding.

(iv) Insurance amounting to ₹ 100 is prepaid.

(v) Write off a further ₹ 100 as Bad-Debts and provision for Doubtful Debts is to be made equal to 5% on Sundry Debtors.

(vi) Half of the stationery was used by the proprietor for his personal purposes.

Discussion

11103.	ntThe relative error in the measurement of the side of a cube is 0.027. The relative error in the measurement of its volume is ?n
Answer» ntThe relative error in the measurement of the side of a cube is 0.027. The relative error in the measurement of its volume is ?n

Discussion

11104.	A piggy bank contains hundred 50 p coins, seventy ₹1 coin, fifty ₹2 coins and thirty ₹5 coins. If it is equally likely that one of the coins will fall out when the bank is turned upside down, what is the probability that the coin(i) will be a ₹1 coin?(ii) will not be a ₹5 coin?(iii) will be a 50 p or a ₹2 coin?
Answer» A piggy bank contains hundred 50 p coins, seventy ₹1 coin, fifty ₹2 coins and thirty ₹5 coins. If it is equally likely that one of the coins will fall out when the bank is turned upside down, what is the probability that the coin (i) will be a ₹1 coin? (ii) will not be a ₹5 coin? (iii) will be a 50 p or a ₹2 coin?

Discussion

11105.	If the ratio of volume to total surface area of a solid sphere is 8 : 1, then radius of the sphere is ___.
Answer» If the ratio of volume to total surface area of a solid sphere is 8 : 1, then radius of the sphere is ___.

Discussion

11106.	In a circle of radius 21 cm, an arc subtendeds as an angle of 60∘ at the centre. Find (i) the length of the arc (ii) area of the sector formed by the arc. (Use π=227)
Answer» In a circle of radius 21 cm, an arc subtendeds as an angle of $60^{\circ}$ at the centre. Find (i) the length of the arc (ii) area of the sector formed by the arc. (Use $π = \frac{22}{7}$ )

Discussion

11107.	Question 45 Two adjacent angles of a parallelogram are in the ratio 1 : 5. Then, all the angles of the parallelogram are a) 30∘,150∘,30∘,150∘ b) 85∘,95∘,85∘,95∘ c) 45∘,135∘,45∘,135∘ d) 30∘,180∘,30∘,180∘
Answer» Question 45 Two adjacent angles of a parallelogram are in the ratio 1 : 5. Then, all the angles of the parallelogram are a) $30^{\circ}, 150^{\circ}, 30^{\circ}, 150^{\circ}$ b) $85^{\circ}, 95^{\circ}, 85^{\circ}, 95^{\circ}$ c) $45^{\circ}, 135^{\circ}, 45^{\circ}, 135^{\circ}$ d) $30^{\circ}, 180^{\circ}, 30^{\circ}, 180^{\circ}$

Discussion

11108.	A solid metallic sphere of diameter 28 cm is melted and recast into a number of smaller cones, each of diameter 423 cm and height 3 cm. Find the number of cones so formed.
Answer» A solid metallic sphere of diameter 28 cm is melted and recast into a number of smaller cones, each of diameter $4 \frac{2}{3}$ cm and height 3 cm. Find the number of cones so formed.

Discussion

11109.	If 5 and -5 are two zeroes of the polynomial x3 + 3x2 − 5x − 15, then its third zero is(a) 3(b) −3(c) 5(d) −5
Answer» If $\sqrt{5} and - \sqrt{5}$ are two zeroes of the polynomial x³ + 3x² − 5x − 15, then its third zero is (a) 3 (b) −3 (c) 5 (d) −5

Discussion

11110.	The sum of two natural numbers is 9 and the sum of their reciprocals is 12. Find the numbers. [CBSE 2012]
Answer» The sum of two natural numbers is 9 and the sum of their reciprocals is $\frac{1}{2}$ . Find the numbers. [CBSE 2012]

Discussion

11111.	∣∣∣x126∣∣∣=46Find the value of x?
Answer» $∣ ∣ ∣ \begin{matrix} x & 1 2 & 6 \end{matrix} ∣ ∣ ∣ = 46$ Find the value of x?

Discussion

11112.	Let s denotes the semi – perimeter of a ∆ ABC, in which BC=a, CA=b and AB=c , if a circle touches the sides BC, CA , AB at D,E,F respectively prove that BD = s - b.
Answer» Let s denotes the semi – perimeter of a ∆ ABC, in which BC=a, CA=b and AB=c , if a circle touches the sides BC, CA , AB at D,E,F respectively prove that BD = s - b.

Discussion

11113.	11 years from now, the age of Peter will be half the square of the age he was 13 years ago. Calculate the current age of Peter.
Answer» 11 years from now, the age of Peter will be half the square of the age he was 13 years ago. Calculate the current age of Peter.

Discussion

11114.	The construction of triangle ΔA'C'B similar to triangle ΔACB is shown in the figure below. Then
Answer» The construction of triangle ΔA'C'B similar to triangle ΔACB is shown in the figure below. Then

Discussion

11115.	Question 10 (i)Show that a1,a2……,an,…… form an AP where an is defined as below.(i) an=3+4nAlso find the sum of the first 15 terms in each case.
Answer» Question 10 (i) Show that $a_{1}, a_{2} \dots \dots, a_{n}, \dots \dots$ form an AP where $a_{n}$ is defined as below. (i) $a_{n} = 3 + 4 n$ Also find the sum of the first 15 terms in each case.

Discussion

11116.	In a right triangle ABC, the right angle is at B. What is the length of the missing side in the figure?
Answer» In a right triangle ABC, the right angle is at B. What is the length of the missing side in the figure?

11116.

In a right triangle ABC, the right angle is at B. What is the length of the missing side in the figure?

Answer»

In a right triangle ABC, the right angle is at B. What is the length of the missing side in the figure?

Discussion

11117.	There are 40 students in a class of whom 25 are girls and 15 are boys. The class teacher has to select one student as a class representative. He writes the name of each student on a separate card, the cards being identical. Then she puts cards in a bag and stirs them thoroughly. She then draws one card from the bag. What is the probability that the name written on the card is the name of (i) a girl? (ii) a boy?
Answer» There are $40$ students in a class of whom $25$ are girls and $15$ are boys. The class teacher has to select one student as a class representative. He writes the name of each student on a separate card, the cards being identical. Then she puts cards in a bag and stirs them thoroughly. She then draws one card from the bag. What is the probability that the name written on the card is the name of (i) a girl? (ii) a boy?

Discussion

11118.	Solve each of the following equations by using the method of completing the square:2x2-5x+2=0
Answer» Solve each of the following equations by using the method of completing the square: $\frac{2}{x^{2}} - \frac{5}{x} + 2 = 0$

Discussion

11119.	{ Comment upon the nature of roots of the quadratic equation }x^2+2x=k+∫_0^1\vert t+k\vert dt depending on the value }}{ of }k∈ R.
Answer» { Comment upon the nature of roots of the quadratic equation }x^2+2x=k+∫_0^1\vert t+k\vert dt depending on the value }}{ of }k∈ R.

Discussion

11120.	A sphere of radius 6 cm is dropped into a cylindrical vessel partly filled with water. The radius of the vessel is 8 cm. If the sphere is submerged completely, then the surface of the water rises by(a) 4.5 cm(b) 3(c) 4 cm(d) 2 cm
Answer» A sphere of radius 6 cm is dropped into a cylindrical vessel partly filled with water. The radius of the vessel is 8 cm. If the sphere is submerged completely, then the surface of the water rises by (a) 4.5 cm (b) 3 (c) 4 cm (d) 2 cm

Discussion

11121.	Use the sign of >, < or = in the box to make the statements true.(−8)+(−4) □ (−8)−(−4)
Answer» Use the sign of >, < or = in the box to make the statements true. $(- 8) + (- 4) □ (- 8) - (- 4)$

Discussion

11122.	Corrigez les fautes.1. Je me ne réveilles pas tot le dimanche.2. Elle a tombé de l'arbre et elle s'a cassé son jambe.3. Sophie t'es brossés ses chevaux et elles s'es maquillé.4. Ils se son promenées vers le village avec ses femmes.5. Cet dame se est maquillé et elle a sortis avec sa cousine.
Answer» Corrigez les fautes. 1. Je me ne réveilles pas tot le dimanche. 2. Elle a tombé de l'arbre et elle s'a cassé son jambe. 3. Sophie t'es brossés ses chevaux et elles s'es maquillé. 4. Ils se son promenées vers le village avec ses femmes. 5. Cet dame se est maquillé et elle a sortis avec sa cousine.

Discussion

11123.	A bag contains three green marbles, four blue marbles, and two orange marbles, If a marble is picked at random, then the probability that it is not an orange marble is(a) 14(b) 13(c) 49(d) 79
Answer» A bag contains three green marbles, four blue marbles, and two orange marbles, If a marble is picked at random, then the probability that it is not an orange marble is (a) $\frac{1}{4}$ (b) $\frac{1}{3}$ (c) $\frac{4}{9}$ (d) $\frac{7}{9}$

Discussion

11124.	what is Eulerian form of a complex number . explain.
Answer» what is Eulerian form of a complex number . explain.

Discussion

11125.	A tent is of the shape of a right circular cylinder upto a height of 3 metres and then becomes a right circular cone with a maximum height of 13.5 metres above the ground. Calculate the cost of painting the inner side of the tent at the rate of Rs 2 per square metre, if the radius of the base is 14 metres.
Answer» A tent is of the shape of a right circular cylinder upto a height of 3 metres and then becomes a right circular cone with a maximum height of 13.5 metres above the ground. Calculate the cost of painting the inner side of the tent at the rate of Rs 2 per square metre, if the radius of the base is 14 metres.

Discussion

11126.	In the given figure, PT is a tangent to a circle with centre O. If OT = 6 cm and OP = 10 cm, then the length of tangent PT is(a) 8 cm(b) 10 cm(c) 12 cm(d) 16 cm
Answer» In the given figure, PT is a tangent to a circle with centre O. If OT = 6 cm and OP = 10 cm, then the length of tangent PT is (a) 8 cm (b) 10 cm (c) 12 cm (d) 16 cm

Discussion

11127.	Two cars started moving from a point, one toward north at 30 km/hr & other toward East at 40 km/hr : distance b/w them after 2 hr is ___
Answer» Two cars started moving from a point, one toward north at 30 km/hr & other toward East at 40 km/hr : distance b/w them after 2 hr is ___

Discussion

11128.	A conical tent is 10 m high and the radius of its base is 24 m. Find(i) Slant height of the tent.(ii) Cost of the canvas required to make the tent, if the cost of 1m2 canvas is Rs 70. [Assume π=227]
Answer» A conical tent is 10 m high and the radius of its base is 24 m. Find (i) Slant height of the tent. (ii) Cost of the canvas required to make the tent, if the cost of $1 m^{2}$ canvas is Rs 70. $[A s s u m e π = \frac{22}{7}]$

Discussion

11129.	What is the square root of (4x2–361)(4x2+12x+9)(64x2–5776) ?
Answer» What is the square root of $(4 x^{2} - 361) (4 x^{2} + 12 x + 9) (64 x^{2} - 5776)$ ?

Discussion

11130.	O is the centre of the circle. AD and BC are perpendicular to XY. CB cuts the circle at E, then which of the options are correct?
Answer» O is the centre of the circle. AD and BC are perpendicular to XY. CB cuts the circle at E, then which of the options are correct?

11130.

O is the centre of the circle. AD and BC are perpendicular to XY. CB cuts the circle at E, then which of the options are correct?

Answer»

O is the centre of the circle. AD and BC are perpendicular to XY. CB cuts the circle at E, then which of the options are correct?

Discussion

11131.	If sin θ + cos θ = x, prove that sin6θ+cos6θ=4-3 x2-124.
Answer» If sin θ + cos θ = x, prove that $\sin^{6} θ + \cos^{6} θ = \frac{4 - 3 {(x^{2} - 1)}^{2}}{4}$ .

Discussion

11132.	The least number that is divisible by all the numbers from 1 to 10 (both inclusive ) is (a) 10 (b) 100 (c) 504 (d) 2520
Answer» The least number that is divisible by all the numbers from 1 to 10 (both inclusive ) is (a) 10 (b) 100 (c) 504 (d) 2520

Discussion

11133.	If (v1 + v2) is perpendicular to (v1 - v2), then which of the following are/is true? A. v1 is perpendicular to v2 B. magnitude of v1 is equal to magnitude of v2 C. v1 is a null vector D. the angle between v1 and v2 can have any value NOTE: v1 and v2 ARE VECTORS.
Answer» If (v1 + v2) is perpendicular to (v1 - v2), then which of the following are/is true? A. v1 is perpendicular to v2 B. magnitude of v1 is equal to magnitude of v2 C. v1 is a null vector D. the angle between v1 and v2 can have any value NOTE: v1 and v2 ARE VECTORS.

Discussion

11134.	Solve the following quadratic equations by factorization:5+x5-x-5-x5+x=334; x≠5, -5
Answer» Solve the following quadratic equations by factorization: $\frac{5 + x}{5 - x} - \frac{5 - x}{5 + x} = 3 \frac{3}{4}; x \neq 5, - 5$

Discussion

11135.	Which of the following pairs of lines are inconsistent?[1 mark]
Answer» Which of the following pairs of lines are inconsistent? [1 mark]

Discussion

11136.	If the sum of 7 terms of an A.P. is 49 and that of 17 terms is 289, find the sum of n terms.
Answer» If the sum of 7 terms of an A.P. is 49 and that of 17 terms is 289, find the sum of n terms.

Discussion

11137.	How to find Determinant of matrix of order 33 ?
Answer» How to find Determinant of matrix of order 33 ?

Discussion

11138.	How many terms of the arithmetic sequence 5, 7, 9, …. should be added to get 140?
Answer» How many terms of the arithmetic sequence 5, 7, 9, …. should be added to get 140?

Discussion

11139.	The position of a point in a plane is expressed by a pair of numbers called ________________
Answer» The position of a point in a plane is expressed by a pair of numbers called ________________

Discussion

11140.	if (1,1) is the solution of the equation px+qy+(a-b) = 0 and px+qy+(b-c)=0, the find a+c
Answer» if (1,1) is the solution of the equation px+qy+(a-b) = 0 and px+qy+(b-c)=0, the find a+c

Discussion

11141.	Question 158A rangoli has been drawn on the floor of a house. ABCD and PQRS both are in the shape of a rhombus. Find the radius of semi-circle drawn on each side of rhombus ABCD.
Answer» Question 158 A rangoli has been drawn on the floor of a house. ABCD and PQRS both are in the shape of a rhombus. Find the radius of semi-circle drawn on each side of rhombus ABCD.

Discussion

11142.	In a class test, the sum of the marks obtained by P in Mathematics and science is 28. Had he got 3 marks more in mathematics and 4 marks less in Science. The product of his marks would have been 180. Find his marks in two subjects.
Answer» In a class test, the sum of the marks obtained by P in Mathematics and science is 28. Had he got 3 marks more in mathematics and 4 marks less in Science. The product of his marks would have been 180. Find his marks in two subjects.

Discussion

11143.	31. one of the diagonals of a rhombus of a perimeter 140 metres is 60 metres . find its area and length of the Other diagonal
Answer» 31. one of the diagonals of a rhombus of a perimeter 140 metres is 60 metres . find its area and length of the Other diagonal

Discussion

11144.	{ Find quotient and remainder when }8x^4+10x^3-5x^2-4x+1 is divided by }2x^2+x-1 by long division }} method
Answer» { Find quotient and remainder when }8x^4+10x^3-5x^2-4x+1 is divided by }2x^2+x-1 by long division }} method

Discussion

11145.	Find the area of a quadrant of a circle whose circumference is 22 cm.
Answer» Find the area of a quadrant of a circle whose circumference is 22 cm.

Discussion

11146.	Question 7Find the coordinates of a point A, where AB is the diameter of circle whose centre is (2, - 3) and B is (1, 4).
Answer» Question 7 Find the coordinates of a point A, where AB is the diameter of circle whose centre is (2, - 3) and B is (1, 4).

Discussion

11147.	Find the probability of getting at least two heads if three coins are tossed simultaneously.
Answer» Find the probability of getting at least two heads if three coins are tossed simultaneously.

Discussion

11148.	Find the mean of the following data, using Step Deviation method method: Marks110130150170190Number of students102030155
Answer» Find the mean of the following data, using Step Deviation method method: $\begin{matrix} Marks & 110 & 130 & 150 & 170 & 190 Number of students & 10 & 20 & 30 & 15 & 5 \end{matrix}$

Discussion

11149.	On a circular table cover of radius 42 cm, a design is formed by a girl leaving an equilateral triangle ABC in the middle, as shown in the figure. Find the covered area of the design. [Use 3=1.73, π=227] [CBSE 2013C]
Answer» On a circular table cover of radius 42 cm, a design is formed by a girl leaving an equilateral triangle ABC in the middle, as shown in the figure. Find the covered area of the design. [Use $\sqrt{3} = 1.73, π = \frac{22}{7}$ ] [CBSE 2013C]

Discussion

11150.	Prove the following trigonometric identities.cot2 A cosec2 B − cot2 B cosec2 A = cot2 A − cot2 B
Answer» Prove the following trigonometric identities. cot² A cosec² B − cot² B cosec² A = cot² A − cot² B

Discussion

Explore topic-wise InterviewSolutions in .

If ABCD is a cyclic quadrilateral with AB as the diameter of the circle and ∠ACD=50∘, then ∠BAD = ___ degrees.40

ntThe relative error in the measurement of the side of a cube is 0.027. The relative error in the measurement of its volume is ?n

If the ratio of volume to total surface area of a solid sphere is 8 : 1, then radius of the sphere is ___.

In a circle of radius 21 cm, an arc subtendeds as an angle of 60∘ at the centre. Find (i) the length of the arc (ii) area of the sector formed by the arc. (Use π=227)

Question 45 Two adjacent angles of a parallelogram are in the ratio 1 : 5. Then, all the angles of the parallelogram are a) 30∘,150∘,30∘,150∘ b) 85∘,95∘,85∘,95∘ c) 45∘,135∘,45∘,135∘ d) 30∘,180∘,30∘,180∘

A solid metallic sphere of diameter 28 cm is melted and recast into a number of smaller cones, each of diameter 423 cm and height 3 cm. Find the number of cones so formed.

If 5 and -5 are two zeroes of the polynomial x3 + 3x2 − 5x − 15, then its third zero is(a) 3(b) −3(c) 5(d) −5

The sum of two natural numbers is 9 and the sum of their reciprocals is 12. Find the numbers. [CBSE 2012]

∣∣∣x126∣∣∣=46Find the value of x?

Let s denotes the semi – perimeter of a ∆ ABC, in which BC=a, CA=b and AB=c , if a circle touches the sides BC, CA , AB at D,E,F respectively prove that BD = s - b.

11 years from now, the age of Peter will be half the square of the age he was 13 years ago. Calculate the current age of Peter.

The construction of triangle ΔA'C'B similar to triangle ΔACB is shown in the figure below. Then

Question 10 (i)Show that a1,a2……,an,…… form an AP where an is defined as below.(i) an=3+4nAlso find the sum of the first 15 terms in each case.

In a right triangle ABC, the right angle is at B. What is the length of the missing side in the figure?

Solve each of the following equations by using the method of completing the square:2x2-5x+2=0

{ Comment upon the nature of roots of the quadratic equation }x^2+2x=k+∫_0^1\vert t+k\vert dt depending on the value }}{ of }k∈ R.

A sphere of radius 6 cm is dropped into a cylindrical vessel partly filled with water. The radius of the vessel is 8 cm. If the sphere is submerged completely, then the surface of the water rises by(a) 4.5 cm(b) 3(c) 4 cm(d) 2 cm

Use the sign of >, < or = in the box to make the statements true.(−8)+(−4) □ (−8)−(−4)

Corrigez les fautes.1. Je me ne réveilles pas tot le dimanche.2. Elle a tombé de l'arbre et elle s'a cassé son jambe.3. Sophie t'es brossés ses chevaux et elles s'es maquillé.4. Ils se son promenées vers le village avec ses femmes.5. Cet dame se est maquillé et elle a sortis avec sa cousine.

A bag contains three green marbles, four blue marbles, and two orange marbles, If a marble is picked at random, then the probability that it is not an orange marble is(a) 14(b) 13(c) 49(d) 79

what is Eulerian form of a complex number . explain.

In the given figure, PT is a tangent to a circle with centre O. If OT = 6 cm and OP = 10 cm, then the length of tangent PT is(a) 8 cm(b) 10 cm(c) 12 cm(d) 16 cm

Two cars started moving from a point, one toward north at 30 km/hr &amp; other toward East at 40 km/hr : distance b/w them after 2 hr is ___

A conical tent is 10 m high and the radius of its base is 24 m. Find(i) Slant height of the tent.(ii) Cost of the canvas required to make the tent, if the cost of 1m2 canvas is Rs 70. [Assume π=227]

What is the square root of (4x2–361)(4x2+12x+9)(64x2–5776) ?

O is the centre of the circle. AD and BC are perpendicular to XY. CB cuts the circle at E, then which of the options are correct?

If sin θ + cos θ = x, prove that sin6θ+cos6θ=4-3 x2-124.

The least number that is divisible by all the numbers from 1 to 10 (both inclusive ) is (a) 10 (b) 100 (c) 504 (d) 2520

If (v1 + v2) is perpendicular to (v1 - v2), then which of the following are/is true? A. v1 is perpendicular to v2 B. magnitude of v1 is equal to magnitude of v2 C. v1 is a null vector D. the angle between v1 and v2 can have any value NOTE: v1 and v2 ARE VECTORS.

Solve the following quadratic equations by factorization:5+x5-x-5-x5+x=334; x≠5, -5

Which of the following pairs of lines are inconsistent?[1 mark]

If the sum of 7 terms of an A.P. is 49 and that of 17 terms is 289, find the sum of n terms.

How to find Determinant of matrix of order 33 ?

How many terms of the arithmetic sequence 5, 7, 9, …. should be added to get 140?

The position of a point in a plane is expressed by a pair of numbers called ________________

if (1,1) is the solution of the equation px+qy+(a-b) = 0 and px+qy+(b-c)=0, the find a+c

Question 158A rangoli has been drawn on the floor of a house. ABCD and PQRS both are in the shape of a rhombus. Find the radius of semi-circle drawn on each side of rhombus ABCD.

In a class test, the sum of the marks obtained by P in Mathematics and science is 28. Had he got 3 marks more in mathematics and 4 marks less in Science. The product of his marks would have been 180. Find his marks in two subjects.

31. one of the diagonals of a rhombus of a perimeter 140 metres is 60 metres . find its area and length of the Other diagonal

{ Find quotient and remainder when }8x^4+10x^3-5x^2-4x+1 is divided by }2x^2+x-1 by long division }} method

Find the area of a quadrant of a circle whose circumference is 22 cm.

Question 7Find the coordinates of a point A, where AB is the diameter of circle whose centre is (2, - 3) and B is (1, 4).

Find the probability of getting at least two heads if three coins are tossed simultaneously.

Find the mean of the following data, using Step Deviation method method: Marks110130150170190Number of students102030155

On a circular table cover of radius 42 cm, a design is formed by a girl leaving an equilateral triangle ABC in the middle, as shown in the figure. Find the covered area of the design. [Use 3=1.73, π=227] [CBSE 2013C]

Prove the following trigonometric identities.cot2 A cosec2 B − cot2 B cosec2 A = cot2 A − cot2 B

Two cars started moving from a point, one toward north at 30 km/hr & other toward East at 40 km/hr : distance b/w them after 2 hr is ___