32581 + Interview Questions in Mathematics Page 159 InterviewSolution

7901.	The given table shows the Marks obtained by students in Mathematics.MarksNo. of Students0−10310−20720−301230−401540−502050−60960−70870−801680−901490−1006Using the table determine the Number of students who got above 74 % by drawing an ogive curve.
Answer» The given table shows the Marks obtained by students in Mathematics. $\begin{matrix} Marks & No. of Students 0 - 10 & 3 10 - 20 & 7 20 - 30 & 12 30 - 40 & 15 40 - 50 & 20 50 - 60 & 9 60 - 70 & 8 70 - 80 & 16 80 - 90 & 14 90 - 100 & 6 \end{matrix}$ Using the table determine the Number of students who got above 74 % by drawing an ogive curve.

7901.

The given table shows the Marks obtained by students in Mathematics.MarksNo. of Students0−10310−20720−301230−401540−502050−60960−70870−801680−901490−1006Using the table determine the Number of students who got above 74 % by drawing an ogive curve.

Answer»

The given table shows the Marks obtained by students in Mathematics.

$\begin{matrix} Marks & No. of Students 0 - 10 & 3 10 - 20 & 7 20 - 30 & 12 30 - 40 & 15 40 - 50 & 20 50 - 60 & 9 60 - 70 & 8 70 - 80 & 16 80 - 90 & 14 90 - 100 & 6 \end{matrix}$

Using the table determine the Number of students who got above 74 % by drawing an ogive curve.

Discussion

7902.	The length of a rectangular field is 23 m more than its breadth. If the perimeter of the field is 206 m, then its area is(a) 2420 m2(b) 2520 m2(c) 2480 m2(d) 2620 m2
Answer» The length of a rectangular field is 23 m more than its breadth. If the perimeter of the field is 206 m, then its area is (a) 2420 m² (b) 2520 m² (c) 2480 m² (d) 2620 m²

Discussion

7903.	Factorize: a2−b2+2bc−c2
Answer» Factorize: $a^{2} - b^{2} + 2 b c - c^{2}$

7903.

Factorize: a2−b2+2bc−c2

Answer»

Factorize:

$a^{2} - b^{2} + 2 b c - c^{2}$

Discussion

7904.	A hemispherical bowl made of brass has inner radius of 3.5 cm. Find the cost of tin-plating the inner part of the bowl as well as tin plating a plate that exactly fits as a lid for the bowl. Tin plating is done at the rate of ₹10 per 100 sq.cm.
Answer» A hemispherical bowl made of brass has inner radius of 3.5 cm. Find the cost of tin-plating the inner part of the bowl as well as tin plating a plate that exactly fits as a lid for the bowl. Tin plating is done at the rate of ₹10 per 100 sq.cm.

Discussion

7905.	Question 1 (v)Fill in the blanks in the following table, given that a is the first term, d the common difference and an the nth term of the A.P.adnan(v)3.50105……
Answer» Question 1 (v) Fill in the blanks in the following table, given that a is the first term, d the common difference and $a_{n}$ the $n^{t h}$ term of the A.P. $\begin{matrix} a & d & n & a_{n} (v) & 3.5 & 0 & 105 & \dots \dots \end{matrix}$

Discussion

7906.	If the area of a circle is equal to the sum of the areas of two circles of diameters 10 cm and 24 cm, then diameter of the large circle (in cm) is(a) 34(b) 26(c) 17(d) 14
Answer» If the area of a circle is equal to the sum of the areas of two circles of diameters 10 cm and 24 cm, then diameter of the large circle (in cm) is (a) 34 (b) 26 (c) 17 (d) 14

Discussion

7907.	If the perimeter of a square is equal to the circumference of a circle then the ratio of their areas is (a) 4 : π (b) π : 4 (c) π : 7 (d) 7 : π
Answer» If the perimeter of a square is equal to the circumference of a circle then the ratio of their areas is (a) 4 : $π$ (b) $π$ : 4 (c) $π$ : 7 (d) 7 : $π$

7907.

If the perimeter of a square is equal to the circumference of a circle then the ratio of their areas is (a) 4 : π (b) π : 4 (c) π : 7 (d) 7 : π

Answer»

If the perimeter of a square is equal to the circumference of a circle then the ratio of their areas is

(a) 4 : $π$ (b) $π$ : 4 (c) $π$ : 7 (d) 7 : $π$

Discussion

7908.	solve by elimination: ax-by=a^2-b^2; x+y=ab
Answer» solve by elimination: ax-by=a^2-b^2; x+y=ab

Discussion

7909.	Find the missing quantity. 1 l=350 ml + _____ ml.650
Answer» Find the missing quantity. $1 l = 350 m l +$ _____ $m l .$ 650

Discussion

7910.	Cards numbered 1 to 30 are put in a bag. A card is drawn at random from this bag. Find the probability that the number on the drawn card is(i) not divisible by 3(ii) a prime number greater than 7(iii) not a perfect square number [CBSE 2014]
Answer» Cards numbered 1 to 30 are put in a bag. A card is drawn at random from this bag. Find the probability that the number on the drawn card is (i) not divisible by 3 (ii) a prime number greater than 7 (iii) not a perfect square number [CBSE 2014]

Discussion

7911.	In the figure, O is the centre of circumcircle of triangle XYZ. Tangents at X and Y intersect at T. Given ∠XTY = 80o and ∠XOZ = 140o, calculate the value of ∠ZXY.
Answer» In the figure, O is the centre of circumcircle of triangle XYZ. Tangents at X and Y intersect at T. Given ∠XTY = 80^o and ∠XOZ = 140^o, calculate the value of ∠ZXY.

7911.

In the figure, O is the centre of circumcircle of triangle XYZ. Tangents at X and Y intersect at T. Given ∠XTY = 80o and ∠XOZ = 140o, calculate the value of ∠ZXY.

Answer»

In the figure, O is the centre of circumcircle of triangle XYZ. Tangents at X and Y intersect at T. Given ∠XTY = 80^o and ∠XOZ = 140^o, calculate the value of ∠ZXY.

Discussion

7912.	Except for one face of a given cube, identical cubes are glued to all the other faces of the given cube. If each side of the given cube measures 3 cm, what is the total surface area of the solid body thus formed?
Answer» Except for one face of a given cube, identical cubes are glued to all the other faces of the given cube. If each side of the given cube measures 3 cm, what is the total surface area of the solid body thus formed?

Discussion

7913.	Without solving the following quadratic equation, find the value of 'm' for which the given equation has real and equal roots. x2+2(m−1)x+(m+5)=0 [4 MARKS]
Answer» Without solving the following quadratic equation, find the value of 'm' for which the given equation has real and equal roots. $x^{2} + 2 (m - 1) x + (m + 5) = 0$ [4 MARKS]

Discussion

7914.	Find the number that is to be added to x2+12x to make it a perfect square.36
Answer» Find the number that is to be added to $x^{2} + 12 x$ to make it a perfect square. 36

Discussion

7915.

Find the mean of each of the following frequency distributions : Class interval: 50-70 70-90 90-110 110-130 130-150 150-170 Frequency: 18 12 13 27 8 22

Answer» Find the mean of each of the following frequency distributions :

Class interval:	50-70	70-90	90-110	110-130	130-150	150-170
Frequency:	18	12	13	27	8	22

Discussion

7916.	The sum of the zeros and the product of zeros of a quadratic polynomial are −12 and −3 respectively. Write the polynomial.
Answer» The sum of the zeros and the product of zeros of a quadratic polynomial are $\frac{- 1}{2} a n d - 3$ respectively. Write the polynomial.

Discussion

7917.	Let M×[1102]=[12], where M is a matrix. a) State the order of the matrix M. b) Find the matrix M
Answer» Let M $\times [\begin{matrix} 1 & 1 0 & 2 \end{matrix}] = [\begin{matrix} 1 & 2 \end{matrix}]$ , where M is a matrix. a) State the order of the matrix M. b) Find the matrix M

7917.

Let M×[1102]=[12], where M is a matrix. a) State the order of the matrix M. b) Find the matrix M

Answer»

Let M $\times [\begin{matrix} 1 & 1 0 & 2 \end{matrix}] = [\begin{matrix} 1 & 2 \end{matrix}]$ , where M is a matrix.

a) State the order of the matrix M.

b) Find the matrix M

Discussion

7918.	Question 5 (iii) In a circle of radius 21 cm, an arc subtends an angle of 60∘ at the centre. Find: (iii) area of the segment formed by the corresponding chord
Answer» Question 5 (iii) In a circle of radius 21 cm, an arc subtends an angle of $60^{\circ}$ at the centre. Find: (iii) area of the segment formed by the corresponding chord

Discussion

7919.	E and F were partners in a firm sharing profits in the ratio of 3 : 1. They admitted G as a new partner on 1st April, 2019 for 1/3rd share. It was decided that E, F and G will share future profits equally. G brought ₹ 50,000 in cash and machinery valued at ₹ 70,000 as premium for goodwill.Pass necessary Journal entries in the books of the firm.
Answer» E and F were partners in a firm sharing profits in the ratio of 3 : 1. They admitted G as a new partner on 1st April, 2019 for 1/3rd share. It was decided that E, F and G will share future profits equally. G brought ₹ 50,000 in cash and machinery valued at ₹ 70,000 as premium for goodwill. Pass necessary Journal entries in the books of the firm.

Discussion

7920.

A and B are partners in a firm sharing profits and losses in the ratio 3 : 1. They admit C for 1/4th share on 31st March, 2014 when their Balance Sheet was as follows: Liabilities ₹ Assets ₹ Employees Provident Fund 17,000 Cash 6,100 Workmen Compensation Reserve 6,000 Stock 15,000 Investment Fluctuation Reserve 4,100 Debtors 50,000 Capital's A/cs: Less : Provision for Doubtful Debts 2,000 48,000 A 54,000 B 35,000 89,000 Investments 7,000 Goodwill 40,000 1,16,100 1,16,100 The following adjustments were agreed upon:(a) C brings in ₹ 16,000 as goodwill and proportionate capital.(b) Bad debts amounted to ₹ 3,000.(c) Market value of investment is ₹ 4,500.(d) Liability on account of Workmen Compensation Reserve amounted to ₹ 2,000.Prepare Revaluation Account and Partners' Capital Accounts.

Answer» A and B are partners in a firm sharing profits and losses in the ratio 3 : 1. They admit C for 1/4th share on 31st March, 2014 when their Balance Sheet was as follows:


Liabilities		₹	Assets		₹
Employees Provident Fund		17,000	Cash		6,100
Workmen Compensation Reserve		6,000	Stock		15,000
Investment Fluctuation Reserve		4,100	Debtors	50,000
Capital's A/cs:			Less : Provision for Doubtful Debts	2,000	48,000
A	54,000
B	35,000	89,000	Investments		7,000
			Goodwill		40,000

		1,16,100			1,16,100

The following adjustments were agreed upon:

(a) C brings in ₹ 16,000 as goodwill and proportionate capital.

(b) Bad debts amounted to ₹ 3,000.

(c) Market value of investment is ₹ 4,500.

(d) Liability on account of Workmen Compensation Reserve amounted to ₹ 2,000.

Prepare Revaluation Account and Partners' Capital Accounts.

Discussion

7921.	54. Water flows at the rate of 5 m per sec. Through a cylindrical pipe whose diameter is 7 cm .How long will it take to fill the conical vessel having base diameter to be 21 m. And depth 12 m.
Answer» 54. Water flows at the rate of 5 m per sec. Through a cylindrical pipe whose diameter is 7 cm .How long will it take to fill the conical vessel having base diameter to be 21 m. And depth 12 m.

Discussion

7922.	If(4x2 + xy) : (3xy - y2) =12:5 , find (x+2y) : (2x + y). x2 - square of x y2 - square of y
Answer» If(4x2 + xy) : (3xy - y2) =12:5 , find (x+2y) : (2x + y). x2 - square of x y2 - square of y

Discussion

7923.	The marks obtained by the students of a class, in an exam which was out of 50 marks is given below : MarksNumber of students5172112163215246283325348396434452493 Find the mean for the ungrouped data.
Answer» The marks obtained by the students of a class, in an exam which was out of 50 marks is given below : $\begin{matrix} M a r k s & N u m b e r o f s t u d e n t s 5 & 1 7 & 2 11 & 2 16 & 3 21 & 5 24 & 6 28 & 3 32 & 5 34 & 8 39 & 6 43 & 4 45 & 2 49 & 3 \end{matrix}$ Find the mean for the ungrouped data.

7923.

The marks obtained by the students of a class, in an exam which was out of 50 marks is given below : MarksNumber of students5172112163215246283325348396434452493 Find the mean for the ungrouped data.

Answer»

The marks obtained by the students of a class, in an exam which was out of 50 marks is given below :

$\begin{matrix} M a r k s & N u m b e r o f s t u d e n t s 5 & 1 7 & 2 11 & 2 16 & 3 21 & 5 24 & 6 28 & 3 32 & 5 34 & 8 39 & 6 43 & 4 45 & 2 49 & 3 \end{matrix}$

Find the mean for the ungrouped data.

Discussion

7924.	Find the solution of the pair of linear equationsx+2y=5 and 7x+3y=13.
Answer» Find the solution of the pair of linear equations $x + 2 y = 5$ and $7 x + 3 y = 13.$

Discussion

7925.	Prove the following trigonometric identities.If Tn=sinn θ+cosn θ, prove that T3-T5T1=T5-T7T3
Answer» Prove the following trigonometric identities. $If T_{n} = \sin^{n} θ + \cos^{n} θ, prove that \frac{T_{3} - T_{5}}{T_{1}} = \frac{T_{5} - T_{7}}{T_{3}}$

Discussion

7926.	35. Find the length of the altitude of the triangle , coordinates of whose vertices are (5,1) ; (2,4); (-1,-1).
Answer» 35. Find the length of the altitude of the triangle , coordinates of whose vertices are (5,1) ; (2,4); (-1,-1).

Discussion

7927.	Question 3Verify whether the following are zeroes of the polynomial, indicated against them.(i) p(x) = 3x + 1, x = −13(ii) p(x)=5x−π,x=45(iii) p(x)=x2−1,x=1,−1(iv) p(x) = (x +1) (x -2), x = - 1, 2(v) p(x)=x2,x=0(vi) p(x)=ix+m,x=−mi(vii) p(x)=3x2−1,x=−1√3,2√3(viii) p(x)=2x+1,x=12
Answer» Question 3 Verify whether the following are zeroes of the polynomial, indicated against them. (i) p(x) = 3x + 1, x = $- \frac{1}{3}$ (ii) $p (x) = 5 x - π, x = \frac{4}{5}$ (iii) $p (x) = x^{2} - 1, x = 1, - 1$ (iv) p(x) = (x +1) (x -2), x = - 1, 2 (v) $p (x) = x^{2}, x = 0$ (vi) $p (x) = i x + m, x = - \frac{m}{i}$ (vii) $p (x) = 3 x^{2} - 1, x = - \frac{1}{\sqrt{3}}, \frac{2}{\sqrt{3}}$ (viii) $p (x) = 2 x + 1, x = \frac{1}{2}$

Discussion

7928.	The diameter of a roller 120 cm long is 84 cm. If it takes 500 complete revolutions to level a playground, determine the cost of levelling at the rate of Rs 50 per square metre.[Use π =227]
Answer» The diameter of a roller 120 cm long is 84 cm. If it takes 500 complete revolutions to level a playground, determine the cost of levelling at the rate of Rs 50 per square metre. [Use π = $\frac{22}{7}$ ]

Discussion

7929.	If α and β are the zeroes of the quadratic polynomial 2x2−8x+4, then the value of αβ+βα+2(1α+1β)+3αβ is ___.16
Answer» If $α a n d β$ are the zeroes of the quadratic polynomial $2 x^{2} - 8 x + 4$ , then the value of $\frac{α}{β} + \frac{β}{α} + 2 (\frac{1}{α} + \frac{1}{β}) + 3 α β$ is ___. 16

Discussion

7930.	9. A hemispherical tank has an inner radius of 2.8 m. Find its capacity in litres.
Answer» 9. A hemispherical tank has an inner radius of 2.8 m. Find its capacity in litres.

Discussion

7931.	A square pyramid covers an area of 400 m2 on the ground.If the height of the pyramid is 10 m, then find the total surface area of the pyramid.
Answer» A square pyramid covers an area of $400 m^{2}$ on the ground. If the height of the pyramid is 10 m, then find the total surface area of the pyramid.

Discussion

7932.	Find the area of the region bounded by the curve y 2 = x and the lines x = 1, x = 4 and the x -axis.
Answer» Find the area of the region bounded by the curve y 2 = x and the lines x = 1, x = 4 and the x -axis.

Discussion

7933.	Nidhi constructed a square pyramid of base edge 10cm and height 6cm. Rahul made a square pyramid of base edge 5cm and height 24cm. What is the ratio of the volumes of the pyramids constructed by Nidhi and Rahul?
Answer» Nidhi constructed a square pyramid of base edge 10cm and height 6cm. Rahul made a square pyramid of base edge 5cm and height 24cm. What is the ratio of the volumes of the pyramids constructed by Nidhi and Rahul?

Discussion

7934.	Solve the following system of linear equations by using the method of substitution:2x−3y=2,x+2y=8
Answer» Solve the following system of linear equations by using the method of substitution: $2 x - 3 y = 2, x + 2 y = 8$

Discussion

7935.	Determine, graphically whether the system of equations x - 2y = 2, 4x - 2y = 5 is consistent or in-consistent.
Answer» Determine, graphically whether the system of equations x - 2y = 2, 4x - 2y = 5 is consistent or in-consistent.

Discussion

7936.	Write an equation of a line passing through the point representing solution of the pair of linear equations x + y =2 and 2x - y = 1 . How many such lines can we find ?
Answer» Write an equation of a line passing through the point representing solution of the pair of linear equations $x + y = 2 and 2 x - y = 1$ . How many such lines can we find ?

Discussion

7937.	Manikanta invested ₹1000 in an oil company. The nominal value of the share is ₹9 and the market value is ₹10. The company is paying 8% dividend per annum. The number of shares bought by him and his income from the investment are respectively ____.
Answer» Manikanta invested ₹1000 in an oil company. The nominal value of the share is ₹9 and the market value is ₹10. The company is paying 8% dividend per annum. The number of shares bought by him and his income from the investment are respectively ____.

Discussion

7938.	If x=2sin θ1+sin 2θ+cos 2θ and θ=45°, then find the value of x.
Answer» If $x = \frac{2 s i n θ}{1 + s i n 2 θ + c o s 2 θ}$ and $θ = 45 °,$ then find the value of $x$ .

Discussion

7939.	If PQ, the distance between the center of two circles, measures 8 units, what is the length of the red curve?
Answer» If PQ, the distance between the center of two circles, measures 8 units, what is the length of the red curve?

Discussion

7940.	A hemisphere of radius 21cm, made up of iron is melted and moulded to form a cone of height 21 cm. What is the ratio of the curved surface area of the cone to that of the hemisphere?
Answer» A hemisphere of radius 21cm, made up of iron is melted and moulded to form a cone of height 21 cm. What is the ratio of the curved surface area of the cone to that of the hemisphere?

Discussion

7941.	In triangle ABC, if BC=AC and ∠B=40∘. Then ∠C is equal to ___ degrees.
Answer» In triangle ABC, if $B C = A C$ and $∠ B = 40^{\circ}$ . Then $∠ C$ is equal to ___ degrees.

Discussion

7942.	Let R be a relation over the set N×n and it is defined by (a, b) R (c, d) ⇒ a+ d = b + c. Then, R is
Answer» Let R be a relation over the set $N \times n$ and it is defined by (a, b) R (c, d) $\Rightarrow$ a+ d = b + c. Then, R is

Discussion

7943.	In the picture below, O is the centre of the circle and the line OD is parallel to the line CA.Prove that OD bisects ∠AOB.
Answer» In the picture below, O is the centre of the circle and the line OD is parallel to the line CA. Prove that OD bisects ∠AOB.

7943.

In the picture below, O is the centre of the circle and the line OD is parallel to the line CA.Prove that OD bisects ∠AOB.

Answer»

In the picture below, O is the centre of the circle and the line OD is parallel to the line CA.

Prove that OD bisects ∠AOB.

Discussion

7944.	Prove that the tangents at the extremities of any chord make equal angles with the chord. [3 MARKS]
Answer» Prove that the tangents at the extremities of any chord make equal angles with the chord. [3 MARKS]

Discussion

7945.	Prove the following trigonometric identities.(1 + cot A − cosec A) (1 + tan A + sec A) = 2
Answer» Prove the following trigonometric identities. (1 + cot A − cosec A) (1 + tan A + sec A) = 2

Discussion

7946.	Write five solutions of the equation x + y = 7.
Answer» Write five solutions of the equation x + y = 7.

Discussion

7947.	Divide 27 into two parts such that the sum of their reciprocals is 320.
Answer» Divide 27 into two parts such that the sum of their reciprocals is $\frac{3}{20}$ .

Discussion

7948.	In ΔABC, ∠C=50⁰ and ∠A = ∠B. What is the measure of ∠A?
Answer» In ΔABC, ∠C=50⁰ and ∠A = ∠B. What is the measure of ∠A?

Discussion

7949.	Find x and y If [2−3y2x]=[215−8]
Answer» Find x and y If $[\begin{matrix} 2 & - 3 y & 2 x \end{matrix}] = [\begin{matrix} 2 & 15 & - 8 \end{matrix}]$

Discussion

7950.	51.AB is a diameter and AC is a chord of a circle such that angle BAC=30 degrees. If the tangent at C intersects AB produced at D, then prove that BC=BD
Answer» 51.AB is a diameter and AC is a chord of a circle such that angle BAC=30 degrees. If the tangent at C intersects AB produced at D, then prove that BC=BD

Discussion

Explore topic-wise InterviewSolutions in .

The given table shows the Marks obtained by students in Mathematics.MarksNo. of Students0−10310−20720−301230−401540−502050−60960−70870−801680−901490−1006Using the table determine the Number of students who got above 74 % by drawing an ogive curve.

The length of a rectangular field is 23 m more than its breadth. If the perimeter of the field is 206 m, then its area is(a) 2420 m2(b) 2520 m2(c) 2480 m2(d) 2620 m2

Factorize: a2−b2+2bc−c2

A hemispherical bowl made of brass has inner radius of 3.5 cm. Find the cost of tin-plating the inner part of the bowl as well as tin plating a plate that exactly fits as a lid for the bowl. Tin plating is done at the rate of ₹10 per 100 sq.cm.

Question 1 (v)Fill in the blanks in the following table, given that a is the first term, d the common difference and an the nth term of the A.P.adnan(v)3.50105……

If the area of a circle is equal to the sum of the areas of two circles of diameters 10 cm and 24 cm, then diameter of the large circle (in cm) is(a) 34(b) 26(c) 17(d) 14

If the perimeter of a square is equal to the circumference of a circle then the ratio of their areas is (a) 4 : π (b) π : 4 (c) π : 7 (d) 7 : π

solve by elimination: ax-by=a^2-b^2; x+y=ab

Find the missing quantity. 1 l=350 ml + _____ ml.650

Cards numbered 1 to 30 are put in a bag. A card is drawn at random from this bag. Find the probability that the number on the drawn card is(i) not divisible by 3(ii) a prime number greater than 7(iii) not a perfect square number [CBSE 2014]

In the figure, O is the centre of circumcircle of triangle XYZ. Tangents at X and Y intersect at T. Given ∠XTY = 80o and ∠XOZ = 140o, calculate the value of ∠ZXY.

Except for one face of a given cube, identical cubes are glued to all the other faces of the given cube. If each side of the given cube measures 3 cm, what is the total surface area of the solid body thus formed?

Without solving the following quadratic equation, find the value of 'm' for which the given equation has real and equal roots. x2+2(m−1)x+(m+5)=0 [4 MARKS]

Find the number that is to be added to x2+12x to make it a perfect square.36

Find the mean of each of the following frequency distributions : Class interval: 50-70 70-90 90-110 110-130 130-150 150-170 Frequency: 18 12 13 27 8 22

The sum of the zeros and the product of zeros of a quadratic polynomial are −12 and −3 respectively. Write the polynomial.

Let M×[1102]=[12], where M is a matrix. a) State the order of the matrix M. b) Find the matrix M

Question 5 (iii) In a circle of radius 21 cm, an arc subtends an angle of 60∘ at the centre. Find: (iii) area of the segment formed by the corresponding chord

54. Water flows at the rate of 5 m per sec. Through a cylindrical pipe whose diameter is 7 cm .How long will it take to fill the conical vessel having base diameter to be 21 m. And depth 12 m.

If(4x2 + xy) : (3xy - y2) =12:5 , find (x+2y) : (2x + y). x2 - square of x y2 - square of y

The marks obtained by the students of a class, in an exam which was out of 50 marks is given below : MarksNumber of students5172112163215246283325348396434452493 Find the mean for the ungrouped data.

Find the solution of the pair of linear equationsx+2y=5 and 7x+3y=13.

Prove the following trigonometric identities.If Tn=sinn θ+cosn θ, prove that T3-T5T1=T5-T7T3

35. Find the length of the altitude of the triangle , coordinates of whose vertices are (5,1) ; (2,4); (-1,-1).

Question 3Verify whether the following are zeroes of the polynomial, indicated against them.(i) p(x) = 3x + 1, x = −13(ii) p(x)=5x−π,x=45(iii) p(x)=x2−1,x=1,−1(iv) p(x) = (x +1) (x -2), x = - 1, 2(v) p(x)=x2,x=0(vi) p(x)=ix+m,x=−mi(vii) p(x)=3x2−1,x=−1√3,2√3(viii) p(x)=2x+1,x=12

The diameter of a roller 120 cm long is 84 cm. If it takes 500 complete revolutions to level a playground, determine the cost of levelling at the rate of Rs 50 per square metre.[Use π =227]

If α and β are the zeroes of the quadratic polynomial 2x2−8x+4, then the value of αβ+βα+2(1α+1β)+3αβ is ___.16

9. A hemispherical tank has an inner radius of 2.8 m. Find its capacity in litres.

A square pyramid covers an area of 400 m2 on the ground.If the height of the pyramid is 10 m, then find the total surface area of the pyramid.

Find the area of the region bounded by the curve y 2 = x and the lines x = 1, x = 4 and the x -axis.

Nidhi constructed a square pyramid of base edge 10cm and height 6cm. Rahul made a square pyramid of base edge 5cm and height 24cm. What is the ratio of the volumes of the pyramids constructed by Nidhi and Rahul?

Solve the following system of linear equations by using the method of substitution:2x−3y=2,x+2y=8

Determine, graphically whether the system of equations x - 2y = 2, 4x - 2y = 5 is consistent or in-consistent.

Write an equation of a line passing through the point representing solution of the pair of linear equations x + y =2 and 2x - y = 1 . How many such lines can we find ?

Manikanta invested ₹1000 in an oil company. The nominal value of the share is ₹9 and the market value is ₹10. The company is paying 8% dividend per annum. The number of shares bought by him and his income from the investment are respectively ____.

If x=2sin θ1+sin 2θ+cos 2θ and θ=45°, then find the value of x.

If PQ, the distance between the center of two circles, measures 8 units, what is the length of the red curve?

A hemisphere of radius 21cm, made up of iron is melted and moulded to form a cone of height 21 cm. What is the ratio of the curved surface area of the cone to that of the hemisphere?

In triangle ABC, if BC=AC and ∠B=40∘. Then ∠C is equal to ___ degrees.

Let R be a relation over the set N×n and it is defined by (a, b) R (c, d) ⇒ a+ d = b + c. Then, R is

In the picture below, O is the centre of the circle and the line OD is parallel to the line CA.Prove that OD bisects ∠AOB.

Prove that the tangents at the extremities of any chord make equal angles with the chord. [3 MARKS]

Prove the following trigonometric identities.(1 + cot A − cosec A) (1 + tan A + sec A) = 2

Write five solutions of the equation x + y = 7.

Divide 27 into two parts such that the sum of their reciprocals is 320.

In ΔABC, ∠C=50⁰ and ∠A = ∠B. What is the measure of ∠A?

Find x and y If [2−3y2x]=[215−8]

51.AB is a diameter and AC is a chord of a circle such that angle BAC=30 degrees. If the tangent at C intersects AB produced at D, then prove that BC=BD