32581 + Interview Questions in Mathematics

1.	Four numbers are in A.P. If their sum is 20 and the sum of their square is 120, then the middle terms are
Answer» Four numbers are in A.P. If their sum is 20 and the sum of their square is 120, then the middle terms are

Discussion

2.	The line x+y=10 divides line segment AB in the ratio a:1. Find the value of a.
Answer» The line $x + y = 10$ divides line segment $A B$ in the ratio $a : 1$ . Find the value of $a$ .

Discussion

3.	Five years ago, a woman’s age was the square of her son’s age. Ten years hence her age will be twice that of her son’s age. Find
Answer» Five years ago, a woman’s age was the square of her son’s age. Ten years hence her age will be twice that of her son’s age. Find

Discussion

4.	In the given right angle triangle if AC=10cm and θ = 30∘ .The vertical height of given triangle is…………………cm __
Answer» In the given right angle triangle if AC=10cm and $θ$ = $30^{\circ}$ .The vertical height of given triangle is…………………cm __

4.

In the given right angle triangle if AC=10cm and θ = 30∘ .The vertical height of given triangle is…………………cm __

Answer»

In the given right angle triangle if AC=10cm and $θ$ = $30^{\circ}$ .The vertical height of given triangle is…………………cm

__

Discussion

5.	Two triangles BAC and BDC right angled at A and D respectively, are drawn on the same base BC and on the same side of BC. If AC and DB intersect at P, prove that AP × PC = DP × PB.
Answer» Two triangles BAC and BDC right angled at A and D respectively, are drawn on the same base BC and on the same side of BC. If AC and DB intersect at P, prove that AP × PC = DP × PB.

Discussion

6.	Solve the following quadratic equations by factorization method : (i) x2+10ix−21=0 (ii) x2+(1−2i)x−2i=0 (iii) x2−(2√3+3i)x+6√3i=0 (iv)6x2−17ix−12=0
Answer» Solve the following quadratic equations by factorization method : (i) $x^{2} + 10 i x - 21 = 0$ (ii) $x^{2} + (1 - 2 i) x - 2 i = 0$ (iii) $x^{2} - (2 \sqrt{3} + 3 i) x + 6 \sqrt{3} i = 0$ (iv) $6 x^{2} - 17 i x - 12 = 0$

6.

Solve the following quadratic equations by factorization method : (i) x2+10ix−21=0 (ii) x2+(1−2i)x−2i=0 (iii) x2−(2√3+3i)x+6√3i=0 (iv)6x2−17ix−12=0

Answer»

Solve the following quadratic equations by factorization method :

(i) $x^{2} + 10 i x - 21 = 0$

(ii) $x^{2} + (1 - 2 i) x - 2 i = 0$

(iii) $x^{2} - (2 \sqrt{3} + 3 i) x + 6 \sqrt{3} i = 0$

(iv) $6 x^{2} - 17 i x - 12 = 0$

Discussion

7.	The sums of n terms of two arithmetic progressions are in the ratio 5n + 4 : 9n + 6. Find the ratio of their 18th terms.
Answer» The sums of n terms of two arithmetic progressions are in the ratio 5n + 4 : 9n + 6. Find the ratio of their 18^th terms.

Discussion

8.	Question 3 A plumbline ( Sahul) is the combination of ( see figure) (A) a cone and a cylinder (B) a hemisphere and a cone (C) frustum of a cone and a cylinder (D) sphere and cylinder
Answer» Question 3 A plumbline ( Sahul) is the combination of ( see figure) (A) a cone and a cylinder (B) a hemisphere and a cone (C) frustum of a cone and a cylinder (D) sphere and cylinder

Discussion

9.	In a school, there are two bells, one in the primary school and the other in the secondary school. Both the bells ring after every class. The primary school has classes 45 minutes each whereas the secondary school has classes every 1 hour. Find when both the bells ring at the same time again if both classes start at the same time?
Answer» In a school, there are two bells, one in the primary school and the other in the secondary school. Both the bells ring after every class. The primary school has classes 45 minutes each whereas the secondary school has classes every 1 hour. Find when both the bells ring at the same time again if both classes start at the same time?

Discussion

10.	If alpha and beta are zeroes of the quadratic polynomial x2-5x+4, then find all the quadratic polynomials whose zeroes are alpha+1/beta and beta+1/alpha.
Answer» If alpha and beta are zeroes of the quadratic polynomial x2-5x+4, then find all the quadratic polynomials whose zeroes are alpha+1/beta and beta+1/alpha.

Discussion

11.	Find the common difference of the given AP. 10, 20, 30, 40, ...
Answer» Find the common difference of the given AP. 10, 20, 30, 40, ...

11.

Find the common difference of the given AP. 10, 20, 30, 40, ...

Answer»

Find the common difference of the given AP.

10, 20, 30, 40, ...

Discussion

12.	A cylindrical pencil sharpened at one edge is the combination of
Answer» A cylindrical pencil sharpened at one edge is the combination of

Discussion

13.	Area of a sector of a circle of radius 36 cm is 54π cm2. The length of the corresponding arc of the sector is:
Answer» Area of a sector of a circle of radius 36 cm is 54π cm². The length of the corresponding arc of the sector is:

Discussion

14.	In fig. 1, ABCD is a rectangle. Find the values of x and y.
Answer» In fig. 1, ABCD is a rectangle. Find the values of x and y.

Discussion

15.	Calculate the height of an equilateral triangle each of whose sides measures 12 cm.
Answer» Calculate the height of an equilateral triangle each of whose sides measures 12 cm.

Discussion

16.	Solve the following systems of equations: 99x+101y=499 101x+99y=501
Answer» Solve the following systems of equations: 99x+101y=499 101x+99y=501

16.

Solve the following systems of equations: 99x+101y=499 101x+99y=501

Answer»

Solve the following systems of equations:

99x+101y=499

101x+99y=501

Discussion

17.	In figure AB is a diameter of a circle with centre O and AT is a tangent. If ∠AOQ=58∘, find ∠ATQ.
Answer» In figure AB is a diameter of a circle with centre O and AT is a tangent. If $∠ A O Q = 58^{\circ}$ , find $∠ A T Q$ .

Discussion

18.	Find three numbers in AP whose sum is 15 and product is 80.
Answer» Find three numbers in AP whose sum is 15 and product is 80.

Discussion

19.	A heap of rice in the form of a cone of diameter 9 m and height 3.5 m. Find the volume of rice.How much canvas cloth is required to cover the heap?
Answer» A heap of rice in the form of a cone of diameter 9 m and height 3.5 m. Find the volume of rice.How much canvas cloth is required to cover the heap?

Discussion

20.	Find the mean of the following data, using assumed-mean method: Marks100−120120−140140−160160−180180−200Number of students102030155
Answer» Find the mean of the following data, using assumed-mean method: $\begin{matrix} Marks & 100 - 120 & 120 - 140 & 140 - 160 & 160 - 180 & 180 - 200 Number of students & 10 & 20 & 30 & 15 & 5 \end{matrix}$

Discussion

21.	If a square and a rhombus stand on the same base, then what is the ratio of the areas of the square and the rhombus respectively?
Answer» If a square and a rhombus stand on the same base, then what is the ratio of the areas of the square and the rhombus respectively?

Discussion

22.	Solve for x and y: 4x+6y=3xy,8x+9y=5xy (x≠0,y≠0).
Answer» Solve for x and y: $4 x + 6 y = 3 x y, 8 x + 9 y = 5 x y (x \neq 0, y \neq 0) .$

22.

Solve for x and y: 4x+6y=3xy,8x+9y=5xy (x≠0,y≠0).

Answer»

Solve for x and y:

$4 x + 6 y = 3 x y, 8 x + 9 y = 5 x y (x \neq 0, y \neq 0) .$

Discussion

23.	Solve the following systems of equations: 0.4x+0.3y=1.7 0.7x-0.2y=0.8
Answer» Solve the following systems of equations: 0.4x+0.3y=1.7 0.7x-0.2y=0.8

23.

Solve the following systems of equations: 0.4x+0.3y=1.7 0.7x-0.2y=0.8

Answer»

Solve the following systems of equations:

0.4x+0.3y=1.7

0.7x-0.2y=0.8

Discussion

24.	Solve the following systems of equations: x+yxy=2 x−yxy=6
Answer» Solve the following systems of equations: $\frac{x + y}{x y} = 2$ $\frac{x - y}{x y} = 6$

24.

Solve the following systems of equations: x+yxy=2 x−yxy=6

Answer»

Solve the following systems of equations:

$\frac{x + y}{x y} = 2$

$\frac{x - y}{x y} = 6$

Discussion

25.	The co-ordinates of the point which divides the line joining the points (– 2, – 2) and (– 5, 7) in the ratio 2 : 1 is:
Answer» The co-ordinates of the point which divides the line joining the points (– 2, – 2) and (– 5, 7) in the ratio 2 : 1 is:

Discussion

26.	In △ABC, the medians BE and CF intersect at G. AGD is a line meeting BC at D. If GD is 1.5 cm, then AD is equal to -
Answer» In $△ A B C,$ the medians $B E$ and $C F$ intersect at $G . A G D$ is a line meeting $B C$ at $D .$ If $G D$ is $1.5 c m,$ then $A D$ is equal to -

26.

In △ABC, the medians BE and CF intersect at G. AGD is a line meeting BC at D. If GD is 1.5 cm, then AD is equal to -

Answer»

In $△ A B C,$ the medians $B E$ and $C F$ intersect at $G . A G D$ is a line meeting $B C$ at $D .$ If $G D$ is $1.5 c m,$ then $A D$ is equal to -

Discussion

27.	A wooden toy was made by scooping out a hemisphere of same radius from each end of a solid cylinder. If the height of the cylinder is 10 cm, and its base is of radius 3.5 cm, find the volume of wood in the toy [Use π=227]
Answer» A wooden toy was made by scooping out a hemisphere of same radius from each end of a solid cylinder. If the height of the cylinder is 10 cm, and its base is of radius 3.5 cm, find the volume of wood in the toy $[U s e π = \frac{22}{7}]$

Discussion

28.	Factorise : 24a3+37a2−5a
Answer» Factorise : $24 a^{3} + 37 a^{2} - 5 a$

28.

Factorise : 24a3+37a2−5a

Answer»

Factorise :

$24 a^{3} + 37 a^{2} - 5 a$

Discussion

29.	Fill in the blanks with the help of options given I.___ of a circle subtend equal angles at the center II. The length of tangents drawn from an external point to a circle are___ III. If PAB is a secant to a circle, intersecting the circle at A and B and PT is a tangent segment, then PT2 =___. IV. If two tangents are drawn from an external point, then they subtend ___ at the center. Options:(i)Equal angles (ii)equal (iii) dissimilar (iv)similar (v)PA×PB (vi)PA+PB (vii)equal chords
Answer» Fill in the blanks with the help of options given I.___ of a circle subtend equal angles at the center II. The length of tangents drawn from an external point to a circle are___ III. If PAB is a secant to a circle, intersecting the circle at A and B and PT is a tangent segment, then $P T^{2}$ =___. IV. If two tangents are drawn from an external point, then they subtend ___ at the center. Options:(i)Equal angles (ii)equal (iii) dissimilar (iv)similar (v) $P A \times P B$ (vi)PA+PB (vii)equal chords

Discussion

30.	If three circles of radius a each, are drawn such that each touches the other two, prove that the area included between them is equal to 425 a2. [ Take √3=1.73 and π=3.14.]
Answer» If three circles of radius $a$ each, are drawn such that each touches the other two, prove that the area included between them is equal to $\frac{4}{25}$ $a^{2}$ . [ Take $\sqrt{3} = 1.73 a n d π = 3.14.$ ]

30.

If three circles of radius a each, are drawn such that each touches the other two, prove that the area included between them is equal to 425 a2. [ Take √3=1.73 and π=3.14.]

Answer»

If three circles of radius $a$ each, are drawn such that each touches the other two, prove that the area included between them is equal to $\frac{4}{25}$ $a^{2}$ .

[ Take $\sqrt{3} = 1.73 a n d π = 3.14.$ ]

Discussion

31.	If the angle between two tangents drawn from an external point P to a circle of radius' a ' and centre O, the 60o the find the length of OP.
Answer» If the angle between two tangents drawn from an external point P to a circle of radius' a ' and centre O, the $60^{o}$ the find the length of OP.

Discussion

32.	A man saved 33000 in 10 months. In each month after the first, he saved 100 more than he did in the preceding month. How much did he have in the first month?
Answer» A man saved 33000 in 10 months. In each month after the first, he saved 100 more than he did in the preceding month. How much did he have in the first month?

Discussion

33.	Question 5 Is 0 a term of the AP 31, 28, 25, …? Justify your answer.
Answer» Question 5 Is 0 a term of the AP 31, 28, 25, …? Justify your answer.

Discussion

34.	P-1:-tan1.tan2.tan3......tan87.tan88.tan89=1
Answer» P-1:-tan1.tan2.tan3......tan87.tan88.tan89=1

Discussion

35.	A chord of a circle of radius 12cm subtend an angle of 120° at the centre. Find the area of corresponding segment of the circle.
Answer» A chord of a circle of radius 12cm subtend an angle of 120° at the centre. Find the area of corresponding segment of the circle.

Discussion

36.	ax^2 + bx + c = k(x-α)(x- β). Why we take K as a constant.Give me answer with example?
Answer» ax^2 + bx + c = k(x-α)(x- β). Why we take K as a constant.Give me answer with example?

Discussion

37.	Which of the following statements always holds true?
Answer» Which of the following statements always holds true?

Discussion

38.	A cylindrical container of radius 6cm and height 15cm is filled with chocolate. The chocolate is to be filled into cones of height 12cm and radius 3cm having a hemispherical shape on the top. Find the number of cones that can be filled with the chocolate?
Answer» A cylindrical container of radius 6cm and height 15cm is filled with chocolate. The chocolate is to be filled into cones of height 12cm and radius 3cm having a hemispherical shape on the top. Find the number of cones that can be filled with the chocolate?

Discussion

39.	The point P(x, y) divides the line joining (– 2, – 2) and (– 5, 7) in the ratio 2 : 1. The value of x + y is\N
Answer» The point P(x, y) divides the line joining (– 2, – 2) and (– 5, 7) in the ratio 2 : 1. The value of x + y is \N

Discussion

40.	If m and n are the zeros of the polynomial, find the value of m/n+n/m
Answer» If m and n are the zeros of the polynomial, find the value of m/n+n/m

Discussion

41.	If the sum of first m terms of an AP is (2m2+3m) then what is its second term?
Answer» If the sum of first m terms of an AP is $(2 m^{2} + 3 m)$ then what is its second term?

Discussion

42.	Solve each of the following given systems of equations graphically and find the vertices and area of the triangle formed by these lines and the x-axis: 5x−y−7=0,x−y+1=0.
Answer» Solve each of the following given systems of equations graphically and find the vertices and area of the triangle formed by these lines and the x-axis: $5 x - y - 7 = 0, x - y + 1 = 0.$

Discussion

43.	A box contains 90 discs, numbered from 1 to 90. If one disc is drawn at random from the box, the probability that it bears prime number less than 23 is (a) 790 (b) 19 (c) 445 (d) 889
Answer» A box contains 90 discs, numbered from 1 to 90. If one disc is drawn at random from the box, the probability that it bears prime number less than 23 is (a) $\frac{7}{90}$ (b) $\frac{1}{9}$ (c) $\frac{4}{45}$ (d) $\frac{8}{89}$

Discussion

44.	How many terms of the AP 63, 60, 57, 54, ... must be taken so that their sum is 693. Explain the double answer.
Answer» How many terms of the AP 63, 60, 57, 54, ... must be taken so that their sum is 693. Explain the double answer.

Discussion

45.	If cot θ=34, show that √secθ−cosecθsecθ+cosecθ=1√7
Answer» If $c o t θ = \frac{3}{4}$ , show that $\sqrt{\frac{s e c θ - c o s e c θ}{s e c θ + c o s e c θ}} = \frac{1}{\sqrt{7}}$

Discussion

46.	Find the values of a and b for which rach of the following systems of linear equations has an infinite number of equations: 2x+3y=7,2ax+(a+b)y=28.
Answer» Find the values of a and b for which rach of the following systems of linear equations has an infinite number of equations: $2 x + 3 y = 7, 2 a x + (a + b) y = 28.$

46.

Find the values of a and b for which rach of the following systems of linear equations has an infinite number of equations: 2x+3y=7,2ax+(a+b)y=28.

Answer»

Find the values of a and b for which rach of the following systems of linear equations has an infinite number of equations:

$2 x + 3 y = 7, 2 a x + (a + b) y = 28.$

Discussion

47.	Find the roots of each of the following equations, if they exist, by applying the quadratic formula: a2b2x2−(4b4−3a4)x−12a2b2=0,a≠0 and b≠0
Answer» Find the roots of each of the following equations, if they exist, by applying the quadratic formula: $a^{2} b^{2} x^{2} - (4 b^{4} - 3 a^{4}) x - 12 a^{2} b^{2} = 0, a \neq 0 a n d b \neq 0$

Discussion

48.	Mode=? (a)xk+h.{(fk−1−fk)(2fk−fk−1−fk+1)} (b) xk+h.{(fk−fk−1)(2fk−fk−1−fk+1)}(c) xk+h.{(fk−fk−1)(fk−2fk−1−fk+1)} (d) xk+h.{(fk−fk−1)(fk−fk−1−2fk+1)}
Answer» Mode=? $(a) x_{k} + h . {\frac{(f_{k - 1} - f_{k})}{(2 f_{k} - f_{k - 1} - f_{k + 1})}} (b) x_{k} + h . {\frac{(f_{k} - f_{k - 1})}{(2 f_{k} - f_{k - 1} - f_{k + 1})}} (c) x_{k} + h . {\frac{(f_{k} - f_{k - 1})}{(f_{k} - 2 f_{k - 1} - f_{k + 1})}} (d) x_{k} + h . {\frac{(f_{k} - f_{k - 1})}{(f_{k} - f_{k - 1} - 2 f_{k + 1})}}$

48.

Mode=? (a)xk+h.{(fk−1−fk)(2fk−fk−1−fk+1)} (b) xk+h.{(fk−fk−1)(2fk−fk−1−fk+1)}(c) xk+h.{(fk−fk−1)(fk−2fk−1−fk+1)} (d) xk+h.{(fk−fk−1)(fk−fk−1−2fk+1)}

Answer»

Mode=?

$(a) x_{k} + h . {\frac{(f_{k - 1} - f_{k})}{(2 f_{k} - f_{k - 1} - f_{k + 1})}} (b) x_{k} + h . {\frac{(f_{k} - f_{k - 1})}{(2 f_{k} - f_{k - 1} - f_{k + 1})}} (c) x_{k} + h . {\frac{(f_{k} - f_{k - 1})}{(f_{k} - 2 f_{k - 1} - f_{k + 1})}} (d) x_{k} + h . {\frac{(f_{k} - f_{k - 1})}{(f_{k} - f_{k - 1} - 2 f_{k + 1})}}$

Discussion

49.	A metallic cylinder has radius 3 cm & height 5 cm. It is made of metal A. To reduce its weight, a conical hole is drilled at the top-centre of the cylinder, and then completely filled with a lighter metal B. The conical hole has a radius of 1.5 cm & depth of 8/9 cm. Calculate the ratio of volume of metal A to volume of metal B.
Answer» A metallic cylinder has radius 3 cm & height 5 cm. It is made of metal A. To reduce its weight, a conical hole is drilled at the top-centre of the cylinder, and then completely filled with a lighter metal B. The conical hole has a radius of 1.5 cm & depth of ⁸/₉ cm. Calculate the ratio of volume of metal A to volume of metal B.

Discussion

50.	A (4, 2), B (6, 5) and C (1, 4) are the vertices of △ABC. (i) The median from A meets BC in D. Find the coordinates of the point D. (ii) Find the coordinates of point P on AD such that AP : PD = 2:1. (iii) Find the coordinates of the points Q and R on medians BE and CF respectively such that BQ : QE = 2 :1 and RF = 2 :1. (iv) What do you observe?
Answer» A (4, 2), B (6, 5) and C (1, 4) are the vertices of $△$ ABC. (i) The median from A meets BC in D. Find the coordinates of the point D. (ii) Find the coordinates of point P on AD such that AP : PD = 2:1. (iii) Find the coordinates of the points Q and R on medians BE and CF respectively such that BQ : QE = 2 :1 and RF = 2 :1. (iv) What do you observe?

50.

A (4, 2), B (6, 5) and C (1, 4) are the vertices of △ABC. (i) The median from A meets BC in D. Find the coordinates of the point D. (ii) Find the coordinates of point P on AD such that AP : PD = 2:1. (iii) Find the coordinates of the points Q and R on medians BE and CF respectively such that BQ : QE = 2 :1 and RF = 2 :1. (iv) What do you observe?

Answer»

A (4, 2), B (6, 5) and C (1, 4) are the vertices of $△$ ABC.

(i) The median from A meets BC in D. Find the coordinates of the point D.

(ii) Find the coordinates of point P on AD such that AP : PD = 2:1.

(iii) Find the coordinates of the points Q and R on medians BE and CF respectively such that BQ : QE = 2 :1 and RF = 2 :1.

(iv) What do you observe?

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Four numbers are in A.P. If their sum is 20 and the sum of their square is 120, then the middle terms are

The line x+y=10 divides line segment AB in the ratio a:1. Find the value of a.

Five years ago, a woman’s age was the square of her son’s age. Ten years hence her age will be twice that of her son’s age. Find

In the given right angle triangle if AC=10cm and θ = 30∘ .The vertical height of given triangle is…………………cm __

Two triangles BAC and BDC right angled at A and D respectively, are drawn on the same base BC and on the same side of BC. If AC and DB intersect at P, prove that AP × PC = DP × PB.

Solve the following quadratic equations by factorization method : (i) x2+10ix−21=0 (ii) x2+(1−2i)x−2i=0 (iii) x2−(2√3+3i)x+6√3i=0 (iv)6x2−17ix−12=0

The sums of n terms of two arithmetic progressions are in the ratio 5n + 4 : 9n + 6. Find the ratio of their 18th terms.

Question 3 A plumbline ( Sahul) is the combination of ( see figure) (A) a cone and a cylinder (B) a hemisphere and a cone (C) frustum of a cone and a cylinder (D) sphere and cylinder

If alpha and beta are zeroes of the quadratic polynomial x2-5x+4, then find all the quadratic polynomials whose zeroes are alpha+1/beta and beta+1/alpha.

Find the common difference of the given AP. 10, 20, 30, 40, ...

A cylindrical pencil sharpened at one edge is the combination of

Area of a sector of a circle of radius 36 cm is 54π cm2. The length of the corresponding arc of the sector is:

In fig. 1, ABCD is a rectangle. Find the values of x and y.

Calculate the height of an equilateral triangle each of whose sides measures 12 cm.

Solve the following systems of equations: 99x+101y=499 101x+99y=501

In figure AB is a diameter of a circle with centre O and AT is a tangent. If ∠AOQ=58∘, find ∠ATQ.

Find three numbers in AP whose sum is 15 and product is 80.

A heap of rice in the form of a cone of diameter 9 m and height 3.5 m. Find the volume of rice.How much canvas cloth is required to cover the heap?

Find the mean of the following data, using assumed-mean method: Marks100−120120−140140−160160−180180−200Number of students102030155

If a square and a rhombus stand on the same base, then what is the ratio of the areas of the square and the rhombus respectively?

Solve for x and y: 4x+6y=3xy,8x+9y=5xy (x≠0,y≠0).

Solve the following systems of equations: 0.4x+0.3y=1.7 0.7x-0.2y=0.8

Solve the following systems of equations: x+yxy=2 x−yxy=6

The co-ordinates of the point which divides the line joining the points (– 2, – 2) and (– 5, 7) in the ratio 2 : 1 is:

In △ABC, the medians BE and CF intersect at G. AGD is a line meeting BC at D. If GD is 1.5 cm, then AD is equal to -

A wooden toy was made by scooping out a hemisphere of same radius from each end of a solid cylinder. If the height of the cylinder is 10 cm, and its base is of radius 3.5 cm, find the volume of wood in the toy [Use π=227]

Factorise : 24a3+37a2−5a

If three circles of radius a each, are drawn such that each touches the other two, prove that the area included between them is equal to 425 a2. [ Take √3=1.73 and π=3.14.]

If the angle between two tangents drawn from an external point P to a circle of radius' a ' and centre O, the 60o the find the length of OP.

A man saved 33000 in 10 months. In each month after the first, he saved 100 more than he did in the preceding month. How much did he have in the first month?

Question 5 Is 0 a term of the AP 31, 28, 25, …? Justify your answer.

P-1:-tan1.tan2.tan3......tan87.tan88.tan89=1

A chord of a circle of radius 12cm subtend an angle of 120° at the centre. Find the area of corresponding segment of the circle.

ax^2 + bx + c = k(x-α)(x- β). Why we take K as a constant.Give me answer with example?

Which of the following statements always holds true?

A cylindrical container of radius 6cm and height 15cm is filled with chocolate. The chocolate is to be filled into cones of height 12cm and radius 3cm having a hemispherical shape on the top. Find the number of cones that can be filled with the chocolate?

The point P(x, y) divides the line joining (– 2, – 2) and (– 5, 7) in the ratio 2 : 1. The value of x + y is\N

If m and n are the zeros of the polynomial, find the value of m/n+n/m

If the sum of first m terms of an AP is (2m2+3m) then what is its second term?

Solve each of the following given systems of equations graphically and find the vertices and area of the triangle formed by these lines and the x-axis: 5x−y−7=0,x−y+1=0.

A box contains 90 discs, numbered from 1 to 90. If one disc is drawn at random from the box, the probability that it bears prime number less than 23 is (a) 790 (b) 19 (c) 445 (d) 889

How many terms of the AP 63, 60, 57, 54, ... must be taken so that their sum is 693. Explain the double answer.

If cot θ=34, show that √secθ−cosecθsecθ+cosecθ=1√7

Find the values of a and b for which rach of the following systems of linear equations has an infinite number of equations: 2x+3y=7,2ax+(a+b)y=28.

Find the roots of each of the following equations, if they exist, by applying the quadratic formula: a2b2x2−(4b4−3a4)x−12a2b2=0,a≠0 and b≠0

Mode=? (a)xk+h.{(fk−1−fk)(2fk−fk−1−fk+1)} (b) xk+h.{(fk−fk−1)(2fk−fk−1−fk+1)}(c) xk+h.{(fk−fk−1)(fk−2fk−1−fk+1)} (d) xk+h.{(fk−fk−1)(fk−fk−1−2fk+1)}