32581 + Interview Questions in Mathematics

1.	7(y+3)-2(x+2)=14 4(y-2)+3(x-3)=2 Solve the system of equation
Answer» 7(y+3)-2(x+2)=14 4(y-2)+3(x-3)=2 Solve the system of equation

1.

7(y+3)-2(x+2)=14 4(y-2)+3(x-3)=2 Solve the system of equation

Answer»

7(y+3)-2(x+2)=14

4(y-2)+3(x-3)=2

Solve the system of equation

Discussion

2.	Posted by Joseph Georgeabout 2 hours ago (l+3)(b-4) = lb - 67 lb - 4l + 3b - 12 = lb - 67 -4l + 3b = -55 it can also be written as 4l-3b = 55 ---(1) (l-1)(b+4) = lb + 89 lb +4l - b +4 = lb +89 4l - b = 85 ---(2) subtracting 2 from 1 4l - 4l -3b +b = 55 - 85 -2b = -30 b = 15 putting this in 1 4l - 3(15) = 55 4l - 45 = 55 4l = 100 l= 25 lenght = 25 m bredth = 15 m..see this was the solution sir and i want to ask that (l-1)(b+4) openings means how to open it ..my ans is coming as-4 but here +4.plz clear itttt
Answer» Posted by Joseph Georgeabout 2 hours ago (l+3)(b-4) = lb - 67 lb - 4l + 3b - 12 = lb - 67 -4l + 3b = -55 it can also be written as 4l-3b = 55 ---(1) (l-1)(b+4) = lb + 89 lb +4l - b +4 = lb +89 4l - b = 85 ---(2) subtracting 2 from 1 4l - 4l -3b +b = 55 - 85 -2b = -30 b = 15 putting this in 1 4l - 3(15) = 55 4l - 45 = 55 4l = 100 l= 25 lenght = 25 m bredth = 15 m..see this was the solution sir and i want to ask that (l-1)(b+4) openings means how to open it ..my ans is coming as-4 but here +4.plz clear itttt

2.

Posted by Joseph Georgeabout 2 hours ago (l+3)(b-4) = lb - 67 lb - 4l + 3b - 12 = lb - 67 -4l + 3b = -55 it can also be written as 4l-3b = 55 ---(1) (l-1)(b+4) = lb + 89 lb +4l - b +4 = lb +89 4l - b = 85 ---(2) subtracting 2 from 1 4l - 4l -3b +b = 55 - 85 -2b = -30 b = 15 putting this in 1 4l - 3(15) = 55 4l - 45 = 55 4l = 100 l= 25 lenght = 25 m bredth = 15 m..see this was the solution sir and i want to ask that (l-1)(b+4) openings means how to open it ..my ans is coming as-4 but here +4.plz clear itttt

Answer»

Posted by Joseph Georgeabout 2 hours ago

(l+3)(b-4) = lb - 67
lb - 4l + 3b - 12 = lb - 67
-4l + 3b = -55
it can also be written as
4l-3b = 55 ---(1)

(l-1)(b+4) = lb + 89
lb +4l - b +4 = lb +89
4l - b = 85 ---(2)

subtracting 2 from 1

4l - 4l -3b +b = 55 - 85
-2b = -30
b = 15

putting this in 1

4l - 3(15) = 55
4l - 45 = 55
4l = 100
l= 25

lenght = 25 m
bredth = 15 m..see this was the solution sir and i want to ask that (l-1)(b+4) openings means how to open it ..my ans is coming as-4 but here +4.plz clear itttt

Discussion

3.	Find the ratio in which P(4, m) divides the line segment joining the points A(2, 3) and B(6, -3). Hence find m.
Answer» Find the ratio in which P(4, m) divides the line segment joining the points A(2, 3) and B(6, -3). Hence find m.

Discussion

4.	Prove 7√11 /3 as irrational ?
Answer» Prove 7√11 /3 as irrational ?

Discussion

5.	I have a car moving which covers a distance of 20 m in 20 seconds. What is its speed?
Answer» I have a car moving which covers a distance of 20 m in 20 seconds. What is its speed?

Discussion

6.	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: x−y+1=0, 3x+2y−12=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: $x - y + 1 = 0, 3 x + 2 y - 12 = 0.$

6.

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: x−y+1=0, 3x+2y−12=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:

$x - y + 1 = 0, 3 x + 2 y - 12 = 0.$

Discussion

7.	If one zero of polynomial (a2+9)x2+13x+6a is reciprocal of other find value of a.
Answer» If one zero of polynomial (a²+9)x²+13x+6a is reciprocal of other find value of a.

Discussion

8.	Let f:(0,∞)→R be a differentiable function such that f′(x)=2−f(x)x for all xϵ(0,∞) and f(1)≠1. Then
Answer» Let $f : (0, \infty) \to R$ be a differentiable function such that $f^{'} (x) = 2 - \frac{f (x)}{x}$ for all $x ϵ (0, \infty)$ and $f (1) \neq 1$ . Then

Discussion

9.	Find the sum of all integers between 84 and 719, which are multiples of 5.
Answer» Find the sum of all integers between 84 and 719, which are multiples of 5.

Discussion

10.	The following figure shows a parallelogram ABCD whose side AB is parallel to the x-axis, ∠A = 60∘ and vertex C = (7, 5). Find the equation of BC and CD.
Answer» The following figure shows a parallelogram ABCD whose side AB is parallel to the x-axis, $∠$ A = $60^{\circ}$ and vertex C = (7, 5). Find the equation of BC and CD.

10.

The following figure shows a parallelogram ABCD whose side AB is parallel to the x-axis, ∠A = 60∘ and vertex C = (7, 5). Find the equation of BC and CD.

Answer»

The following figure shows a parallelogram ABCD whose side AB is parallel to the x-axis, $∠$ A = $60^{\circ}$ and vertex C = (7, 5). Find the equation of BC and CD.

Discussion

11.	If sec θ = 135, find the value of BC and tanθ
Answer» If sec $θ$ = $\frac{13}{5}$ , find the value of BC and tan $θ$

11.

If sec θ = 135, find the value of BC and tanθ

Answer»

If sec $θ$ = $\frac{13}{5}$ , find the value of BC and tan $θ$

Discussion

12.	If 1/a, 1/b, 1/c, are in a.p prove that BC, ca, an are in a.p hints: prove that ab- ca =ca- BC Using 1/c - 1/b = 1/b - 1/a.
Answer» If 1/a, 1/b, 1/c, are in a.p prove that BC, ca, an are in a.p hints: prove that ab- ca =ca- BC Using 1/c - 1/b = 1/b - 1/a.

Discussion

13.	A solid wooden toy is in the shape of a right circular cone mounted on a hemisphere. If the radius of the hemisphere is 4.2 cm and the total height of the toy is 10.2 cm, find the volume of the wooden toy.
Answer» A solid wooden toy is in the shape of a right circular cone mounted on a hemisphere. If the radius of the hemisphere is 4.2 cm and the total height of the toy is 10.2 cm, find the volume of the wooden toy.

Discussion

14.	A man has a choice to invest in hundred - rupee shares of two companies A & B. Shares of company A are available at 20 % premium and pays 8 % dividend whereas shares of company B are available at a discount of 10% and it pays 7% dividend. If the man invested equally in both the companies and the sum of the return from there is ₹ 936, then how much, in all does he invest?
Answer» A man has a choice to invest in hundred - rupee shares of two companies A & B. Shares of company A are available at 20 % premium and pays 8 % dividend whereas shares of company B are available at a discount of 10% and it pays 7% dividend. If the man invested equally in both the companies and the sum of the return from there is ₹ 936, then how much, in all does he invest?

Discussion

15.	If AB is a chord which passes through the centre O of a circle, then what is AB known as?
Answer» If AB is a chord which passes through the centre O of a circle, then what is AB known as?

Discussion

16.	A cone of radius 10 cm divided into two parts by drawing a plane through the mid-point of its axis, parallel to its base. Compare the volume of the two parts.
Answer» A cone of radius 10 cm divided into two parts by drawing a plane through the mid-point of its axis, parallel to its base. Compare the volume of the two parts.

Discussion

17.	Construct a triangle ABC with side BC = 7 cm , ∠B=45∘,∠A=105∘. Then cnstruct another triangle whose sides are 34 times the corresponding sides of the ΔABC
Answer» Construct a triangle ABC with side BC = 7 cm , $∠ B = 45^{\circ}, ∠ A = 105^{\circ}$ . Then cnstruct another triangle whose sides are $\frac{3}{4}$ times the corresponding sides of the $Δ A B C$

Discussion

18.	An A. P. consists of 57 terms of which 7th term is 13 and the last term is 108. Find the 45th term of this A. P.
Answer» An A. P. consists of 57 terms of which $7^{t h}$ term is 13 and the last term is 108. Find the $45^{t h}$ term of this A. P.

Discussion

19.	Write the matrix form for linear equations: 3x+4y=54x+5y=9
Answer» Write the matrix form for linear equations: $3 x + 4 y = 5 4 x + 5 y = 9$

Discussion

20.	When a boy weighing 20 kg sits at one end of a 4 m long see-saw, it gets depressed at this end. How can it be brought to the horizontal position by an another boy weighing 40 kg?
Answer» When a boy weighing 20 kg sits at one end of a 4 m long see-saw, it gets depressed at this end. How can it be brought to the horizontal position by an another boy weighing 40 kg?

Discussion

21.	If the roots of the equation (a – b)x2 + (b – c)x + (c – a) = 0 are equal, then prove that 2a = b + c.
Answer» If the roots of the equation (a – b) $x^{2}$ + (b – c)x + (c – a) = 0 are equal, then prove that 2a = b + c.

Discussion

22.	A tent is in the form of a cylinder of diameter 4.2 m and height 4 m, surmounted by a cone of equal base and height 2.8 m. find the cost of canvas for making the tent at ₹ 100 per sq.m.
Answer» A tent is in the form of a cylinder of diameter $4.2 m$ and height $4 m$ , surmounted by a cone of equal base and height $2.8 m$ . find the cost of canvas for making the tent at ₹ $100$ per sq.m.

Discussion

23.	Which statement is not true about the sentence? Each of the men working in the factory leaves when they complete their 12-hour shift.
Answer» Which statement is not true about the sentence? Each of the men working in the factory leaves when they complete their 12-hour shift.

Discussion

24.	A man observes the angle of elevation of the top of a building to be 30o. He walks towards it in a horizontal line through its base. On covering 60 m the ∠ of elevation changes to 60o. Find the height of the building correct to the nearest metre.
Answer» A man observes the angle of elevation of the top of a building to be 30^o. He walks towards it in a horizontal line through its base. On covering 60 m the ∠ of elevation changes to 60^o. Find the height of the building correct to the nearest metre.

Discussion

25.	16 glass spheres each of radius 2 cm are packed into a cuboidal box of internal dimensions 16 cm×8 cm×8 cm and then the box is filled with water. Find the volume of water filled in the box.
Answer» 16 glass spheres each of radius 2 cm are packed into a cuboidal box of internal dimensions $16 c m \times 8 c m \times 8 c m$ and then the box is filled with water. Find the volume of water filled in the box.

Discussion

26.	Solve each of the following quadratic equations: 22x−3.2(x+2)+32=0
Answer» Solve each of the following quadratic equations: $2^{2 x} - {3.2}^{(x + 2)} + 32 = 0$

Discussion

27.	The sum of first three terms of an AP is 48. If the product of first and second terms exceeds 4 times the third term by 12. find the AP.
Answer» The sum of first three terms of an AP is 48. If the product of first and second terms exceeds 4 times the third term by 12. find the AP.

Discussion

28.	If 4x+6y=3xy and 8x+9y=5xy then (a) x=2,y=3 (b) x=1,y=2 (c) x=3,y=4 (d) x=1,y=-1
Answer» If $4 x + 6 y = 3 x y a n d 8 x + 9 y = 5 x y$ then (a) x=2,y=3 (b) x=1,y=2 (c) x=3,y=4 (d) x=1,y=-1

28.

If 4x+6y=3xy and 8x+9y=5xy then (a) x=2,y=3 (b) x=1,y=2 (c) x=3,y=4 (d) x=1,y=-1

Answer»

If $4 x + 6 y = 3 x y a n d 8 x + 9 y = 5 x y$ then

(a) x=2,y=3 (b) x=1,y=2 (c) x=3,y=4 (d) x=1,y=-1

Discussion

29.	IF an denotes the nth term of the AP 2, 7, 12, 17, ..., find the value of (a30−a20).
Answer» IF $a_{n}$ denotes the nth term of the AP 2, 7, 12, 17, ..., find the value of $(a_{30} - a_{20})$ .

Discussion

30.	An A.P. consists of 60 terms. If the first and the last terms be 7 and 125 respectively, find 32nd term.
Answer» An A.P. consists of 60 terms. If the first and the last terms be 7 and 125 respectively, find 32nd term.

Discussion

31.	In figure, there are two concentric circles with centre O. PRT and PQS are tangents to the inner circle from a point P lying on the outer circle. If PR = 5 cm, find the length of PS.
Answer» In figure, there are two concentric circles with centre O. PRT and PQS are tangents to the inner circle from a point P lying on the outer circle. If PR = 5 cm, find the length of PS.

Discussion

32.	If 3 cos θ - 4 sin θ = 2 cos θ + sin θ, find tan θ.
Answer» If 3 cos $θ$ - 4 sin $θ$ = 2 cos $θ$ + sin $θ$ , find tan $θ$ .

Discussion

33.	Find the value of k for which the following system of equations has no solution: (20-25): 2x - ky + 3 = 0 3x + 2y - 1 = 0
Answer» Find the value of k for which the following system of equations has no solution: (20-25): 2x - ky + 3 = 0 3x + 2y - 1 = 0

33.

Find the value of k for which the following system of equations has no solution: (20-25): 2x - ky + 3 = 0 3x + 2y - 1 = 0

Answer»

Find the value of k for which the following system of equations has no solution: (20-25):

2x - ky + 3 = 0

3x + 2y - 1 = 0

Discussion

34.	How many spherical bullets each of 5 cm in diameter can be cast from a rectangular block of metal 11 dm × 1 m×5 dm?
Answer» How many spherical bullets each of 5 cm in diameter can be cast from a rectangular block of metal $11 d m \times 1 m \times 5 d m$ ?

Discussion

35.	The first and the last terms of an A.P. are 7 and 49 respectively. If sum of all its terms is 420, find its common difference.
Answer» The first and the last terms of an A.P. are 7 and 49 respectively. If sum of all its terms is 420, find its common difference.

Discussion

36.	The nth term of a sequence is (2n -3), find its fifteenth term.
Answer» The $n^{t h}$ term of a sequence is (2n -3), find its fifteenth term.

Discussion

37.	What is perimeter of a circle called?
Answer» What is perimeter of a circle called?

Discussion

38.	point p(5,-3) is one of the two pints of trisection of the line segment joining the points a(7,-2) & b(-1,5) near to a. find the coordinates of the other point of trisection Solution A---------p----------Q------------B let Q is the unknown point because according to question AP=PQ=QB In the question it is not given that Q is the mid point of QB.then how con we presume it?
Answer» point p(5,-3) is one of the two pints of trisection of the line segment joining the points a(7,-2) & b(-1,5) near to a. find the coordinates of the other point of trisection Solution A---------p----------Q------------B let Q is the unknown point because according to question AP=PQ=QB In the question it is not given that Q is the mid point of QB.then how con we presume it?

Discussion

39.	The value of sin 30∘ is?
Answer» The value of $sin$ 30 $^{\circ}$ is?

Discussion

40.	An electric belt is placed around the rim of a pulley of radius 5 cm. From one point C on the belt, the elastic belt is pulled directly away from the centre O of the pulley until it is at P, 10 cm from the point O. Find the length of the belt that is still in contact with the pulley. Also find the shaded area. Use π=3.14 and √3=1.73.
Answer» An electric belt is placed around the rim of a pulley of radius 5 cm. From one point C on the belt, the elastic belt is pulled directly away from the centre O of the pulley until it is at P, 10 cm from the point O. Find the length of the belt that is still in contact with the pulley. Also find the shaded area. Use $π = 3.14$ and $\sqrt{3} = 1.73$ .

Discussion

41.	Neha has a recurring deposit account in a bank and deposits Rs. 400 per month for 2.5 years. The rate of interest paid by bank if the maturity value of this account is Rs. 13240 will be
Answer» Neha has a recurring deposit account in a bank and deposits Rs. 400 per month for 2.5 years. The rate of interest paid by bank if the maturity value of this account is Rs. 13240 will be

Discussion

42.	1 newton = _________ dyne.
Answer» 1 newton = _________ dyne.

Discussion

43.	The sum of first n terms of an ap is 4n²+2n find the value of this ap
Answer» The sum of first n terms of an ap is 4n²+2n find the value of this ap

Discussion

44.	A two digit number is 4 times the sum of its digit and twice the product of the digit .find the number
Answer» A two digit number is 4 times the sum of its digit and twice the product of the digit .find the number

Discussion

45.	Find the sum of the sequence −13, 1, −3, 9,............ upto 8 terms.
Answer» Find the sum of the sequence $- \frac{1}{3}, 1, - 3, 9,$ ............ upto 8 terms.

Discussion

46.	The area of a rectangle increases by 200 sq m, if the length is increased by 8 m and breadth by 3 m. The area increases by 255 sq m, If the length is increased by 3m and breadth by 8 m, find the length and breadth of the rectangle.
Answer» The area of a rectangle increases by 200 sq m, if the length is increased by 8 m and breadth by 3 m. The area increases by 255 sq m, If the length is increased by 3m and breadth by 8 m, find the length and breadth of the rectangle.

Discussion

47.	Solve the following system of equations graphically: Shade the region between the lines and the y-axis 4x - y = 4 3x + 2y = 14
Answer» Solve the following system of equations graphically: Shade the region between the lines and the y-axis 4x - y = 4 3x + 2y = 14

47.

Solve the following system of equations graphically: Shade the region between the lines and the y-axis 4x - y = 4 3x + 2y = 14

Answer»

Solve the following system of equations graphically:

Shade the region between the lines and the y-axis

4x - y = 4

3x + 2y = 14

Discussion

48.	If z1,z2,z3.....nn are nth, roots of unity, then for k = 1, 2, ....., n
Answer» If $z_{1}, z_{2}, z_{3} . . . . . n_{n}$ are n^th, roots of unity, then for k = 1, 2, ....., n

Discussion

49.	Jagadish buys goods worth Rs 6,650. He gets a rebate of 6% on it. After getting the rebate, he pays sales tax at 10%. Find: (i) The amount of sales tax paid (ii) The total amount to be paid by Jagadish. [4 MARKS]
Answer» Jagadish buys goods worth Rs 6,650. He gets a rebate of 6% on it. After getting the rebate, he pays sales tax at 10 $%$ . Find: (i) The amount of sales tax paid (ii) The total amount to be paid by Jagadish. [4 MARKS]

Discussion

50.	A toy is in the form of a cone mounted on a hemisphere of diameter 7 cm. The total height of the toy is 14.5 cm. The total surface area of the toy will be
Answer» A toy is in the form of a cone mounted on a hemisphere of diameter 7 cm. The total height of the toy is 14.5 cm. The total surface area of the toy will be

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

7(y+3)-2(x+2)=14 4(y-2)+3(x-3)=2 Solve the system of equation

Find the ratio in which P(4, m) divides the line segment joining the points A(2, 3) and B(6, -3). Hence find m.

Prove 7√11 /3 as irrational ?

I have a car moving which covers a distance of 20 m in 20 seconds. What is its speed?

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: x−y+1=0, 3x+2y−12=0.

If one zero of polynomial (a​​​​​​2​​​​​+9)x​​​​​​2+13x+6a is reciprocal of other find value of a.

Let f:(0,∞)→R be a differentiable function such that f′(x)=2−f(x)x for all xϵ(0,∞) and f(1)≠1. Then

Find the sum of all integers between 84 and 719, which are multiples of 5.

The following figure shows a parallelogram ABCD whose side AB is parallel to the x-axis, ∠A = 60∘ and vertex C = (7, 5). Find the equation of BC and CD.

If sec θ = 135, find the value of BC and tanθ

If 1/a, 1/b, 1/c, are in a.p prove that BC, ca, an are in a.p hints: prove that ab- ca =ca- BC Using 1/c - 1/b = 1/b - 1/a.

A solid wooden toy is in the shape of a right circular cone mounted on a hemisphere. If the radius of the hemisphere is 4.2 cm and the total height of the toy is 10.2 cm, find the volume of the wooden toy.

If AB is a chord which passes through the centre O of a circle, then what is AB known as?

A cone of radius 10 cm divided into two parts by drawing a plane through the mid-point of its axis, parallel to its base. Compare the volume of the two parts.

Construct a triangle ABC with side BC = 7 cm , ∠B=45∘,∠A=105∘. Then cnstruct another triangle whose sides are 34 times the corresponding sides of the ΔABC

An A. P. consists of 57 terms of which 7th term is 13 and the last term is 108. Find the 45th term of this A. P.

Write the matrix form for linear equations: 3x+4y=54x+5y=9

When a boy weighing 20 kg sits at one end of a 4 m long see-saw, it gets depressed at this end. How can it be brought to the horizontal position by an another boy weighing 40 kg?

If the roots of the equation (a – b)x2 + (b – c)x + (c – a) = 0 are equal, then prove that 2a = b + c.

A tent is in the form of a cylinder of diameter 4.2 m and height 4 m, surmounted by a cone of equal base and height 2.8 m. find the cost of canvas for making the tent at ₹ 100 per sq.m.

Which statement is not true about the sentence? Each of the men working in the factory leaves when they complete their 12-hour shift.

A man observes the angle of elevation of the top of a building to be 30o. He walks towards it in a horizontal line through its base. On covering 60 m the ∠ of elevation changes to 60o. Find the height of the building correct to the nearest metre.

16 glass spheres each of radius 2 cm are packed into a cuboidal box of internal dimensions 16 cm×8 cm×8 cm and then the box is filled with water. Find the volume of water filled in the box.

Solve each of the following quadratic equations: 22x−3.2(x+2)+32=0

The sum of first three terms of an AP is 48. If the product of first and second terms exceeds 4 times the third term by 12. find the AP.

If 4x+6y=3xy and 8x+9y=5xy then (a) x=2,y=3 (b) x=1,y=2 (c) x=3,y=4 (d) x=1,y=-1

IF an denotes the nth term of the AP 2, 7, 12, 17, ..., find the value of (a30−a20).

An A.P. consists of 60 terms. If the first and the last terms be 7 and 125 respectively, find 32nd term.

In figure, there are two concentric circles with centre O. PRT and PQS are tangents to the inner circle from a point P lying on the outer circle. If PR = 5 cm, find the length of PS.

If 3 cos θ - 4 sin θ = 2 cos θ + sin θ, find tan θ.

Find the value of k for which the following system of equations has no solution: (20-25): 2x - ky + 3 = 0 3x + 2y - 1 = 0

How many spherical bullets each of 5 cm in diameter can be cast from a rectangular block of metal 11 dm × 1 m×5 dm?

The first and the last terms of an A.P. are 7 and 49 respectively. If sum of all its terms is 420, find its common difference.

The nth term of a sequence is (2n -3), find its fifteenth term.

What is perimeter of a circle called?

The value of sin 30∘ is?

Neha has a recurring deposit account in a bank and deposits Rs. 400 per month for 2.5 years. The rate of interest paid by bank if the maturity value of this account is Rs. 13240 will be

1 newton = _________ dyne.

The sum of first n terms of an ap is 4n²+2n find the value of this ap

A two digit number is 4 times the sum of its digit and twice the product of the digit .find the number

Find the sum of the sequence −13, 1, −3, 9,............ upto 8 terms.

The area of a rectangle increases by 200 sq m, if the length is increased by 8 m and breadth by 3 m. The area increases by 255 sq m, If the length is increased by 3m and breadth by 8 m, find the length and breadth of the rectangle.

Solve the following system of equations graphically: Shade the region between the lines and the y-axis 4x - y = 4 3x + 2y = 14

If z1,z2,z3.....nn are nth, roots of unity, then for k = 1, 2, ....., n

Jagadish buys goods worth Rs 6,650. He gets a rebate of 6% on it. After getting the rebate, he pays sales tax at 10%. Find: (i) The amount of sales tax paid (ii) The total amount to be paid by Jagadish. [4 MARKS]

A toy is in the form of a cone mounted on a hemisphere of diameter 7 cm. The total height of the toy is 14.5 cm. The total surface area of the toy will be

If one zero of polynomial (a2+9)x2+13x+6a is reciprocal of other find value of a.