32581 + Interview Questions in Mathematics Page 173 InterviewSolution

8601.	70.The sum of the roots of an equation is 2 and sum of their cube is 98,then form the quadratic equation
Answer» 70.The sum of the roots of an equation is 2 and sum of their cube is 98,then form the quadratic equation

Discussion

8602.	Factorise each of the following expression:(i)a3x+a2(x–y)–a(y+z)–z(ii)(x2+3x)2–5(x2+3x)–y(x2+3x)+5y
Answer» Factorise each of the following expression: $(i) a^{3} x + a^{2} (x - y) - a (y + z) - z$ $(i i) (x^{2} + 3 x)^{2} - 5 (x^{2} + 3 x) - y (x^{2} + 3 x) + 5 y$

Discussion

8603.	Prove that the length of the tangents drawn from an external point to a circle are equal.
Answer» Prove that the length of the tangents drawn from an external point to a circle are equal.

Discussion

8604.	In the given figure, O is the centre of a circle, AOC is its diameter such that ∠ ACB = 50o . If AT is the tangent to the circle at the point A then ∠ BAT = ? (a) 40o (b) 50o (c) 60o (d) 65o
Answer» In the given figure, O is the centre of a circle, AOC is its diameter such that $∠$ ACB = $50^{o}$ . If AT is the tangent to the circle at the point A then $∠$ BAT = ? (a) $40^{o}$ (b) $50^{o}$ (c) $60^{o}$ (d) $65^{o}$

8604.

In the given figure, O is the centre of a circle, AOC is its diameter such that ∠ ACB = 50o . If AT is the tangent to the circle at the point A then ∠ BAT = ? (a) 40o (b) 50o (c) 60o (d) 65o

Answer»

In the given figure, O is the centre of a circle, AOC is its diameter such that $∠$ ACB = $50^{o}$ . If AT is the tangent to the circle at the point A then $∠$ BAT = ?

(a) $40^{o}$ (b) $50^{o}$ (c) $60^{o}$ (d) $65^{o}$

Discussion

8605.	22. Find the equation of the parabola whose vertex is at (3,-2) and focus is at (6,2)
Answer» 22. Find the equation of the parabola whose vertex is at (3,-2) and focus is at (6,2)

Discussion

8606.	The adjacent figure shows two arcs P and Q. Arc P is part of the circle with centre O and radius OA. Arc Q is a part of the circle with centre M and radius AM, where M is the mid-point of AB. Area enclosed by the arc AQB and chord AB
Answer» The adjacent figure shows two arcs P and Q. Arc P is part of the circle with centre O and radius OA. Arc Q is a part of the circle with centre M and radius AM, where M is the mid-point of AB. Area enclosed by the arc AQB and chord AB

Discussion

8607.	Show that the following system of equations has a unique solution and solve it:2x-3y=174x+y=13
Answer» Show that the following system of equations has a unique solution and solve it: $2 x - 3 y = 17 4 x + y = 13$

Discussion

8608.	If one of the zeroes of the cubic polynomial ax^3+bx^2+d is zero. Then find product of other two zeroes
Answer» If one of the zeroes of the cubic polynomial ax^3+bx^2+d is zero. Then find product of other two zeroes

Discussion

8609.	Question 193 Construct a parallelogram POUR in which PO = 5.5 cm, OU = 7.2 cm and ∠O=70∘.
Answer» Question 193 Construct a parallelogram POUR in which PO = 5.5 cm, OU = 7.2 cm and $∠ O = 70^{\circ}$ .

Discussion

8610.	If 2/√3 and -2/√3 are roots of polynomial 3x^4-12x^3+5x^2+16x-12, thenfind the other two roots.
Answer» If 2/√3 and -2/√3 are roots of polynomial 3x^4-12x^3+5x^2+16x-12, thenfind the other two roots.

Discussion

8611.	For what value of k does the following pair of linear equations have no solution? 10x+5y−(k−5)=0 and 20x+10y−k=0.
Answer» For what value of k does the following pair of linear equations have no solution? $10 x + 5 y - (k - 5) = 0 a n d 20 x + 10 y - k = 0.$

8611.

For what value of k does the following pair of linear equations have no solution? 10x+5y−(k−5)=0 and 20x+10y−k=0.

Answer»

For what value of k does the following pair of linear equations have no solution?

$10 x + 5 y - (k - 5) = 0 a n d 20 x + 10 y - k = 0.$

Discussion

8612.	if the weight of a solid hemisphere is 6/5 that of a solid sphere of same material. the ratio of their radii will be
Answer» if the weight of a solid hemisphere is 6/5 that of a solid sphere of same material. the ratio of their radii will be

Discussion

8613.	If ∫dx(x+100)√x+99=f(x)+C, then f(x) is equal to (where C is integration constant)
Answer» If $\int \frac{d x}{(x + 100) \sqrt{x + 99}} = f (x) + C,$ then $f (x)$ is equal to (where $C$ is integration constant)

Discussion

8614.	Evaluate each of the followingsin2 30° cos2 45° + 4 tan2 30° + 12 sin2 90°-2 cos2 90°+124 cos2 0°
Answer» Evaluate each of the following sin² 30° cos² 45° + 4 tan² 30° + $\frac{1}{2} \sin^{2} 90 ° - 2 \cos^{2} 90 ° + \frac{1}{24} \cos^{2} 0 °$

Discussion

8615.	8. A circle of max area is inscribed in an ellipse. If p is the probability factor that a point within the ellipse chosen at random lies outside the circles ,then the eccentrcity of the ellipse is
Answer» 8. A circle of max area is inscribed in an ellipse. If p is the probability factor that a point within the ellipse chosen at random lies outside the circles ,then the eccentrcity of the ellipse is

Discussion

8616.	(1)State whether the following quadratic equation have two distinct real roots. Justify your answer.(i) x2−3x+4=0(2)State whether the following quadratic equation have two distinct real roots. Justify your answer.(ii) 2x2+x−1=0(3)State whether the following quadratic equation have two distinct real roots. Justify your answer.(iii) 2x2−6x+92=0(4)State whether the following quadratic equation have two distinct real roots. Justify your answer.(iv) 3x2−4x+1=0(5)State whether the following quadratic equation have two distinct real roots. Justify your answer.(v) (x+4)2−8x=0(6)State whether the following quadratic equation have two distinct real roots. Justify your answer.(vi) (x−√2)2−2(x+1)=0(7)State whether the following quadratic equation have two distinct real roots. Justify your answer.(vii) √2x2−3√2x+1√2=0(8)State whether the following quadratic equation have two distinct real roots. Justify your answer.(viii) x(1−x)−2=0(9)State whether the following quadratic equation have two distinct real roots. Justify your answer(ix) (x−1)(x+2)+2=0(10)State whether the following quadratic equation have two distinct real roots. Justify your answer.(x) (x+1)(x−2)+x=0
Answer» (1) State whether the following quadratic equation have two distinct real roots. Justify your answer. (i) $x^{2} - 3 x + 4 = 0$ (2) State whether the following quadratic equation have two distinct real roots. Justify your answer. (ii) $2 x^{2} + x - 1 = 0$ (3) State whether the following quadratic equation have two distinct real roots. Justify your answer. (iii) $2 x^{2} - 6 x + \frac{9}{2} = 0$ (4) State whether the following quadratic equation have two distinct real roots. Justify your answer. (iv) $3 x^{2} - 4 x + 1 = 0$ (5) State whether the following quadratic equation have two distinct real roots. Justify your answer. (v) $(x + 4)^{2} - 8 x = 0$ (6) State whether the following quadratic equation have two distinct real roots. Justify your answer. (vi) $(x - \sqrt{2})^{2} - 2 (x + 1) = 0$ (7) State whether the following quadratic equation have two distinct real roots. Justify your answer. (vii) $\sqrt{2} x^{2} - \frac{3}{\sqrt{2}} x + \frac{1}{\sqrt{2}} = 0$ (8) State whether the following quadratic equation have two distinct real roots. Justify your answer. (viii) $x (1 - x) - 2 = 0$ (9) State whether the following quadratic equation have two distinct real roots. Justify your answer (ix) $(x - 1) (x + 2) + 2 = 0$ (10) State whether the following quadratic equation have two distinct real roots. Justify your answer. (x) $(x + 1) (x - 2) + x = 0$

Discussion

8617.	63.Find the area of the shaded portion and the whole figure as shown
Answer» 63.Find the area of the shaded portion and the whole figure as shown

Discussion

8618.	Solve the following systems of equations:44x+y+30x-y=1055x+y+40x-y=13
Answer» Solve the following systems of equations: $\frac{44}{x + y} + \frac{30}{x - y} = 10 \frac{55}{x + y} + \frac{40}{x - y} = 13$

Discussion

8619.	Solve the equation 4x2+ 7x = 1 by the method of completing the square. In one of the options the positive root and the converted form of the equation after completing the square is given. Select this option.
Answer» Solve the equation 4 $x^{2}$ + 7x = 1 by the method of completing the square. In one of the options the positive root and the converted form of the equation after completing the square is given. Select this option.

Discussion

8620.	The sum of the digits of a two-digit number is 9. If 27 is added to it, the digits of the number get reversed. The number is
Answer» The sum of the digits of a two-digit number is 9. If 27 is added to it, the digits of the number get reversed. The number is

Discussion

8621.	The sum of a number and its reciprocals is. What are the numbers?
Answer» The sum of a number and its reciprocals is. What are the numbers?

Discussion

8622.	The following data gives the information on the observed lifetime (in hours) of 225 electrical components:Life time (in hours)0−2020−4040−6060−8080−100100−120Number of components103552613829Determine the modal lifetime of the components.
Answer» The following data gives the information on the observed lifetime (in hours) of 225 electrical components: $\begin{matrix} L i f e t i m e (i n h o u r s) & 0 - 20 & 20 - 40 & 40 - 60 & 60 - 80 & 80 - 100 & 100 - 120 N u m b e r o f c o m p o n e n t s & 10 & 35 & 52 & 61 & 38 & 29 \end{matrix}$ Determine the modal lifetime of the components.

Discussion

8623.	In the given triangle find sec 60 , if ACBC = 2
Answer» In the given triangle find sec 60 , if $\frac{A C}{B C}$ = 2

8623.

In the given triangle find sec 60 , if ACBC = 2

Answer»

In the given triangle find sec 60 , if $\frac{A C}{B C}$ = 2

Discussion

8624.	If the mean of the following data is 18.75, then the value of P is
Answer» If the mean of the following data is 18.75, then the value of P is

8624.

If the mean of the following data is 18.75, then the value of P is

Answer»

If the mean of the following data is 18.75, then the value of P is

Discussion

8625.	A Sumo Wrestler wants to gain weight. He eats 5 Eggs on day 1. He increases the number by 3 on day 2. He repeats the same thing for 'n' number of days. If the total number of Eggs consumed by him in 'n' days is 185, find 'n'.
Answer» A Sumo Wrestler wants to gain weight. He eats 5 Eggs on day 1. He increases the number by 3 on day 2. He repeats the same thing for 'n' number of days. If the total number of Eggs consumed by him in 'n' days is 185, find 'n'.

Discussion

8626.	In a ∆ABC, AB = BC = CA = 2a and AD ⊥ BC. Prove that(i) AD=a3(ii) Area ∆ABC=3 a2
Answer» In a ∆ABC, AB = BC = CA = 2a and AD ⊥ BC. Prove that (i) $AD = a \sqrt{3}$ (ii) $A r e a (∆ A B C) = \sqrt{3} a^{2}$

Discussion

8627.	In the adjoining figure, the crescent is formed by circles which touch at the point A. O is the centre the bigger circle. If CB =9 cm and ED =5 cm. Find the area of the shaded region.
Answer» In the adjoining figure, the crescent is formed by circles which touch at the point A. O is the centre the bigger circle. If CB =9 cm and ED =5 cm. Find the area of the shaded region.

Discussion

8628.	If the numbers x − 2, 4x − 1 and 5x + 2 are in A.P. find the value of x.
Answer» If the numbers x − 2, 4x − 1 and 5x + 2 are in A.P. find the value of x.

Discussion

8629.	If A+B+C=180degree. Prove that sin2A+sin2B+sin2C=4×sinA×sinB×sinC.
Answer» If A+B+C=180degree. Prove that sin2A+sin2B+sin2C=4×sinA×sinB×sinC.

Discussion

8630.	A sphere and a cube have equal surface areas. What is the ratio of the volume of the sphere to that of the cube?
Answer» A sphere and a cube have equal surface areas. What is the ratio of the volume of the sphere to that of the cube?

Discussion

8631.	In Figure 2, ABCD is a parallelogram. Find the values of x and y.
Answer» In Figure 2, ABCD is a parallelogram. Find the values of x and y.

Discussion

8632.	The equation x2+4x+c=0 has real roots, then
Answer» The equation $x^{2} + 4 x + c = 0$ has real roots, then

Discussion

8633.	Without using distance formula, show that the points (-2, -1), (4, 0), (3, 3) and (-3, 2) arc the vertices .of a parallelogram.
Answer» Without using distance formula, show that the points (-2, -1), (4, 0), (3, 3) and (-3, 2) arc the vertices .of a parallelogram.

Discussion

8634.	If SecA + tanA = x. Find secA-tanA in terms of x.
Answer» If SecA + tanA = x. Find secA-tanA in terms of x.

Discussion

8635.	A frustum of height 14 cm and radii 3 cm and 9 cm is filled with water upto the brim. Find the quantity of water in the frustum.
Answer» A frustum of height 14 cm and radii 3 cm and 9 cm is filled with water upto the brim. Find the quantity of water in the frustum.

Discussion

8636.	The sum of three consecutive even numbers is 336. Find them.
Answer» The sum of three consecutive even numbers is 336. Find them.

Discussion

8637.	33. If D is the HCF of 105 and 18 then find X and Y satisfying d=18 x + 105 y where x and y are integers
Answer» 33. If D is the HCF of 105 and 18 then find X and Y satisfying d=18 x + 105 y where x and y are integers

Discussion

8638.	How many coins 1.75 cm in diameter and 2 mm thick must be melted to form a cuboid 11 cm × 10 cm × 7 cm?
Answer» How many coins 1.75 cm in diameter and 2 mm thick must be melted to form a cuboid 11 cm × 10 cm × 7 cm?

Discussion

8639.	A solid cuboid of iron with dimensions 53 cm ⨯ 40 cm ⨯ 15 cm is melted and recast into a cylindrical pipe. The outer and inner diameters of pipe are 8 cm and 7 cm respectively. Find the length of pipe. [CBSE 2015]
Answer» A solid cuboid of iron with dimensions 53 cm ⨯ 40 cm ⨯ 15 cm is melted and recast into a cylindrical pipe. The outer and inner diameters of pipe are 8 cm and 7 cm respectively. Find the length of pipe. [CBSE 2015]

Discussion

8640.	Solve for x:(i) x-1x-2+x-3x-4=313; x≠2, 4(ii) 1x-1x-2=3, x≠0, 2(iii) x+1x=3, x≠0(iv) 16x-1=15x+1, x≠0, -1(v) 1x-3-1x+5=16, x≠3,-5
Answer» Solve for x: (i) $\frac{x - 1}{x - 2} + \frac{x - 3}{x - 4} = 3 \frac{1}{3}; x \neq 2, 4$ (ii) $\frac{1}{x} - \frac{1}{x - 2} = 3, x \neq 0, 2$ (iii) $x + \frac{1}{x} = 3, x \neq 0$ (iv) $\frac{16}{x} - 1 = \frac{15}{x + 1}, x \neq 0, - 1$ (v) $\frac{1}{x - 3} - \frac{1}{x + 5} = \frac{1}{6}, x \neq 3, - 5$

Discussion

8641.	If ∆=1xx21yy21zz2, ∆1=111yzzxxyxyz, then prove that ∆+∆1=0.
Answer» $If ∆ = \|\begin{matrix} 1 & x & x^{2} \\ 1 & y & y^{2} \\ 1 & z & z^{2} \end{matrix}\|, ∆_{1} = \|\begin{matrix} 1 & 1 & 1 \\ y z & z x & x y \\ x & y & z \end{matrix}\|, then prove that ∆ + ∆_{1} = 0 .$

Discussion

8642.	Solve the following: A lady went to a bank with Rs. 100000. She asked the cashier to give her Rs. 500 and Rs. 1000 currency notes in return. She got 175 currency notes in all. Find the number of each kind of currency notes.
Answer» Solve the following: A lady went to a bank with Rs. 100000. She asked the cashier to give her Rs. 500 and Rs. 1000 currency notes in return. She got 175 currency notes in all. Find the number of each kind of currency notes.

8642.

Solve the following: A lady went to a bank with Rs. 100000. She asked the cashier to give her Rs. 500 and Rs. 1000 currency notes in return. She got 175 currency notes in all. Find the number of each kind of currency notes.

Answer»

Solve the following:

A lady went to a bank with Rs. 100000. She asked the cashier to give her Rs. 500 and Rs. 1000 currency notes in return. She got 175 currency notes in all. Find the number of each kind of currency notes.

Discussion

8643.	Find the values of k for which the roots are real and equal in each of the following equations:(i) kx2+4x+1=0(ii) kx2-25x+4=0(iii) 3x2-5x+2k=0(iv) 4x2+kx+9=0(v) 2kx2-40x+25=0(vi) 9x2-24x+k=0(vii) 4x2-3kx+1=0(viii) x2-25+2kx+37+10k=0(ix) 3k+1x2+2k+1x+k=0(x) kx2+kx+1=-4x2-x(xi) k+1x2+2k+3x+k+8=0(xii) x2-2kx+7k-12=0(xiii) k+1x2-23k+1x+8k+1=0(xiv) 2k+1x2+2k+3x+k+5=0(xvii) 4x2-2k+1x+k+4=0
Answer» Find the values of k for which the roots are real and equal in each of the following equations: (i) $k x^{2} + 4 x + 1 = 0$ (ii) $k x^{2} - 2 \sqrt{5} x + 4 = 0$ (iii) $3 x^{2} - 5 x + 2 k = 0$ (iv) $4 x^{2} + k x + 9 = 0$ (v) $2 k x^{2} - 40 x + 25 = 0$ (vi) $9 x^{2} - 24 x + k = 0$ (vii) $4 x^{2} - 3 k x + 1 = 0$ (viii) $x^{2} - 2 (5 + 2 k) x + 3 (7 + 10 k) = 0$ (ix) $(3 k + 1) x^{2} + 2 (k + 1) x + k = 0$ (x) $k x^{2} + k x + 1 = - 4 x^{2} - x$ (xi) $(k + 1) x^{2} + 2 (k + 3) x + (k + 8) = 0$ (xii) $x^{2} - 2 k x + 7 k - 12 = 0$ (xiii) $(k + 1) x^{2} - 2 (3 k + 1) x + 8 k + 1 = 0$ (xiv) $(2 k + 1) x^{2} + 2 (k + 3) x + (k + 5) = 0$ (xvii) $4 x^{2} - 2 (k + 1) x + (k + 4) = 0$

Discussion

8644.	A person distributes his total property among his three sons. The ratio of the total property, share of the first son and share of the second son is 15:3:7: . Find the central angle which represents the share of the third son?
Answer» A person distributes his total property among his three sons. The ratio of the total property, share of the first son and share of the second son is 15:3:7: . Find the central angle which represents the share of the third son?

Discussion

8645.	In the given figure, O is the centre of the circle. Find x.
Answer» In the given figure, O is the centre of the circle. Find $x$ .

8645.

In the given figure, O is the centre of the circle. Find x.

Answer»

In the given figure, O is the centre of the circle. Find $x$ .

Discussion

8646.	Question 163(i)Supply the missing information for each diagram.
Answer» Question 163(i) Supply the missing information for each diagram.

8646.

Question 163(i)Supply the missing information for each diagram.

Answer»

Question 163(i)

Supply the missing information for each diagram.

Discussion

8647.	The zeros of the quadratic polynomial x^2+99x+127 is equal toA.both positiveB.both negativeC.one positive and one negativeD. Both equal.
Answer» The zeros of the quadratic polynomial x^2+99x+127 is equal to A.both positive B.both negative C.one positive and one negative D. Both equal.

Discussion

8648.	Question 12How many spherical lead shots of diameter 4 cm can be made out of a solid cube of lead whose edge measures 44 cm
Answer» Question 12 How many spherical lead shots of diameter 4 cm can be made out of a solid cube of lead whose edge measures 44 cm

Discussion

8649.	In ΔABC, if D is a point on the side AB such that ABAD=3, then ADDB = .
Answer» In $Δ A B C$ , if D is a point on the side AB such that $\frac{A B}{A D} = 3$ , then $\frac{A D}{D B}$ = .

Discussion

8650.	In the given figure ABCD is a rectangle of dimensions 21 cm × 14 cm. A semicircle is drawn with BC as diameter. Find the area and the perimeter of the shaded region in the figure.
Answer» In the given figure ABCD is a rectangle of dimensions 21 cm $\times$ 14 cm. A semicircle is drawn with BC as diameter. Find the area and the perimeter of the shaded region in the figure.

Discussion

Explore topic-wise InterviewSolutions in .

70.The sum of the roots of an equation is 2 and sum of their cube is 98,then form the quadratic equation

Factorise each of the following expression:(i)a3x+a2(x–y)–a(y+z)–z(ii)(x2+3x)2–5(x2+3x)–y(x2+3x)+5y

Prove that the length of the tangents drawn from an external point to a circle are equal.

In the given figure, O is the centre of a circle, AOC is its diameter such that ∠ ACB = 50o . If AT is the tangent to the circle at the point A then ∠ BAT = ? (a) 40o (b) 50o (c) 60o (d) 65o

22. Find the equation of the parabola whose vertex is at (3,-2) and focus is at (6,2)

The adjacent figure shows two arcs P and Q. Arc P is part of the circle with centre O and radius OA. Arc Q is a part of the circle with centre M and radius AM, where M is the mid-point of AB. Area enclosed by the arc AQB and chord AB

Show that the following system of equations has a unique solution and solve it:2x-3y=174x+y=13

If one of the zeroes of the cubic polynomial ax^3+bx^2+d is zero. Then find product of other two zeroes

Question 193 Construct a parallelogram POUR in which PO = 5.5 cm, OU = 7.2 cm and ∠O=70∘.

If 2/√3 and -2/√3 are roots of polynomial 3x^4-12x^3+5x^2+16x-12, thenfind the other two roots.

For what value of k does the following pair of linear equations have no solution? 10x+5y−(k−5)=0 and 20x+10y−k=0.

if the weight of a solid hemisphere is 6/5 that of a solid sphere of same material. the ratio of their radii will be

If ∫dx(x+100)√x+99=f(x)+C, then f(x) is equal to (where C is integration constant)

Evaluate each of the followingsin2 30° cos2 45° + 4 tan2 30° + 12 sin2 90°-2 cos2 90°+124 cos2 0°

8. A circle of max area is inscribed in an ellipse. If p is the probability factor that a point within the ellipse chosen at random lies outside the circles ,then the eccentrcity of the ellipse is

63.Find the area of the shaded portion and the whole figure as shown

Solve the following systems of equations:44x+y+30x-y=1055x+y+40x-y=13

Solve the equation 4x2+ 7x = 1 by the method of completing the square. In one of the options the positive root and the converted form of the equation after completing the square is given. Select this option.

The sum of the digits of a two-digit number is 9. If 27 is added to it, the digits of the number get reversed. The number is

The sum of a number and its reciprocals is. What are the numbers?

The following data gives the information on the observed lifetime (in hours) of 225 electrical components:Life time (in hours)0−2020−4040−6060−8080−100100−120Number of components103552613829Determine the modal lifetime of the components.

In the given triangle find sec 60 , if ACBC = 2

If the mean of the following data is 18.75, then the value of P is

A Sumo Wrestler wants to gain weight. He eats 5 Eggs on day 1. He increases the number by 3 on day 2. He repeats the same thing for 'n' number of days. If the total number of Eggs consumed by him in 'n' days is 185, find 'n'.

In a ∆ABC, AB = BC = CA = 2a and AD ⊥ BC. Prove that(i) AD=a3(ii) Area ∆ABC=3 a2

In the adjoining figure, the crescent is formed by circles which touch at the point A. O is the centre the bigger circle. If CB =9 cm and ED =5 cm. Find the area of the shaded region.

If the numbers x − 2, 4x − 1 and 5x + 2 are in A.P. find the value of x.

If A+B+C=180degree. Prove that sin2A+sin2B+sin2C=4×sinA×sinB×sinC.

A sphere and a cube have equal surface areas. What is the ratio of the volume of the sphere to that of the cube?

In Figure 2, ABCD is a parallelogram. Find the values of x and y.

The equation x2+4x+c=0 has real roots, then

Without using distance formula, show that the points (-2, -1), (4, 0), (3, 3) and (-3, 2) arc the vertices .of a parallelogram.

If SecA + tanA = x. Find secA-tanA in terms of x.

A frustum of height 14 cm and radii 3 cm and 9 cm is filled with water upto the brim. Find the quantity of water in the frustum.

The sum of three consecutive even numbers is 336. Find them.

33. If D is the HCF of 105 and 18 then find X and Y satisfying d=18 x + 105 y where x and y are integers

How many coins 1.75 cm in diameter and 2 mm thick must be melted to form a cuboid 11 cm × 10 cm × 7 cm?

A solid cuboid of iron with dimensions 53 cm ⨯ 40 cm ⨯ 15 cm is melted and recast into a cylindrical pipe. The outer and inner diameters of pipe are 8 cm and 7 cm respectively. Find the length of pipe. [CBSE 2015]

Solve for x:(i) x-1x-2+x-3x-4=313; x≠2, 4(ii) 1x-1x-2=3, x≠0, 2(iii) x+1x=3, x≠0(iv) 16x-1=15x+1, x≠0, -1(v) 1x-3-1x+5=16, x≠3,-5

If ∆=1xx21yy21zz2, ∆1=111yzzxxyxyz, then prove that ∆+∆1=0.

Solve the following: A lady went to a bank with Rs. 100000. She asked the cashier to give her Rs. 500 and Rs. 1000 currency notes in return. She got 175 currency notes in all. Find the number of each kind of currency notes.

A person distributes his total property among his three sons. The ratio of the total property, share of the first son and share of the second son is 15:3:7: . Find the central angle which represents the share of the third son?

In the given figure, O is the centre of the circle. Find x.

Question 163(i)Supply the missing information for each diagram.

The zeros of the quadratic polynomial x^2+99x+127 is equal toA.both positiveB.both negativeC.one positive and one negativeD. Both equal.

Question 12How many spherical lead shots of diameter 4 cm can be made out of a solid cube of lead whose edge measures 44 cm

In ΔABC, if D is a point on the side AB such that ABAD=3, then ADDB = .

In the given figure ABCD is a rectangle of dimensions 21 cm × 14 cm. A semicircle is drawn with BC as diameter. Find the area and the perimeter of the shaded region in the figure.