32581 + Interview Questions in Mathematics Page 67 InterviewSolution

3301.	In a right angled triangle with sides a and b hypotenuse c, the altitude drawn on the hypotenuse is x. Prove that ab = cx.
Answer» In a right angled triangle with sides a and b hypotenuse c, the altitude drawn on the hypotenuse is x. Prove that ab = cx.

Discussion

3302.	The incenter of a triangle is :
Answer» The incenter of a triangle is :

Discussion

3303.	Find ∠ABF from the given figure.
Answer» Find $∠ A B F$ from the given figure.

3303.

Find ∠ABF from the given figure.

Answer»

Find $∠ A B F$ from the given figure.

Discussion

3304.	Solve: a) a)x2+6x=0 b) (x–4)(5x+2)=0 c) x2+3x–18=0
Answer» Solve: a) $a) x^{2} + 6 x = 0$ b) $(x - 4) (5 x + 2) = 0$ c) $x^{2} + 3 x - 18 = 0$

Discussion

3305.	Range Frequency Cumulative frequency 0−105(b)10−20(a)820−302(c)30−406(d)Fill in the missing slots and find the value of (a)+(b)+(c)+(d).
Answer» $\begin{matrix} R a n g e & F r e q u e n c y & C u m u l a t i v e f r e q u e n c y 0 - 10 & 5 & (b) 10 - 20 & (a) & 8 20 - 30 & 2 & (c) 30 - 40 & 6 & (d) \end{matrix}$ Fill in the missing slots and find the value of $(a) + (b) + (c) + (d)$ .

3305.

Range Frequency Cumulative frequency 0−105(b)10−20(a)820−302(c)30−406(d)Fill in the missing slots and find the value of (a)+(b)+(c)+(d).

Answer»

$\begin{matrix} R a n g e & F r e q u e n c y & C u m u l a t i v e f r e q u e n c y 0 - 10 & 5 & (b) 10 - 20 & (a) & 8 20 - 30 & 2 & (c) 30 - 40 & 6 & (d) \end{matrix}$

Fill in the missing slots and find the value of $(a) + (b) + (c) + (d)$ .

Discussion

3306.	Find the zeroes of the following polynomials by factorization method and verify the relations between the zeroes and the coefficient of the polynomials. 4x2+5√2x−3
Answer» Find the zeroes of the following polynomials by factorization method and verify the relations between the zeroes and the coefficient of the polynomials. $4 x^{2} + 5 \sqrt{2} x - 3$

Discussion

3307.	The two lines a1x + b1y = c1 and a2x + b2y = c2 are perpendicular if(a) a1a2 + b1b2 = 0(b) a1b2 + a2b1(c) a1b1 + a2b2 = 0(d) a1b2 + a2b1 = 0
Answer» The two lines a₁x + b₁y = c₁ and a₂x + b₂y = c₂ are perpendicular if (a) a₁a₂ + b₁b₂ = 0 (b) a₁b₂ + a₂b₁ (c) a₁b₁ + a₂b₂ = 0 (d) a₁b₂ + a₂b₁ = 0

Discussion

3308.	The volume of the greatest sphere that can be cut off from a cylindrical log of wood of base radius 1 cm and height 5 cm is(a) 43π(b) 103π(c) 5π(d) 203π
Answer» The volume of the greatest sphere that can be cut off from a cylindrical log of wood of base radius 1 cm and height 5 cm is (a) $\frac{4}{3} π$ (b) $\frac{10}{3} π$ (c) 5 $π$ (d) $\frac{20}{3} π$

Discussion

3309.	A group consists of 12 persons, of which 3 are extremely patient, other 6 are extremely honest and rest are extremely kind. A person from the group is selected at random. Assuming that each person is equally likely to be selected, find the probability of selecting a person who is (i) extremely patient, (ii) extremely kind or honest.
Answer» A group consists of 12 persons, of which 3 are extremely patient, other 6 are extremely honest and rest are extremely kind. A person from the group is selected at random. Assuming that each person is equally likely to be selected, find the probability of selecting a person who is (i) extremely patient, (ii) extremely kind or honest.

Discussion

3310.	Let Z be the set ofall integers and A={(x,y);x4–y4=175,x,y∈ Z}B={(x,y);x>y,x,y∈ Z}Then,the number of elementsinA∩ Bis
Answer» Let Z be the set ofall integers and A={(x,y);x4–y4=175,x,y∈ Z}B={(x,y);x>y,x,y∈ Z}Then,the number of elementsinA∩ Bis

Discussion

3311.

Two dice, one blue and one grey, are thrown at the same time. Complete the following table: Event: 'Sum on two dice' 2 3 4 5 6 7 8 9 10 11 12 Probability From the above table a student argues that there are 11 possible outcomes 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12. Therefore, each of them has a probability 111. Do you agree with this argument?

Answer» Two dice, one blue and one grey, are thrown at the same time. Complete the following table:

Event: 'Sum on two dice'	2	3	4	5	6	7	8	9	10	11	12
Probability

From the above table a student argues that there are 11 possible outcomes 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12. Therefore, each of them has a probability

\frac{1}{11} .

Do you agree with this argument?

Discussion

3312.	Solve the following quadratic equation: x2=18x−77
Answer» Solve the following quadratic equation: $x^{2} = 18 x - 77$

Discussion

3313.	A cylindrical container of radius 6 cm and height 15 cm is filled with ice cream. The whole ice cream has to be distributed to 10 children in equal cones with hemispherical tops. If the height of the conical portion is 4 times the radius of its base, find the radius of the ice cream cone.
Answer» A cylindrical container of radius 6 cm and height 15 cm is filled with ice cream. The whole ice cream has to be distributed to 10 children in equal cones with hemispherical tops. If the height of the conical portion is 4 times the radius of its base, find the radius of the ice cream cone.

Discussion

3314.	P, Q, R and S were partners in a firm sharing profits in the ratio of 5 : 3 : 1 : 1. On 1st January, 2019, S retired from the firm. On S's retirement, goodwill of the firm was valued at ₹ 4,20,000. New profit-sharing ratio among P, Q and R will be 4 : 3 : 3.Showing your working notes clearly, pass necessary Journal entry for the treatment of goodwill in the books of the firm on S's retirement.
Answer» P, Q, R and S were partners in a firm sharing profits in the ratio of 5 : 3 : 1 : 1. On 1st January, 2019, S retired from the firm. On S's retirement, goodwill of the firm was valued at ₹ 4,20,000. New profit-sharing ratio among P, Q and R will be 4 : 3 : 3. Showing your working notes clearly, pass necessary Journal entry for the treatment of goodwill in the books of the firm on S's retirement.

Discussion

3315.

If the median of the distribution is given below is 28.5, find the values of x and y. Class interval Frequency 0 − 10 5 10 − 20 x 20 − 30 20 30 − 40 15 40 − 50 y 50 − 60 5 Total 60

Answer»

If the median of the distribution is given below is 28.5, find the values of x and y.

Class interval	Frequency
0 − 10	5
10 − 20	x
20 − 30	20
30 − 40	15
40 − 50	y
50 − 60	5
Total	60

Discussion

3316.	consider set A = {x1, x2, x3, x4, x5} and set B = {y1, y2, y3} function f is defined from A to B.1.> number of onto functions from A to B such that f(x1)=y1
Answer» consider set A = {x1, x2, x3, x4, x5} and set B = {y1, y2, y3} function f is defined from A to B. 1.> number of onto functions from A to B such that f(x1)=y1

Discussion

3317.	The area of the triangle formed by the lines joining the vertex of the parabola x2 = 12y to the ends of its latusrectum is(a) 12 sq. units(b) 16 sq. units(c) 18 sq. units(d) 24 sq. units
Answer» The area of the triangle formed by the lines joining the vertex of the parabola x² = 12y to the ends of its latusrectum is (a) 12 sq. units (b) 16 sq. units (c) 18 sq. units (d) 24 sq. units

Discussion

3318.	In Fig. 7.243, if ∠ACB = ∠CDA, AC = 8 cm and AD = 3 cm, then BD = ________.
Answer» In Fig. 7.243, if ∠ACB = ∠CDA, AC = 8 cm and AD = 3 cm, then BD = ________.

Discussion

3319.	IF CIRCLES X^2 +Y^2 =9 AND X^2 +Y^2+2AX+2Y+1=0 TOUCH EACH OTHER INTERNALLY THEN A = +OR- 4/314/3-4/3
Answer» IF CIRCLES X^2 +Y^2 =9 AND X^2 +Y^2+2AX+2Y+1=0 TOUCH EACH OTHER INTERNALLY THEN A = +OR- 4/3 1 4/3 -4/3

Discussion

3320.	The area of a rhombus is 72 cm² . If it's perimeter is 32 cm, find the altitude .
Answer» The area of a rhombus is 72 cm² . If it's perimeter is 32 cm, find the altitude .

Discussion

3321.	A solid frustum is of height 8 cm. If the radii of its lower and upper ends are 3 cm and 9 cm respectively, then its slant height is(a) 15 cm(b) 12 cm(c) 10 cm(d) 17 cm
Answer» A solid frustum is of height 8 cm. If the radii of its lower and upper ends are 3 cm and 9 cm respectively, then its slant height is (a) 15 cm (b) 12 cm (c) 10 cm (d) 17 cm

Discussion

3322.	The angles of depression of two ships from the top of a light house and on the same side of it are found to be 45° and 30° respectively. If the ships are 200 m apart, find the height of the light house. [CBSE 2012]
Answer» The angles of depression of two ships from the top of a light house and on the same side of it are found to be 45° and 30° respectively. If the ships are 200 m apart, find the height of the light house. [CBSE 2012]

Discussion

3323.	A kite is flying at a height of 30 m above the ground. The string attached to the kite is temporarily tied to a point on the ground. The inclination of the string with the ground is 30∘. Find the length of the string(in meters), assuming that there is no slack in the string.
Answer» A kite is flying at a height of 30 m above the ground. The string attached to the kite is temporarily tied to a point on the ground. The inclination of the string with the ground is $30^{\circ}$ . Find the length of the string(in meters), assuming that there is no slack in the string.

Discussion

3324.	In an A.P. if mth term is n and nth term is m, where m≠n, find the pth term.
Answer» In an $A . P .$ if $m^{t h}$ term is $n$ and $n^{t h}$ term is $m$ , where $m \neq n,$ find the $p^{t h}$ term.

Discussion

3325.	A room is 16 m long and 13.5 m broad. Find the cost of covering its floor with 75-m-wide carpet at ₹60 per metre.
Answer» A room is 16 m long and 13.5 m broad. Find the cost of covering its floor with 75-m-wide carpet at ₹60 per metre.

Discussion

3326.	Solve for x: 3x−2+33−x=4
Answer» Solve for x: $3^{x - 2} + 3^{3 - x} = 4$

Discussion

3327.	LetP=(−1,0),Q=(0,0) and R=(3,3√3) be three points, then the equation of the bisector of the ∠ PQR is -
Answer» Let $P = (- 1, 0), Q = (0, 0)$ and $R = (3, 3 \sqrt{3})$ be three points, then the equation of the bisector of the $∠$ PQR is -

Discussion

3328.	Aman invests ₹.20020 in shares of par value ₹ 26 at 10% premium. The dividend is 15% per annum. Calculate: (i) the number of shares (ii) the dividend received by him annually (iii) the rate of interest he gets on his money.
Answer» Aman invests ₹.20020 in shares of par value ₹ 26 at $10 %$ premium. The dividend is 15% per annum. Calculate: (i) the number of shares (ii) the dividend received by him annually (iii) the rate of interest he gets on his money.

Discussion

3329.	If α,β and γ are the zeroes of the polynomial x3−5x2−2x+24, which of the following is the difference of two zeroes?
Answer» If $α, β$ and $γ$ are the zeroes of the polynomial $x^{3} - 5 x^{2} - 2 x + 24$ , which of the following is the difference of two zeroes?

Discussion

3330.	Question 1 (iii)Find the nature of the roots of the following quadratic equations. If the real roots exist, find them;(iii)2x2−6x+3=0
Answer» Question 1 (iii) Find the nature of the roots of the following quadratic equations. If the real roots exist, find them; $(i i i) 2 x^{2} - 6 x + 3 = 0$

Discussion

3331.	The capital invested by 3 people A, B and C are in the ratio of 1: 2 : 3 and profit earned by A is Rs.50 less than that earned by B. Calculate the total profit in the business.
Answer» The capital invested by 3 people A, B and C are in the ratio of 1: 2 : 3 and profit earned by A is Rs.50 less than that earned by B. Calculate the total profit in the business.

Discussion

3332.	In △ABC, D, E and F are mid points of sides AB, BC and AC respectively.How many pairs of similar triangles are there in the figure formed after joining D, E, F?
Answer» In $△ A B C$ , D, E and F are mid points of sides AB, BC and AC respectively.How many pairs of similar triangles are there in the figure formed after joining D, E, F?

Discussion

3333.	Write the coordinates of the point dividing line segment joining points (2, 3) and (3, 4) internally in the ratio 1 : 5.
Answer» Write the coordinates of the point dividing line segment joining points (2, 3) and (3, 4) internally in the ratio 1 : 5.

Discussion

3334.	A spherical shell of lead, whose external diameter is 18 cm, is melted and recast into a right circular cylinder, whose height is 8 cm and diameter 12 cm. The internal diameter of the shell is:
Answer» A spherical shell of lead, whose external diameter is 18 cm, is melted and recast into a right circular cylinder, whose height is 8 cm and diameter 12 cm. The internal diameter of the shell is:

Discussion

3335.	If the equation x2+2(k+2)x+9k=0 has real equal roots, then values of k are
Answer» If the equation $x^{2} + 2 (k + 2) x + 9 k = 0$ has real equal roots, then values of $k$ are

Discussion

3336.	Find the volume of a sphere whose diameter is:(i) 14 cm(ii) 3.5 dm(iii) 2.1 m
Answer» Find the volume of a sphere whose diameter is: (i) 14 cm (ii) 3.5 dm (iii) 2.1 m

Discussion

3337.	A cylinder is surmounted by a cone as shown in the figure. Find the total surface area solid formed. (in cm2). (Take π=3.14)
Answer» A cylinder is surmounted by a cone as shown in the figure. Find the total surface area solid formed. (in $c m^{2}$ ). (Take $π = 3.14$ )

3337.

A cylinder is surmounted by a cone as shown in the figure. Find the total surface area solid formed. (in cm2). (Take π=3.14)

Answer»

A cylinder is surmounted by a cone as shown in the figure. Find the total surface area solid formed. (in $c m^{2}$ ). (Take $π = 3.14$ )

Discussion

3338.	Given that √2 is irrational, prove that (5+3√2) is an irrational number.
Answer» Given that $\sqrt{2}$ is irrational, prove that $(5 + 3 \sqrt{2})$ is an irrational number.

Discussion

3339.	Which among the following is the correct histogram for the following data: Class interval600−640640−680680−720720−760760−800800−840Frequency184515328817163
Answer» Which among the following is the correct histogram for the following data: $\begin{matrix} Class interval & 600 - 640 & 640 - 680 & 680 - 720 & 720 - 760 & 760 - 800 & 800 - 840 Frequency & 18 & 45 & 153 & 288 & 171 & 63 \end{matrix}$

3339.

Which among the following is the correct histogram for the following data: Class interval600−640640−680680−720720−760760−800800−840Frequency184515328817163

Answer»

Which among the following is the correct histogram for the following data:

$\begin{matrix} Class interval & 600 - 640 & 640 - 680 & 680 - 720 & 720 - 760 & 760 - 800 & 800 - 840 Frequency & 18 & 45 & 153 & 288 & 171 & 63 \end{matrix}$

Discussion

3340.	Prove that the area of a circular path of uniform width h surrounding a circular region of radius r is πh(2r+h).
Answer» Prove that the area of a circular path of uniform width h surrounding a circular region of radius r is $π h (2 r + h)$ .

Discussion

3341.	One of the roots of the quadratic equation x2+2√2x−16=0 is
Answer» One of the roots of the quadratic equation $x^{2} + 2 \sqrt{2 x} - 16 = 0$ is

Discussion

3342.	cosA - sinA +1/cosA + sinA -1 =cosecA + cotA
Answer» cosA - sinA +1/cosA + sinA -1 =cosecA + cotA

Discussion

3343.	In the following figure find the area of the shaded region. (Use π = 3.14)
Answer» In the following figure find the area of the shaded region. (Use π = 3.14)

Discussion

3344.	△ABC is an isosceles triangle in which AB = AC = 13 cm. If area of △ADC is 169 m2, then area of △EFB is equal to
Answer» $△ A B C$ is an isosceles triangle in which AB = AC = 13 cm. If area of $△ A D C$ is $169 m^{2}$ , then area of $△ E F B$ is equal to

3344.

△ABC is an isosceles triangle in which AB = AC = 13 cm. If area of △ADC is 169 m2, then area of △EFB is equal to

Answer»

$△ A B C$ is an isosceles triangle in which AB = AC = 13 cm. If area of $△ A D C$ is $169 m^{2}$ , then area of $△ E F B$ is equal to

Discussion

3345.	In the given figure, ∠GHE=∠DFE=90∘,DH=8 cm,DF=12 cm,DG=(3x−1) cm and DE=(4x+2)cm. find the length of segments DG and DE. [4 MARKS]
Answer» In the given figure, $∠ G H E = ∠ D F E = 90^{\circ}, D H = 8 c m, D F = 12 c m, D G = (3 x - 1) c m$ and $D E = (4 x + 2) c m$ . find the length of segments DG and DE. [4 MARKS]

Discussion

3346.	A man goes 24 m due west and then 7 m due north. How far is he from the starting point?(a) 31 m(b) 17 m(c) 25 m(d) 26 m
Answer» A man goes 24 m due west and then 7 m due north. How far is he from the starting point? (a) 31 m (b) 17 m (c) 25 m (d) 26 m

Discussion

3347.	For the following A.P.s, write thefirst term and the common difference.(i) 3, 1, − 1, −3 …(ii) − 5, −1, 3, 7 …(iii) (iv) 0.6, 1.7, 2.8, 3.9…
Answer» For the following A.P.s, write the first term and the common difference. (i) 3, 1, − 1, − 3 … (ii) − 5, − 1, 3, 7 … (iii) (iv) 0.6, 1.7, 2.8, 3.9 …

3347.

For the following A.P.s, write thefirst term and the common difference.(i) 3, 1, − 1, −3 …(ii) − 5, −1, 3, 7 …(iii) (iv) 0.6, 1.7, 2.8, 3.9…

Answer»

For the following A.P.s, write the
first term and the common difference.

(i) 3, 1, − 1, −
3 …

(ii) − 5, −
1, 3, 7 …

(iii)

(iv) 0.6, 1.7, 2.8, 3.9
…

Discussion

3348.	at 273^oC, the rate of a reaction is 'x' and at 293^oC, rate cons†an t becomes 9x. what is value of rate cons†an t at 313^oC?
Answer» at 273^oC, the rate of a reaction is 'x' and at 293^oC, rate cons†an t becomes 9x. what is value of rate cons†an t at 313^oC?

Discussion

3349.	Find the values of k for which the given quadratic equation has real and distinct roots:(a) kx2 + 2x + 1 = 0(b) kx2 + 6x + 1 = 0(c) x2 − kx + 9 = 0
Answer» Find the values of k for which the given quadratic equation has real and distinct roots: (a) kx² + 2x + 1 = 0 (b) kx² + 6x + 1 = 0 (c) x² − kx + 9 = 0

Discussion

3350.	A circular ground of radius 50 m has to be covered with water proof sheet. The same amount of water proof sheet is also used for making conical tents. If the base area of tent is 625 m2then the height of tent is____cm2
Answer» A circular ground of radius 50 m has to be covered with water proof sheet. The same amount of water proof sheet is also used for making conical tents. If the base area of tent is 625 $m^{2}$ then the height of tent is____ ${c m}^{2}$

Discussion

Explore topic-wise InterviewSolutions in .

In a right angled triangle with sides a and b hypotenuse c, the altitude drawn on the hypotenuse is x. Prove that ab = cx.

The incenter of a triangle is :

Find ∠ABF from the given figure.

Solve: a) a)x2+6x=0 b) (x–4)(5x+2)=0 c) x2+3x–18=0

Range Frequency Cumulative frequency 0−105(b)10−20(a)820−302(c)30−406(d)Fill in the missing slots and find the value of (a)+(b)+(c)+(d).

Find the zeroes of the following polynomials by factorization method and verify the relations between the zeroes and the coefficient of the polynomials. 4x2+5√2x−3

The two lines a1x + b1y = c1 and a2x + b2y = c2 are perpendicular if(a) a1a2 + b1b2 = 0(b) a1b2 + a2b1(c) a1b1 + a2b2 = 0(d) a1b2 + a2b1 = 0

The volume of the greatest sphere that can be cut off from a cylindrical log of wood of base radius 1 cm and height 5 cm is(a) 43π(b) 103π(c) 5π(d) 203π

Let Z be the set ofall integers and A={(x,y);x4–y4=175,x,y∈ Z}B={(x,y);x>y,x,y∈ Z}Then,the number of elementsinA∩ Bis

Solve the following quadratic equation: x2=18x−77

A cylindrical container of radius 6 cm and height 15 cm is filled with ice cream. The whole ice cream has to be distributed to 10 children in equal cones with hemispherical tops. If the height of the conical portion is 4 times the radius of its base, find the radius of the ice cream cone.

If the median of the distribution is given below is 28.5, find the values of x and y. Class interval Frequency 0 − 10 5 10 − 20 x 20 − 30 20 30 − 40 15 40 − 50 y 50 − 60 5 Total 60

consider set A = {x1, x2, x3, x4, x5} and set B = {y1, y2, y3} function f is defined from A to B.1.> number of onto functions from A to B such that f(x1)=y1

The area of the triangle formed by the lines joining the vertex of the parabola x2 = 12y to the ends of its latusrectum is(a) 12 sq. units(b) 16 sq. units(c) 18 sq. units(d) 24 sq. units

In Fig. 7.243, if ∠ACB = ∠CDA, AC = 8 cm and AD = 3 cm, then BD = ________.

IF CIRCLES X^2 +Y^2 =9 AND X^2 +Y^2+2AX+2Y+1=0 TOUCH EACH OTHER INTERNALLY THEN A = +OR- 4/314/3-4/3

The area of a rhombus is 72 cm² . If it's perimeter is 32 cm, find the altitude .

A solid frustum is of height 8 cm. If the radii of its lower and upper ends are 3 cm and 9 cm respectively, then its slant height is(a) 15 cm(b) 12 cm(c) 10 cm(d) 17 cm

The angles of depression of two ships from the top of a light house and on the same side of it are found to be 45° and 30° respectively. If the ships are 200 m apart, find the height of the light house. [CBSE 2012]

A kite is flying at a height of 30 m above the ground. The string attached to the kite is temporarily tied to a point on the ground. The inclination of the string with the ground is 30∘. Find the length of the string(in meters), assuming that there is no slack in the string.

In an A.P. if mth term is n and nth term is m, where m≠n, find the pth term.

A room is 16 m long and 13.5 m broad. Find the cost of covering its floor with 75-m-wide carpet at ₹60 per metre.

Solve for x: 3x−2+33−x=4

LetP=(−1,0),Q=(0,0) and R=(3,3√3) be three points, then the equation of the bisector of the ∠ PQR is -

Aman invests ₹.20020 in shares of par value ₹ 26 at 10% premium. The dividend is 15% per annum. Calculate: (i) the number of shares (ii) the dividend received by him annually (iii) the rate of interest he gets on his money.

If α,β and γ are the zeroes of the polynomial x3−5x2−2x+24, which of the following is the difference of two zeroes?

Question 1 (iii)Find the nature of the roots of the following quadratic equations. If the real roots exist, find them;(iii)2x2−6x+3=0

The capital invested by 3 people A, B and C are in the ratio of 1: 2 : 3 and profit earned by A is Rs.50 less than that earned by B. Calculate the total profit in the business.

In △ABC, D, E and F are mid points of sides AB, BC and AC respectively.How many pairs of similar triangles are there in the figure formed after joining D, E, F?

Write the coordinates of the point dividing line segment joining points (2, 3) and (3, 4) internally in the ratio 1 : 5.

A spherical shell of lead, whose external diameter is 18 cm, is melted and recast into a right circular cylinder, whose height is 8 cm and diameter 12 cm. The internal diameter of the shell is:

If the equation x2+2(k+2)x+9k=0 has real equal roots, then values of k are

Find the volume of a sphere whose diameter is:(i) 14 cm(ii) 3.5 dm(iii) 2.1 m

A cylinder is surmounted by a cone as shown in the figure. Find the total surface area solid formed. (in cm2). (Take π=3.14)

Given that √2 is irrational, prove that (5+3√2) is an irrational number.

Which among the following is the correct histogram for the following data: Class interval600−640640−680680−720720−760760−800800−840Frequency184515328817163

Prove that the area of a circular path of uniform width h surrounding a circular region of radius r is πh(2r+h).

One of the roots of the quadratic equation x2+2√2x−16=0 is

cosA - sinA +1/cosA + sinA -1 =cosecA + cotA

In the following figure find the area of the shaded region. (Use π = 3.14)

△ABC is an isosceles triangle in which AB = AC = 13 cm. If area of △ADC is 169 m2, then area of △EFB is equal to

In the given figure, ∠GHE=∠DFE=90∘,DH=8 cm,DF=12 cm,DG=(3x−1) cm and DE=(4x+2)cm. find the length of segments DG and DE. [4 MARKS]

A man goes 24 m due west and then 7 m due north. How far is he from the starting point?(a) 31 m(b) 17 m(c) 25 m(d) 26 m

For the following A.P.s, write thefirst term and the common difference.(i) 3, 1, − 1, −3 …(ii) − 5, −1, 3, 7 …(iii) (iv) 0.6, 1.7, 2.8, 3.9…

at 273^oC, the rate of a reaction is 'x' and at 293^oC, rate cons†an t becomes 9x. what is value of rate cons†an t at 313^oC?

Find the values of k for which the given quadratic equation has real and distinct roots:(a) kx2 + 2x + 1 = 0(b) kx2 + 6x + 1 = 0(c) x2 − kx + 9 = 0

A circular ground of radius 50 m has to be covered with water proof sheet. The same amount of water proof sheet is also used for making conical tents. If the base area of tent is 625 m2then the height of tent is____cm2