24740 + Interview Questions in Mathematics

1.	The smallest rational number by which 13should be multiplied so that its decimal expansion terminates after one place of decimal, is(a) 310(b) 110(c) 3(d) 3100
Answer» The smallest rational number by which $\frac{1}{3}$ should be multiplied so that its decimal expansion terminates after one place of decimal, is (a) $\frac{3}{10}$ (b) $\frac{1}{10}$ (c) 3 (d) $\frac{3}{100}$

Discussion

2.	The number of end point(s) in a line segment is/are2
Answer» The number of end point(s) in a line segment is/are 2

Discussion

3.	Question 11 (ii)In ΔABC and ΔDEF ,AB=DE, AB \|\| DE, BC =EF and BC \|\| EF. Vertices A, B and C are joined to vertices D,E and F respectively ( see the given figure). Show that Quadrilateral BEFC is a parallelogram.
Answer» Question 11 (ii) In $Δ A B C$ and $Δ D E F$ ,AB=DE, AB \|\| DE, BC =EF and BC \|\| EF. Vertices A, B and C are joined to vertices D,E and F respectively ( see the given figure). Show that Quadrilateral BEFC is a parallelogram.

Discussion

4.	In the given figure, △ABC∼△PQR and AM and PN are medians of △ABC and △PQR respectively. Find the value of Area of △ ABCArea of △ PQR .
Answer» In the given figure, $△ A B C \sim △$ PQR and AM and PN are medians of $△$ ABC and $△$ PQR respectively. Find the value of $\frac{A r e a o f △ A B C}{A r e a o f △ P Q R}$ .

4.

In the given figure, △ABC∼△PQR and AM and PN are medians of △ABC and △PQR respectively. Find the value of Area of △ ABCArea of △ PQR .

Answer»

In the given figure, $△ A B C \sim △$ PQR and AM and PN are medians of $△$ ABC and $△$ PQR respectively. Find the value of $\frac{A r e a o f △ A B C}{A r e a o f △ P Q R}$ .

Discussion

5.	A right triangle has two sides of lengths 4 m and 4 m respectively. Find the length of the hypotenuse by using ratio of sides concept.
Answer» A right triangle has two sides of lengths 4 m and 4 m respectively. Find the length of the hypotenuse by using ratio of sides concept.

Discussion

6.	If A and B are two sets such that A={x:x∈N,x is a factor of 20} and B={y:y∈N,y is a factor of 30}, then find the A∩B
Answer» If $A$ and $B$ are two sets such that $A = {x : x \in N, x is a factor of 20}$ and $B = {y : y \in N, y is a factor of 30}$ , then find the $A \cap B$

Discussion

7.	Point (0,4) lies:
Answer» Point (0,4) lies:

Discussion

8.	If the side of a rhombus is 10 cm and one diagonal is 16 cm, then its area is _________.
Answer» If the side of a rhombus is 10 cm and one diagonal is 16 cm, then its area is _________.

Discussion

9.	If the polynomials 2x3 + ax2 + 3x − 5 and x3 + x2 − 4x +a leave the same remainder when divided by x −2, find the value of a.
Answer» If the polynomials 2x³ + ax² + 3x − 5 and x³ + x² − 4x +a leave the same remainder when divided by x −2, find the value of a.

Discussion

10.	ABCD is a parallelogram. W, X, Y and Z are points on sides AB, BC, CD, and DA respectively, such that AW=DY. If ar(ABCD)=400 cm2, what is the area of quadrilateral WXYZ?
Answer» ABCD is a parallelogram. W, X, Y and Z are points on sides AB, BC, CD, and DA respectively, such that $A W = D Y$ . If ar $(A B C D) = 400 c m^{2}$ , what is the area of quadrilateral WXYZ?

Discussion

11.	Factorize each of the following expressions: p3 + 27
Answer» Factorize each of the following expressions: p³ + 27

Discussion

12.	Let →a=i+2j+k,→b=i−j+k and →c=i+j−k, a vector in the plane →a and →b whose projection on →c is 1√3is........
Answer» Let $\to a = i + 2 j + k, \to b = i - j + k a n d \to c = i + j - k,$ a vector in the plane $\to a a n d \to b$ whose projection on $\to c i s \frac{1}{\sqrt{3}} i s . . . . . . . .$

12.

Let →a=i+2j+k,→b=i−j+k and →c=i+j−k, a vector in the plane →a and →b whose projection on →c is 1√3is........

Answer»

Let $\to a = i + 2 j + k, \to b = i - j + k a n d \to c = i + j - k,$ a vector in the plane $\to a a n d \to b$ whose projection on $\to c i s \frac{1}{\sqrt{3}} i s . . . . . . . .$

Discussion

13.	Solve for x, 2/(x-1) is less than or equal to 3/(2x-3) using wavy curve method
Answer» Solve for x, 2/(x-1) is less than or equal to 3/(2x-3) using wavy curve method

Discussion

14.	Arrange the given data in ungrouped frequency table : 10 ,20 ,30 ,10 ,50 ,40 ,30 ,90 ,20 ,30 ,10 ,30 ,40 ,90 ,100 ,20 ,30 ,20 ,10 ,10
Answer» Arrange the given data in ungrouped frequency table : 10 ,20 ,30 ,10 ,50 ,40 ,30 ,90 ,20 ,30 ,10 ,30 ,40 ,90 ,100 ,20 ,30 ,20 ,10 ,10

Discussion

15.	(a) A had a capital of ₹ 75,000 on 1st April, 2018. He had also goods amounting to ₹ 15,000 which he had purchased on credit and the payment had not been made. Find out the value of the total assets of the business.(b ) After a period of one month, he came to know that he had suffered a loss of ₹ 1,700. He withdrew ₹ 800 for his personal use. Find out his capital and assets of the business.
Answer» (a) A had a capital of ₹ 75,000 on 1st April, 2018. He had also goods amounting to ₹ 15,000 which he had purchased on credit and the payment had not been made. Find out the value of the total assets of the business. (b ) After a period of one month, he came to know that he had suffered a loss of ₹ 1,700. He withdrew ₹ 800 for his personal use. Find out his capital and assets of the business.

Discussion

16.	In the given circle, identify the center, radii, diameter and chords.
Answer» In the given circle, identify the center, radii, diameter and chords.

16.

In the given circle, identify the center, radii, diameter and chords.

Answer»

In the given circle, identify the center, radii, diameter and chords.

Discussion

17.	Question 1 (iii)Solve the following pair of linear equations by the elimination method and the substitution method:3x - 5y - 4 = 0 and 9x = 2y + 7
Answer» Question 1 (iii) Solve the following pair of linear equations by the elimination method and the substitution method: 3x - 5y - 4 = 0 and 9x = 2y + 7

Discussion

18.	In figure, which of the following statement is true?
Answer» In figure, which of the following statement is true?

18.

In figure, which of the following statement is true?

Answer»

In figure, which of the following statement is true?

Discussion

19.	In the following figure, ΔODC ∼ ΔOBA, ∠BOC = 125° and ∠CDO = 70°. Find ∠DOC, ∠DCO and ∠OAB
Answer» In the following figure, ΔODC ∼ ΔOBA, ∠BOC = 125° and ∠CDO = 70°. Find ∠DOC, ∠DCO and ∠OAB

19.

In the following figure, ΔODC ∼ ΔOBA, ∠BOC = 125° and ∠CDO = 70°. Find ∠DOC, ∠DCO and ∠OAB

Answer»

In the following figure, ΔODC ∼ ΔOBA, ∠BOC = 125° and ∠CDO = 70°. Find ∠DOC, ∠DCO and ∠OAB

Discussion

20.	Question 1 (ii) Does the following figure lie on the same base and between the same parallels? If yes, write the common base and two parallels.
Answer» Question 1 (ii) Does the following figure lie on the same base and between the same parallels? If yes, write the common base and two parallels.

Discussion

21.	Rationalize sqrt5/2sqrt3
Answer» Rationalize sqrt5/2sqrt3

Discussion

22.

Choose correct alternative for each of the following questions(1) To draw graph of 4x +5y = 19, Find y when x = 1. A) 4 (B) 3 (C) 2 (D) –3 (2) For simultaneous equations in variables x and y, Dx = 49, Dy = –63, D = 7 then what is x ? A) 7 (B) –7 (C) 17 (D) -17 (3) Find the value of 53-7-4 A) –1 (B) –41 (C) 41 (D) 1 (4) To solve x + y = 3 ; 3x – 2y – 4 = 0 by determinant method find D. A) 5 (B) 1 (C) –5 (D) –1 (5) ax + by = c and mx + ny = d and an ≠ bm then these simultaneous equations have - (A) Only one common solution. (A) No solution. (C) Infinite number of solutions. (D) Only two solution.

Answer»

Choose correct alternative for each of the following questions

(1) To draw graph of 4x +5y = 19, Find y when x = 1.

A) 4

(B) 3

(C) 2

(D) –3

(2) For simultaneous equations in variables x and y, D_x= 49, D_y = –63, D = 7 then what is x ?

A) 7

(B) –7

(C)

\frac{1}{7}

(D)

\frac{- 1}{7}

(3) Find the value of

|\begin{matrix} 5 & 3 \\ - 7 & - 4 \end{matrix}|

A) –1

(B) –41

(C) 41

(D) 1

(4) To solve x + y = 3 ; 3x – 2y – 4 = 0 by determinant method find D.

A) 5

(B) 1

(C) –5

(D) –1

(5) ax + by = c and mx + ny = d and an ≠ bm then these simultaneous equations have -

(A)	Only one common solution.	(A)	No solution.
(C)	Infinite number of solutions.	(D)	Only two solution.

Discussion

23.	Question 6Draw a triangle ABC with side BC=7 cm,∠B=45∘,∠A=105∘. Then, construct a triangle whose sides are 4/3 times the corresponding sides of ΔABC.
Answer» Question 6 Draw a triangle ABC with side $B C = 7 c m, ∠ B = 45^{\circ}, ∠ A = 105^{\circ}$ . Then, construct a triangle whose sides are 4/3 times the corresponding sides of $Δ A B C$ .

Discussion

24.	The total surface area of a cube is 1176 cm2. Find its volume.
Answer» The total surface area of a cube is $1176 c m^{2}$ . Find its volume.

Discussion

25.	What is the least rationalizing factor of √24?
Answer» What is the least rationalizing factor of $\sqrt{24}$ ?

Discussion

26.	Expand (x+5)(x−5).
Answer» Expand $(x + 5) (x - 5)$ .

Discussion

27.	This question consists of two statements,namely,Assertion (A) and Reason (R).For selecting the correct answer,use the following code: (a) Both Assertion (A) and Reason (R) are true and Reason (R) correct explanation of Assertion (A). (b) Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A). (c) Assertion (A) is true and Reason (R) is false. (d) Assertion (A) is false and Reason (R) is true. Assertion (A)Reason (R)If ABCD is a rhombus whose one Median of a triangle divides itangle is 60∘then the ratio of the into two triangles of equal area.lenghts of its diagonals is √3:1. The correct answer is :(a) /(b)/(c)/(d).
Answer» This question consists of two statements,namely,Assertion (A) and Reason (R).For selecting the correct answer,use the following code: (a) Both Assertion (A) and Reason (R) are true and Reason (R) correct explanation of Assertion (A). (b) Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A). (c) Assertion (A) is true and Reason (R) is false. (d) Assertion (A) is false and Reason (R) is true. $\begin{matrix} A s s e r t i o n (A) & R e a s o n (R) If ABCD is a rhombus whose one & Median of a triangle divides it angle is 60^{\circ} then the ratio of the & into two triangles of equal area. lenghts of its diagonals is \sqrt{3} : 1. \end{matrix}$ The correct answer is :(a) /(b)/(c)/(d).

27.

This question consists of two statements,namely,Assertion (A) and Reason (R).For selecting the correct answer,use the following code: (a) Both Assertion (A) and Reason (R) are true and Reason (R) correct explanation of Assertion (A). (b) Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A). (c) Assertion (A) is true and Reason (R) is false. (d) Assertion (A) is false and Reason (R) is true. Assertion (A)Reason (R)If ABCD is a rhombus whose one Median of a triangle divides itangle is 60∘then the ratio of the into two triangles of equal area.lenghts of its diagonals is √3:1. The correct answer is :(a) /(b)/(c)/(d).

Answer»

This question consists of two statements,namely,Assertion (A) and Reason (R).For selecting the correct answer,use the following code:

(a) Both Assertion (A) and Reason (R) are true and Reason (R) correct explanation of Assertion (A).

(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).

(c) Assertion (A) is true and Reason (R) is false.

(d) Assertion (A) is false and Reason (R) is true.

$\begin{matrix} A s s e r t i o n (A) & R e a s o n (R) If ABCD is a rhombus whose one & Median of a triangle divides it angle is 60^{\circ} then the ratio of the & into two triangles of equal area. lenghts of its diagonals is \sqrt{3} : 1. \end{matrix}$

The correct answer is :(a) /(b)/(c)/(d).

Discussion

28.	Which of the following polynomials has x+1 as one of the factors?
Answer» Which of the following polynomials has $x + 1$ as one of the factors?

Discussion

29.	Factorize: 27x3 – 125y3
Answer» Factorize: 27x³ – 125y³

Discussion

30.	2 numbers are less than 60 and 3 numbers are more than 60. The numbers which are less have a difference of 10 and 20, respectively, from 60.The numbers which are more, have a difference of 10, 20 and 30, from 60. What is the average of these numbers (including 60)?
Answer» 2 numbers are less than 60 and 3 numbers are more than 60. The numbers which are less have a difference of 10 and 20, respectively, from 60. The numbers which are more, have a difference of 10, 20 and 30, from 60. What is the average of these numbers (including 60)?

30.

2 numbers are less than 60 and 3 numbers are more than 60. The numbers which are less have a difference of 10 and 20, respectively, from 60.The numbers which are more, have a difference of 10, 20 and 30, from 60. What is the average of these numbers (including 60)?

Answer»

2 numbers are less than 60 and 3 numbers are more than 60. The numbers which are less have a difference of 10 and 20, respectively, from 60.

The numbers which are more, have a difference of 10, 20 and 30, from 60. What is the average of these numbers (including 60)?

Discussion

31.

From the following Receipts and Payments Account of Kapil Dev Club and from the given additional information, prepare Income and Expenditure Account for the year ending 31st December, 2019 and the Balance Sheet as at that date: RECEIPTS AND PAYMENTS ACCOUNT for the year ended 31st March, 2019 Dr. Cr. Receipts ₹ Payments ₹ To Balance b/d 1,90,000 By Salaries 3,30,000 To Subscriptions 6,60,000 By Sports Material 4,00,000 To Interest on Investment 40,000 By Balance c/d 1,60,000 8% p.a. for full year 8,90,000 8,90,000 Additional Information:(i) The club had received ₹ 20,000 for subscription in 2017-18 for 2018-19.(ii) Salaries had been paid only for 11 months.(iii) Stock of sports materials on 31st March, 2018 was ₹ 3,00,000 and on 31st March, 2019 ₹ 6,50,000.

Answer» From the following Receipts and Payments Account of Kapil Dev Club and from the given additional information, prepare Income and Expenditure Account for the year ending 31st December, 2019 and the Balance Sheet as at that date:

RECEIPTS AND PAYMENTS ACCOUNT for the year ended 31st March, 2019
Dr.				Cr.
Receipts	₹	Payments	₹

To Balance b/d	1,90,000	By Salaries	3,30,000
To Subscriptions	6,60,000	By Sports Material	4,00,000
To Interest on Investment	40,000	By Balance c/d	1,60,000
8% p.a. for full year
	8,90,000		8,90,000

Additional Information:

(i) The club had received ₹ 20,000 for subscription in 2017-18 for 2018-19.

(ii) Salaries had been paid only for 11 months.

(iii) Stock of sports materials on 31st March, 2018 was ₹ 3,00,000 and on 31st March, 2019 ₹ 6,50,000.

Discussion

32.	Question 15If two solid hemispheres of same base radius r are joined together along their bases the curved surface area of this new solid is(A) 4πr2(B) 6πr2(C) 3πr2(D) 8πr2
Answer» Question 15 If two solid hemispheres of same base radius r are joined together along their bases the curved surface area of this new solid is (A) $4 π r^{2}$ (B) $6 π r^{2}$ (C) $3 π r^{2}$ (D) $8 π r^{2}$

Discussion

33.	(a − b)3 + (b − c)3 + (c − a)3 =(a) (a + b + c) (a2 + b2 + c2 − ab − bc − ca)(b) (a − b) (b − c) (c − a)(c) 3(a − b) ( b− c) (c − a)(d) none of these
Answer» (a − b)³ + (b − c)³ + (c − a)³ = (a) (a + b + c) (a² + b²+ c² − ab − bc − ca) (b) (a − b) (b − c) (c − a) (c) 3(a − b) ( b− c) (c − a) (d) none of these

Discussion

34.	The inner diameter of a cylindrical wooden pipe is 24 cm and its outer diameter is 28 cm. The length of the pipe is 35 cm. Find the mass of the pipe, if 1 cm3 of wood has a mass of 0.6 g.
Answer» The inner diameter of a cylindrical wooden pipe is 24 cm and its outer diameter is 28 cm. The length of the pipe is 35 cm. Find the mass of the pipe, if 1 cm³ of wood has a mass of 0.6 g.

Discussion

35.

1500 families with 2 children were selected randomly, and the following data were recorded: Number of girls in a family 2 1 0 Number of families 475 814 211 Compute the probability of a family, chosen at random, having(i) 2 girls (ii) 1 girl (iii) No girlAlso check whether the sum of these probabilities is 1.

Answer»

1500 families with 2 children were selected randomly, and the following data were recorded:

Number of girls in a family	2	1	0
Number of families	475	814	211

Compute the probability of a family, chosen at random, having

(i) 2 girls (ii) 1 girl (iii) No girl

Also check whether the sum of these probabilities is 1.

Discussion

36.	Question 157In the following figure of a ship, ABDH and CEFG are two parallelograms. Find the value of x.
Answer» Question 157 In the following figure of a ship, ABDH and CEFG are two parallelograms. Find the value of x.

Discussion

37.	Question 9 (iii) A right circular cylinder just encloses a sphere of radius r (see figure). Find: (iii) the ratio of the areas obtained in (i) and (ii).
Answer» Question 9 (iii) A right circular cylinder just encloses a sphere of radius r (see figure). Find: (iii) the ratio of the areas obtained in (i) and (ii).

37.

Question 9 (iii) A right circular cylinder just encloses a sphere of radius r (see figure). Find: (iii) the ratio of the areas obtained in (i) and (ii).

Answer»

Question 9 (iii)
A right circular cylinder just encloses a sphere of radius r (see figure). Find:

(iii) the ratio of the areas obtained in (i) and (ii).

Discussion

38.	In the given parallelogram ABCD, DP = BQ and ∠ADP=∠CBQ. To which triangle is ΔADP congruent to?
Answer» In the given parallelogram ABCD, DP = BQ and $∠ A D P = ∠ C B Q$ . To which triangle is $Δ A D P$ congruent to?

Discussion

39.	In a sample survey of 645 people, it was found that 516 people have a high school certificate. If a person is chosen at random, what is the probability that he / she has a high school certificate?(a) 12(b) 35(c) 710(d) 45
Answer» In a sample survey of 645 people, it was found that 516 people have a high school certificate. If a person is chosen at random, what is the probability that he / she has a high school certificate? (a) $\frac{1}{2}$ (b) $\frac{3}{5}$ (c) $\frac{7}{10}$ (d) $\frac{4}{5}$

Discussion

40.	If x + 1 is a factor of the polynomial ax3 + x2 – 2x + 4a – 9, then a = __________.
Answer» If x + 1 is a factor of the polynomial ax³ + x² – 2x + 4a – 9, then a = __________.

Discussion

41.	An isosceles right angled triangle is inscribed in the circle x2+y2=r2. If the coordinates of an end of the hypotenuse are (a, b), the coordinates of the vertex are
Answer» An isosceles right angled triangle is inscribed in the circle $x^{2} + y^{2} = r^{2} .$ If the coordinates of an end of the hypotenuse are (a, b), the coordinates of the vertex are

Discussion

42.	A card is drawn at random from a well shuffled deck of playing cards. The probability that the card drawn is neither a king nor a queen is
Answer» A card is drawn at random from a well shuffled deck of playing cards. The probability that the card drawn is neither a king nor a queen is

Discussion

43.	The monthly electricity bill of a family for the year 2018 is; 250 200 300 500 750 1000 1200 795 600 500 300 150. Find the range.
Answer» The monthly electricity bill of a family for the year 2018 is; 250 200 300 500 750 1000 1200 795 600 500 300 150. Find the range.

43.

The monthly electricity bill of a family for the year 2018 is; 250 200 300 500 750 1000 1200 795 600 500 300 150. Find the range.

Answer»

The monthly electricity bill of a family for the year 2018 is; 250 200 300 500 750 1000 1200 795 600 500 300 150.

Find the range.

Discussion

44.	Question 12 Is it possible to construct a triangle with lengths of its sides as 8 cm, 7 cm and 4 cm? Give reason for your answer.
Answer» Question 12 Is it possible to construct a triangle with lengths of its sides as 8 cm, 7 cm and 4 cm? Give reason for your answer.

Discussion

45.	Let α, β, γ be non zero non coplanar vectors such that γ.β =0 and α+ (γ×β) = γ×α. If angle between α and β lies between (π/4, π/6) then arithmetic mean of maximum and minimum values of \|γ\|² is
Answer» Let α, β, γ be non zero non coplanar vectors such that γ.β =0 and α+ (γ×β) = γ×α. If angle between α and β lies between (π/4, π/6) then arithmetic mean of maximum and minimum values of \|γ\|² is

Discussion

46.	Find the area of triangle in cm2 whose base is 4 cm long and the height corresponding to the base measures 12 cm.24
Answer» Find the area of triangle in ${cm}^{2}$ whose base is 4 cm long and the height corresponding to the base measures 12 cm. 24

Discussion

47.	A coin tossed 15 times and observed that head comes up 11 times . find the probabilistically of that a tail comes up
Answer» A coin tossed 15 times and observed that head comes up 11 times . find the probabilistically of that a tail comes up

Discussion

48.	18. AB is a diameter. of x2 + 9y2 = 25. The eccentric angle of A is 3%. Then the eccentric angle of B is
Answer» 18. AB is a diameter. of x2 + 9y2 = 25. The eccentric angle of A is 3%. Then the eccentric angle of B is

Discussion

49.	Question 3A metal pipe is 77 cm long. The inner diameter of a cross-section is 4 cm, the outer diameter being 4.4 cm.Find its,(i) Inner curved surface area(ii) Outer curved surface area(iii) Total surface area. [Assume π=227]
Answer» Question 3 A metal pipe is 77 cm long. The inner diameter of a cross-section is 4 cm, the outer diameter being 4.4 cm. Find its, (i) Inner curved surface area (ii) Outer curved surface area (iii) Total surface area. $[A s s u m e π = \frac{22}{7}]$

Discussion

50.	The perimeter of a triangular field is 420 m and its sides are in the ratio 6:7:8. Find the area of the triangular field.
Answer» The perimeter of a triangular field is 420 m and its sides are in the ratio 6:7:8. Find the area of the triangular field.

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

The smallest rational number by which 13should be multiplied so that its decimal expansion terminates after one place of decimal, is(a) 310(b) 110(c) 3(d) 3100

The number of end point(s) in a line segment is/are2

Question 11 (ii)In ΔABC and ΔDEF ,AB=DE, AB || DE, BC =EF and BC || EF. Vertices A, B and C are joined to vertices D,E and F respectively ( see the given figure). Show that Quadrilateral BEFC is a parallelogram.

In the given figure, △ABC∼△PQR and AM and PN are medians of △ABC and △PQR respectively. Find the value of Area of △ ABCArea of △ PQR .

A right triangle has two sides of lengths 4 m and 4 m respectively. Find the length of the hypotenuse by using ratio of sides concept.

If A and B are two sets such that A={x:x∈N,x is a factor of 20} and B={y:y∈N,y is a factor of 30}, then find the A∩B

Point (0,4) lies:

If the side of a rhombus is 10 cm and one diagonal is 16 cm, then its area is _________.

If the polynomials 2x3 + ax2 + 3x − 5 and x3 + x2 − 4x +a leave the same remainder when divided by x −2, find the value of a.

ABCD is a parallelogram. W, X, Y and Z are points on sides AB, BC, CD, and DA respectively, such that AW=DY. If ar(ABCD)=400 cm2, what is the area of quadrilateral WXYZ?

Factorize each of the following expressions: p3 + 27

Let →a=i+2j+k,→b=i−j+k and →c=i+j−k, a vector in the plane →a and →b whose projection on →c is 1√3is........

Solve for x, 2/(x-1) is less than or equal to 3/(2x-3) using wavy curve method

Arrange the given data in ungrouped frequency table : 10 ,20 ,30 ,10 ,50 ,40 ,30 ,90 ,20 ,30 ,10 ,30 ,40 ,90 ,100 ,20 ,30 ,20 ,10 ,10

In the given circle, identify the center, radii, diameter and chords.

Question 1 (iii)Solve the following pair of linear equations by the elimination method and the substitution method:3x - 5y - 4 = 0 and 9x = 2y + 7

In figure, which of the following statement is true?

In the following figure, ΔODC ∼ ΔOBA, ∠BOC = 125° and ∠CDO = 70°. Find ∠DOC, ∠DCO and ∠OAB

Question 1 (ii) Does the following figure lie on the same base and between the same parallels? If yes, write the common base and two parallels.

Rationalize sqrt5/2sqrt3

Question 6Draw a triangle ABC with side BC=7 cm,∠B=45∘,∠A=105∘. Then, construct a triangle whose sides are 4/3 times the corresponding sides of ΔABC.

The total surface area of a cube is 1176 cm2. Find its volume.

What is the least rationalizing factor of √24?

Expand (x+5)(x−5).

Which of the following polynomials has x+1 as one of the factors?

Factorize: 27x3 – 125y3

2 numbers are less than 60 and 3 numbers are more than 60. The numbers which are less have a difference of 10 and 20, respectively, from 60.The numbers which are more, have a difference of 10, 20 and 30, from 60. What is the average of these numbers (including 60)?

Question 15If two solid hemispheres of same base radius r are joined together along their bases the curved surface area of this new solid is(A) 4πr2(B) 6πr2(C) 3πr2(D) 8πr2

(a − b)3 + (b − c)3 + (c − a)3 =(a) (a + b + c) (a2 + b2 + c2 − ab − bc − ca)(b) (a − b) (b − c) (c − a)(c) 3(a − b) ( b− c) (c − a)(d) none of these

The inner diameter of a cylindrical wooden pipe is 24 cm and its outer diameter is 28 cm. The length of the pipe is 35 cm. Find the mass of the pipe, if 1 cm3 of wood has a mass of 0.6 g.

Question 157In the following figure of a ship, ABDH and CEFG are two parallelograms. Find the value of x.

Question 9 (iii) A right circular cylinder just encloses a sphere of radius r (see figure). Find: (iii) the ratio of the areas obtained in (i) and (ii).

In the given parallelogram ABCD, DP = BQ and ∠ADP=∠CBQ. To which triangle is ΔADP congruent to?

In a sample survey of 645 people, it was found that 516 people have a high school certificate. If a person is chosen at random, what is the probability that he / she has a high school certificate?(a) 12(b) 35(c) 710(d) 45

If x + 1 is a factor of the polynomial ax3 + x2 – 2x + 4a – 9, then a = __________.

An isosceles right angled triangle is inscribed in the circle x2+y2=r2. If the coordinates of an end of the hypotenuse are (a, b), the coordinates of the vertex are

A card is drawn at random from a well shuffled deck of playing cards. The probability that the card drawn is neither a king nor a queen is

The monthly electricity bill of a family for the year 2018 is; 250 200 300 500 750 1000 1200 795 600 500 300 150. Find the range.

Question 12 Is it possible to construct a triangle with lengths of its sides as 8 cm, 7 cm and 4 cm? Give reason for your answer.

Let α, β, γ be non zero non coplanar vectors such that γ.β =0 and α+ (γ×β) = γ×α. If angle between α and β lies between (π/4, π/6) then arithmetic mean of maximum and minimum values of |γ|² is

Find the area of triangle in cm2 whose base is 4 cm long and the height corresponding to the base measures 12 cm.24

A coin tossed 15 times and observed that head comes up 11 times . find the probabilistically of that a tail comes up

18. AB is a diameter. of x2 + 9y2 = 25. The eccentric angle of A is 3%. Then the eccentric angle of B is

Question 3A metal pipe is 77 cm long. The inner diameter of a cross-section is 4 cm, the outer diameter being 4.4 cm.Find its,(i) Inner curved surface area(ii) Outer curved surface area(iii) Total surface area. [Assume π=227]

The perimeter of a triangular field is 420 m and its sides are in the ratio 6:7:8. Find the area of the triangular field.