32581 + Interview Questions in Mathematics

1.	A bag contains 100 identical marble stones numbered from 1 to 100. What is the probability of drawing a marble having a number divisible by both 4 and 5?
Answer» A bag contains 100 identical marble stones numbered from 1 to 100. What is the probability of drawing a marble having a number divisible by both 4 and 5?

Discussion

2.	The above picture are few natural examples of parabolic shape which is represented by a quadratic polynomial. A parabolic arch is an arch in the shape of a parabola. In structures, their curve represents an efficient method of load, and so can be found in bridges and in architecture in a variety of forms.Based on the above information, answer the following questions. Find a quadratic polynomial with 18 as the sum and 2 as product of its zeroes.
Answer» The above picture are few natural examples of parabolic shape which is represented by a quadratic polynomial. A parabolic arch is an arch in the shape of a parabola. In structures, their curve represents an efficient method of load, and so can be found in bridges and in architecture in a variety of forms. Based on the above information, answer the following questions. Find a quadratic polynomial with $\frac{1}{8}$ as the sum and 2 as product of its zeroes.

Discussion

3.	48. A chord of a circle is equal to the radius of the circle find the angle subtended by the chord at a point on the minor arc and also at a point on the major arc
Answer» 48. A chord of a circle is equal to the radius of the circle find the angle subtended by the chord at a point on the minor arc and also at a point on the major arc

Discussion

4.	A pair of straight lines x2−8x+12=0 and y2−14y+45=0 are forming a square. Co-ordinates of the center of the circle inscribed in the square are
Answer» A pair of straight lines $x^{2} - 8 x + 12 = 0$ and $y^{2} - 14 y + 45 = 0$ are forming a square. Co-ordinates of the center of the circle inscribed in the square are

Discussion

5.	In a test, an examinee either guesses or copies or knows the answer to a multiple choice question with four choices. The probability that he makes a guess is 13 and the probability that he copies the answer is 16. The probability that his answer is correct given that he copied it is 18. Find the probability that he knew the answer to the question, given that he answered it correctly.
Answer» In a test, an examinee either guesses or copies or knows the answer to a multiple choice question with four choices. The probability that he makes a guess is $\frac{1}{3}$ and the probability that he copies the answer is $\frac{1}{6}$ . The probability that his answer is correct given that he copied it is $\frac{1}{8} .$ Find the probability that he knew the answer to the question, given that he answered it correctly.

Discussion

6.	AB and CD are two equal chords of a circle with centre at O. If OP ⊥ AB and OQ ⊥ CD, where P and Q are points on the chords AB and CD respectively and if ∠POQ=100∘, the measure of ∠APQ is:
Answer» AB and CD are two equal chords of a circle with centre at O. If OP $⊥$ AB and OQ $⊥$ CD, where P and Q are points on the chords AB and CD respectively and if $∠ P O Q = 100^{\circ}$ , the measure of $∠ A P Q$ is:

Discussion

7.	A 8 cm cube is cut into as many 2 cm cubes as possible. Then, the ratio of the surface area of the larger cube to that of the sum of the surface areas of the smaller cubes, is
Answer» A 8 cm cube is cut into as many 2 cm cubes as possible. Then, the ratio of the surface area of the larger cube to that of the sum of the surface areas of the smaller cubes, is

Discussion

8.	Question 5The first term of an AP is 5, the last term is 45 and the sum is 400. Find the number of terms and the common difference.
Answer» Question 5 The first term of an AP is 5, the last term is 45 and the sum is 400. Find the number of terms and the common difference.

Discussion

9.	Raghu had to make a cylindrical tube with an aluminium cover. What is the area of the aluminium sheet he needs to cover the tube if the tube has a length of 1 m and base radius 3.5 cm?(Take π=22/7)
Answer» Raghu had to make a cylindrical tube with an aluminium cover. What is the area of the aluminium sheet he needs to cover the tube if the tube has a length of 1 m and base radius 3.5 cm? (Take π=22/7)

Discussion

10.

Pankaj, Naresh and Saurabh are partners sharing profits in the ratio of 3 : 2 : 1. On 1st April, 2019, Naresh retired on that date, Balance Sheet of the firm was as follows: Liabilities Amount (₹) Assets Amount (₹) General Reserve 12,000 Bank 7,600 Sundry Creditors 15,000 Debtors 6,000 Bills Payable 12,000 Less: Provision for Doubtful Debts 400 5,600 Outstanding Salary 2,200 Stock 9,000 Provision for Legal Damages 6,000 Furniture 41,000 Capital A/cs: Premises 80,000 Pankaj 46,000 Naresh 30,000 Saurabh 20,000 96,000 1,43,200 1,43,200 Additional Information:(a) Premises have appreciated by 20%, stock depreciated by 10% and provision for doubtful debts was to be made 5% on debtors. Further, provision for legal damages is to be made for ₹ 1,200 and furniture to be brought up to ₹ 45,000. (b) Goodwill of the firm be valued at ₹ 42,000.(c) ₹ 26,000 from Naresh's Capital Account be transferred to his Loan Account and balance be paid through bank: if required, necessary loan may be obtained from bank.(d) New profit-sharing ratio of Pankaj and Saurabh is decided to be 5 : 1.Give the necessary Ledger Accounts and Balance Sheet of the firm after Naresh's retirement.

Answer» Pankaj, Naresh and Saurabh are partners sharing profits in the ratio of 3 : 2 : 1. On 1st April, 2019, Naresh retired on that date, Balance Sheet of the firm was as follows:

Liabilities		Amount (₹)	Assets		Amount (₹)
General Reserve		12,000	Bank		7,600
Sundry Creditors		15,000	Debtors	6,000
Bills Payable		12,000	Less: Provision for Doubtful Debts	400	5,600
Outstanding Salary		2,200	Stock		9,000
Provision for Legal Damages		6,000	Furniture		41,000
Capital A/cs:			Premises		80,000
Pankaj	46,000
Naresh	30,000
Saurabh	20,000	96,000

		1,43,200			1,43,200

Additional Information:

(a) Premises have appreciated by 20%, stock depreciated by 10% and provision for doubtful debts was to be made 5% on debtors. Further, provision for legal damages is to be made for ₹ 1,200 and furniture to be brought up to ₹ 45,000.

(b) Goodwill of the firm be valued at ₹ 42,000.

(c) ₹ 26,000 from Naresh's Capital Account be transferred to his Loan Account and balance be paid through bank: if required, necessary loan may be obtained from bank.

(d) New profit-sharing ratio of Pankaj and Saurabh is decided to be 5 : 1.

Give the necessary Ledger Accounts and Balance Sheet of the firm after Naresh's retirement.

Discussion

11.	The line through A(–2, 3) & B(4, b) is perpendicular to the line 2 – 4y = 5. Find the value of ‘b’
Answer» The line through A(–2, 3) & B(4, b) is perpendicular to the line 2 – 4y = 5. Find the value of ‘b’

Discussion

12.	At θ=90∘, which of the two angles are not defined?
Answer» At $θ = 90^{\circ}$ , which of the two angles are not defined?

Discussion

13.	25. Water flows at rate of 10 m per minute from a cylinderical pipe 5 mm in diameter. Hw long will it take up to a conical vessel whose diameter at base is 40 cm and depth 24 cm ? (a) 48 minutes 15 sec (b) 51 minutes 12 sec (c) 52 minutes 1 sec (d) 55 minutes
Answer» 25. Water flows at rate of 10 m per minute from a cylinderical pipe 5 mm in diameter. Hw long will it take up to a conical vessel whose diameter at base is 40 cm and depth 24 cm ? (a) 48 minutes 15 sec (b) 51 minutes 12 sec (c) 52 minutes 1 sec (d) 55 minutes

Discussion

14.	In a rain water harvesting system, the rain water from a roof of 22×20 meter drains into a cylindrical tank having diameter of base 2m and height of 3.5m. If the tank is full, find the rainfall in cm.
Answer» In a rain water harvesting system, the rain water from a roof of 22×20 meter drains into a cylindrical tank having diameter of base 2m and height of 3.5m. If the tank is full, find the rainfall in cm.

Discussion

15.	3x–4y=1...(1)5x–6y=7...(2) In the above equations, which of the following step can to be done to numerically equate the coefficients of x?
Answer» $3 x - 4 y = 1$ ...(1) $5 x - 6 y = 7$ ...(2) In the above equations, which of the following step can to be done to numerically equate the coefficients of $x$ ?

Discussion

16.	ABCD is a rectangle with AB = 14 cm and BC = 7 cm. Taking DC, BC and AD as diameters, three semi-circles are drawn as shown in the figure. Find the area of the shaded region.
Answer» ABCD is a rectangle with AB = 14 cm and BC = 7 cm. Taking DC, BC and AD as diameters, three semi-circles are drawn as shown in the figure. Find the area of the shaded region.

16.

ABCD is a rectangle with AB = 14 cm and BC = 7 cm. Taking DC, BC and AD as diameters, three semi-circles are drawn as shown in the figure. Find the area of the shaded region.

Answer»

ABCD is a rectangle with AB = 14 cm and BC = 7 cm. Taking DC, BC and AD as diameters, three semi-circles are drawn as shown in the figure. Find the area of the shaded region.

Discussion

17.	How many irrational numbers exist between two rational numbers?
Answer» How many irrational numbers exist between two rational numbers?

Discussion

18.	The sum of the digits in a two digits number is 9.The number obtained by interchanging the digits exceeds the original number by 27 . Find the two digit number.
Answer» The sum of the digits in a two digits number is 9.The number obtained by interchanging the digits exceeds the original number by 27 . Find the two digit number.

Discussion

19.	how to draw an astroid which has a equation (x)^2/3 + (y)^2/3 = a^2/3
Answer» how to draw an astroid which has a equation (x)^2/3 + (y)^2/3 = a^2/3

Discussion

20.	Use Euclid's division lemma to show that the square of any positive integers is either of the form 3m or 3m+1 for some integer m
Answer» Use Euclid's division lemma to show that the square of any positive integers is either of the form 3m or 3m+1 for some integer m

Discussion

21.	cos 12°sin 78°+tan 23°cot 67°=?(a) 0(b) 1(c) 2(d) 32
Answer» $\frac{\cos 12 °}{\sin 78 °} + \frac{\tan 23 °}{\cot 67 °} = ?$ (a) 0 (b) 1 (c) 2 (d) $\frac{3}{2}$

Discussion

22.	26. If the area of a circle and a square are equalso,then the ratio of theIrish perimeters is:
Answer» 26. If the area of a circle and a square are equalso,then the ratio of theIrish perimeters is:

Discussion

23.	The value of π upto 50 decimal place is3.14159265358979323846264338327950288419716939937510(1) Make a frequency distribution table of digits from 0 to 9 after the decimal place.(2) Which are the most and least occuring digits ?
Answer» The value of $π$ upto 50 decimal place is 3.1415926535897932384626433832795028841971693 9937510 (1) Make a frequency distribution table of digits from 0 to 9 after the decimal place. (2) Which are the most and least occuring digits ?

Discussion

24.	Find the value of cos38° cosec52°tan18° tan35° tan60° tan72° tan55°.
Answer» $Find the value of \frac{\cos 38 ° cosec 52 °}{\tan 18 ° \tan 35 ° \tan 60 ° \tan 72 ° \tan 55 °} .$

Discussion

25.	how to simplify (sinAcosB+cosAsinB)/(cosAcosB-sinAsinB) to (tanA+tanB)/(1-tanAtanB)?
Answer» how to simplify (sinAcosB+cosAsinB)/(cosAcosB-sinAsinB) to (tanA+tanB)/(1-tanAtanB)?

Discussion

26.	A rectangle sheet of paper 44 cm × 18 cm is rolled once along its length and a cylinder is formed. The volume of the cylinder so formed is equal to
Answer» A rectangle sheet of paper 44 cm × 18 cm is rolled once along its length and a cylinder is formed. The volume of the cylinder so formed is equal to

Discussion

27.	If α, β, γ are the zeros of the polynomial f(x) = ax3 + bx2 + cx + d, then 1α+1β+1γ=(a) -bd(b) cd(c) -cd(d) -ca
Answer» If α, β, γ are the zeros of the polynomial f(x) = ax³ + bx² + cx + d, then $\frac{1}{α} + \frac{1}{β} + \frac{1}{γ} =$ (a) $- \frac{b}{d}$ (b) $\frac{c}{d}$ (c) $- \frac{c}{d}$ (d) $- \frac{c}{a}$

Discussion

28.	In the picture below, the radius of the circle is 15 centimetres. Compute the lengths of the tangents PQ and PR(i) The point P is equidistant from A and B(ii) The line OP bisects the line AB and the angle APB
Answer» In the picture below, the radius of the circle is 15 centimetres. Compute the lengths of the tangents PQ and PR (i) The point P is equidistant from A and B (ii) The line OP bisects the line AB and the angle APB

28.

In the picture below, the radius of the circle is 15 centimetres. Compute the lengths of the tangents PQ and PR(i) The point P is equidistant from A and B(ii) The line OP bisects the line AB and the angle APB

Answer»

In the picture below, the radius of the circle is 15 centimetres. Compute the lengths of the tangents PQ and PR

(i) The point P is equidistant from A and B

(ii) The line OP bisects the line AB and the angle APB

Discussion

29.	In the figure given below, what is the value of tan θ in terms of a,b and c?
Answer» In the figure given below, what is the value of $t a n θ$ in terms of a,b and c?

Discussion

30.	Question 2 In figure, if OA = 5 cm, AB = 8 cm and OD is perpendicular to AB, then CD is equal to (A) 2 cm (B) 3 cm (C) 4 cm (D) 5 cm
Answer» Question 2 In figure, if OA = 5 cm, AB = 8 cm and OD is perpendicular to AB, then CD is equal to (A) 2 cm (B) 3 cm (C) 4 cm (D) 5 cm

Discussion

31.	Let ABC be a right triangle in which AB = 3 cm, BC = 4 cm and ∠ B = 90∘. BD is the perpendicular from B on AC. The circle through B, C, D is drawn. Construct the tangents from A to this circle. [4 MARKS]
Answer» Let ABC be a right triangle in which AB = 3 cm, BC = 4 cm and $∠$ B = $90^{\circ}$ . BD is the perpendicular from B on AC. The circle through B, C, D is drawn. Construct the tangents from A to this circle. [4 MARKS]

Discussion

32.	If P(2, 4), Q(0, 3), R(3, 6) and S(5, y) are the vertices of a parallelogram PQRS, then the value of y is(a) 7 (b) 5 (c) −7 (d) −8 [CBSE 2014]
Answer» If P(2, 4), Q(0, 3), R(3, 6) and S(5, y) are the vertices of a parallelogram PQRS, then the value of y is (a) 7 (b) 5 (c) −7 (d) −8 [CBSE 2014]

Discussion

33.	In the adjoining figure P,M,Q,R are collinear and PM = MQ = MS, SR2 = PR . QR. Then
Answer» In the adjoining figure P,M,Q,R are collinear and PM = MQ = MS, SR² = PR . QR. Then

33.

In the adjoining figure P,M,Q,R are collinear and PM = MQ = MS, SR2 = PR . QR. Then

Answer»

In the adjoining figure P,M,Q,R are collinear and

PM = MQ = MS, SR² = PR . QR. Then

Discussion

34.	ABCD is a rectangle formed by joining the points A (−1, −1), B(−1 4) C (5 4) and D (5, −1). P, Q, R and S are the mid-points of sides AB, BC, CD and DA respectively. Is the quadrilateral PQRS a square? a rectangle? or a rhombus? Justify your answer.
Answer» ABCD is a rectangle formed by joining the points A (−1, −1), B(−1 4) C (5 4) and D (5, −1). P, Q, R and S are the mid-points of sides AB, BC, CD and DA respectively. Is the quadrilateral PQRS a square? a rectangle? or a rhombus? Justify your answer.

Discussion

35.	Draw a circle of a diameter 7 cm. Take a point A as the end point of diameter. Draw a tangent to the circle at the point A. [3 MARKS]
Answer» Draw a circle of a diameter 7 cm. Take a point A as the end point of diameter. Draw a tangent to the circle at the point A. [3 MARKS]

Discussion

36.	Which of the following statement is true for the inequation 2x+5>27?
Answer» Which of the following statement is true for the inequation $2 x + 5 > 27$ ?

Discussion

37.	Find the sum of the roots of the equation x2–8x+2=0.
Answer» Find the sum of the roots of the equation $x^{2} - 8 x + 2 = 0$ .

Discussion

38.	Question 4 (iii)Choose the correct option. Justify your choice.(iii) (sec A + tan A) (1 - sin A) =(A) sec A(B) sin A(C) cosec A(D) cos A
Answer» Question 4 (iii) Choose the correct option. Justify your choice. (iii) (sec A + tan A) (1 - sin A) = (A) sec A (B) sin A (C) cosec A (D) cos A

Discussion

39.

Prepare Simple Cash book of Gopal of Amritsar from the following transactions: 2019 ₹ April 1 Gopal commenced business introducing cash ₹ 60,000 and ₹ 1,50,000 by taking a loan from the Allahabad Bank. April 4 Purchased following assets for business: Computer ₹ 16,000; Furniture ₹ 18,500 and Machinery ₹ 32,000 plus CGST and SGST 6% each, paid by cheque. April 6 Purchased goods of ₹ 40,000 plus CGST and SGST 6% each from Bhushan, Amritsar, half of the value paid in cash. April 8 Paid wages for installation of Machinery 4,000 April 12 Computer repair charges ₹ 1,900 paid along with CGST and SGST 6% each April 15 Paid wages 15,000 Purchased Postage Stamps 150 Paid for stationery of ₹ 2,700 along with CGST and SGST 6% each April 19 Sold for cash half the goods purchased from Bhushan to Anil Krishna at a profit of 25% and allowed him Trade Discount of 5%. Charged CGST and SGST 6% each April 24 Payment to carpenter for repairs to personal furniture 350 April 26 Paid for medical expenses of Smt. Gopal 1,800 April 30 Paid for shop rent ₹ 2,000 along with CGST and SGST 6% each.

Answer» Prepare Simple Cash book of Gopal of Amritsar from the following transactions:

2019		₹
April 1	Gopal commenced business introducing cash ₹ 60,000 and ₹ 1,50,000 by taking a loan from the Allahabad Bank.
April 4	Purchased following assets for business: Computer ₹ 16,000; Furniture ₹ 18,500 and Machinery ₹ 32,000 plus CGST and SGST 6% each, paid by cheque.
April 6	Purchased goods of ₹ 40,000 plus CGST and SGST 6% each from Bhushan, Amritsar, half of the value paid in cash.
April 8	Paid wages for installation of Machinery	4,000
April 12	Computer repair charges ₹ 1,900 paid along with CGST and SGST 6% each
April 15	Paid wages	15,000
	Purchased Postage Stamps	150
	Paid for stationery of ₹ 2,700 along with CGST and SGST 6% each
April 19	Sold for cash half the goods purchased from Bhushan to Anil Krishna at a profit of 25% and allowed him Trade Discount of 5%. Charged CGST and SGST 6% each
April 24	Payment to carpenter for repairs to personal furniture	350
April 26	Paid for medical expenses of Smt. Gopal	1,800
April 30	Paid for shop rent ₹ 2,000 along with CGST and SGST 6% each.

Discussion

40.	ABC is a triangle and PQ is a straight linemeeting AB in P and AC in. Q. If A P= 1cm, PB = 3 cm, AQ = 1.5 cm, QC =4.5 m, prove that area of ΔAPQ is one- sixteenth of the area of ΔABC
Answer» ABC is a triangle and PQ is a straight linemeeting AB in P and AC in. Q. If A P= 1cm, PB = 3 cm, AQ = 1.5 cm, QC =4.5 m, prove that area of $Δ A P Q$ is one- sixteenth of the area of $Δ A B C$

Discussion

41.	Base of a triangle is 9 cm and the height is 5 cm. Base of another triangle is 10 cm and height is 6 cm. Find the ratio of areas of these triangles.
Answer» Base of a triangle is 9 cm and the height is 5 cm. Base of another triangle is 10 cm and height is 6 cm. Find the ratio of areas of these triangles.

Discussion

42.	Question 3Find area of a triangle formed by joining mid-points of sides of another triangle whose vertices are (0, -1), (2, 1) and (0, 3). Find ratio of this area to the area of the given triangle.
Answer» Question 3 Find area of a triangle formed by joining mid-points of sides of another triangle whose vertices are (0, -1), (2, 1) and (0, 3). Find ratio of this area to the area of the given triangle.

Discussion

43.	A person standing on the bank of a river observes that the angle of elevation of the top of a tree standing on the opposite bank is 60∘. When he moves 30 metres away from the bank, he finds the angle of elevation to be 30∘. Find the height of the tree and the width of the river. [Take √3=1.732]
Answer» A person standing on the bank of a river observes that the angle of elevation of the top of a tree standing on the opposite bank is $60^{\circ}$ . When he moves 30 metres away from the bank, he finds the angle of elevation to be $30^{\circ}$ . Find the height of the tree and the width of the river. [Take $\sqrt{3} = 1.732$ ]

Discussion

44.	M is a point on the side BC of a parallelogram ABCD. DM when produced meets AB produced at N. Prove that (i) DMMN=DCBN (ii) DNDM=ANDC.
Answer» M is a point on the side BC of a parallelogram ABCD. DM when produced meets AB produced at N. Prove that (i) $\frac{D M}{M N} = \frac{D C}{B N}$ (ii) $\frac{D N}{D M} = \frac{A N}{D C}$ .

44.

M is a point on the side BC of a parallelogram ABCD. DM when produced meets AB produced at N. Prove that (i) DMMN=DCBN (ii) DNDM=ANDC.

Answer»

M is a point on the side BC of a parallelogram ABCD. DM when produced meets AB produced at N. Prove that

(i) $\frac{D M}{M N} = \frac{D C}{B N}$

(ii) $\frac{D N}{D M} = \frac{A N}{D C}$ .

Discussion

45.	Find the roots of each of the following equations, if they exist, by applying the quadratic formula:x-1x=3, x≠0 [CBSE 2010]
Answer» Find the roots of each of the following equations, if they exist, by applying the quadratic formula: $x - \frac{1}{x} = 3, x \neq 0$ [CBSE 2010]

Discussion

46.	Question 6The first and the last term of an AP are 17 and 350 respectively. If the common difference is 9, how many terms are there and what is their sum?
Answer» Question 6 The first and the last term of an AP are 17 and 350 respectively. If the common difference is 9, how many terms are there and what is their sum?

Discussion

47.	Question 8AB is a diameter and AC is a chord of a circle with centre O such that ∠BAC=30∘. The tangent at c intersects extended AB at a point D. Prove that BC = BD.
Answer» Question 8 AB is a diameter and AC is a chord of a circle with centre O such that $∠ B A C = 30^{\circ}$ . The tangent at c intersects extended AB at a point D. Prove that BC = BD.

Discussion

48.	If (x+a) is a factor of (2x2+2ax+5x+10), find the value of a.
Answer» If (x+a) is a factor of $(2 x^{2} + 2 a x + 5 x + 10)$ , find the value of a.

Discussion

49.	Following are the lives in hours of 15 pieces of the components of aircraft engine. Find the median:715, 724, 725, 710, 729, 745, 694, 699, 696, 712, 734, 728, 716, 705, 719
Answer» Following are the lives in hours of 15 pieces of the components of aircraft engine. Find the median: 715, 724, 725, 710, 729, 745, 694, 699, 696, 712, 734, 728, 716, 705, 719

Discussion

50.	Solve the following inequation and represent the solution set on the number line: −3+x≤8x3+2≤143+2x, where xϵI [4 MARKS]
Answer» Solve the following inequation and represent the solution set on the number line: $- 3 + x \leq \frac{8 x}{3} + 2 \leq \frac{14}{3} + 2 x$ , where $x ϵ I$ [4 MARKS]

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

A bag contains 100 identical marble stones numbered from 1 to 100. What is the probability of drawing a marble having a number divisible by both 4 and 5?

48. A chord of a circle is equal to the radius of the circle find the angle subtended by the chord at a point on the minor arc and also at a point on the major arc

A pair of straight lines x2−8x+12=0 and y2−14y+45=0 are forming a square. Co-ordinates of the center of the circle inscribed in the square are

AB and CD are two equal chords of a circle with centre at O. If OP ⊥ AB and OQ ⊥ CD, where P and Q are points on the chords AB and CD respectively and if ∠POQ=100∘, the measure of ∠APQ is:

A 8 cm cube is cut into as many 2 cm cubes as possible. Then, the ratio of the surface area of the larger cube to that of the sum of the surface areas of the smaller cubes, is

Question 5The first term of an AP is 5, the last term is 45 and the sum is 400. Find the number of terms and the common difference.

Raghu had to make a cylindrical tube with an aluminium cover. What is the area of the aluminium sheet he needs to cover the tube if the tube has a length of 1 m and base radius 3.5 cm?(Take π=22/7)

The line through A(–2, 3) &amp; B(4, b) is perpendicular to the line 2 – 4y = 5. Find the value of ‘b’

At θ=90∘, which of the two angles are not defined?

25. Water flows at rate of 10 m per minute from a cylinderical pipe 5 mm in diameter. Hw long will it take up to a conical vessel whose diameter at base is 40 cm and depth 24 cm ? (a) 48 minutes 15 sec (b) 51 minutes 12 sec (c) 52 minutes 1 sec (d) 55 minutes

In a rain water harvesting system, the rain water from a roof of 22×20 meter drains into a cylindrical tank having diameter of base 2m and height of 3.5m. If the tank is full, find the rainfall in cm.

3x–4y=1...(1)5x–6y=7...(2) In the above equations, which of the following step can to be done to numerically equate the coefficients of x?

ABCD is a rectangle with AB = 14 cm and BC = 7 cm. Taking DC, BC and AD as diameters, three semi-circles are drawn as shown in the figure. Find the area of the shaded region.

How many irrational numbers exist between two rational numbers?

The sum of the digits in a two digits number is 9.The number obtained by interchanging the digits exceeds the original number by 27 . Find the two digit number.

how to draw an astroid which has a equation (x)^2/3 + (y)^2/3 = a^2/3

Use Euclid's division lemma to show that the square of any positive integers is either of the form 3m or 3m+1 for some integer m

cos 12°sin 78°+tan 23°cot 67°=?(a) 0(b) 1(c) 2(d) 32

26. If the area of a circle and a square are equalso,then the ratio of theIrish perimeters is:

The value of π upto 50 decimal place is3.14159265358979323846264338327950288419716939937510(1) Make a frequency distribution table of digits from 0 to 9 after the decimal place.(2) Which are the most and least occuring digits ?

Find the value of cos38° cosec52°tan18° tan35° tan60° tan72° tan55°.

how to simplify (sinAcosB+cosAsinB)/(cosAcosB-sinAsinB) to (tanA+tanB)/(1-tanAtanB)?

A rectangle sheet of paper 44 cm × 18 cm is rolled once along its length and a cylinder is formed. The volume of the cylinder so formed is equal to

If α, β, γ are the zeros of the polynomial f(x) = ax3 + bx2 + cx + d, then 1α+1β+1γ=(a) -bd(b) cd(c) -cd(d) -ca

In the picture below, the radius of the circle is 15 centimetres. Compute the lengths of the tangents PQ and PR(i) The point P is equidistant from A and B(ii) The line OP bisects the line AB and the angle APB

In the figure given below, what is the value of tan θ in terms of a,b and c?

Question 2 In figure, if OA = 5 cm, AB = 8 cm and OD is perpendicular to AB, then CD is equal to (A) 2 cm (B) 3 cm (C) 4 cm (D) 5 cm

Let ABC be a right triangle in which AB = 3 cm, BC = 4 cm and ∠ B = 90∘. BD is the perpendicular from B on AC. The circle through B, C, D is drawn. Construct the tangents from A to this circle. [4 MARKS]

If P(2, 4), Q(0, 3), R(3, 6) and S(5, y) are the vertices of a parallelogram PQRS, then the value of y is(a) 7 (b) 5 (c) −7 (d) −8 [CBSE 2014]

In the adjoining figure P,M,Q,R are collinear and PM = MQ = MS, SR2 = PR . QR. Then

ABCD is a rectangle formed by joining the points A (−1, −1), B(−1 4) C (5 4) and D (5, −1). P, Q, R and S are the mid-points of sides AB, BC, CD and DA respectively. Is the quadrilateral PQRS a square? a rectangle? or a rhombus? Justify your answer.

Draw a circle of a diameter 7 cm. Take a point A as the end point of diameter. Draw a tangent to the circle at the point A. [3 MARKS]

Which of the following statement is true for the inequation 2x+5&gt;27?

Find the sum of the roots of the equation x2–8x+2=0.

Question 4 (iii)Choose the correct option. Justify your choice.(iii) (sec A + tan A) (1 - sin A) =(A) sec A(B) sin A(C) cosec A(D) cos A

ABC is a triangle and PQ is a straight linemeeting AB in P and AC in. Q. If A P= 1cm, PB = 3 cm, AQ = 1.5 cm, QC =4.5 m, prove that area of ΔAPQ is one- sixteenth of the area of ΔABC

Base of a triangle is 9 cm and the height is 5 cm. Base of another triangle is 10 cm and height is 6 cm. Find the ratio of areas of these triangles.

Question 3Find area of a triangle formed by joining mid-points of sides of another triangle whose vertices are (0, -1), (2, 1) and (0, 3). Find ratio of this area to the area of the given triangle.

M is a point on the side BC of a parallelogram ABCD. DM when produced meets AB produced at N. Prove that (i) DMMN=DCBN (ii) DNDM=ANDC.

Find the roots of each of the following equations, if they exist, by applying the quadratic formula:x-1x=3, x≠0 [CBSE 2010]

Question 6The first and the last term of an AP are 17 and 350 respectively. If the common difference is 9, how many terms are there and what is their sum?

Question 8AB is a diameter and AC is a chord of a circle with centre O such that ∠BAC=30∘. The tangent at c intersects extended AB at a point D. Prove that BC = BD.

If (x+a) is a factor of (2x2+2ax+5x+10), find the value of a.

Following are the lives in hours of 15 pieces of the components of aircraft engine. Find the median:715, 724, 725, 710, 729, 745, 694, 699, 696, 712, 734, 728, 716, 705, 719

Solve the following inequation and represent the solution set on the number line: −3+x≤8x3+2≤143+2x, where xϵI [4 MARKS]

The line through A(–2, 3) & B(4, b) is perpendicular to the line 2 – 4y = 5. Find the value of ‘b’

Which of the following statement is true for the inequation 2x+5>27?