32581 + Interview Questions in Mathematics

1.	“Price of a commodity is not equivalent to its value. Let us assume that one day the price of everything i.e. diesel, vegetables, courier costs, daily wage, the cost of flats, etc. got doubled. Prices then would certainly rise, but values of all things except one would not.” If prices of all things got doubled, then according to the passage which one of the following will be correct?
Answer» “Price of a commodity is not equivalent to its value. Let us assume that one day the price of everything i.e. diesel, vegetables, courier costs, daily wage, the cost of flats, etc. got doubled. Prices then would certainly rise, but values of all things except one would not.” If prices of all things got doubled, then according to the passage which one of the following will be correct?

Discussion

2.	At 4.30 pm, the equation of line along minute hand is ( x=0 ) . Therefore, a this instant, the equation of line along the hour hand will be.1- x+y = 02- x-y = 03- y = root2 x4- y = x/root2
Answer» At 4.30 pm, the equation of line along minute hand is ( x=0 ) . Therefore, a this instant, the equation of line along the hour hand will be. 1- x+y = 0 2- x-y = 0 3- y = root2 x 4- y = x/root2

Discussion

3.	Mark the correct alternative in each of the following:If y=1+x1!+x22!+x33!+..., then dydx=(a) y + 1 (b) y − 1 (c) y (d) y2
Answer» Mark the correct alternative in each of the following: If $y = 1 + \frac{x}{1!} + \frac{x^{2}}{2!} + \frac{x^{3}}{3!} + . . .$ , then $\frac{d y}{d x} =$ (a) y + 1 (b) y − 1 (c) y (d) y²

Discussion

4.

Prepare a Cash Book with Cash and Bank columns from the following information for the month of December 2011 in the Books of O'Neil: 2016 Dec. 1 Cash in Hand ₹ 2,780; Bank Overdraft ₹ 3,125. 2 Cheque worth ₹ 400 issued to the petty cashier. 5 ₹ 350 was paid to Hari & Sons for the supply of stationery on this day. 7 Received a cheque worth ₹ 600 from Pramod against sale of goods. 10 Received ₹ 1,200 for sale of goods. 11 The cheque which was received from Pramod on 7th December was endorsed as favour of Morgan together with ₹ 1,400 in cash. 15 Received ₹ 950 from Sheila. 23 Murarilal paid ₹ 2,000 in cash and ₹ 3,000 in cheque after receiving a discount of ₹ 200 for goods sold to him in November. The cheque was immediately deposited into the Bank. 26 Bought goods worth ₹ 1,700 from Rustom and paid by cheque after receiving a discount of ₹ 170. 30 Interest on overdraft ₹ 50 was charged by the Bank. 30 Cash in excess of ₹ 1,000 was deposited into the Bank.

Answer» Prepare a Cash Book with Cash and Bank columns from the following information for the month of December 2011 in the Books of O'Neil:

2016
Dec. 1	Cash in Hand ₹ 2,780; Bank Overdraft ₹ 3,125.
2	Cheque worth ₹ 400 issued to the petty cashier.
5	₹ 350 was paid to Hari & Sons for the supply of stationery on this day.
7	Received a cheque worth ₹ 600 from Pramod against sale of goods.
10	Received ₹ 1,200 for sale of goods.
11	The cheque which was received from Pramod on 7th December was endorsed as favour of Morgan together with ₹ 1,400 in cash.
15	Received ₹ 950 from Sheila.
23	Murarilal paid ₹ 2,000 in cash and ₹ 3,000 in cheque after receiving a discount of ₹ 200 for goods sold to him in November. The cheque was immediately deposited into the Bank.
26	Bought goods worth ₹ 1,700 from Rustom and paid by cheque after receiving a discount of ₹ 170.
30	Interest on overdraft ₹ 50 was charged by the Bank.
30	Cash in excess of ₹ 1,000 was deposited into the Bank.

Discussion

5.	Question 12If an event cannot occur, then its probability is(a) 1(b) 34(c) 12(d) 0
Answer» Question 12 If an event cannot occur, then its probability is (a) 1 (b) $\frac{3}{4}$ (c) $\frac{1}{2}$ (d) 0

Discussion

6.	Note Take π=227, unless stated otherwise.Volume and surface area of a solid hemisphere are numerically equal. What is the diameter of the hemisphere?
Answer» Note Take $π = \frac{22}{7}$ , unless stated otherwise. Volume and surface area of a solid hemisphere are numerically equal. What is the diameter of the hemisphere?

Discussion

7.	The area of an equilateral triangle ABC is 17320.5 cm2. With each vertex of the triangle as centre, a circle is drawn with radius equal to half the length of the side of the triangle (See the given figure). Find the area of shaded region. [Use π = 3.14 and]
Answer» The area of an equilateral triangle ABC is 17320.5 cm². With each vertex of the triangle as centre, a circle is drawn with radius equal to half the length of the side of the triangle (See the given figure). Find the area of shaded region. [Use π = 3.14 and]

7.

The area of an equilateral triangle ABC is 17320.5 cm2. With each vertex of the triangle as centre, a circle is drawn with radius equal to half the length of the side of the triangle (See the given figure). Find the area of shaded region. [Use π = 3.14 and]

Answer»

The area of an equilateral triangle ABC is 17320.5 cm². With each vertex of the triangle as centre, a circle is drawn with radius equal to half the length of the side of the triangle (See the given figure). Find the area of shaded region. [Use π = 3.14 and]

Discussion

8.	If 3 and -3 are two zeros of the polynomial (x4+x3−11x2−9x+18), find all the zeros of the given polynomial.
Answer» If 3 and -3 are two zeros of the polynomial $(x^{4} + x^{3} - 11 x^{2} - 9 x + 18)$ , find all the zeros of the given polynomial.

Discussion

9.	If the points (a, 0), (0, b) and (1, 1) are collinear, then which of the following is true?
Answer» If the points (a, 0), (0, b) and (1, 1) are collinear, then which of the following is true?

Discussion

10.	Let Sn denote the sum of n terms of an A.P. whose first term is a. If the common difference d is given by d=Sn−k Sn−1+Sn−2, then k =
Answer» Let $S_{n}$ denote the sum of n terms of an A.P. whose first term is a. If the common difference d is given by $d = S_{n} - k S_{n - 1} + S_{n - 2}$ , then k =

Discussion

11.	Question 11 An aeroplane leaves an airport and flies due north at a speed of 1000 km per hour. At the same time, another aeroplane leaves the same airport and flies due west at a speed of 1200 km per hour. How far apart will the two planes be after 112 hours?
Answer» Question 11 An aeroplane leaves an airport and flies due north at a speed of 1000 km per hour. At the same time, another aeroplane leaves the same airport and flies due west at a speed of 1200 km per hour. How far apart will the two planes be after $1 \frac{1}{2}$ hours?

Discussion

12.	Get the algebraic expression in the following case using variables, constants, and arithmetic operations:Numbers x and y both squared and added.
Answer» Get the algebraic expression in the following case using variables, constants, and arithmetic operations: Numbers $x$ and $y$ both squared and added.

12.

Get the algebraic expression in the following case using variables, constants, and arithmetic operations:Numbers x and y both squared and added.

Answer»

Get the algebraic expression in the following case using variables, constants, and arithmetic operations:

Numbers $x$ and $y$ both squared and added.

Discussion

13.	Choose the correct answer in each of the following questions:What is 20th term from the end of the AP 3, 8, 13, ..., 253?(a) 163 (b) 158 (c) 153 (d) 148
Answer» Choose the correct answer in each of the following questions: What is 20th term from the end of the AP 3, 8, 13, ..., 253? (a) 163 (b) 158 (c) 153 (d) 148

Discussion

14.	Which of the following ratio relates to opposite side of an angle and the hypotenuse in a right-angled triangle?
Answer» Which of the following ratio relates to opposite side of an angle and the hypotenuse in a right-angled triangle?

Discussion

15.

Let N be the set of natural numbers, Define a real valued functionf:N→N by f(x)=2x+1.Using this definition, complete the table given below. x 1 2 3 4 5 6 7 y f(1)= f(2)= f(3)= f(4)= f(5)= f(6)= f(7)=

Answer» Let N be the set of natural numbers, Define a real valued function

f : N \to N

by

f (x) = 2 x + 1

.

Using this definition, complete the table given below.

x	1	2	3	4	5	6	7
y	f(1)=	f(2)=	f(3)=	f(4)=	f(5)=	f(6)=	f(7)=

Discussion

16.	Number of CupsFrequencyCumulative Frequency2113344−−−−957166420 For the above given frequency table, find the missing frequency.
Answer» $\begin{matrix} N u m b e r o f C u p s & F r e q u e n c y & C u m u l a t i v e F r e q u e n c y 2 & 1 & 1 3 & 3 & 4 4 & - - - - & 9 5 & 7 & 16 6 & 4 & 20 \end{matrix}$ For the above given frequency table, find the missing frequency.

16.

Number of CupsFrequencyCumulative Frequency2113344−−−−957166420 For the above given frequency table, find the missing frequency.

Answer»

$\begin{matrix} N u m b e r o f C u p s & F r e q u e n c y & C u m u l a t i v e F r e q u e n c y 2 & 1 & 1 3 & 3 & 4 4 & - - - - & 9 5 & 7 & 16 6 & 4 & 20 \end{matrix}$

For the above given frequency table, find the missing frequency.

Discussion

17.	The diameter of the cone is 14 cm and slant height is 9 cm. Find the total surface area of the cone.
Answer» The diameter of the cone is 14 cm and slant height is 9 cm. Find the total surface area of the cone.

17.

The diameter of the cone is 14 cm and slant height is 9 cm. Find the total surface area of the cone.

Answer»

The diameter of the cone is 14 cm and slant height is 9 cm. Find the total surface area of the cone.

Discussion

18.	34. What are the conditions for common root or roots of 2 Quadratic equations?
Answer» 34. What are the conditions for common root or roots of 2 Quadratic equations?

Discussion

19.	Question 8The price of a TV is Rs 13,000. The sales tax charged on it is at the rate of 12%. Find the amount that Vinod will have to pay if he buys it.
Answer» Question 8 The price of a TV is Rs 13,000. The sales tax charged on it is at the rate of 12%. Find the amount that Vinod will have to pay if he buys it.

Discussion

20.	Question 8 Zero of the zero polynomial is A) 0 B) 1 C) Any real number D) Not defined
Answer» Question 8 Zero of the zero polynomial is A) 0 B) 1 C) Any real number D) Not defined

Discussion

21.

Pass entries in the books of Ganguli & Sons. assuming all transactions have been entered in the state of West Bengal: (i) Purchased goods for ₹ 2,00,000 and payment made by cheque. (ii) Sold goods for ₹ 1,60,000 to Devki Nandan & Sons. (iii) Purchased goods for ₹ 50,000 on credit. (iv) Paid for printing and stationery ₹ 4,000. (v) Received interest ₹ 5,000. (vi) Paid for advertisement ₹ 30,000 by cheque. Assume CGST 6% and SGST 6%.

Answer» Pass entries in the books of Ganguli & Sons. assuming all transactions have been entered in the state of West Bengal:

(i)	Purchased goods for ₹ 2,00,000 and payment made by cheque.
(ii)	Sold goods for ₹ 1,60,000 to Devki Nandan & Sons.
(iii)	Purchased goods for ₹ 50,000 on credit.
(iv)	Paid for printing and stationery ₹ 4,000.
(v)	Received interest ₹ 5,000.
(vi)	Paid for advertisement ₹ 30,000 by cheque.

Assume CGST 6% and SGST 6%.

Discussion

22.	In a triangle ABC,a3cos(B−C)+b3cos(C−A)+c3cos(A−B)=
Answer» In a triangle $A B C, a^{3} c o s (B - C) + b^{3} c o s (C - A) + c^{3} c o s (A - B) =$

Discussion

23.	The length of the tangent from an external point P to a circle of radius 5 cm is 10 cm. The distance of the point from the centre of the circle is _______.
Answer» The length of the tangent from an external point P to a circle of radius 5 cm is 10 cm. The distance of the point from the centre of the circle is _______.

Discussion

24.	What must be added to f(x)=4x3+8x2−7x+3 so that resulting polynomial is divisible by g(x)=x2−x+2?
Answer» What must be added to $f (x) = 4 x^{3} + 8 x^{2} - 7 x + 3 so that resulting polynomial is divisible b y g (x) = x^{2} - x + 2 ?$

Discussion

25.	The values of x satisfying the inequality [tan−1x]2−[tan−1x]−2≤0, where [.] denotes integer part function, is
Answer» The values of $x$ satisfying the inequality $[{tan}^{- 1} x]^{2} - [{tan}^{- 1} x] - 2 \leq 0$ , where $[.]$ denotes integer part function, is

Discussion

26.

Enter the following transactions in subsidiary books, post them into Ledger and prepare a Trial Balance:The following balances existed in Sunil Bros. books on April 1, 2017:Assets : Cash in hand ₹ 27,500; Bank Balance ₹ 40,000; Debtors : Ashok ₹ 18,000, Bahadur ₹ 25,000, Charu ₹ 30,000; Stock ₹ 1,60,000 and Furniture ₹ 40,000.Liabilities : Creditors : Dinesh ₹ 20,000 and Ekta ₹ 15,000. 2017 April 1 Cash Sales ₹ 18,000. 2 Deposited into Bank ₹ 20,000. 3 Purchased from Dinesh : 300 metres Cotton ₹ 60 per metre 200 metres Silk ₹ 100 per metre 5 Cheque issued to Dinesh for ₹ 25,000. 6 Accepted a bill at one month for ₹ 15,000 drawn by Dinesh. 8 Sold to Ashok : 400 metres Cotton ₹ 80 per metre 250 metres Silk ₹ 140 per metre 10 Returned by Ashok 50 metres Silk. 12 Received Cash ₹ 8,000 and a Cheque for ₹ 40,000 from Ashok. Cheque was immediately sent to Bank. 13 Received a B/R from Bahadur for ₹ 20,000 at one month. 15 Accepted a bill at two months drawn by Ekta for the amount due to her. 16 Purchased a Computer for office use from Shiva Ltd. for ₹ 45,000 on Credit. 18 Cash purchases ₹ 10,000. 19 Received full payment from Charu by cheque, sent it to Bank. Discount allowed 2%. 20 Issued a cheque to Dinesh in full payment of his account after deducting 1% discount. 22 Settled the account of Shiva Ltd. by a cheque. 24 Proprietor took away goods worth ₹ 5,000 and Cash ₹ 6,000. 25 Purchased from Ganesh 200 metres Cotton ₹ 70 per metre subject to trade discount of 5%. 27 Paid Rent ₹ 3,000 and Salaries ₹ 8,000. 30 Interest allowed by bank ₹ 600.

Answer» Enter the following transactions in subsidiary books, post them into Ledger and prepare a Trial Balance:

The following balances existed in Sunil Bros. books on April 1, 2017:

Assets : Cash in hand ₹ 27,500; Bank Balance ₹ 40,000; Debtors : Ashok ₹ 18,000, Bahadur ₹ 25,000, Charu ₹ 30,000; Stock ₹ 1,60,000 and Furniture ₹ 40,000.

Liabilities : Creditors : Dinesh ₹ 20,000 and Ekta ₹ 15,000.

2017
April 1		Cash Sales ₹ 18,000.
2		Deposited into Bank ₹ 20,000.
3		Purchased from Dinesh :
		300 metres Cotton ₹ 60 per metre
		200 metres Silk ₹ 100 per metre
5		Cheque issued to Dinesh for ₹ 25,000.
6		Accepted a bill at one month for ₹ 15,000 drawn by Dinesh.
8		Sold to Ashok :
		400 metres Cotton ₹ 80 per metre
		250 metres Silk ₹ 140 per metre
10		Returned by Ashok 50 metres Silk.
12		Received Cash ₹ 8,000 and a Cheque for ₹ 40,000 from Ashok. Cheque was immediately sent to Bank.
13		Received a B/R from Bahadur for ₹ 20,000 at one month.
15		Accepted a bill at two months drawn by Ekta for the amount due to her.
16		Purchased a Computer for office use from Shiva Ltd. for ₹ 45,000 on Credit.
18		Cash purchases ₹ 10,000.
19		Received full payment from Charu by cheque, sent it to Bank. Discount allowed 2%.
20		Issued a cheque to Dinesh in full payment of his account after deducting 1% discount.
22		Settled the account of Shiva Ltd. by a cheque.
24		Proprietor took away goods worth ₹ 5,000 and Cash ₹ 6,000.
25		Purchased from Ganesh 200 metres Cotton ₹ 70 per metre subject to trade discount of 5%.
27		Paid Rent ₹ 3,000 and Salaries ₹ 8,000.
30		Interest allowed by bank ₹ 600.

Discussion

27.	Evaluate each of the following (cosec2 45o sec2 30o)(sin2 30o+4 cot2 45o−sec2 60o)
Answer» Evaluate each of the following $(c o s e c^{2} 45^{o} s e c^{2} 30^{o}) (s i n^{2} 30^{o} + 4 c o t^{2} 45^{o} - s e c^{2} 60^{o})$

27.

Evaluate each of the following (cosec2 45o sec2 30o)(sin2 30o+4 cot2 45o−sec2 60o)

Answer»

Evaluate each of the following

$(c o s e c^{2} 45^{o} s e c^{2} 30^{o}) (s i n^{2} 30^{o} + 4 c o t^{2} 45^{o} - s e c^{2} 60^{o})$

Discussion

28.	A wooden article was made by scooping out a hemisphere from each end of a cylinder, as shown in the figure. If the height of the cylinder is 20cm and its base is of diameter 7cm, find the total surface area of the article when it is ready.
Answer» A wooden article was made by scooping out a hemisphere from each end of a cylinder, as shown in the figure. If the height of the cylinder is $20 c m$ and its base is of diameter $7 c m$ , find the total surface area of the article when it is ready.

28.

A wooden article was made by scooping out a hemisphere from each end of a cylinder, as shown in the figure. If the height of the cylinder is 20cm and its base is of diameter 7cm, find the total surface area of the article when it is ready.

Answer»

A wooden article was made by scooping out a hemisphere from each end of a cylinder, as shown in the figure. If the height of the cylinder is $20 c m$ and its base is of diameter $7 c m$ , find the total surface area of the article when it is ready.

Discussion

29.	Let ABCD be a trapezium with AD parallel to BC. Assume there is a point M in the interior of the segment BC such that AB = AM and DC = DM. Then the ratio of the area of the trapezium to the area of triangle AMD is.
Answer» Let ABCD be a trapezium with AD parallel to BC. Assume there is a point M in the interior of the segment BC such that AB = AM and DC = DM. Then the ratio of the area of the trapezium to the area of triangle AMD is.

Discussion

30.	A bag contains 3 red, 3 white and 3 green balls. One ball is taken out of the bag at random. What is the probability that the ball drawn is –(1) red.(2) not red(3) either red or white.
Answer» A bag contains 3 red, 3 white and 3 green balls. One ball is taken out of the bag at random. What is the probability that the ball drawn is – (1) red. (2) not red (3) either red or white.

Discussion

31.	In the given figure, if AOB is the diameter and MPQ is a tangent at P, then the value of ∠MPA is
Answer» In the given figure, if AOB is the diameter and MPQ is a tangent at P, then the value of $∠ M P A$ is

Discussion

32.	All red face cards are removed from a pack of playing cards. The remaining cards are well shuffled and then a card is drawn at random from them. Find the probability that the drawn card is: (i) a red card (ii) a face card and (iii) a card of clubs.
Answer» All red face cards are removed from a pack of playing cards. The remaining cards are well shuffled and then a card is drawn at random from them. Find the probability that the drawn card is: (i) a red card (ii) a face card and (iii) a card of clubs.

Discussion

33.	Let the base of the triangle be b. Let the height (altitude) be h. Then the area (A) of that triangle varies as :
Answer» Let the base of the triangle be b. Let the height (altitude) be h. Then the area (A) of that triangle varies as :

Discussion

34.	Solve the following quadratic equations by factorization:a+b2 x2-4abx-a-b2=0
Answer» Solve the following quadratic equations by factorization: ${(a + b)}^{2} x^{2} - 4 a b x - {(a - b)}^{2} = 0$

Discussion

35.	From the information given in the figure, prove that PM = PN = 3 × a
Answer» From the information given in the figure, prove that PM = PN = $\sqrt{3}$ × a

Discussion

36.	If sec θ=54, find the value of sin θ-2 cos θtan θ-cot θ.
Answer» If $\sec θ = \frac{5}{4}$ , find the value of $\frac{\sin θ - 2 \cos θ}{\tan θ - \cot θ}$ .

Discussion

37.	Chord ED is parallel to the diameter AC of the circle. Given ∠CBE=55°, calculate ∠DEC.
Answer» Chord ED is parallel to the diameter AC of the circle. Given ∠CBE=55°, calculate ∠DEC.

37.

Chord ED is parallel to the diameter AC of the circle. Given ∠CBE=55°, calculate ∠DEC.

Answer»

Chord ED is parallel to the diameter AC of the circle. Given ∠CBE=55°, calculate ∠DEC.

Discussion

38.	A conical vessel of radius 6 cm and height 8 cm is completely filled with water. A sphere is lowered into the water such that when it touches the sides it is just immersed. What fraction of water overflows?
Answer» A conical vessel of radius 6 cm and height 8 cm is completely filled with water. A sphere is lowered into the water such that when it touches the sides it is just immersed. What fraction of water overflows?

Discussion

39.	A fraction becomes 13 when 2 is subtracted from the numerator and it becomes 12 when 1 is subtracted from the denominator. Find the fraction.
Answer» A fraction becomes $\frac{1}{3}$ when 2 is subtracted from the numerator and it becomes $\frac{1}{2}$ when 1 is subtracted from the denominator. Find the fraction.

Discussion

40.	Which of the following trigonometric ratios will have the same value as cot 53∘?
Answer» Which of the following trigonometric ratios will have the same value as cot $53^{\circ}$ ?

Discussion

41.	Find the value ofsinθ cosθ [sin(90∘−θ) cosecθ + cos(90∘−θ) secθ]
Answer» Find the value of $s i n θ$ $c o s θ$ [ $s i n (90^{\circ} - θ)$ $c o s e c θ$ + $c o s (90^{\circ} - θ)$ $s e c θ$ ]

Discussion

42.	Question 1 (ii) In the following figure (ii), DE \|\| BC. Find AD.
Answer» Question 1 (ii) In the following figure (ii), DE \|\| BC. Find AD.

Discussion

43.	The angles of a triangle are in A.P. If the greatest angle is twice the least, find the greatest angle.
Answer» The angles of a triangle are in A.P. If the greatest angle is twice the least, find the greatest angle.

Discussion

44.	Question 2 (iv)Find the roots of the quadratic equations given in Q.1 above by applying the quadratic formula.(iv) 2x2+x+4=0
Answer» Question 2 (iv) Find the roots of the quadratic equations given in Q.1 above by applying the quadratic formula. (iv) $2 x^{2} + x + 4 = 0$

Discussion

45.	In the given figure, □ABCD is a parallelogram, P and Q are midpoints of side AB and DC respectively, then prove □APCQ is a parallelogram.
Answer» In the given figure, $□$ ABCD is a parallelogram, P and Q are midpoints of side AB and DC respectively, then prove $□$ APCQ is a parallelogram.

Discussion

46.	Which of the following sequence is not in arithmetic progression?
Answer» Which of the following sequence is not in arithmetic progression?

Discussion

47.	23. If the sum of a G.P with common ratio 3 is 364 and last term is 243, then find the number of terms ?
Answer» 23. If the sum of a G.P with common ratio 3 is 364 and last term is 243, then find the number of terms ?

Discussion

48.

Which of the following pairs of linear equations are consistent/ inconsistent? If consistent, obtain the solution graphically:

Answer»

Which of the following pairs of linear equations are consistent/ inconsistent? If consistent, obtain the solution graphically:

Discussion

49.	If sec2A = cosec(A - 42°), where 2A is an acute angle, then find the value of A. [CBSE2008]
Answer» If sec2A = cosec(A $-$ 42 $°$ ), where 2A is an acute angle, then find the value of A. [CBSE2008]

Discussion

50.	Express sinπ5+i1-cosπ5 in polar form.
Answer» Express $\sin \frac{π}{5} + i (1 - \cos \frac{π}{5})$ in polar form.

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

At 4.30 pm, the equation of line along minute hand is ( x=0 ) . Therefore, a this instant, the equation of line along the hour hand will be.1- x+y = 02- x-y = 03- y = root2 x4- y = x/root2

Mark the correct alternative in each of the following:If y=1+x1!+x22!+x33!+..., then dydx=(a) y + 1 (b) y − 1 (c) y (d) y2

Question 12If an event cannot occur, then its probability is(a) 1(b) 34(c) 12(d) 0

Note Take π=227, unless stated otherwise.Volume and surface area of a solid hemisphere are numerically equal. What is the diameter of the hemisphere?

The area of an equilateral triangle ABC is 17320.5 cm2. With each vertex of the triangle as centre, a circle is drawn with radius equal to half the length of the side of the triangle (See the given figure). Find the area of shaded region. [Use π = 3.14 and]

If 3 and -3 are two zeros of the polynomial (x4+x3−11x2−9x+18), find all the zeros of the given polynomial.

If the points (a, 0), (0, b) and (1, 1) are collinear, then which of the following is true?

Let Sn denote the sum of n terms of an A.P. whose first term is a. If the common difference d is given by d=Sn−k Sn−1+Sn−2, then k =

Question 11 An aeroplane leaves an airport and flies due north at a speed of 1000 km per hour. At the same time, another aeroplane leaves the same airport and flies due west at a speed of 1200 km per hour. How far apart will the two planes be after 112 hours?

Get the algebraic expression in the following case using variables, constants, and arithmetic operations:Numbers x and y both squared and added.

Choose the correct answer in each of the following questions:What is 20th term from the end of the AP 3, 8, 13, ..., 253?(a) 163 (b) 158 (c) 153 (d) 148

Which of the following ratio relates to opposite side of an angle and the hypotenuse in a right-angled triangle?

Let N be the set of natural numbers, Define a real valued functionf:N→N by f(x)=2x+1.Using this definition, complete the table given below. x 1 2 3 4 5 6 7 y f(1)= f(2)= f(3)= f(4)= f(5)= f(6)= f(7)=

Number of CupsFrequencyCumulative Frequency2113344−−−−957166420 For the above given frequency table, find the missing frequency.

The diameter of the cone is 14 cm and slant height is 9 cm. Find the total surface area of the cone.

34. What are the conditions for common root or roots of 2 Quadratic equations?

Question 8The price of a TV is Rs 13,000. The sales tax charged on it is at the rate of 12%. Find the amount that Vinod will have to pay if he buys it.

Question 8 Zero of the zero polynomial is A) 0 B) 1 C) Any real number D) Not defined

In a triangle ABC,a3cos(B−C)+b3cos(C−A)+c3cos(A−B)=

The length of the tangent from an external point P to a circle of radius 5 cm is 10 cm. The distance of the point from the centre of the circle is _______.

What must be added to f(x)=4x3+8x2−7x+3 so that resulting polynomial is divisible by g(x)=x2−x+2?

The values of x satisfying the inequality [tan−1x]2−[tan−1x]−2≤0, where [.] denotes integer part function, is

Evaluate each of the following (cosec2 45o sec2 30o)(sin2 30o+4 cot2 45o−sec2 60o)

A wooden article was made by scooping out a hemisphere from each end of a cylinder, as shown in the figure. If the height of the cylinder is 20cm and its base is of diameter 7cm, find the total surface area of the article when it is ready.

Let ABCD be a trapezium with AD parallel to BC. Assume there is a point M in the interior of the segment BC such that AB = AM and DC = DM. Then the ratio of the area of the trapezium to the area of triangle AMD is.

A bag contains 3 red, 3 white and 3 green balls. One ball is taken out of the bag at random. What is the probability that the ball drawn is –(1) red.(2) not red(3) either red or white.

In the given figure, if AOB is the diameter and MPQ is a tangent at P, then the value of ∠MPA is

All red face cards are removed from a pack of playing cards. The remaining cards are well shuffled and then a card is drawn at random from them. Find the probability that the drawn card is: (i) a red card (ii) a face card and (iii) a card of clubs.

Let the base of the triangle be b. Let the height (altitude) be h. Then the area (A) of that triangle varies as :

Solve the following quadratic equations by factorization:a+b2 x2-4abx-a-b2=0

From the information given in the figure, prove that PM = PN = 3 × a

If sec θ=54, find the value of sin θ-2 cos θtan θ-cot θ.

Chord ED is parallel to the diameter AC of the circle. Given ∠CBE=55°, calculate ∠DEC.

A conical vessel of radius 6 cm and height 8 cm is completely filled with water. A sphere is lowered into the water such that when it touches the sides it is just immersed. What fraction of water overflows?

A fraction becomes 13 when 2 is subtracted from the numerator and it becomes 12 when 1 is subtracted from the denominator. Find the fraction.

Which of the following trigonometric ratios will have the same value as cot 53∘?

Find the value ofsinθ cosθ [sin(90∘−θ) cosecθ + cos(90∘−θ) secθ]

Question 1 (ii) In the following figure (ii), DE || BC. Find AD.

The angles of a triangle are in A.P. If the greatest angle is twice the least, find the greatest angle.

Question 2 (iv)Find the roots of the quadratic equations given in Q.1 above by applying the quadratic formula.(iv) 2x2+x+4=0

In the given figure, □ABCD is a parallelogram, P and Q are midpoints of side AB and DC respectively, then prove □APCQ is a parallelogram.

Which of the following sequence is not in arithmetic progression?

23. If the sum of a G.P with common ratio 3 is 364 and last term is 243, then find the number of terms ?

Which of the following pairs of linear equations are consistent/ inconsistent? If consistent, obtain the solution graphically:

If sec2A = cosec(A - 42°), where 2A is an acute angle, then find the value of A. [CBSE2008]

Express sinπ5+i1-cosπ5 in polar form.