32581 + Interview Questions in Mathematics Page 204 InterviewSolution

10151.	(a) Without using trigonometric tables evaluate: sin 35∘ cos 55∘+cos 35∘ sin 55∘cosec2 10∘−tan2 80∘ (b) Evaluate without using trigonometric tables: cos2 26∘+cos 64∘ sin 26∘+tan 36∘cot 54∘ [6 MARKS]
Answer» (a) Without using trigonometric tables evaluate: $\frac{s i n 35^{\circ} c o s 55^{\circ} + c o s 35^{\circ} s i n 55^{\circ}}{c o s e c^{2} 10^{\circ} - t a n^{2} 80^{\circ}}$ (b) Evaluate without using trigonometric tables: $c o s^{2} 26^{\circ} + c o s 64^{\circ} s i n 26^{\circ} + \frac{t a n 36^{\circ}}{c o t 54^{\circ}}$ [6 MARKS]

Discussion

10152.	If the area bounded by the parabola x2=4y, the x−axis and the line x=4 is divided into two equal areas by the line x=α, then the value of α3 is
Answer» If the area bounded by the parabola $x^{2} = 4 y,$ the $x -$ axis and the line $x = 4$ is divided into two equal areas by the line $x = α,$ then the value of $α^{3}$ is

Discussion

10153.	From a solid cylinder of height 2.8 cm and diameter 4.2 cm,a conical cavity of the same height and same diameter is hollowed out.Find the total surface area of the remaining solid.(Take π= 22/7)
Answer» From a solid cylinder of height 2.8 cm and diameter 4.2 cm,a conical cavity of the same height and same diameter is hollowed out.Find the total surface area of the remaining solid. $(T a k e π = 22 / 7)$

Discussion

10154.

Sh. Param Bhushan does not maintain proper books of accounts. From the following, prepare his trading and profit & loss account for the year ended 31st March, 2015, together with balance sheet as at that date: BALANCE SHEET as at 31st March, 2014 Liabilities (₹) Assets (₹) Sundry Creditors 80,000 Cash 22,000 Outstanding Salaries 4,000 Sundry Debtors 1,50,000 Capital 8,08,000 Stock 1,20,000 Plant and Machinery 2,00,000 Freehold Premises 4,00,000 8,92,000 8,92,000 Cash book analysis shows the following: ₹ Payment to Creditors 4,00,000 Staff Salaries 76,000 Rent Paid 17,300 General Expenses (including insurance premium of ₹ 2,400 paid on 1st January 2015 to run for one year) 8,700 Personal Withdrawals 12,000 Received from Debtors 5,50,000 Cash Sales 1,10,000 Purchase of Computers (on 1st January, 2015) 40,000 Purchase of Furniture (on 1st January, 2015) 60,000 The following further information is available:Closing Stock ₹ 1,35,000; Closing Debtors ₹ 1,92,000; Closing Creditors ₹ 72,000; Outstanding Salaries at the end ₹ 6,000; General Expenses include ₹ 5,000 for house rent of Sh. Param Bhushan and Cash Sale include ₹ 30,000 for sale of his personal jewellery.Create a provision of 212% for doubtful debts and depreciate plant and machinery by 10% p.a. and computers and furniture by 20% p.a. Also provide 5% for group incentive commission to staff on net profit after charging such commission.

Answer» Sh. Param Bhushan does not maintain proper books of accounts. From the following, prepare his trading and profit & loss account for the year ended 31st March, 2015, together with balance sheet as at that date:

BALANCE SHEET

as at 31st March, 2014
Liabilities	(₹)	Assets	(₹)
Sundry Creditors	80,000	Cash	22,000
Outstanding Salaries	4,000	Sundry Debtors	1,50,000
Capital	8,08,000	Stock	1,20,000
		Plant and Machinery	2,00,000
		Freehold Premises	4,00,000

	8,92,000		8,92,000

Cash book analysis shows the following:

	₹
Payment to Creditors	4,00,000
Staff Salaries	76,000
Rent Paid	17,300
General Expenses (including insurance premium of ₹ 2,400 paid on 1st January 2015 to run for one year)	8,700
Personal Withdrawals	12,000
Received from Debtors	5,50,000
Cash Sales	1,10,000
Purchase of Computers (on 1st January, 2015)	40,000
Purchase of Furniture (on 1st January, 2015)	60,000

The following further information is available:

Closing Stock ₹ 1,35,000; Closing Debtors ₹ 1,92,000; Closing Creditors ₹ 72,000; Outstanding Salaries at the end ₹ 6,000; General Expenses include ₹ 5,000 for house rent of Sh. Param Bhushan and Cash Sale include ₹ 30,000 for sale of his personal jewellery.

Create a provision of

2 \frac{1}{2} %

for doubtful debts and depreciate plant and machinery by 10% p.a. and computers and furniture by 20% p.a. Also provide 5% for group incentive commission to staff on net profit after charging such commission.

Discussion

10155.	3 boxes contain 2 balls each . First contains 2 red balls second contains 1 red and 1 black ball and third contains two black balls . All 3 boxes are fully covered and mislabelled u are only permitted to remove one ball at a time , how many minimum balls you must remove to be able to label the three boxes correctly.
Answer» 3 boxes contain 2 balls each . First contains 2 red balls second contains 1 red and 1 black ball and third contains two black balls . All 3 boxes are fully covered and mislabelled u are only permitted to remove one ball at a time , how many minimum balls you must remove to be able to label the three boxes correctly.

Discussion

10156.	What is the value of 6 tan2θ-6cos2θ.
Answer» What is the value of $6 \tan^{2} θ - \frac{6}{\cos^{2} θ}$ .

Discussion

10157.	The distance between the points (a cos θ + b sin θ, 0) and (0, a sin θ − b cos θ) is(a) a2 + b2(b) a + b(c) a2 − b2(d) a2 + b2
Answer» The distance between the points (a cos θ + b sin θ, 0) and (0, a sin θ − b cos θ) is (a) a² + b² (b) a + b (c) a² − b² (d) $\sqrt{a 2 + b 2}$

Discussion

10158.	The number of two digit numbers divisible by 5 is
Answer» The number of two digit numbers divisible by 5 is

Discussion

10159.	Question 1 (i)Find the nature of the roots of the following quadratic equations. If the real roots exist, find them;(i) 2x2−3x+5=0
Answer» Question 1 (i) Find the nature of the roots of the following quadratic equations. If the real roots exist, find them; (i) $2 x^{2} - 3 x + 5 = 0$

Discussion

10160.	In the given figure, quad. ABCD is circumscribed, touching the circle at P, Q, R and S. If AP = 5 cm, BC = 7 cm adn CS = 3 cm. Then, the length AB = ? (a) 9 cm (b) 10 cm (c) 12 cm (d) 8 cm
Answer» In the given figure, quad. ABCD is circumscribed, touching the circle at P, Q, R and S. If AP = 5 cm, BC = 7 cm adn CS = 3 cm. Then, the length AB = ? (a) 9 cm (b) 10 cm (c) 12 cm (d) 8 cm

10160.

In the given figure, quad. ABCD is circumscribed, touching the circle at P, Q, R and S. If AP = 5 cm, BC = 7 cm adn CS = 3 cm. Then, the length AB = ? (a) 9 cm (b) 10 cm (c) 12 cm (d) 8 cm

Answer»

In the given figure, quad. ABCD is circumscribed, touching the circle at P, Q, R and S. If AP = 5 cm, BC = 7 cm adn CS = 3 cm. Then, the length AB = ?

(a) 9 cm (b) 10 cm (c) 12 cm (d) 8 cm

Discussion

10161.	The 20th term of an arithmetic sequence is 80 and its 21st term is 84. then difference between any two terms could be
Answer» The 20th term of an arithmetic sequence is 80 and its 21st term is 84. then difference between any two terms could be

Discussion

10162.	What is the graphical representation of the demand schedule called?
Answer» What is the graphical representation of the demand schedule called?

Discussion

10163.	Find the maximum value of x that satisfies −23<−x3+1, x∈W. 4
Answer» Find the maximum value of $x$ that satisfies $- \frac{2}{3} < - \frac{x}{3} + 1$ , $x \in W .$ 4

Discussion

10164.	Three cards are drawn successively, without replacement from a pack of 52 well-shuffled cards. What is the probability that the third card drawn is a queen given that first card is king of spades while second card is an ace?
Answer» Three cards are drawn successively, without replacement from a pack of 52 well-shuffled cards. What is the probability that the third card drawn is a queen given that first card is king of spades while second card is an ace?

Discussion

10165.	If 2x+y+25=3x-y+13=3x+2y+16 then(a) x = 1, y = 1 (b) x = − 1, y = − 1 (c) x = 1, y = 2 (d) x = 2, y = 1
Answer» If $\frac{2 x + y + 2}{5} = \frac{3 x - y + 1}{3} = \frac{3 x + 2 y + 1}{6}$ then (a) x = 1, y = 1 (b) x = − 1, y = − 1 (c) x = 1, y = 2 (d) x = 2, y = 1

Discussion

10166.	A round table cover has six equal designs as shown in the given figure. If the radius of the cover is 35 cm then find the total area of the design. [ Use √31.732andπ=3.14]
Answer» A round table cover has six equal designs as shown in the given figure. If the radius of the cover is 35 cm then find the total area of the design. [ Use $\sqrt{3} 1.732 a n d π = 3.14$ ]

10166.

A round table cover has six equal designs as shown in the given figure. If the radius of the cover is 35 cm then find the total area of the design. [ Use √31.732andπ=3.14]

Answer»

A round table cover has six equal designs as shown in the given figure. If the radius of the cover is 35 cm then find the total area of the design. [ Use $\sqrt{3} 1.732 a n d π = 3.14$ ]

Discussion

10167.	Prove that: cos6x=32cos6x−48cos4x+18cos2x−1
Answer» Prove that: $cos 6 x = 32 {cos}^{6} x - 48 {cos}^{4} x + 18 {cos}^{2} x - 1$

Discussion

10168.	The ___ of the screw is the distance between two successive screw threads.
Answer» The ___ of the screw is the distance between two successive screw threads.

Discussion

10169.	The entries of a savings bank account are given below: DateParticularsWithdrawals (in Rs.)Deposits (in Rs.)Balance (in Rs.)01.01.03B/F−−1400001.02.03By Cash−115002550012.02.03By Cheque5000−2050005.04.03By Cash−37502425015.04.03By Cheque4250−2000009.05.03By Cash−15002150004.06.03By cash−150023000 Find the interest for six months (that is from January to June) at 8% per annum on the minimum balance on or after the tenth of every month.
Answer» The entries of a savings bank account are given below: $\begin{matrix} D a t e & P a r t i c u l a r s & W i t h d r a w a l s (i n R s .) & D e p o s i t s (i n R s .) & B a l a n c e (i n R s .) 01.01.03 & B / F & - & - & 14000 01.02.03 & B y C a s h & - & 11500 & 25500 12.02.03 & B y C h e q u e & 5000 & - & 20500 05.04.03 & B y C a s h & - & 3750 & 24250 15.04.03 & B y C h e q u e & 4250 & - & 20000 09.05.03 & B y C a s h & - & 1500 & 21500 04.06.03 & B y c a s h & - & 1500 & 23000 \end{matrix}$ Find the interest for six months (that is from January to June) at 8% per annum on the minimum balance on or after the tenth of every month.

10169.

The entries of a savings bank account are given below: DateParticularsWithdrawals (in Rs.)Deposits (in Rs.)Balance (in Rs.)01.01.03B/F−−1400001.02.03By Cash−115002550012.02.03By Cheque5000−2050005.04.03By Cash−37502425015.04.03By Cheque4250−2000009.05.03By Cash−15002150004.06.03By cash−150023000 Find the interest for six months (that is from January to June) at 8% per annum on the minimum balance on or after the tenth of every month.

Answer»

The entries of a savings bank account are given below:

$\begin{matrix} D a t e & P a r t i c u l a r s & W i t h d r a w a l s (i n R s .) & D e p o s i t s (i n R s .) & B a l a n c e (i n R s .) 01.01.03 & B / F & - & - & 14000 01.02.03 & B y C a s h & - & 11500 & 25500 12.02.03 & B y C h e q u e & 5000 & - & 20500 05.04.03 & B y C a s h & - & 3750 & 24250 15.04.03 & B y C h e q u e & 4250 & - & 20000 09.05.03 & B y C a s h & - & 1500 & 21500 04.06.03 & B y c a s h & - & 1500 & 23000 \end{matrix}$

Find the interest for six months (that is from January to June) at 8% per annum on the minimum balance on or after the tenth of every month.

Discussion

10170.	If f(x)= ax^2 + bx + c has no real zeros and a+b+c < 0, then a)c=0b)c>0c)c
Answer» If f(x)= ax^2 + bx + c has no real zeros and a+b+c < 0, then a)c=0 b)c>0 c)c<0 d)None of these

Discussion

10171.	If the diameters of the concentric circles shown in the figure below are in the ratio 1 : 2 : 3 then find the ratio of the areas of three regions.
Answer» If the diameters of the concentric circles shown in the figure below are in the ratio 1 : 2 : 3 then find the ratio of the areas of three regions.

Discussion

10172.	The sum of the squares of two consecutive positive even numbers is 348. Represent this in equation form.
Answer» The sum of the squares of two consecutive positive even numbers is 348. Represent this in equation form.

Discussion

10173.	Check whether the following are quadratic equations 1) (x-3) (2x+1) = x(x+5) 2) x2+3x+1=(x-2)2
Answer» Check whether the following are quadratic equations 1) (x-3) (2x+1) = x(x+5) 2) x2+3x+1=(x-2)2

10173.

Check whether the following are quadratic equations 1) (x-3) (2x+1) = x(x+5) 2) x2+3x+1=(x-2)2

Answer»

Check whether the following are quadratic equations

1) (x-3) (2x+1) = x(x+5)

2) x*2+3x+1=(x-2)*2

Discussion

10174.	A circular pond is 17.5 m in diameter. It is surrounded by a 2m wide path, Find the cost of constructing the path at the rate of ₹ 25 per m2 .
Answer» A circular pond is 17.5 m in diameter. It is surrounded by a 2m wide path, Find the cost of constructing the path at the rate of ₹ 25 per m².

Discussion

10175.	Question 3 (iv)Form the pair of linear equations for the following problems and find their solution by substitution method:The taxi charges in a city consisting of a fixed charge together with the charge for the distance covered. For a distance of 10 km, the charge paid is Rs 105 and for a journey of 15 km, the charge paid is Rs 155. What are the fixed charges and the charge per km? How much does a person have to pay for travelling a distance of 25 km?
Answer» Question 3 (iv) Form the pair of linear equations for the following problems and find their solution by substitution method: The taxi charges in a city consisting of a fixed charge together with the charge for the distance covered. For a distance of 10 km, the charge paid is Rs 105 and for a journey of 15 km, the charge paid is Rs 155. What are the fixed charges and the charge per km? How much does a person have to pay for travelling a distance of 25 km?

Discussion

10176.	Prove that the area of the equilateral triangle drawn on the hypotenuse of a right angled triangle is equal to the sum of the areas of the equilateral triangle drawn on the other two sides of the triangle.
Answer» Prove that the area of the equilateral triangle drawn on the hypotenuse of a right angled triangle is equal to the sum of the areas of the equilateral triangle drawn on the other two sides of the triangle.

Discussion

10177.	From the top of a lighthouse H m tall, a person observes the angle of depression of a boat to be 60∘. Another person who is H3 m from the top of a lighthouse observes the angle of depression of another boat directly behind the first boat to be 45∘. Find the distance between the two boats. (Take √3 = 1.7)
Answer» From the top of a lighthouse H m tall, a person observes the angle of depression of a boat to be $60^{\circ}$ . Another person who is $\frac{H}{3}$ m from the top of a lighthouse observes the angle of depression of another boat directly behind the first boat to be $45^{\circ}$ . Find the distance between the two boats. (Take $\sqrt{3}$ = 1.7)

10177.

From the top of a lighthouse H m tall, a person observes the angle of depression of a boat to be 60∘. Another person who is H3 m from the top of a lighthouse observes the angle of depression of another boat directly behind the first boat to be 45∘. Find the distance between the two boats. (Take √3 = 1.7)

Answer»

From the top of a lighthouse H m tall, a person observes the angle of depression of a boat to be $60^{\circ}$ . Another person who is $\frac{H}{3}$ m from the top of a lighthouse observes the angle of depression of another boat directly behind the first boat to be $45^{\circ}$ . Find the distance between the two boats.

(Take $\sqrt{3}$ = 1.7)

Discussion

10178.	A man observes a car from the top of a tower, which is moving towards the tower with a uniform speed. If the angle of depression of the car changes from 30° to 45° in 12 minutes, find the time taken by the car now to reach the tower. [CBSE 2017]
Answer» A man observes a car from the top of a tower, which is moving towards the tower with a uniform speed. If the angle of depression of the car changes from 30° to 45° in 12 minutes, find the time taken by the car now to reach the tower. [CBSE 2017]

Discussion

10179.	Three consecutive positive integers are taken such that sum of square of the first number and the product of other two numbers is 232. Find the numbers?
Answer» Three consecutive positive integers are taken such that sum of square of the first number and the product of other two numbers is 232. Find the numbers?

Discussion

10180.

Enter the following transactions in the Cash Book of Chandrika of Chandigarh: 2019 ₹ Jan. 1 Chandrika commences business with cash 1,00,000 Jan. 3 She opened a Bank Current Account with her Savings Account cheque 19,00,000 Jan. 4 She receives cheque from Kirti & Co. on account 60,000 Jan. 7 She pays Kirti & Co.'s cheque into Bank Jan. 10 She advanced Ratan & Co. by cheque 35,000 Jan. 12 Tripathi & Co. pays into her Bank A/c 47,500 Jan. 15 She receives cheque from Warsi and allows him discount ₹ 3,500 45,000 Jan. 20 She receives cash ₹ 7,500 and cheque ₹ 10,000 from Kalyan against credit balance Jan. 25 She pays into Bank, including cheques received on 15th and 20th January 1,00,000 Jan. 27 She pays by cheque for purchases of ₹ 27,500 plus CGST and SGST 6% each Jan. 28 Cheque received from Warsi was dishonoured Jan. 30 She pays sundry expenses in cash 50 Jan. 30 She pays John & Co. in cash and is allowed discount ₹ 3,500 37,500 Jan. 31 She pays office rent ₹ 20,000 plus CGST and SGST 6% each by cheque Jan. 31 She draws a cheque for office use 40,000 Jan. 31 She pays staff salaries by cheque 30,000 Jan. 31 She pays cash for stationery ₹ 2,500 plus CGST and SGST 6% each Jan. 31 She purchases goods for cash ₹ 12,500 plus CGST and SGST 6% each Jan. 31 She pays Jagpal by cheque for commission ₹ 30,000 plus CGST and SGST 6% each Jan. 31 She receives cheque for commission of ₹ 50,000 plus CGST and SGST 6% each from Raghubir & Co. and pays the same into Bank Jan. 31 Cash sales ₹ 45,000 plus CGST and SGST 6% each

Answer» Enter the following transactions in the Cash Book of Chandrika of Chandigarh:


2019		₹
Jan. 1	Chandrika commences business with cash	1,00,000
Jan. 3	She opened a Bank Current Account with her Savings Account cheque	19,00,000
Jan. 4	She receives cheque from Kirti & Co. on account	60,000
Jan. 7	She pays Kirti & Co.'s cheque into Bank
Jan. 10	She advanced Ratan & Co. by cheque	35,000
Jan. 12	Tripathi & Co. pays into her Bank A/c	47,500
Jan. 15	She receives cheque from Warsi and allows him discount ₹ 3,500	45,000
Jan. 20	She receives cash ₹ 7,500 and cheque ₹ 10,000 from Kalyan against credit balance
Jan. 25	She pays into Bank, including cheques received on 15th and 20th January	1,00,000
Jan. 27	She pays by cheque for purchases of ₹ 27,500 plus CGST and SGST 6% each
Jan. 28	Cheque received from Warsi was dishonoured
Jan. 30	She pays sundry expenses in cash	50
Jan. 30	She pays John & Co. in cash and is allowed discount ₹ 3,500	37,500
Jan. 31	She pays office rent ₹ 20,000 plus CGST and SGST 6% each by cheque
Jan. 31	She draws a cheque for office use	40,000
Jan. 31	She pays staff salaries by cheque	30,000
Jan. 31	She pays cash for stationery ₹ 2,500 plus CGST and SGST 6% each
Jan. 31	She purchases goods for cash ₹ 12,500 plus CGST and SGST 6% each
Jan. 31	She pays Jagpal by cheque for commission ₹ 30,000 plus CGST and SGST 6% each
Jan. 31	She receives cheque for commission of ₹ 50,000 plus CGST and SGST 6% each from Raghubir & Co. and pays the same into Bank
Jan. 31	Cash sales ₹ 45,000 plus CGST and SGST 6% each

Discussion

10181.	Draw a histogram to represent the following information:Marks0−1010−3030−4545−5050−60Number of students83218106
Answer» Draw a histogram to represent the following information: $\begin{matrix} Marks & 0 - 10 & 10 - 30 & 30 - 45 & 45 - 50 & 50 - 60 Number of students & 8 & 32 & 18 & 10 & 6 \end{matrix}$

Discussion

10182.	Solve for x and y: 7(y+3)−2(x+2)=14,4(y−2)+3(x−3)=2
Answer» Solve for x and y: $7 (y + 3) - 2 (x + 2) = 14, 4 (y - 2) + 3 (x - 3) = 2$

10182.

Solve for x and y: 7(y+3)−2(x+2)=14,4(y−2)+3(x−3)=2

Answer»

Solve for x and y:

$7 (y + 3) - 2 (x + 2) = 14, 4 (y - 2) + 3 (x - 3) = 2$

Discussion

10183.	Equation of the circle passing through (2,3) and centre at the origin is .
Answer» Equation of the circle passing through $(2, 3)$ and centre at the origin is .

Discussion

10184.	The two tangents drawn from an external point to a circle are _______ to the segment joining the centre to the point.
Answer» The two tangents drawn from an external point to a circle are _______ to the segment joining the centre to the point.

Discussion

10185.	Use Euclid's division algorithm to find the HCF of: 867 and 255
Answer» Use Euclid's division algorithm to find the HCF of: 867 and 255

Discussion

10186.	If a=23×32×5 and b=24×3×72, then which of the following is true?
Answer» If $a = 2^{3} \times 3^{2} \times 5$ and $b = 2^{4} \times 3 \times 7^{2}$ , then which of the following is true?

Discussion

10187.	A question was asked in a class”The points A(5, 5), B(4, 4) and C(3, 3) form which triangle?”.Unfortunately, no student could get it right.What type of triangle will be formed if the points are joined ?
Answer» A question was asked in a class ”The points A(5, 5), B(4, 4) and C(3, 3) form which triangle?”. Unfortunately, no student could get it right. What type of triangle will be formed if the points are joined ?

Discussion

10188.	4 If 4 points are made by the intersection of lines 2x-y+1=0, x-2y+3=0, with coordinate axis are concyclic then center of circle is
Answer» 4 If 4 points are made by the intersection of lines 2x-y+1=0, x-2y+3=0, with coordinate axis are concyclic then center of circle is

Discussion

10189.	A company with 4000 shares of nominal value of Rs 110 each declares an annual dividend of 15%, Calculate: (i) the total amount of dividend paid by the company. (ii) the annual income of Shahrukh who hold 88 shares in the company. (iii) if he received only 10% on his investment, find the price Shahrukh paid for each share.
Answer» A company with 4000 shares of nominal value of Rs 110 each declares an annual dividend of $15 %$ , Calculate: (i) the total amount of dividend paid by the company. (ii) the annual income of Shahrukh who hold 88 shares in the company. (iii) if he received only $10 %$ on his investment, find the price Shahrukh paid for each share.

Discussion

10190.	There are two examination rooms A and B. If 10 candidates are sent from A to B, the number of students in each room is same. If 20 candidates are sent from B to A, the number of students in A is double the number of students in B. Find the number of students in each room.
Answer» There are two examination rooms A and B. If 10 candidates are sent from A to B, the number of students in each room is same. If 20 candidates are sent from B to A, the number of students in A is double the number of students in B. Find the number of students in each room.

Discussion

10191.	{ 8 In a triangle }ABC,AB=AC and }D is a point on side }AC such that }BC^2=AC× CD}{ Prove that }BD=BC .
Answer» { 8 In a triangle }ABC,AB=AC and }D is a point on side }AC such that }BC^2=AC× CD}{ Prove that }BD=BC .

Discussion

10192.	In an A.P, the firstterm is 2 and the sum of the first five terms is one-fourth of thenext five terms. Show that 20th term is –112.
Answer» In an A.P, the first term is 2 and the sum of the first five terms is one-fourth of the next five terms. Show that 20^th term is –112.

Discussion

10193.	Calculate ∑fiui∑fi for the given data using step-deviation method. Class intervalFrequency(fi)Class mark(xi)di=xi−aui=dih0−1004050−200−2100−20039150−100−1200−3003425000300−400303501001400−500454502002
Answer» Calculate $\frac{\sum f_{i} u_{i}}{\sum f_{i}}$ for the given data using step-deviation method. $\begin{matrix} Class interval & Frequency (f_{i}) & Class mark (x_{i}) & d_{i} = x_{i} - a & u_{i} = \frac{d_{i}}{h} 0 - 100 & 40 & 50 & - 200 & - 2 100 - 200 & 39 & 150 & - 100 & - 1 200 - 300 & 34 & 250 & 0 & 0 300 - 400 & 30 & 350 & 100 & 1 400 - 500 & 45 & 450 & 200 & 2 \end{matrix}$

Discussion

10194.	Every odd integer is of the form 2m − 1, where m is an integer (True/False).
Answer» Every odd integer is of the form 2m − 1, where m is an integer (True/False).

Discussion

10195.	A right angled triangle with sides 3 cm and 4 cm is revolved around its hypotenuse. Find the volume of the double cone thus generated.
Answer» A right angled triangle with sides 3 cm and 4 cm is revolved around its hypotenuse. Find the volume of the double cone thus generated.

Discussion

10196.	The top of a 15m high tower makes an angle of depression of 60∘ with the bottom of an electronic pole and angle of depression of 30∘ with the top of the pole. What is the height of the electric pole?
Answer» The top of a $15 m$ high tower makes an angle of depression of $60^{\circ}$ with the bottom of an electronic pole and angle of depression of $30^{\circ}$ with the top of the pole. What is the height of the electric pole?

Discussion

10197.	Draw a circle of radius 2.7 cm. Draw a tangent to the circle at any point on it.
Answer» Draw a circle of radius 2.7 cm. Draw a tangent to the circle at any point on it.

Discussion

10198.	Construct a triangle with sides 5 cm, 6 cm and 7 cm and then another triangle whose sides are 75 of the corresponding sides of first triangle.
Answer» Construct a triangle with sides 5 cm, 6 cm and 7 cm and then another triangle whose sides are $\frac{7}{5}$ of the corresponding sides of first triangle.

Discussion

10199.	Solve the following quadratic equations by factorization:6x2 + 11x + 3 = 0
Answer» Solve the following quadratic equations by factorization: 6x² + 11x + 3 = 0

Discussion

10200.	What number should be added to polynomial x2-5x+4 so that 3 is the zero of polynomial?
Answer» What number should be added to polynomial x2-5x+4 so that 3 is the zero of polynomial?

Discussion

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(a) Without using trigonometric tables evaluate: sin 35∘ cos 55∘+cos 35∘ sin 55∘cosec2 10∘−tan2 80∘ (b) Evaluate without using trigonometric tables: cos2 26∘+cos 64∘ sin 26∘+tan 36∘cot 54∘ [6 MARKS]

If the area bounded by the parabola x2=4y, the x−axis and the line x=4 is divided into two equal areas by the line x=α, then the value of α3 is

From a solid cylinder of height 2.8 cm and diameter 4.2 cm,a conical cavity of the same height and same diameter is hollowed out.Find the total surface area of the remaining solid.(Take π= 22/7)

What is the value of 6 tan2θ-6cos2θ.

The distance between the points (a cos θ + b sin θ, 0) and (0, a sin θ − b cos θ) is(a) a2 + b2(b) a + b(c) a2 − b2(d) a2 + b2

The number of two digit numbers divisible by 5 is

Question 1 (i)Find the nature of the roots of the following quadratic equations. If the real roots exist, find them;(i) 2x2−3x+5=0

In the given figure, quad. ABCD is circumscribed, touching the circle at P, Q, R and S. If AP = 5 cm, BC = 7 cm adn CS = 3 cm. Then, the length AB = ? (a) 9 cm (b) 10 cm (c) 12 cm (d) 8 cm

The 20th term of an arithmetic sequence is 80 and its 21st term is 84. then difference between any two terms could be

What is the graphical representation of the demand schedule called?

Find the maximum value of x that satisfies −23&lt;−x3+1, x∈W. 4

Three cards are drawn successively, without replacement from a pack of 52 well-shuffled cards. What is the probability that the third card drawn is a queen given that first card is king of spades while second card is an ace?

If 2x+y+25=3x-y+13=3x+2y+16 then(a) x = 1, y = 1 (b) x = − 1, y = − 1 (c) x = 1, y = 2 (d) x = 2, y = 1

A round table cover has six equal designs as shown in the given figure. If the radius of the cover is 35 cm then find the total area of the design. [ Use √31.732andπ=3.14]

Prove that: cos6x=32cos6x−48cos4x+18cos2x−1

The ___ of the screw is the distance between two successive screw threads.

If f(x)= ax^2 + bx + c has no real zeros and a+b+c < 0, then a)c=0b)c>0c)c

If the diameters of the concentric circles shown in the figure below are in the ratio 1 : 2 : 3 then find the ratio of the areas of three regions.

The sum of the squares of two consecutive positive even numbers is 348. Represent this in equation form.

Check whether the following are quadratic equations 1) (x-3) (2x+1) = x(x+5) 2) x*2+3x+1=(x-2)*2

A circular pond is 17.5 m in diameter. It is surrounded by a 2m wide path, Find the cost of constructing the path at the rate of ₹ 25 per m2 .

Prove that the area of the equilateral triangle drawn on the hypotenuse of a right angled triangle is equal to the sum of the areas of the equilateral triangle drawn on the other two sides of the triangle.

A man observes a car from the top of a tower, which is moving towards the tower with a uniform speed. If the angle of depression of the car changes from 30° to 45° in 12 minutes, find the time taken by the car now to reach the tower. [CBSE 2017]

Three consecutive positive integers are taken such that sum of square of the first number and the product of other two numbers is 232. Find the numbers?

Draw a histogram to represent the following information:Marks0−1010−3030−4545−5050−60Number of students83218106

Solve for x and y: 7(y+3)−2(x+2)=14,4(y−2)+3(x−3)=2

Equation of the circle passing through (2,3) and centre at the origin is .

The two tangents drawn from an external point to a circle are _______ to the segment joining the centre to the point.

Use Euclid's division algorithm to find the HCF of: 867 and 255

If a=23×32×5 and b=24×3×72, then which of the following is true?

A question was asked in a class”The points A(5, 5), B(4, 4) and C(3, 3) form which triangle?”.Unfortunately, no student could get it right.What type of triangle will be formed if the points are joined ?

4 If 4 points are made by the intersection of lines 2x-y+1=0, x-2y+3=0, with coordinate axis are concyclic then center of circle is

There are two examination rooms A and B. If 10 candidates are sent from A to B, the number of students in each room is same. If 20 candidates are sent from B to A, the number of students in A is double the number of students in B. Find the number of students in each room.

{ 8 In a triangle }ABC,AB=AC and }D is a point on side }AC such that }BC^2=AC× CD}{ Prove that }BD=BC .

In an A.P, the firstterm is 2 and the sum of the first five terms is one-fourth of thenext five terms. Show that 20th term is –112.

Calculate ∑fiui∑fi for the given data using step-deviation method. Class intervalFrequency(fi)Class mark(xi)di=xi−aui=dih0−1004050−200−2100−20039150−100−1200−3003425000300−400303501001400−500454502002

Every odd integer is of the form 2m − 1, where m is an integer (True/False).

A right angled triangle with sides 3 cm and 4 cm is revolved around its hypotenuse. Find the volume of the double cone thus generated.

The top of a 15m high tower makes an angle of depression of 60∘ with the bottom of an electronic pole and angle of depression of 30∘ with the top of the pole. What is the height of the electric pole?

Draw a circle of radius 2.7 cm. Draw a tangent to the circle at any point on it.

Construct a triangle with sides 5 cm, 6 cm and 7 cm and then another triangle whose sides are 75 of the corresponding sides of first triangle.

Solve the following quadratic equations by factorization:6x2 + 11x + 3 = 0

What number should be added to polynomial x2-5x+4 so that 3 is the zero of polynomial?

Find the maximum value of x that satisfies −23<−x3+1, x∈W. 4

Check whether the following are quadratic equations 1) (x-3) (2x+1) = x(x+5) 2) x2+3x+1=(x-2)2