32581 + Interview Questions in Mathematics

1.	Prove the following trigonometric identities: (1+tan2A)+(1+1tan2A)=1sin2A−sin4A
Answer» Prove the following trigonometric identities: $(1 + t a n^{2} A) + (1 + \frac{1}{t a n^{2} A}) = \frac{1}{s i n^{2} A - s i n^{4} A}$

1.

Prove the following trigonometric identities: (1+tan2A)+(1+1tan2A)=1sin2A−sin4A

Answer»

Prove the following trigonometric identities:

$(1 + t a n^{2} A) + (1 + \frac{1}{t a n^{2} A}) = \frac{1}{s i n^{2} A - s i n^{4} A}$

2.	A lending library has a fixed charge for the first three days and additional charge for each day thereafter. Saritha paid Rs 27 for a book kept for seven days, while Susy paid Rs 21 for the book she kept for five days. Find the fixed charge and the charge for each extra day.
Answer» A lending library has a fixed charge for the first three days and additional charge for each day thereafter. Saritha paid Rs 27 for a book kept for seven days, while Susy paid Rs 21 for the book she kept for five days. Find the fixed charge and the charge for each extra day.

Discussion

3.	Question 4 (iv)Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method:Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of the two cars?
Answer» Question 4 (iv) Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method: Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of the two cars?

Discussion

4.	A cubical block of side 10 cm is surmounted by a hemisphere. What is the largest diameter that the hemisphere can have? Find the cost of painting the total surface area of the solid so formed, at the rate of ₹5 per 100 sq cm. [Use π = 3.14] [CBSE 2015]
Answer» A cubical block of side 10 cm is surmounted by a hemisphere. What is the largest diameter that the hemisphere can have? Find the cost of painting the total surface area of the solid so formed, at the rate of ₹5 per 100 sq cm. [Use $π$ = 3.14] [CBSE 2015]

Discussion

5.	Construct a triangle similar to a given ΔABC such that each of its sides is (2/3)rd of the corresponding sides of ΔABC. It is given that BC = 6 cm, ∠B = 50° and ∠C = 60°.
Answer» Construct a triangle similar to a given ΔABC such that each of its sides is (2/3)^rd of the corresponding sides of ΔABC. It is given that BC = 6 cm, ∠B = 50° and ∠C = 60°.

Discussion

6.	Water flows at the rate of 10 metre per minute from a cylindrical pipe 5 mm in diameter. How long will it take to fill up a conical vessel whose diameter at the 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» Water flows at the rate of 10 metre per minute from a cylindrical pipe 5 mm in diameter. How long will it take to fill up a conical vessel whose diameter at the 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

7.	If H.C.F and L.C.M of two numbers is x and y respectively, if one of the numbers is b then the other number is?
Answer» If H.C.F and L.C.M of two numbers is x and y respectively, if one of the numbers is b then the other number is?

Discussion

8.	Find the value(s) of x, if the distance between the points A(0,0) and B(x,–4) is 5 units.
Answer» Find the value(s) of $x$ , if the distance between the points $A (0, 0)$ and $B (x, - 4)$ is $5$ units.

Discussion

9.	In a class interval if only lower limit of the class interval is included in the class limit then that class interval is called ___.
Answer» In a class interval if only lower limit of the class interval is included in the class limit then that class interval is called ___.

Discussion

10.	Find the area in cm2 of the shaded region if PQ = 24cm, PR = 7cm and O is the centre of the circle. [3 MARKS]
Answer» Find the area in $c m^{2}$ of the shaded region if PQ = 24cm, PR = 7cm and O is the centre of the circle. [3 MARKS]

10.

Find the area in cm2 of the shaded region if PQ = 24cm, PR = 7cm and O is the centre of the circle. [3 MARKS]

Answer»

Find the area in $c m^{2}$ of the shaded region if PQ = 24cm, PR = 7cm and O is the centre of the circle. [3 MARKS]

Discussion

11.	5. The angles of elevation of the top of thetower from two points at distances a unit and b unitfrom the base and in the same straight line with itare complementary. The height of the tower is (a) a+b unit (b) \sqrt{ab} unit (c) ab unit (d) a\sqrt b unit
Answer» 5. The angles of elevation of the top of thetower from two points at distances a unit and b unitfrom the base and in the same straight line with itare complementary. The height of the tower is (a) a+b unit (b) \sqrt{ab} unit (c) ab unit (d) a\sqrt b unit

Discussion

12.	From a well-shuffled deck of 52 cards, a card is picked at random. (i) Find the probability of the card being a queen of spades. (ii) If the card drawn at first is a queen of spade and is not replaced, what is the probability of getting a card which is a spade?
Answer» From a well-shuffled deck of 52 cards, a card is picked at random. (i) Find the probability of the card being a queen of spades. (ii) If the card drawn at first is a queen of spade and is not replaced, what is the probability of getting a card which is a spade?

Discussion

13.	19. From the point a(0,3) is inscribed in the region common to two circles x2+y2-4x-12=0 and x2+y2+4x-12=0 with two pf its vertices on the line joining the centres of the circles.the area of rhombus is
Answer» 19. From the point a(0,3) is inscribed in the region common to two circles x2+y2-4x-12=0 and x2+y2+4x-12=0 with two pf its vertices on the line joining the centres of the circles.the area of rhombus is

Discussion

14.	On a certain commodity, rate of CGST =14% and rate of SGST =14%. What is the rate of GST?
Answer» On a certain commodity, rate of CGST $= 14 %$ and rate of SGST $= 14 %$ . What is the rate of GST?

Discussion

15.	21. Four different integers form an increasing AP. One of these numbers is equal to the sum of squares of the other three numbers. Find the numbers
Answer» 21. Four different integers form an increasing AP. One of these numbers is equal to the sum of squares of the other three numbers. Find the numbers

Discussion

16.	Write the value of k for which the system of equations 3x−2y=0 and kx+5y=0 has infinitely many solutions.
Answer» Write the value of $k$ for which the system of equations $3 x - 2 y = 0$ and $k x + 5 y = 0$ has infinitely many solutions.

Discussion

17.	cos256∘+cos234∘sin256∘+sin234∘+3tan256∘×tan234∘=___
Answer» $\frac{c o s^{2} 56^{\circ} + c o s^{2} 34^{\circ}}{s i n^{2} 56^{\circ} + s i n^{2} 34^{\circ}} + 3 t a n^{2} 56^{\circ} \times t a n^{2} 34^{\circ} =$ ___

Discussion

18.	In ∆ABC, ray AD bisects ∠A and intersects BC in D. If BC = a, AC = b and AC = c, prove that(i) BD=acb+c(ii) DC=abb+c
Answer» In ∆ABC, ray AD bisects ∠A and intersects BC in D. If BC = a, AC = b and AC = c, prove that (i) $BD = \frac{a c}{b + c}$ (ii) $DC = \frac{a b}{b + c}$

Discussion

19.	1cos θ−1(sec θ+tan θ)
Answer» $\frac{1}{c o s θ} - \frac{1}{(s e c θ + t a n θ)}$

Discussion

20.	A person started walking towards the east and covered a distance of 9 m and turned towards the north and covered a distance of 30 m. Then, he turned towards the west and covered 2 m and finally turned towards the south and walked a distance of 6 m. The distance between the initial and final positions of the person is: [1 mark]
Answer» A person started walking towards the east and covered a distance of 9 m and turned towards the north and covered a distance of 30 m. Then, he turned towards the west and covered 2 m and finally turned towards the south and walked a distance of 6 m. The distance between the initial and final positions of the person is: [1 mark]

Discussion

21.	Prove that √2 is irrational.
Answer» Prove that $\sqrt{2}$ is irrational.

Discussion

22.	If 13-a10=8+5, then a=(a) −5(b) −6(c) −4(d) −2
Answer» If $\sqrt{13 - a \sqrt{10}} = \sqrt{8} + \sqrt{5}, then a =$ (a) −5 (b) −6 (c) −4 (d) −2

Discussion

23.	(1) Draw the graph of y = x2 and y = 2x + 3 and hence solve the equation x2 − 2x − 3 = 0.(2) Draw the graph of y = 2x2 and y = 3 − x and hence solve the equation 2x2 + x − 3 = 0.(3) Draw the graph of y = 2x2 and y = 3 + x and hence solve the equation 2x2 − x − 3 = 0.
Answer» (1) Draw the graph of y = x² and y = 2x + 3 and hence solve the equation x² − 2x − 3 = 0. (2) Draw the graph of y = 2x²and y = 3 − x and hence solve the equation 2x² + x − 3 = 0. (3) Draw the graph of y = 2x² and y = 3 + x and hence solve the equation 2x² − x − 3 = 0.

23.

(1) Draw the graph of y = x2 and y = 2x + 3 and hence solve the equation x2 − 2x − 3 = 0.(2) Draw the graph of y = 2x2 and y = 3 − x and hence solve the equation 2x2 + x − 3 = 0.(3) Draw the graph of y = 2x2 and y = 3 + x and hence solve the equation 2x2 − x − 3 = 0.

Answer»

(1) Draw the graph of y = x² and y = 2x + 3 and hence solve the equation x² − 2x − 3 = 0.

(2) Draw the graph of y = 2x²and y = 3 − x and hence solve the equation 2x² + x − 3 = 0.

(3) Draw the graph of y = 2x² and y = 3 + x and hence solve the equation 2x² − x − 3 = 0.

Discussion

24.

Find the Mean, Median and Mode of the following data using Assumed Mean Method and verify using the Emperical Formula. Asecending Order of Data : 156, 156, 156, 156, 158, 158, 160,160, 162, 163, 163,164, 165, 166, 168, 168, 172, 172, 174, 174, 175, 175, 177, 178, 178, 178, 180, 190

Answer»

Find the Mean, Median and Mode of the following data using Assumed Mean Method and verify using the Emperical Formula.

Asecending Order of Data : 156, 156, 156, 156, 158, 158, 160,160, 162, 163, 163,164, 165, 166, 168, 168, 172, 172, 174, 174, 175, 175, 177, 178, 178, 178, 180, 190

Discussion

25.

The following balances were extracted from the books of Shri Krishan Kumar as at 31st March, 2017: Dr. (₹) Cr. (₹) Capital 24,500 Drawings 2,000 General Expenses 2,500 Buildings 11,000 Machinery 9,340 Stock (1-4-2016) 16,200 Power 2,240 Taxes and Insurance 1,315 Wages 7,200 Sundry Debtors 6,280 Sundry Creditors 2,500 Charity 105 Bad-debts 550 Bank Overdraft 11,180 Sales 65,360 Purchases 47,000 Scooter 2,000 Scooter Expenses 500 Bad-debts Provision 900 Commission 1,320 Trade Expenses 1,280 Bills Payable 3,850 Cash 100 1,09,610 1,09,610 Adjustments:-(i) Stock on 31st March, 2017 was valued at ₹ 23,500.(ii) 15th of general expenses and taxes & insurance to be charged to factory and the balance to the office.(iii) Write off a further Bad-debts of ₹ 160 and maintain the provision for Bad-debts at 5% on Debtors.(iv) Depreciate Machinery at 10% and Scooter by ₹ 240.(v) Provide ₹ 700 for outstanding interest on Bank Overdraft.(vi) Prepaid Insurance is to the extent of ₹ 50.(vii) Provide for Manager's Commission at 10% on the Net Profit after charging such Commission.Prepare final accounts for the year ended 31st March, 2017 after giving effect to the above adjustments.

Answer» The following balances were extracted from the books of Shri Krishan Kumar as at 31st March, 2017:

	Dr. (₹)	Cr. (₹)
Capital		24,500
Drawings	2,000
General Expenses	2,500
Buildings	11,000
Machinery	9,340
Stock (1-4-2016)	16,200
Power	2,240
Taxes and Insurance	1,315
Wages	7,200
Sundry Debtors	6,280
Sundry Creditors		2,500
Charity	105
Bad-debts	550
Bank Overdraft		11,180
Sales		65,360
Purchases	47,000
Scooter	2,000
Scooter Expenses	500
Bad-debts Provision		900
Commission		1,320
Trade Expenses	1,280
Bills Payable		3,850
Cash	100
	1,09,610	1,09,610

Adjustments:-

(i) Stock on 31st March, 2017 was valued at ₹ 23,500.

(ii)

\frac{1}{5} th

of general expenses and taxes & insurance to be charged to factory and the balance to the office.

(iii) Write off a further Bad-debts of ₹ 160 and maintain the provision for Bad-debts at 5% on Debtors.

(iv) Depreciate Machinery at 10% and Scooter by ₹ 240.

(v) Provide ₹ 700 for outstanding interest on Bank Overdraft.

(vi) Prepaid Insurance is to the extent of ₹ 50.

(vii) Provide for Manager's Commission at 10% on the Net Profit after charging such Commission.

Prepare final accounts for the year ended 31st March, 2017 after giving effect to the above adjustments.

Discussion

26.

In the following data, find the values of p and q. Also, find the median class and modal class. Class Frequency (f) Cumulative frequency (cf) 100−200 11 11 200−300 12 p 300−400 10 33 400−500 q 46 500−600 20 66 600−700 14 80

Answer» In the following data, find the values of p and q. Also, find the median class and modal class.

Class	Frequency (f)	Cumulative frequency (cf)
100−200	11	11
200−300	12	p
300−400	10	33
400−500	q	46
500−600	20	66
600−700	14	80

Discussion

27.	Prove the following identities: cot2A(sec A−1)1+sin A=sec2 A(1−sin A1+sec A)
Answer» Prove the following identities: $\frac{c o t^{2} A (s e c A - 1)}{1 + s i n A} = s e c^{2} A (\frac{1 - s i n A}{1 + s e c A})$

27.

Prove the following identities: cot2A(sec A−1)1+sin A=sec2 A(1−sin A1+sec A)

Answer»

Prove the following identities:

$\frac{c o t^{2} A (s e c A - 1)}{1 + s i n A} = s e c^{2} A (\frac{1 - s i n A}{1 + s e c A})$

Discussion

28.	The number (1+√3)2 is a/an ____________.
Answer» The number ${(1 + \sqrt{3})}^{2}$ is a/an ____________.

Discussion

29.

The median of the following data is 525. Find the missing frequency, if it is given that there are 100 observations in the data: Class intervalFrequency Class interval Frequency 0−100 2 500−600 20 100−200 5 600−700 f2 200−300 f1 700−800 9 300−400 12 800−900 7 400−500 17 900−1000 4

Answer»

The median of the following data is 525. Find the missing frequency, if it is given that there are 100 observations in the data:

Class interval	Frequency	Class interval	Frequency
$0 - 100$	2	$500 - 600$	20
$100 - 200$	5	$600 - 700$	$f_{2}$
$200 - 300$	$f_{1}$	$700 - 800$	9
$300 - 400$	12	$800 - 900$	7
$400 - 500$	17	$900 - 1000$	4

Discussion

30.	What is the nature of roots of the quadratic equation if the discriminant is 4.
Answer» What is the nature of roots of the quadratic equation if the discriminant is 4.

Discussion

31.	Find a quadratic polynomial for the given numbers as the sum and product of its zeroes respectively.√2,13
Answer» Find a quadratic polynomial for the given numbers as the sum and product of its zeroes respectively. $\sqrt{2}, \frac{1}{3}$

31.

Find a quadratic polynomial for the given numbers as the sum and product of its zeroes respectively.√2,13

Answer»

Find a quadratic polynomial for the given numbers as the sum and product of its zeroes respectively.

$\sqrt{2}, \frac{1}{3}$

Discussion

32.	In Q. No. 14, write the sign of c.
Answer» In Q. No. 14, write the sign of c.

Discussion

33.	If a=b×c+0(where a,b,c€N), then find the H.C.F of a and b
Answer» If a=b×c+0(where a,b,c€N), then find the H.C.F of a and b

Discussion

34.	If the volumes of two cones are in the ratio of 1 : 4 and their diameters are in the ratio of 4 : 5, find the ratio of their heights.
Answer» If the volumes of two cones are in the ratio of 1 : 4 and their diameters are in the ratio of 4 : 5, find the ratio of their heights.

Discussion

35.	(H): In }△ ABC,D is mid point of }\overline{BC} . }E is foot of perpendicular } from }C on external angle bisector of }\angle BAC . prove 2 DE = } AB+ AC
Answer» (H): In }△ ABC,D is mid point of }\overline{BC} . }E is foot of perpendicular } from }C on external angle bisector of }\angle BAC . prove 2 DE = } AB+ AC

Discussion

36.

From the following extracts from the Cash Book and the Pass Book for the month of January, 2019, prepare Bank Reconciliation Statement: CASH BOOK (BANK COLUMNS ONLY) Dr. Cr. Date Particulars L.F. Bank (₹) Date Particulars L.F. Bank (₹) 2019 2019 Jan.01 To Balance b/d 4,510 Jan.02 By S. Gidwani & Co. 1,230 Jan.03 To Cash 300 Jan.06 By Wages 3,000 Jan.10 To G. Basu & Co. 1,000 Jan.14 By Basu & Co. (Cheque dishonoured) 1,000 Jan.15 To Mohan & Co. 2,300 Jan.15 By V. Kumar & Co. 300 Jan.17 To Cash 600 Jan.18 By S. Sharda & Sons 470 Jan.20 To M. Mohan & Bros. 1,550 Jan.24 By Cash 400 Jan.24 To T.P. Bhalla & Co. 740 Jan.28 By R. Ramdas & Co. 780 Jan.31 To S. Leader & Sons 2,130 Jan.31 By B. Bansal & Bros. 340 Jan.31 By Balance c/d 5,610 13,130 13,130 2019 Feb. To Balance b/d 5,610 PASS BOOK Date Particulars Withdrawals (₹) Deposits (₹) Dr. or Cr. Balance (₹) 2019 Jan.01 By Balance Cr. 4,510 Jan.03 By Cash 300 Cr. 4,810 Jan.06 To Selves–Cash 3,000 Cr. 1,810 Jan.10 To S. Gidwani & Co. 1,230 Cr. 580 Jan.16 By Mohan & Co. 2,300 Cr. 2,880 Jan.17 By Cash 600 Cr. 3,480 Jan.20 To S. Sharda & Sons 470 Cr. 3,010 Jan.24 To Cash 400 Cr. 2,610 Jan.31 To Bank Charges 10 Cr. 2,600 Jan.31 To Life insurance Premium as per instructions 250 Cr. 2,350 Jan.31 By Interest on Government Securities 300 Cr. 2,650

Answer» From the following extracts from the Cash Book and the Pass Book for the month of January, 2019, prepare Bank Reconciliation Statement:

CASH BOOK (BANK COLUMNS ONLY)
Dr.							Cr.
Date	Particulars	L.F.	Bank (₹)	Date	Particulars	L.F.	Bank (₹)
2019				2019
Jan.01	To Balance b/d		4,510	Jan.02	By S. Gidwani & Co.		1,230
Jan.03	To Cash		300	Jan.06	By Wages		3,000
Jan.10	To G. Basu & Co.		1,000	Jan.14	By Basu & Co. (Cheque dishonoured)		1,000
Jan.15	To Mohan & Co.		2,300	Jan.15	By V. Kumar & Co.		300
Jan.17	To Cash		600	Jan.18	By S. Sharda & Sons		470
Jan.20	To M. Mohan & Bros.		1,550	Jan.24	By Cash		400
Jan.24	To T.P. Bhalla & Co.		740	Jan.28	By R. Ramdas & Co.		780
Jan.31	To S. Leader & Sons		2,130	Jan.31	By B. Bansal & Bros.		340
				Jan.31	By Balance c/d		5,610
			13,130				13,130
2019
Feb.	To Balance b/d		5,610

PASS BOOK
Date	Particulars	Withdrawals (₹)	Deposits (₹)	Dr. or Cr.	Balance (₹)
2019
Jan.01	By Balance			Cr.	4,510
Jan.03	By Cash		300	Cr.	4,810
Jan.06	To Selves–Cash	3,000		Cr.	1,810
Jan.10	To S. Gidwani & Co.	1,230		Cr.	580
Jan.16	By Mohan & Co.		2,300	Cr.	2,880
Jan.17	By Cash		600	Cr.	3,480
Jan.20	To S. Sharda & Sons	470		Cr.	3,010
Jan.24	To Cash	400		Cr.	2,610
Jan.31	To Bank Charges	10		Cr.	2,600
Jan.31	To Life insurance Premium as per instructions	250		Cr.	2,350
Jan.31	By Interest on Government Securities		300	Cr.	2,650

Discussion

37.	Question 7Two cones with same base radius 8 cm and height 15 cm are joined together along their bases. Find the surface area of the shape so formed.
Answer» Question 7 Two cones with same base radius 8 cm and height 15 cm are joined together along their bases. Find the surface area of the shape so formed.

Discussion

38.	If the sum of 99 terms of AP is 198, then what is the value of the 50th term?
Answer» If the sum of 99 terms of AP is 198, then what is the value of the 50th term?

Discussion

39.	Find the inner surface area of the above vessel. 572
Answer» Find the inner surface area of the above vessel. 572

Discussion

40.	Ten years ago, a father was twelve times as old as his son and ten years hence, he will be twice as old as his son will be then. Find their present ages.
Answer» Ten years ago, a father was twelve times as old as his son and ten years hence, he will be twice as old as his son will be then. Find their present ages.

Discussion

41.	Reena has. Pens and pencils which together are 40 in number. If she has 5 more pencils and 5 less pens,then number of pencils would become 4 times the number of pens . Find original number of pens and pencils.
Answer» Reena has. Pens and pencils which together are 40 in number. If she has 5 more pencils and 5 less pens,then number of pencils would become 4 times the number of pens . Find original number of pens and pencils.

Discussion

42.	15. The points A(3,0) B(a,2) and C(4,1) are the vertices of triangle ABC right angled at vertex A.Find the value of a.
Answer» 15. The points A(3,0) B(a,2) and C(4,1) are the vertices of triangle ABC right angled at vertex A.Find the value of a.

Discussion

43.	Question 1 (v) Which of the following form an AP? Justify your answer. 12,13,14,⋯
Answer» Question 1 (v) Which of the following form an AP? Justify your answer. $\frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \dots$

Discussion

44.	The areas of two similar triangles are 121 cm2 and 64 cm2 respectively. If the median of the first triangle is 12.1 cm, find the corresponding median of the other.
Answer» The areas of two similar triangles are 121 cm² and 64 cm² respectively. If the median of the first triangle is 12.1 cm, find the corresponding median of the other.

Discussion

45.	P(t1) and P(t2) are the points t1and t2 on the parabola }y^2=4ax . The normals at }P and }Q meet on } the parabola. Show that the middle point of }PQ lies on the }{ parabola }y^2=2a(x+2a) .
Answer» P(t1) and P(t2) are the points t1and t2 on the parabola }y^2=4ax . The normals at }P and }Q meet on } the parabola. Show that the middle point of }PQ lies on the }{ parabola }y^2=2a(x+2a) .

Discussion

46.	When the price of a commodity falls, the consumer will have greater purchasing power
Answer» When the price of a commodity falls, the consumer will have greater purchasing power

Discussion

47.	Fill in the blanks.Point G is the centroid of ∆ ABC.(1) If l(RG) = 2.5 then l(GC) = ......(2) If l(BG) = 6 then l(BQ) = ......(3) If l(AP) =6 then l(AG) = ...... and l(GP) = ........
Answer» Fill in the blanks. Point G is the centroid of ∆ ABC. (1) If l(RG) = 2.5 then l(GC) = ...... (2) If l(BG) = 6 then l(BQ) = ...... (3) If l(AP) =6 then l(AG) = ...... and l(GP) = ........

Discussion

48.	If x-y=2 and 2x+y=15 then(a) x = 4, y = 2 (b) x = 5, y = 3 (c) x = 6, y = 4 (d) x = 7, y = 5
Answer» If $x - y = 2 and \frac{2}{x + y} = \frac{1}{5}$ then (a) x = 4, y = 2 (b) x = 5, y = 3 (c) x = 6, y = 4 (d) x = 7, y = 5

Discussion

49.	To construct a square from a given triangle, we need to make a rectangle of length and breadth equal to ______ and _______ of the triangle.
Answer» To construct a square from a given triangle, we need to make a rectangle of length and breadth equal to ______ and _______ of the triangle.

Discussion

50.	Choose the correct answer of the following question:The area of a rhombus is 480 cm2 and the length of one of its diagonals is 20 cm. The length of each side of the rhombus is(a) 24 cm (b) 30 cm (c) 26 cm (d) 28 cm
Answer» Choose the correct answer of the following question: The area of a rhombus is 480 cm² and the length of one of its diagonals is 20 cm. The length of each side of the rhombus is (a) 24 cm (b) 30 cm (c) 26 cm (d) 28 cm

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Prove the following trigonometric identities: (1+tan2A)+(1+1tan2A)=1sin2A−sin4A

A lending library has a fixed charge for the first three days and additional charge for each day thereafter. Saritha paid Rs 27 for a book kept for seven days, while Susy paid Rs 21 for the book she kept for five days. Find the fixed charge and the charge for each extra day.

A cubical block of side 10 cm is surmounted by a hemisphere. What is the largest diameter that the hemisphere can have? Find the cost of painting the total surface area of the solid so formed, at the rate of ₹5 per 100 sq cm. [Use π = 3.14] [CBSE 2015]

Construct a triangle similar to a given ΔABC such that each of its sides is (2/3)rd of the corresponding sides of ΔABC. It is given that BC = 6 cm, ∠B = 50° and ∠C = 60°.

Water flows at the rate of 10 metre per minute from a cylindrical pipe 5 mm in diameter. How long will it take to fill up a conical vessel whose diameter at the 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

If H.C.F and L.C.M of two numbers is x and y respectively, if one of the numbers is b then the other number is?

Find the value(s) of x, if the distance between the points A(0,0) and B(x,–4) is 5 units.

In a class interval if only lower limit of the class interval is included in the class limit then that class interval is called ___.

Find the area in cm2 of the shaded region if PQ = 24cm, PR = 7cm and O is the centre of the circle. [3 MARKS]

5. The angles of elevation of the top of thetower from two points at distances a unit and b unitfrom the base and in the same straight line with itare complementary. The height of the tower is (a) a+b unit (b) \sqrt{ab} unit (c) ab unit (d) a\sqrt b unit

From a well-shuffled deck of 52 cards, a card is picked at random. (i) Find the probability of the card being a queen of spades. (ii) If the card drawn at first is a queen of spade and is not replaced, what is the probability of getting a card which is a spade?

19. From the point a(0,3) is inscribed in the region common to two circles x2+y2-4x-12=0 and x2+y2+4x-12=0 with two pf its vertices on the line joining the centres of the circles.the area of rhombus is

On a certain commodity, rate of CGST =14% and rate of SGST =14%. What is the rate of GST?

21. Four different integers form an increasing AP. One of these numbers is equal to the sum of squares of the other three numbers. Find the numbers

Write the value of k for which the system of equations 3x−2y=0 and kx+5y=0 has infinitely many solutions.

cos256∘+cos234∘sin256∘+sin234∘+3tan256∘×tan234∘=___

In ∆ABC, ray AD bisects ∠A and intersects BC in D. If BC = a, AC = b and AC = c, prove that(i) BD=acb+c(ii) DC=abb+c

1cos θ−1(sec θ+tan θ)

Prove that √2 is irrational.

If 13-a10=8+5, then a=(a) −5(b) −6(c) −4(d) −2

(1) Draw the graph of y = x2 and y = 2x + 3 and hence solve the equation x2 − 2x − 3 = 0.(2) Draw the graph of y = 2x2 and y = 3 − x and hence solve the equation 2x2 + x − 3 = 0.(3) Draw the graph of y = 2x2 and y = 3 + x and hence solve the equation 2x2 − x − 3 = 0.

Find the Mean, Median and Mode of the following data using Assumed Mean Method and verify using the Emperical Formula. Asecending Order of Data : 156, 156, 156, 156, 158, 158, 160,160, 162, 163, 163,164, 165, 166, 168, 168, 172, 172, 174, 174, 175, 175, 177, 178, 178, 178, 180, 190

In the following data, find the values of p and q. Also, find the median class and modal class. Class Frequency (f) Cumulative frequency (cf) 100−200 11 11 200−300 12 p 300−400 10 33 400−500 q 46 500−600 20 66 600−700 14 80

Prove the following identities: cot2A(sec A−1)1+sin A=sec2 A(1−sin A1+sec A)

The number (1+√3)2 is a/an ____________.

What is the nature of roots of the quadratic equation if the discriminant is 4.

Find a quadratic polynomial for the given numbers as the sum and product of its zeroes respectively.√2,13

In Q. No. 14, write the sign of c.

If a=b×c+0(where a,b,c€N), then find the H.C.F of a and b

If the volumes of two cones are in the ratio of 1 : 4 and their diameters are in the ratio of 4 : 5, find the ratio of their heights.

(H): In }△ ABC,D is mid point of }\overline{BC} . }E is foot of perpendicular } from }C on external angle bisector of }\angle BAC . prove 2 DE = } AB+ AC

Question 7Two cones with same base radius 8 cm and height 15 cm are joined together along their bases. Find the surface area of the shape so formed.

If the sum of 99 terms of AP is 198, then what is the value of the 50th term?

Find the inner surface area of the above vessel. 572

Ten years ago, a father was twelve times as old as his son and ten years hence, he will be twice as old as his son will be then. Find their present ages.

Reena has. Pens and pencils which together are 40 in number. If she has 5 more pencils and 5 less pens,then number of pencils would become 4 times the number of pens . Find original number of pens and pencils.

15. The points A(3,0) B(a,2) and C(4,1) are the vertices of triangle ABC right angled at vertex A.Find the value of a.

Question 1 (v) Which of the following form an AP? Justify your answer. 12,13,14,⋯

The areas of two similar triangles are 121 cm2 and 64 cm2 respectively. If the median of the first triangle is 12.1 cm, find the corresponding median of the other.

P(t1) and P(t2) are the points t1and t2 on the parabola }y^2=4ax . The normals at }P and }Q meet on } the parabola. Show that the middle point of }PQ lies on the }{ parabola }y^2=2a(x+2a) .

When the price of a commodity falls, the consumer will have greater purchasing power

Fill in the blanks.Point G is the centroid of ∆ ABC.(1) If l(RG) = 2.5 then l(GC) = ......(2) If l(BG) = 6 then l(BQ) = ......(3) If l(AP) =6 then l(AG) = ...... and l(GP) = ........

If x-y=2 and 2x+y=15 then(a) x = 4, y = 2 (b) x = 5, y = 3 (c) x = 6, y = 4 (d) x = 7, y = 5

To construct a square from a given triangle, we need to make a rectangle of length and breadth equal to ______ and _______ of the triangle.

Choose the correct answer of the following question:The area of a rhombus is 480 cm2 and the length of one of its diagonals is 20 cm. The length of each side of the rhombus is(a) 24 cm (b) 30 cm (c) 26 cm (d) 28 cm

To construct a square from a given triangle, we need to make a rectangle of length and breadth equal to and _ of the triangle.