32581 + Interview Questions in Mathematics

1.	The power of P(1,2) with respect to the circle x2+y2+4x+2y+3 = 0 is double the power of P with respect to x2+y2+2x+y+k = 0 then the value of k is
Answer» The power of P(1,2) with respect to the circle $x^{2} + y^{2} + 4 x + 2 y + 3$ = 0 is double the power of P with respect to $x^{2} + y^{2} + 2 x + y + k$ = 0 then the value of k is

Discussion

2.	6.solve : \|x+1\|+\|x-4 \|
Answer» 6.solve : \|x+1\|+\|x-4 \|<7

Discussion

3.	The sum of a number and its square is 634, find the numbers.
Answer» The sum of a number and its square is $\frac{63}{4}$ , find the numbers.

Discussion

4.

Grouped frequency distribution of supply of milk to hotels and the number of hotels is given in the following table. Find the mode of the supply of milk. Milk (Litre) 1 - 3 3 - 5 5 - 7 7 - 9 9 - 11 11 - 13 No. of hotels 7 5 15 20 35 18

Answer» Grouped frequency distribution of supply of milk to hotels and the number of hotels is given in the following table. Find the mode of the supply of milk.

Milk (Litre)	1 - 3	3 - 5	5 - 7	7 - 9	9 - 11	11 - 13
No. of hotels	7	5	15	20	35	18

Discussion

5.	Question 1 Which one of the following options is true, and why?y=3x+5 has(i) a unique solution(ii) only two solutions(iii) infinitely many solutions
Answer» Question 1 Which one of the following options is true, and why? $y = 3 x + 5$ has (i) a unique solution (ii) only two solutions (iii) infinitely many solutions

Discussion

6.	find HCF and LCM of 404 and 96 and verify that HCF into LCM is equal to product of the two given numbers.
Answer» find HCF and LCM of 404 and 96 and verify that HCF into LCM is equal to product of the two given numbers.

Discussion

7.	If cos θ=1213, show that sin θ (1 − tan θ)=35156.
Answer» If $\cos θ = \frac{12}{13}$ , show that sin θ (1 − tan θ) $= \frac{35}{156}$ .

Discussion

8.	An aeroplane is flying at a height of 300 m above the gound. Flying at this height the angles of depression from the aeroplane of two points on both banks of a river in opposite directions are 45∘ and 60∘ respectively. Find the width of the river. [Use~√3=1.732.]
Answer» An aeroplane is flying at a height of 300 m above the gound. Flying at this height the angles of depression from the aeroplane of two points on both banks of a river in opposite directions are $45^{\circ}$ and $60^{\circ}$ respectively. Find the width of the river. [Use~ $\sqrt{3} = 1.732.$ ]

Discussion

9.	Find the slope of a line passing through the following points:(i) (5, 6) and (2, 3)(ii) (9, -2) and (6, -5)
Answer» Find the slope of a line passing through the following points: (i) (5, 6) and (2, 3) (ii) (9, -2) and (6, -5)

Discussion

10.	36 has _________ number of prime factors.
Answer» 36 has _________ number of prime factors.

Discussion

11.	The surface area of a box which is in the form of a cuboid whose dimensions arel x b x h is:
Answer» The surface area of a box which is in the form of a cuboid whose dimensions are l x b x h is:

Discussion

12.	There are two temples, one on each bank of a river, just opposite to each other. One temple is 50 m high. From the top of this temple, the angles of depression of the top and the foot of the other temple are 30° and 60° respectively. Find the width of the river and the height of the other temple.
Answer» There are two temples, one on each bank of a river, just opposite to each other. One temple is 50 m high. From the top of this temple, the angles of depression of the top and the foot of the other temple are 30° and 60° respectively. Find the width of the river and the height of the other temple.

Discussion

13.	Find the roots of each of the following equations, if they exist, by applying the quadratic formula:mnx2+nm=1-2x
Answer» Find the roots of each of the following equations, if they exist, by applying the quadratic formula: $\frac{m}{n} x^{2} + \frac{n}{m} = 1 - 2 x$

Discussion

14.	An aero-plane takes 1 hr less for a journey of 1200 km. If its speed is increased by 60 km/hr from the initial speed. Find the initial speed of the plane.
Answer» An aero-plane takes 1 hr less for a journey of 1200 km. If its speed is increased by 60 km/hr from the initial speed. Find the initial speed of the plane.

Discussion

15.	In a lottery, there are 8 prizes and 16 blanks. What is the probability of getting a prize? (a) 12 (b) 13 (c) 23 (d) None of these
Answer» In a lottery, there are 8 prizes and 16 blanks. What is the probability of getting a prize? (a) $\frac{1}{2}$ (b) $\frac{1}{3}$ (c) $\frac{2}{3}$ (d) None of these

Discussion

16.

Sugandh Ltd. issued 60,000 shares of ₹ 10 each at a premium of ₹ 2 per share payable as ₹ 3 on application, ₹ 5(including premium) on allotment and the balance on first and final call. Applications were received for 92,000 shares. The Directors resolved to allot as: (i) Applicants of 40,000 shares 30,000 shares, (ii) Applicants of 50,000 shares 30,000 shares, (iii) Applicants of 2,000 shares Nil. Mohan, who had applied for 800 shares in Category(i) and Sohan, who was allotted 600 shares in Category(ii) failed to pay the allotment money. Calculate amount received on allotment.

Answer» Sugandh Ltd. issued 60,000 shares of ₹ 10 each at a premium of ₹ 2 per share payable as ₹ 3 on application, ₹ 5(including premium) on allotment and the balance on first and final call. Applications were received for 92,000 shares. The Directors resolved to allot as:

(i)	Applicants of 40,000 shares	30,000 shares,
(ii)	Applicants of 50,000 shares	30,000 shares,
(iii)	Applicants of 2,000 shares	Nil.

Mohan, who had applied for 800 shares in Category

(i) and Sohan, who was allotted 600 shares in Category

(ii) failed to pay the allotment money. Calculate amount received on allotment.

Discussion

17.	If one of the zeroes of bi-quadratic polynomial fx)x4 ax3 bx2 + cx + d is 1, then the sum ofall the coefficients of the polynomial is(2) -1(4) -d(3) 0
Answer» If one of the zeroes of bi-quadratic polynomial fx)x4 ax3 bx2 + cx + d is 1, then the sum ofall the coefficients of the polynomial is(2) -1(4) -d(3) 0

Discussion

18.	The ratio between the radius of the base and the height of a cylinder is 2 : 3. If the volume of the cylinder is 12936 cm3, then find the radius of the base of the cylinder.
Answer» The ratio between the radius of the base and the height of a cylinder is 2 : 3. If the volume of the cylinder is 12936 cm³, then find the radius of the base of the cylinder.

Discussion

19.	In the given figure, PA and PB are tangents to the circle with centre O such that ∠APB=50°. Write the measure of ∠OAB. [CBSE 2015]
Answer» In the given figure, PA and PB are tangents to the circle with centre O such that $∠ APB = 50 °$ . Write the measure of $∠ OAB .$ [CBSE 2015]

Discussion

20.	Divide 53968 by 267 and check the result by division algorithm
Answer» Divide 53968 by 267 and check the result by division algorithm

Discussion

21.	What does I bands do.
Answer» What does I bands do.

Discussion

22.	Krishna’s family has 4 members. The daily rice consumption of the 4 family members is - 0.5 kg, 0.4 kg, 0.3 kg and 0.6 kg. Krishna wants to find the average rice consumption per family member. What is the measure that will come into use now?
Answer» Krishna’s family has 4 members. The daily rice consumption of the 4 family members is - 0.5 kg, 0.4 kg, 0.3 kg and 0.6 kg. Krishna wants to find the average rice consumption per family member. What is the measure that will come into use now?

Discussion

23.	12. If (2p+1,p) is a solution of equations 2x+5y=20, then find the value of p
Answer» 12. If (2p+1,p) is a solution of equations 2x+5y=20, then find the value of p

Discussion

24.	In a rain-water harvesting system, the rain-water from a roof of 22 m × 20 m drains into a cylindrical tank having diameter of base 2 m and heigth 3.5 m. If the tank is full, find the rainfall in cm. Write your views on water conservation.
Answer» In a rain-water harvesting system, the rain-water from a roof of 22 m $\times$ 20 m drains into a cylindrical tank having diameter of base 2 m and heigth 3.5 m. If the tank is full, find the rainfall in cm. Write your views on water conservation.

Discussion

25.	the volume of 2pvol H2O2 required to get 5 litres of O2 at STPis
Answer» the volume of 2pvol H2O2 required to get 5 litres of O2 at STPis

Discussion

26.	A die and a coin are tossed simultaneously. If a head on the coin is taken to be 1 and a tail is taken to be 0, find the number of outcomes where sum of numbers on the die and the coin is greater than 4.
Answer» A die and a coin are tossed simultaneously. If a head on the coin is taken to be 1 and a tail is taken to be 0, find the number of outcomes where sum of numbers on the die and the coin is greater than 4.

Discussion

27.	ΔABC is right angled at B, given 5×sinA=3. Find cosC + tanA + cosecC.
Answer» $Δ A B C$ is right angled at B, given $5 \times s i n A = 3$ . Find cosC + tanA + cosecC.

Discussion

28.	4x3+4x2−x−1 is a multiple of
Answer» $4 x^{3} + 4 x^{2} - x - 1$ is a multiple of

Discussion

29.	A well of whose diameter is 3m is dug 14m deep. The earth taken out of it is evenly spread out in the form of a circular ring of width 4m to form an embankment. Find the height of the embankment.
Answer» A well of whose diameter is 3m is dug 14m deep. The earth taken out of it is evenly spread out in the form of a circular ring of width 4m to form an embankment. Find the height of the embankment.

29.

A well of whose diameter is 3m is dug 14m deep. The earth taken out of it is evenly spread out in the form of a circular ring of width 4m to form an embankment. Find the height of the embankment.

Answer»

A well of whose diameter is 3m is dug 14m deep. The earth taken out of it is evenly spread out in the form of a circular ring of width 4m to form an embankment. Find the height of the embankment.

Discussion

30.	A wooden toy rocket is in the shape of a cone mounted on a cylinder, as shown in Fig. The height of the entire rocket is 26 cm, while the height of the conical part is 6 cm. The base of the conical portion has a diameter of 5 cm, while the base diameter of the cylindrical portion is 3 cm. If the conical portion is to be painted orange and the cylindrical portion yellow, find the area of the rocket painted with each of these colours. (Take π=3.14) [4 MARKS]
Answer» A wooden toy rocket is in the shape of a cone mounted on a cylinder, as shown in Fig. The height of the entire rocket is 26 cm, while the height of the conical part is 6 cm. The base of the conical portion has a diameter of 5 cm, while the base diameter of the cylindrical portion is 3 cm. If the conical portion is to be painted orange and the cylindrical portion yellow, find the area of the rocket painted with each of these colours. (Take $π = 3.14$ ) [4 MARKS]

30.

A wooden toy rocket is in the shape of a cone mounted on a cylinder, as shown in Fig. The height of the entire rocket is 26 cm, while the height of the conical part is 6 cm. The base of the conical portion has a diameter of 5 cm, while the base diameter of the cylindrical portion is 3 cm. If the conical portion is to be painted orange and the cylindrical portion yellow, find the area of the rocket painted with each of these colours. (Take π=3.14) [4 MARKS]

Answer»

A wooden toy rocket is in the shape of a cone mounted on a cylinder, as shown in Fig. The height of the entire rocket is 26 cm, while the height of the conical part is 6 cm. The base of the conical portion has a diameter of 5 cm, while the base diameter of the cylindrical portion is 3 cm. If the conical portion is to be painted orange and the cylindrical portion yellow, find the area of the rocket painted with each of these colours. (Take $π = 3.14$ ) [4 MARKS]

Discussion

31.	Minimise Z=4x+2ySubject to constraints:3x+y>=27-x-y=30x,y>=0
Answer» Minimise Z=4x+2y Subject to constraints: 3x+y>=27 -x-y<=-21 x+2y>=30 x,y>=0

Discussion

32.	Find the angular elevation of the sun when the shadow of a 10 m long pole is 10√3 m.
Answer» Find the angular elevation of the sun when the shadow of a 10 m long pole is $10 \sqrt{3} m .$

Discussion

33.	In the given figure AP and BP are tangents drawn from an external point.Prove that OP⊥AB
Answer» In the given figure AP and BP are tangents drawn from an external point.Prove that $O P ⊥ A B$

Discussion

34.

R. Chetan has the following balances in his books on 1st March, 2018:Cash ₹ 15,400; Cash at Bank ₹ 82,500; Stock ₹ 1,92,500; Plant and Machinery ₹ 4,40,000.Sundry Debtors: Rajesh ₹ 27,500; James ₹ 13,750.Sundry Creditors: Rao ₹ 19,250, Samanta; ₹ 35,750; Capital ₹ 7,16,650.The following are the transactions for the month of March 2018: 2018 ₹ March 1 Cash Sales* 2,000 March 2 Purchases machinery by cheque* 5,000 March 4 Paid salaries by cheque 2,750 March 7 Paid wages in cash 440 March 9 Rajesh settled his account by cheque less 5% discount March 11 Sold goods on credit to James, Patna 10,000 March 13 Sent a credit note to James for goods returned (Including IGST reversed) 2,240 March 18 Paid Rao by cheque in full settlement 18,000 March 20 Took loan from Bank of Baroda 50,000 March 22 Withdrawn from bank for private purposes 2,500 March 25 Bought goods on credit from Samanta, Delhi** 5,000 March 27 Paid corporation tax by cheque 1,155 March 30 Cash sales (Including CGST and SGST 6% each) and paid into bank 4,480 March 31 All cash in hand, with the exception of ₹ 825 retained for change, was paid into the bank Transactions marked* are intra-state transactions subject to CGST and SGST 6% each. Transactions marked** are inter-state transactions subject to IGST 12%Record these transactions in his subsidiary books, post to the Ledger and prepare a Trail Balance as on 31st March, 2018.

Answer» R. Chetan has the following balances in his books on 1st March, 2018:

Cash ₹ 15,400; Cash at Bank ₹ 82,500; Stock ₹ 1,92,500; Plant and Machinery ₹ 4,40,000.

Sundry Debtors: Rajesh ₹ 27,500; James ₹ 13,750.

Sundry Creditors: Rao ₹ 19,250, Samanta; ₹ 35,750; Capital ₹ 7,16,650.

The following are the transactions for the month of March 2018:

2018		₹
March 1	Cash Sales*	2,000
March 2	Purchases machinery by cheque*	5,000
March 4	Paid salaries by cheque	2,750
March 7	Paid wages in cash	440
March 9	Rajesh settled his account by cheque less 5% discount
March 11	Sold goods on credit to James, Patna**	10,000
March 13	Sent a credit note to James for goods returned** (Including IGST reversed)	2,240
March 18	Paid Rao by cheque in full settlement	18,000
March 20	Took loan from Bank of Baroda	50,000
March 22	Withdrawn from bank for private purposes	2,500
March 25	Bought goods on credit from Samanta, Delhi**	5,000
March 27	Paid corporation tax by cheque	1,155
March 30	Cash sales (Including CGST and SGST 6% each) and paid into bank	4,480
March 31	All cash in hand, with the exception of ₹ 825 retained for change, was paid into the bank

Transactions marked* are intra-state transactions subject to CGST and SGST 6% each. Transactions marked** are inter-state transactions subject to IGST 12%

Record these transactions in his subsidiary books, post to the Ledger and prepare a Trail Balance as on 31st March, 2018.

Discussion

35.	From an external point P, tangents PA and PB are drawn to a circle with centre O. If CD is the tangent to the circle at a point E and PA = 14 cm, find the perimeter of Δ PCD.
Answer» From an external point P, tangents PA and PB are drawn to a circle with centre O. If CD is the tangent to the circle at a point E and PA = 14 cm, find the perimeter of Δ PCD.

Discussion

36.	Choose the correct answer in each of the following questions:The next term of the AP 7, 28, 63, ... is [CBSE 2014](a) 70 (a) 84 (a) 98 (d) 112
Answer» Choose the correct answer in each of the following questions: The next term of the AP $\sqrt{7}, \sqrt{28}, \sqrt{63}, . . .$ is [CBSE 2014] (a) $\sqrt{70}$ (a) $\sqrt{84}$ (a) $\sqrt{98}$ (d) $\sqrt{112}$

Discussion

37.	The ratio of corresponding sides of similar triangles is 3 : 5; then Find the ratio of their areas.
Answer» The ratio of corresponding sides of similar triangles is 3 : 5; then Find the ratio of their areas.

Discussion

38.	Find the area of the trapezium whose parallel sides are 12m and 20m respectively and distance between them is 10m.
Answer» Find the area of the trapezium whose parallel sides are 12m and 20m respectively and distance between them is 10m.

Discussion

39.	Question 7 (i) In the figure, altitudes AD and CE of ΔABC intersect each other at the point P. Show that (i) ΔAEP∼ΔCDP
Answer» Question 7 (i) In the figure, altitudes AD and CE of $Δ A B C$ intersect each other at the point P. Show that (i) $Δ A E P \sim Δ C D P$

Discussion

40.

Write the median class of the following distribution: Class-interval: 0−10 10−20 20−30 30−40 40−50 50−60 60−70 Frequency: 4 4 8 10 12 8 4

Answer» Write the median class of the following distribution:

Class-interval:	0−10	10−20	20−30	30−40	40−50	50−60	60−70
Frequency:	4	4	8	10	12	8	4

Discussion

41.	A line segment AB is divided in the ratio 4:9 by a point C. Find the length AC (in cm) if AB=26 cm. ___
Answer» A line segment AB is divided in the ratio 4:9 by a point C. Find the length AC (in cm) if AB=26 cm. ___

41.

A line segment AB is divided in the ratio 4:9 by a point C. Find the length AC (in cm) if AB=26 cm. ___

Answer»

A line segment AB is divided in the ratio 4:9 by a point C. Find the length AC (in cm) if AB=26 cm.

___

Discussion

42.	Find the roots of the following quadratic equations by the factorization method. 21x2−2x+121=0
Answer» Find the roots of the following quadratic equations by the factorization method. $21 x^{2} - 2 x + \frac{1}{21} = 0$

Discussion

43.	If an iron rod of length 1 unit is always moving with its ends in contact with coordinate axes and the locus of mid point of the rod is x2+y2=k then the value of 16k is
Answer» If an iron rod of length $1$ unit is always moving with its ends in contact with coordinate axes and the locus of mid point of the rod is $x^{2} + y^{2} = k$ then the value of $16 k$ is

Discussion

44.	In the given figure, BD bisects ∠ABC and BD is perpendicular to AC. Find x + y.
Answer» In the given figure, BD bisects $∠ A B C$ and BD is perpendicular to AC. Find x + y.

Discussion

45.	If a chord AB subtends an angle of 60° at the centre of a circle, then the angle between the tangents at A and B is ________.
Answer» If a chord AB subtends an angle of 60° at the centre of a circle, then the angle between the tangents at A and B is ________.

Discussion

46.	Question 30A cube of side 5 cm is cut into 1 cm cubes. The percentage increase in volume after such cutting is ___
Answer» Question 30 A cube of side 5 cm is cut into 1 cm cubes. The percentage increase in volume after such cutting is ___

46.

Question 30A cube of side 5 cm is cut into 1 cm cubes. The percentage increase in volume after such cutting is ___

Answer»

Question 30

A cube of side 5 cm is cut into 1 cm cubes. The percentage increase in volume after such cutting is ___

Discussion

47.

PA and PB are two tangents drawn from an external point P to a circle with centre C and radius 4 cm. If PA & PB are perpendicular to each other, then the length of each tangent is:

Answer»

PA and PB are two tangents drawn from an external point P to a circle with centre C and radius 4 cm. If PA & PB are perpendicular to each other, then the length of each tangent is:

Discussion

48.	A circular park of radius 20 m is situated in a colony. Three boys Ankur, Syed and David are sitting at equal distance on its boundary each having a toy telephone in his hands to talk each other. Find the length of the string of each phone.
Answer» A circular park of radius 20 m is situated in a colony. Three boys Ankur, Syed and David are sitting at equal distance on its boundary each having a toy telephone in his hands to talk each other. Find the length of the string of each phone.

Discussion

49.	Let f : R --43 →R be a function defined as f(x) =4x3x+4 . Show that f : R --43 → Rang (f) is one-one and onto. Hence, find f -1.
Answer» Let f : R $- \{- \frac{4}{3}\} \to$ R be a function defined as f $(x)$ $= \frac{4 x}{3 x + 4}$ . Show that f : R $- \{- \frac{4}{3}\} \to$ Rang (f) is one-one and onto. Hence, find f ^{$-$ 1}.

Discussion

50.	Mark the correct alternative in each of the following:The probability of getting an even number, when a die is thrown once is(a) 12 (b) 13 (c) 16 (d) 56 [CBSE 2013]
Answer» Mark the correct alternative in each of the following: The probability of getting an even number, when a die is thrown once is (a) $\frac{1}{2}$ (b) $\frac{1}{3}$ (c) $\frac{1}{6}$ (d) $\frac{5}{6}$ [CBSE 2013]

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

The power of P(1,2) with respect to the circle x2+y2+4x+2y+3 = 0 is double the power of P with respect to x2+y2+2x+y+k = 0 then the value of k is

6.solve : |x+1|+|x-4 |

The sum of a number and its square is 634, find the numbers.

Grouped frequency distribution of supply of milk to hotels and the number of hotels is given in the following table. Find the mode of the supply of milk. Milk (Litre) 1 - 3 3 - 5 5 - 7 7 - 9 9 - 11 11 - 13 No. of hotels 7 5 15 20 35 18

Question 1 Which one of the following options is true, and why?y=3x+5 has(i) a unique solution(ii) only two solutions(iii) infinitely many solutions

find HCF and LCM of 404 and 96 and verify that HCF into LCM is equal to product of the two given numbers.

If cos θ=1213, show that sin θ (1 − tan θ)=35156.

An aeroplane is flying at a height of 300 m above the gound. Flying at this height the angles of depression from the aeroplane of two points on both banks of a river in opposite directions are 45∘ and 60∘ respectively. Find the width of the river. [Use~√3=1.732.]

Find the slope of a line passing through the following points:(i) (5, 6) and (2, 3)(ii) (9, -2) and (6, -5)

36 has _________ number of prime factors.

The surface area of a box which is in the form of a cuboid whose dimensions arel x b x h is:

There are two temples, one on each bank of a river, just opposite to each other. One temple is 50 m high. From the top of this temple, the angles of depression of the top and the foot of the other temple are 30° and 60° respectively. Find the width of the river and the height of the other temple.

Find the roots of each of the following equations, if they exist, by applying the quadratic formula:mnx2+nm=1-2x

An aero-plane takes 1 hr less for a journey of 1200 km. If its speed is increased by 60 km/hr from the initial speed. Find the initial speed of the plane.

In a lottery, there are 8 prizes and 16 blanks. What is the probability of getting a prize? (a) 12 (b) 13 (c) 23 (d) None of these

If one of the zeroes of bi-quadratic polynomial fx)x4 ax3 bx2 + cx + d is 1, then the sum ofall the coefficients of the polynomial is(2) -1(4) -d(3) 0

The ratio between the radius of the base and the height of a cylinder is 2 : 3. If the volume of the cylinder is 12936 cm3, then find the radius of the base of the cylinder.

In the given figure, PA and PB are tangents to the circle with centre O such that ∠APB=50°. Write the measure of ∠OAB. [CBSE 2015]

Divide 53968 by 267 and check the result by division algorithm

What does I bands do.

Krishna’s family has 4 members. The daily rice consumption of the 4 family members is - 0.5 kg, 0.4 kg, 0.3 kg and 0.6 kg. Krishna wants to find the average rice consumption per family member. What is the measure that will come into use now?

12. If (2p+1,p) is a solution of equations 2x+5y=20, then find the value of p

In a rain-water harvesting system, the rain-water from a roof of 22 m × 20 m drains into a cylindrical tank having diameter of base 2 m and heigth 3.5 m. If the tank is full, find the rainfall in cm. Write your views on water conservation.

the volume of 2pvol H2O2 required to get 5 litres of O2 at STPis

A die and a coin are tossed simultaneously. If a head on the coin is taken to be 1 and a tail is taken to be 0, find the number of outcomes where sum of numbers on the die and the coin is greater than 4.

ΔABC is right angled at B, given 5×sinA=3. Find cosC + tanA + cosecC.

4x3+4x2−x−1 is a multiple of

A well of whose diameter is 3m is dug 14m deep. The earth taken out of it is evenly spread out in the form of a circular ring of width 4m to form an embankment. Find the height of the embankment.

Minimise Z=4x+2ySubject to constraints:3x+y>=27-x-y=30x,y>=0

Find the angular elevation of the sun when the shadow of a 10 m long pole is 10√3 m.

In the given figure AP and BP are tangents drawn from an external point.Prove that OP⊥AB

From an external point P, tangents PA and PB are drawn to a circle with centre O. If CD is the tangent to the circle at a point E and PA = 14 cm, find the perimeter of Δ PCD.

Choose the correct answer in each of the following questions:The next term of the AP 7, 28, 63, ... is [CBSE 2014](a) 70 (a) 84 (a) 98 (d) 112

The ratio of corresponding sides of similar triangles is 3 : 5; then Find the ratio of their areas.

Find the area of the trapezium whose parallel sides are 12m and 20m respectively and distance between them is 10m.

Question 7 (i) In the figure, altitudes AD and CE of ΔABC intersect each other at the point P. Show that (i) ΔAEP∼ΔCDP

Write the median class of the following distribution: Class-interval: 0−10 10−20 20−30 30−40 40−50 50−60 60−70 Frequency: 4 4 8 10 12 8 4

A line segment AB is divided in the ratio 4:9 by a point C. Find the length AC (in cm) if AB=26 cm. ___

Find the roots of the following quadratic equations by the factorization method. 21x2−2x+121=0

If an iron rod of length 1 unit is always moving with its ends in contact with coordinate axes and the locus of mid point of the rod is x2+y2=k then the value of 16k is ​​​​​​​

In the given figure, BD bisects ∠ABC and BD is perpendicular to AC. Find x + y.

If a chord AB subtends an angle of 60° at the centre of a circle, then the angle between the tangents at A and B is ________.

Question 30A cube of side 5 cm is cut into 1 cm cubes. The percentage increase in volume after such cutting is ___

PA and PB are two tangents drawn from an external point P to a circle with centre C and radius 4 cm. If PA &amp; PB are perpendicular to each other, then the length of each tangent is:

A circular park of radius 20 m is situated in a colony. Three boys Ankur, Syed and David are sitting at equal distance on its boundary each having a toy telephone in his hands to talk each other. Find the length of the string of each phone.

Let f : R --43 →R be a function defined as f(x) =4x3x+4 . Show that f : R --43 → Rang (f) is one-one and onto. Hence, find f -1.

Mark the correct alternative in each of the following:The probability of getting an even number, when a die is thrown once is(a) 12 (b) 13 (c) 16 (d) 56 [CBSE 2013]

If an iron rod of length 1 unit is always moving with its ends in contact with coordinate axes and the locus of mid point of the rod is x2+y2=k then the value of 16k is

PA and PB are two tangents drawn from an external point P to a circle with centre C and radius 4 cm. If PA & PB are perpendicular to each other, then the length of each tangent is: