32581 + Interview Questions in Mathematics Page 51 InterviewSolution

2501.	(i) Given that HCF (306, 657) = 9, find LCM (306, 657).(ii) Write the smallest number which is divisible by both 306 and 657.
Answer» (i) Given that HCF (306, 657) = 9, find LCM (306, 657). (ii) Write the smallest number which is divisible by both 306 and 657.

Discussion

2502.	Question 12 The points A(-1, -2), B(4,3), C(2,5) and D(-3,0) in that order form a rectangle.
Answer» Question 12 The points A(-1, -2), B(4,3), C(2,5) and D(-3,0) in that order form a rectangle.

Discussion

2503.	Which formula generates the sequence represented by the graph below?
Answer» Which formula generates the sequence represented by the graph below?

2503.

Which formula generates the sequence represented by the graph below?

Answer»

Which formula generates the sequence represented by the graph below?

Discussion

2504.	AN ELECTRONIC DEVICE MAKES A BEEP AFTER EVERY 60 SECOND ANOTHER DEVICE MAKES A BEEP AFTER EVERY 62 SECOND .THEY BEEPED YOGETHER AT 10 AM AT WHAT TIME THEY WILL BEEP TOGETHER AT EARLIEST
Answer» AN ELECTRONIC DEVICE MAKES A BEEP AFTER EVERY 60 SECOND ANOTHER DEVICE MAKES A BEEP AFTER EVERY 62 SECOND .THEY BEEPED YOGETHER AT 10 AM AT WHAT TIME THEY WILL BEEP TOGETHER AT EARLIEST

Discussion

2505.	If a and b are different positive primes such that(i) a-1b2a2b-47÷a3b-5a-2b3=axby, find x and y.(ii) a+b-1a-1+b-1=axby, find x + y + 2.
Answer» If a and b are different positive primes such that (i) ${(\frac{a^{- 1} b^{2}}{a^{2} b^{- 4}})}^{7} \div (\frac{a^{3} b^{- 5}}{a^{- 2} b^{3}}) = a^{x} b^{y}$ , find x and y. (ii) ${(a + b)}^{- 1} (a^{- 1} + b^{- 1}) = a^{x} b^{y}$ , find x + y + 2.

Discussion

2506.	The angles of elevation of the top of a tower from two points at a distance of 4 m and 9 m from the base of the tower and in the same straight line with it are complementary. The height of the tower is ____m. ___
Answer» The angles of elevation of the top of a tower from two points at a distance of 4 m and 9 m from the base of the tower and in the same straight line with it are complementary. The height of the tower is ____m. ___

Discussion

2507.	A rod bent into an angle is placed with its vertexr at the centre of a circle and it is found that 110 of the circle lies within it. If it is placed with its vertex on the circumference, what part of the circle would be within it ?
Answer» A rod bent into an angle is placed with its vertexr at the centre of a circle and it is found that $\frac{1}{10}$ of the circle lies within it. If it is placed with its vertex on the circumference, what part of the circle would be within it ?

2507.

A rod bent into an angle is placed with its vertexr at the centre of a circle and it is found that 110 of the circle lies within it. If it is placed with its vertex on the circumference, what part of the circle would be within it ?

Answer»

A rod bent into an angle is placed with its vertexr at the centre of a circle and it is found that $\frac{1}{10}$ of the circle lies within it. If it is placed with its vertex on the circumference, what part of the circle would be within it ?

Discussion

2508.	Find all zeros of the polynomial 2x4 – 9x3 + 5x2 +3x – 1, if two of its zeros are 2+3 and 2-3.
Answer» Find all zeros of the polynomial 2x⁴ – 9x³ + 5x² +3x – 1, if two of its zeros are $2 + \sqrt{3} and 2 - \sqrt{3}$ .

Discussion

2509.	Find the area of the shaded region in the given figure, if ABCD is a rectangle with sides 8 cm and 6 cm and O is the centre of the circle. [CBSE 2014]
Answer» Find the area of the shaded region in the given figure, if ABCD is a rectangle with sides 8 cm and 6 cm and O is the centre of the circle. [CBSE 2014]

Discussion

2510.	The expression x4+8x2+16 can be factorised as
Answer» The expression $x^{4} + 8 x^{2} + 16$ can be factorised as

Discussion

2511.	If three matrices A, B and C follows Right Distributive Property, then their orders respectively can be:
Answer» If three matrices A, B and C follows Right Distributive Property, then their orders respectively can be:

Discussion

2512.	Question 45Sate weather the given statement is true or false.When the distance is kept fixed, speed and time vary directly with each other.
Answer» Question 45 Sate weather the given statement is true or false. When the distance is kept fixed, speed and time vary directly with each other.

2512.

Question 45Sate weather the given statement is true or false.When the distance is kept fixed, speed and time vary directly with each other.

Answer»

Question 45

Sate weather the given statement is true or false.

When the distance is kept fixed, speed and time vary directly with each other.

Discussion

2513.	Two numbers have 12 as their HCF and 350 as their LCM (True/False).
Answer» Two numbers have 12 as their HCF and 350 as their LCM (True/False).

Discussion

2514.	The angles of depression of the top and bottom of a tower as seen from the top of a 603-m-high cliff are 45° and 60°, respectively. Find the height of the tower. [CBSE 2012]
Answer» The angles of depression of the top and bottom of a tower as seen from the top of a 60 $\sqrt{3}$ -m-high cliff are 45° and 60°, respectively. Find the height of the tower. [CBSE 2012]

Discussion

2515.	A cylindrical tub of radius 12 cm contains water to a depth of 20 cm. A spherical ball dropped into the tub and the level of the water is raised by 6.75 cm. Find the radius of the ball.
Answer» A cylindrical tub of radius 12 cm contains water to a depth of 20 cm. A spherical ball dropped into the tub and the level of the water is raised by 6.75 cm. Find the radius of the ball.

Discussion

2516.	If 6 couples wanted to travel in 2 different vans having 6 seats each, 3 in front and 3 in back, then the number of ways in which the female sits exactly behind her male patner (arrangement inside the van matters) is
Answer» If $6$ couples wanted to travel in $2$ different vans having $6$ seats each, $3$ in front and $3$ in back, then the number of ways in which the female sits exactly behind her male patner (arrangement inside the van matters) is

Discussion

2517.	Which term of the A.P: 24, 21, 18, 15, ..... is the first negative term?
Answer» Which term of the A.P: 24, 21, 18, 15, ..... is the first negative term?

Discussion

2518.	The perimeter of a rectangular field is 82 m and its area is 400 m2. Find the breadth of the rectangle.
Answer» The perimeter of a rectangular field is 82 m and its area is 400 m². Find the breadth of the rectangle.

Discussion

2519.	In a ∆ABC, ∠B = 90° and tanA = 13. Prove that(i) sinA·cosC + cosA·sinC = 1 (ii) cosA·cosC - sinA·sinC = 0
Answer» In a $∆$ ABC, $∠$ B = 90 $°$ and tanA = $\frac{1}{\sqrt{3}}$ . Prove that (i) sinA $\cdot$ cosC + cosA $\cdot$ sinC = 1 (ii) cosA $\cdot$ cosC $-$ sinA $\cdot$ sinC = 0

Discussion

2520.	A man walks 8 km due North, then 5 km to East and 4 km to North. How far is he from the starting point?
Answer» A man walks 8 km due North, then 5 km to East and 4 km to North. How far is he from the starting point?

Discussion

2521.	Question 1(ii)Find the roots of the following quadratic equations by factorisation:(ii) 2x2+x–6=0
Answer» Question 1(ii) Find the roots of the following quadratic equations by factorisation: (ii) $2 x^{2} + x - 6 = 0$

Discussion

2522.	Explain Euclids division lemma
Answer» Explain Euclids division lemma

Discussion

2523.	If square root of the matrix A=[2000] is in the form of [a00b], then number of possible matrices is
Answer» If square root of the matrix $A = [\begin{matrix} 2 & 0 0 & 0 \end{matrix}]$ is in the form of $[\begin{matrix} a & 0 0 & b \end{matrix}],$ then number of possible matrices is

Discussion

2524.	24. Prove that the point (-1/14,39/14) is the centre of the circle circumscribing the triangle whose angular points are (1,1),(2,3)&(-2,2).
Answer» 24. Prove that the point (-1/14,39/14) is the centre of the circle circumscribing the triangle whose angular points are (1,1),(2,3)&(-2,2).

Discussion

2525.	10. the value of polynomial p(x)=xcube+7xsquare+16x+7 at x=1÷whole root 9+4root 5
Answer» 10. the value of polynomial p(x)=xcube+7xsquare+16x+7 at x=1÷whole root 9+4root 5

Discussion

2526.

Enter the following transactions in a Two Column Cash Book:- 2016 ₹ Dec. 1 Started business with cash 50,000 2 Pays into Bank 29,000 3 Received cheque from Raja & Co. 800 Discount allowed 20 5 Withdrew cash from bank for private use 240 10 Purchased goods for ₹ 1,00,000; IGST 18%; Payment made by Cheque 12 Sold goods for ₹ 1,50,000; Trade Discount 20%; IGST 18%; Payment received by Cheque 14 Received cheque from Kamla 395 Discount allowed 15 16 Kamla's cheque endorsed to Bala in full settlement of her account of ₹ 425 29 Paid rent by cheque 1,000 30 Deposited into bank, balance of cash in excess of 450

Answer» Enter the following transactions in a Two Column Cash Book:-

2016		₹
Dec. 1	Started business with cash	50,000
2	Pays into Bank	29,000
3	Received cheque from Raja & Co.	800
	Discount allowed	20
5	Withdrew cash from bank for private use	240
10	Purchased goods for ₹ 1,00,000; IGST 18%; Payment made by Cheque
12	Sold goods for ₹ 1,50,000; Trade Discount 20%; IGST 18%; Payment received by Cheque
14	Received cheque from Kamla	395
	Discount allowed	15
16	Kamla's cheque endorsed to Bala in full settlement of her account of ₹ 425
29	Paid rent by cheque	1,000
30	Deposited into bank, balance of cash in excess of	450

Discussion

2527.	The train was moving with uniform speed after covering a distance of 30km some defect develop with the engine of the train and for this reason its speed reduced to 4 by 5 of its original speed. The train reaches is destination late by 45 minutes in case the defects had happened after covering 18 km more the train would have reached just 36 minute late find the speed of the train at the start and the distance of Germany
Answer» The train was moving with uniform speed after covering a distance of 30km some defect develop with the engine of the train and for this reason its speed reduced to 4 by 5 of its original speed. The train reaches is destination late by 45 minutes in case the defects had happened after covering 18 km more the train would have reached just 36 minute late find the speed of the train at the start and the distance of Germany

Discussion

2528.	In Fig. 1, the value of the median of the data using the graph of less than ogive and more than ogive is(a) 5(b) 40(c) 80(d) 15
Answer» In Fig. 1, the value of the median of the data using the graph of less than ogive and more than ogive is (a) 5 (b) 40 (c) 80 (d) 15

Discussion

2529.	Question 9 (i)A right circular cylinder just encloses a sphere of radius 'r' (see figure). Find:(i) the surface area of the sphere,
Answer» Question 9 (i) A right circular cylinder just encloses a sphere of radius 'r' (see figure). Find: (i) the surface area of the sphere,

2529.

Question 9 (i)A right circular cylinder just encloses a sphere of radius 'r' (see figure). Find:(i) the surface area of the sphere,

Answer»

Question 9 (i)

A right circular cylinder just encloses a sphere of radius 'r' (see figure). Find:

(i) the surface area of the sphere,

Discussion

2530.	In the given figure, AB∥DC, BO = 6 cm and DO = 8 cm. Find BP×DO.
Answer» In the given figure, $A B ∥ D C$ , BO = 6 cm and DO = 8 cm. Find $B P \times D O$ .

2530.

In the given figure, AB∥DC, BO = 6 cm and DO = 8 cm. Find BP×DO.

Answer»

In the given figure, $A B ∥ D C$ , BO = 6 cm and DO = 8 cm. Find $B P \times D O$ .

Discussion

2531.

Ashu and Harish are partners sharing profit and losses as 3 : 2 . They decided to dissolve the firm on 31st March, 2019. Their Balance Sheet on the above date was: Liabilities Amount (₹) Assets Amount (₹) Capital A/cs: Building 80,000 Ashu 1,08,000 Machinery 70,000 Harish 54,000 1,62,000 Furniture 14,000 Creditors 88,000 Stock 20,000 Bank Overdraft 50,000 Investments 60,000 Debtors 48,000 Cash in Hand 8,000 3,00,000 3,00,000 Ashu is to take over the building at ₹ 95,000 and Machinery and Furniture is taken over by Harish at value of ₹ 80,000. Ashu agreed to pay Creditor and Harish agreed to meet Bank overdraft. Stock and Investments are taken by both partner in profit-sharing ratio. Debtors realised for ₹ 46,000, expenses of realisation amounted to ₹ 3,000. Prepare necessary Ledger Accounts.

Answer» Ashu and Harish are partners sharing profit and losses as 3 : 2 . They decided to dissolve the firm on 31st March, 2019. Their Balance Sheet on the above date was:


Liabilities		Amount (₹)	Assets	Amount (₹)
Capital A/cs:			Building	80,000
Ashu	1,08,000		Machinery	70,000
Harish	54,000	1,62,000	Furniture	14,000
Creditors		88,000	Stock	20,000
Bank Overdraft		50,000	Investments	60,000
			Debtors	48,000
			Cash in Hand	8,000

		3,00,000		3,00,000

Ashu is to take over the building at ₹ 95,000 and Machinery and Furniture is taken over by Harish at value of ₹ 80,000. Ashu agreed to pay Creditor and Harish agreed to meet Bank overdraft. Stock and Investments are taken by both partner in profit-sharing ratio. Debtors realised for ₹ 46,000, expenses of realisation amounted to ₹ 3,000. Prepare necessary Ledger Accounts.

Discussion

2532.	Prove the following trigonometric identities.(i) cot θ-tan θ=2 cos2 θ-1sin θ cos θ(ii) tan θ-cot θ=2 sin2 θ-1sin θ cos θ
Answer» Prove the following trigonometric identities. (i) $\cot θ - \tan θ = \frac{2 \cos^{2} θ - 1}{\sin θ \cos θ}$ (ii) $\tan θ - \cot θ = \frac{2 \sin^{2} θ - 1}{\sin θ \cos θ}$

Discussion

2533.	If m+1th term of an ap is twice the n+1 the term then prove that 3m+1 is twice the m+ n+1 the term
Answer» If m+1th term of an ap is twice the n+1 the term then prove that 3m+1 is twice the m+ n+1 the term

Discussion

2534.	Find the value of a and b . 2x+3y=7 and 2ax+ay=28-by
Answer» Find the value of a and b . 2x+3y=7 and 2ax+ay=28-by

Discussion

2535.	Which of these points lie on the line 7x+8y=61?
Answer» Which of these points lie on the line $7 x + 8 y = 61$ ?

Discussion

2536.	In the given figure, O is the centre of the circle and AB is a tangent to it at point B. If CD and OA intersect at E on the circle and ∠BDC=65∘, then find the measure of ∠BAO.
Answer» In the given figure, O is the centre of the circle and AB is a tangent to it at point B. If CD and OA intersect at E on the circle and $∠ B D C = 65^{\circ}$ , then find the measure of $∠ B A O$ .

Discussion

2537.	Solve and find value of y.3x2−5y3=−2 ; x2+y2=136
Answer» Solve and find value of y. $\frac{3 x}{2} - \frac{5 y}{3} = - 2$ ; $\frac{x}{2} + \frac{y}{2} = \frac{13}{6}$

2537.

Solve and find value of y.3x2−5y3=−2 ; x2+y2=136

Answer»

Solve and find value of y.

$\frac{3 x}{2} - \frac{5 y}{3} = - 2$ ; $\frac{x}{2} + \frac{y}{2} = \frac{13}{6}$

Discussion

2538.	In the given figure, O is the point inside a △MNP such that ∠MOP = 900 , OM = 16 cm and OP = 12 cm. If MN = 21 cm and ∠NMP = 900 thenNP = ?(a) 25 cm(b) 29 cm(c) 33 cm(d) 35 cm
Answer» In the given figure, O is the point inside a △MNP such that ∠MOP = 90⁰ , OM = 16 cm and OP = 12 cm. If MN = 21 cm and ∠NMP = 90⁰ then NP = ? (a) 25 cm (b) 29 cm (c) 33 cm (d) 35 cm

Discussion

2539.	Question 82 Solve the following: Anushka and Arushi are friends. They have equal amount of money in their pockets. Anushka gave 13 of her money to Arushi as her birthday gift. Then, Arushi gave a party at a restaurant and cleared the bill by paying half of the total money with her. If the remaining money in Arushi's pocket is Rs. 1600, then find the sum gifted by anushka.
Answer» Question 82 Solve the following: Anushka and Arushi are friends. They have equal amount of money in their pockets. Anushka gave $\frac{1}{3}$ of her money to Arushi as her birthday gift. Then, Arushi gave a party at a restaurant and cleared the bill by paying half of the total money with her. If the remaining money in Arushi's pocket is Rs. 1600, then find the sum gifted by anushka.

2539.

Question 82 Solve the following: Anushka and Arushi are friends. They have equal amount of money in their pockets. Anushka gave 13 of her money to Arushi as her birthday gift. Then, Arushi gave a party at a restaurant and cleared the bill by paying half of the total money with her. If the remaining money in Arushi's pocket is Rs. 1600, then find the sum gifted by anushka.

Answer»

Question 82

Solve the following:

Anushka and Arushi are friends. They have equal amount of money in their pockets. Anushka gave $\frac{1}{3}$ of her money to Arushi as her birthday gift. Then, Arushi gave a party at a restaurant and cleared the bill by paying half of the total money with her. If the remaining money in Arushi's pocket is Rs. 1600, then find the sum gifted by anushka.

Discussion

2540.	A die is thrown once. Find the probability of getting a number less than 3.
Answer» A die is thrown once. Find the probability of getting a number less than 3.

Discussion

2541.

Calculate the median from the following data: Marks below: 10 20 30 40 50 60 70 80 No. of students: 15 35 60 84 96 127 198 250

Answer» Calculate the median from the following data:

Marks below:	10	20	30	40	50	60	70	80
No. of students:	15	35	60	84	96	127	198	250

Discussion

2542.	In a competitive examination , one mark is awarded for each correct answer while 1/2 mark is deducted for everey wrong answer . Jayanti answered 120 questions and got 90 marks. How many questions did she answer correctly.
Answer» In a competitive examination , one mark is awarded for each correct answer while 1/2 mark is deducted for everey wrong answer . Jayanti answered 120 questions and got 90 marks. How many questions did she answer correctly.

Discussion

2543.	How much should a man invest in Rs 100 shares selling at Rs 110 to obtain an annual income of Rs 1,680, if the dividend declared is 12%?
Answer» How much should a man invest in Rs 100 shares selling at Rs 110 to obtain an annual income of Rs 1,680, if the dividend declared is 12%?

Discussion

2544.	Assuming that the two triangles ABC and PQR are similar, find the value of QR if AB = 10 cm, PQ = 5 cm, and BC = 8 cm.
Answer» Assuming that the two triangles ABC and PQR are similar, find the value of QR if AB = 10 cm, PQ = 5 cm, and BC = 8 cm.

Discussion

2545.	Question 15In the given figure, ∠BAC=90∘ and AD ⊥ BC. The number of right-angled triangles in the figure is a) 1b) 2c) 3d) 4
Answer» Question 15 In the given figure, $∠ B A C$ = $90^{\circ}$ and AD $⊥$ BC. The number of right-angled triangles in the figure is a) 1 b) 2 c) 3 d) 4

2545.

Question 15In the given figure, ∠BAC=90∘ and AD ⊥ BC. The number of right-angled triangles in the figure is a) 1b) 2c) 3d) 4

Answer»

Question 15

In the given figure, $∠ B A C$ = $90^{\circ}$ and AD $⊥$ BC.

The number of right-angled triangles in the figure is

a) 1

b) 2

c) 3

d) 4

Discussion

2546.	Question 10.I toss three coins together. The possible outcomes are no heads, 1 head, 2 head and 3 heads. So, I say that probability of no heads is 14. What is wrong with this conclusion ?
Answer» Question 10. I toss three coins together. The possible outcomes are no heads, 1 head, 2 head and 3 heads. So, I say that probability of no heads is $\frac{1}{4}$ . What is wrong with this conclusion ?

Discussion

2547.	Water flows at the rate of 10 m/minute through a cylindrical pipe 5 mm in diameter. How long would it take to fill a conical vessel whose diameter at the base is 40 cm and depth 24 cm?
Answer» Water flows at the rate of $10 m / m i n u t e$ through a cylindrical pipe $5 m m$ in diameter. How long would it take to fill a conical vessel whose diameter at the base is $40 c m$ and depth $24 c m$ ?

Discussion

2548.	Find 8 (mod 4).
Answer» Find 8 (mod 4).

Discussion

2549.	AB is the diameter and AC is a chord of a circle with centre O such that angle BAC=30o. The tangent to the circle at C intersects AB produced in D. Then,
Answer» AB is the diameter and AC is a chord of a circle with centre O such that angle $B A C = 30^{o}$ . The tangent to the circle at C intersects AB produced in D. Then,

Discussion

2550.	A solid consisting of a right circular cone standing on a hemisphere, is placed upright in a right circular cylinder, full of water and touches the bottom. Find the volume of water left in the cylinder having given that the radius of the cylinder is 3 cm and its height is 6 cm. The radius of hemisphere is 2 cm and the height of the cone is 4 cm. ( Also draw the diagram)
Answer» A solid consisting of a right circular cone standing on a hemisphere, is placed upright in a right circular cylinder, full of water and touches the bottom. Find the volume of water left in the cylinder having given that the radius of the cylinder is 3 cm and its height is 6 cm. The radius of hemisphere is 2 cm and the height of the cone is 4 cm. ( Also draw the diagram)

Discussion

Explore topic-wise InterviewSolutions in .

(i) Given that HCF (306, 657) = 9, find LCM (306, 657).(ii) Write the smallest number which is divisible by both 306 and 657.

Question 12 The points A(-1, -2), B(4,3), C(2,5) and D(-3,0) in that order form a rectangle.

Which formula generates the sequence represented by the graph below?

AN ELECTRONIC DEVICE MAKES A BEEP AFTER EVERY 60 SECOND ANOTHER DEVICE MAKES A BEEP AFTER EVERY 62 SECOND .THEY BEEPED YOGETHER AT 10 AM AT WHAT TIME THEY WILL BEEP TOGETHER AT EARLIEST

If a and b are different positive primes such that(i) a-1b2a2b-47÷a3b-5a-2b3=axby, find x and y.(ii) a+b-1a-1+b-1=axby, find x + y + 2.

The angles of elevation of the top of a tower from two points at a distance of 4 m and 9 m from the base of the tower and in the same straight line with it are complementary. The height of the tower is ____m. ___

A rod bent into an angle is placed with its vertexr at the centre of a circle and it is found that 110 of the circle lies within it. If it is placed with its vertex on the circumference, what part of the circle would be within it ?

Find all zeros of the polynomial 2x4 – 9x3 + 5x2 +3x – 1, if two of its zeros are 2+3 and 2-3.

Find the area of the shaded region in the given figure, if ABCD is a rectangle with sides 8 cm and 6 cm and O is the centre of the circle. [CBSE 2014]

The expression x4+8x2+16 can be factorised as

If three matrices A, B and C follows Right Distributive Property, then their orders respectively can be:

Question 45Sate weather the given statement is true or false.When the distance is kept fixed, speed and time vary directly with each other.

Two numbers have 12 as their HCF and 350 as their LCM (True/False).

The angles of depression of the top and bottom of a tower as seen from the top of a 603-m-high cliff are 45° and 60°, respectively. Find the height of the tower. [CBSE 2012]

A cylindrical tub of radius 12 cm contains water to a depth of 20 cm. A spherical ball dropped into the tub and the level of the water is raised by 6.75 cm. Find the radius of the ball.

If 6 couples wanted to travel in 2 different vans having 6 seats each, 3 in front and 3 in back, then the number of ways in which the female sits exactly behind her male patner (arrangement inside the van matters) is

Which term of the A.P: 24, 21, 18, 15, ..... is the first negative term?

The perimeter of a rectangular field is 82 m and its area is 400 m2. Find the breadth of the rectangle.

In a ∆ABC, ∠B = 90° and tanA = 13. Prove that(i) sinA·cosC + cosA·sinC = 1 (ii) cosA·cosC - sinA·sinC = 0

A man walks 8 km due North, then 5 km to East and 4 km to North. How far is he from the starting point?

Question 1(ii)Find the roots of the following quadratic equations by factorisation:(ii) 2x2+x–6=0

Explain Euclids division lemma

If square root of the matrix A=[2000] is in the form of [a00b], then number of possible matrices is

24. Prove that the point (-1/14,39/14) is the centre of the circle circumscribing the triangle whose angular points are (1,1),(2,3)&(-2,2).

10. the value of polynomial p(x)=xcube+7xsquare+16x+7 at x=1÷whole root 9+4root 5

In Fig. 1, the value of the median of the data using the graph of less than ogive and more than ogive is(a) 5(b) 40(c) 80(d) 15

Question 9 (i)A right circular cylinder just encloses a sphere of radius 'r' (see figure). Find:(i) the surface area of the sphere,

In the given figure, AB∥DC, BO = 6 cm and DO = 8 cm. Find BP×DO.

Prove the following trigonometric identities.(i) cot θ-tan θ=2 cos2 θ-1sin θ cos θ(ii) tan θ-cot θ=2 sin2 θ-1sin θ cos θ

If m+1th term of an ap is twice the n+1 the term then prove that 3m+1 is twice the m+ n+1 the term

Find the value of a and b . 2x+3y=7 and 2ax+ay=28-by

Which of these points lie on the line 7x+8y=61?

In the given figure, O is the centre of the circle and AB is a tangent to it at point B. If CD and OA intersect at E on the circle and ∠BDC=65∘, then find the measure of ∠BAO.

Solve and find value of y.3x2−5y3=−2 ; x2+y2=136

In the given figure, O is the point inside a △MNP such that ∠MOP = 900 , OM = 16 cm and OP = 12 cm. If MN = 21 cm and ∠NMP = 900 thenNP = ?(a) 25 cm(b) 29 cm(c) 33 cm(d) 35 cm

A die is thrown once. Find the probability of getting a number less than 3.

Calculate the median from the following data: Marks below: 10 20 30 40 50 60 70 80 No. of students: 15 35 60 84 96 127 198 250

In a competitive examination , one mark is awarded for each correct answer while 1/2 mark is deducted for everey wrong answer . Jayanti answered 120 questions and got 90 marks. How many questions did she answer correctly.

How much should a man invest in Rs 100 shares selling at Rs 110 to obtain an annual income of Rs 1,680, if the dividend declared is 12%?

Assuming that the two triangles ABC and PQR are similar, find the value of QR if AB = 10 cm, PQ = 5 cm, and BC = 8 cm.

Question 15In the given figure, ∠BAC=90∘ and AD ⊥ BC. The number of right-angled triangles in the figure is a) 1b) 2c) 3d) 4

Question 10.I toss three coins together. The possible outcomes are no heads, 1 head, 2 head and 3 heads. So, I say that probability of no heads is 14. What is wrong with this conclusion ?

Water flows at the rate of 10 m/minute through a cylindrical pipe 5 mm in diameter. How long would it take to fill a conical vessel whose diameter at the base is 40 cm and depth 24 cm?

Find 8 (mod 4).

AB is the diameter and AC is a chord of a circle with centre O such that angle BAC=30o. The tangent to the circle at C intersects AB produced in D. Then,

The angles of elevation of the top of a tower from two points at a distance of 4 m and 9 m from the base of the tower and in the same straight line with it are complementary. The height of the tower is __m. _