32581 + Interview Questions in Mathematics Page 17 InterviewSolution

801.	(i) What is the Range for Probability of any event?(ii) What is impossible event?
Answer» (i) What is the Range for Probability of any event? (ii) What is impossible event?

Discussion

802.	Find the inverse of each of the following matrices by using elementary row transformations:2-3532-411-2
Answer» Find the inverse of each of the following matrices by using elementary row transformations: $[\begin{matrix} 2 & - 3 & 5 \\ 3 & 2 & - 4 \\ 1 & 1 & - 2 \end{matrix}]$

Discussion

803.	10. Find the equation of the line passing through (2,3) and parallel to the line joining the points (2,-2) and (6,4).
Answer» 10. Find the equation of the line passing through (2,3) and parallel to the line joining the points (2,-2) and (6,4).

Discussion

804.	11. If sec theta cos alpha=root 2 and tan theta cot alpha=root 3, then find the values of tan theta and tan alpha that satisfy the equations.
Answer» 11. If sec theta cos alpha=root 2 and tan theta cot alpha=root 3, then find the values of tan theta and tan alpha that satisfy the equations.

Discussion

805.	{104 . The circle }x^2+y^2-4x-4y+4=0 is inscribed in a triangle which has two of its sides }} along the coordinate axes. The locus of the circumcentre of the triangle is }{x+y-xy+k(x^2+y^2)^{1/2}=0. Then }k=}{ 2) }1
Answer» {104 . The circle }x^2+y^2-4x-4y+4=0 is inscribed in a triangle which has two of its sides }} along the coordinate axes. The locus of the circumcentre of the triangle is }{x+y-xy+k(x^2+y^2)^{1/2}=0. Then }k=}{ 2) }1

Discussion

806.	32. A semi-circular sheet of metal diameter 28cm is bent to form an open conical cup. Find the capacity of cup.
Answer» 32. A semi-circular sheet of metal diameter 28cm is bent to form an open conical cup. Find the capacity of cup.

Discussion

807.	In the given figure, ABC is a triangle and PQ is a straight line meeting AB in P and AC in Q. If AP = 1 cm, PB = 3 cm, AQ = 1.5 cm, QC = 4.5 cm, prove that area of ΔAPQ is 116 of the area of ΔABC.
Answer» In the given figure, ABC is a triangle and PQ is a straight line meeting AB in P and AC in Q. If AP = 1 cm, PB = 3 cm, AQ = 1.5 cm, QC = 4.5 cm, prove that area of $Δ A P Q$ is $\frac{1}{16}$ of the area of $Δ A B C$ .

807.

In the given figure, ABC is a triangle and PQ is a straight line meeting AB in P and AC in Q. If AP = 1 cm, PB = 3 cm, AQ = 1.5 cm, QC = 4.5 cm, prove that area of ΔAPQ is 116 of the area of ΔABC.

Answer»

In the given figure, ABC is a triangle and PQ is a straight line meeting AB in P and AC in Q. If AP = 1 cm, PB = 3 cm, AQ = 1.5 cm, QC = 4.5 cm, prove that area of $Δ A P Q$ is $\frac{1}{16}$ of the area of $Δ A B C$ .

Discussion

808.	The probabilities of a student getting grade A, B, C, and D are 0.2, 0.3, 0.15 and 0.35 respectively. Then what is the probability that a student gets at least a C grade?
Answer» The probabilities of a student getting grade A, B, C, and D are 0.2, 0.3, 0.15 and 0.35 respectively. Then what is the probability that a student gets at least a C grade?

Discussion

809.	define radius of gyration. is it a cons†an t quantity
Answer» define radius of gyration. is it a cons†an t quantity

Discussion

810.	If the volume of a hemisphere is four times its total surface area, then find its radius(in cm)?18
Answer» If the volume of a hemisphere is four times its total surface area, then find its radius (in cm)? 18

Discussion

811.	In the given figure, PA and PB are two tangents from an external point P to a circle with centre O. If ∠PBA = 65∘ , find ∠OAB and ∠APB
Answer» In the given figure, PA and PB are two tangents from an external point P to a circle with centre O. If ∠PBA = 65^∘ , find ∠OABand ∠APB

Discussion

812.	If the mean of the following data is 8, find the value of p. x35791113f6815p84
Answer» If the mean of the following data is 8, find the value of p. $\begin{matrix} x & 3 & 5 & 7 & 9 & 11 & 13 f & 6 & 8 & 15 & p & 8 & 4 \end{matrix}$

Discussion

813.	In △ ABC, ∠ACB=90∘,CD⊥AB. Prove that BC2AC2=BDAD
Answer» In $△$ ABC, $∠ A C B = 90^{\circ}, C D ⊥ A B$ . Prove that $\frac{B C^{2}}{A C^{2}} = \frac{B D}{A D}$

Discussion

814.	The list of numbers 5, - 2, -9, -16 ... is ___.
Answer» The list of numbers 5, - 2, -9, -16 ... is ___.

Discussion

815.	One says, “give me hundred, friend! I shall then become twice as rich as you” The other replies, “If you give me ten, I shall be six times as rich as you”. Tell me what is the amount of their respective capital?
Answer» One says, “give me hundred, friend! I shall then become twice as rich as you” The other replies, “If you give me ten, I shall be six times as rich as you”. Tell me what is the amount of their respective capital?

Discussion

816.	Prove that cosθ+sin(270∘+θ)−sin(270∘−θ)+cos(180∘+θ)
Answer» Prove that $cos θ + sin (270^{\circ} + θ) - sin (270^{\circ} - θ) + cos (180^{\circ} + θ)$

Discussion

817.	If x2−y2=18 and x−y=3, then 4xy= _____.27
Answer» If $x^{2} - y^{2} = 18$ and $x - y = 3$ , then $4 x y =$ _____. 27

Discussion

818.	Find the polynomial whose sum of its zeroes is −85 and the products of the zeroes is 75
Answer» Find the polynomial whose sum of its zeroes is $- \frac{8}{5}$ and the products of the zeroes is $\frac{7}{5}$

Discussion

819.	25. A tower stands at the centre of a circular. A and B are the points on the boundary of the park such that AB(=a) subtends an angle of 60 degree at the foot of the tower and the angle of elevation of the top of tower from A orB is 30 degree. Find height of tower
Answer» 25. A tower stands at the centre of a circular. A and B are the points on the boundary of the park such that AB(=a) subtends an angle of 60 degree at the foot of the tower and the angle of elevation of the top of tower from A orB is 30 degree. Find height of tower

Discussion

820.	In the figure ∠B=90∘, D and E trisect BC, Prove that 8AE2=3AC2+5AD2 [4 MARKS]
Answer» In the figure $∠ B = 90^{\circ}$ , D and E trisect BC, Prove that $8 {A E}^{2} = 3 {A C}^{2} + 5 {A D}^{2}$ [4 MARKS]

820.

In the figure ∠B=90∘, D and E trisect BC, Prove that 8AE2=3AC2+5AD2 [4 MARKS]

Answer»

In the figure $∠ B = 90^{\circ}$ , D and E trisect BC, Prove that $8 {A E}^{2} = 3 {A C}^{2} + 5 {A D}^{2}$ [4 MARKS]

Discussion

821.	Question 8 Solve the equation -4 + (-1) + 2 + . . . . . + x = 437.
Answer» Question 8 Solve the equation -4 + (-1) + 2 + . . . . . + x = 437.

Discussion

822.	Question 18 Find the number of revolutions made by a circular wheel of area 1.54 m2 in rolling a distance of 176 m.
Answer» Question 18 Find the number of revolutions made by a circular wheel of area $1.54 m^{2}$ in rolling a distance of 176 m.

Discussion

823.	A card is drawn at random from a pack of 52 playing cards. The probability of getting a face card is
Answer» A card is drawn at random from a pack of 52 playing cards. The probability of getting a face card is

Discussion

824.	A path of width 3.5 m runs around a semi-circular grassy plot whose perimeter is 72 m. Find the area of the path. (Use π=227)
Answer» A path of width 3.5 m runs around a semi-circular grassy plot whose perimeter is 72 m. Find the area of the path. (Use $π = \frac{22}{7}$ )

Discussion

825.	Find angle BOC in the given figure if AOB = 30 degrees and AC is the diameter of the given circle.
Answer» Find angle BOC in the given figure if AOB = 30 degrees and AC is the diameter of the given circle.

Discussion

826.	If 5θ and 4θ are acute angles satisfying sin 5θ = cos 4θ, then 2 sin 3θ − 3 tan 3θ is equal to(a) 1(b) 0(c) −1(d) 1+3
Answer» If 5θ and 4θ are acute angles satisfying sin 5θ = cos 4θ, then 2 sin 3θ − $\sqrt{3} \tan 3 θ$ is equal to (a) 1 (b) 0 (c) −1 (d) $1 + \sqrt{3}$

Discussion

827.	2xcube -xy square -ycube........factorize
Answer» 2xcube -xy square -ycube........factorize

Discussion

828.	A building (toy) is in the form of a cylinder surmounted by a hemispherical dome. The base diameter of the dome is equal to 1/3 of the total height of the building. If the base radius of the cylinder is 6 cm, then the volume of the building is
Answer» A building (toy) is in the form of a cylinder surmounted by a hemispherical dome. The base diameter of the dome is equal to 1/3 of the total height of the building. If the base radius of the cylinder is 6 cm, then the volume of the building is

Discussion

829.	A hemispherical bowl of diameter 7.2 cm is filled completely with chocolate sauce. This sauce is poured into an inverted cone of radius 4.8 cm. Find the height of the cone.
Answer» A hemispherical bowl of diameter 7.2 cm is filled completely with chocolate sauce. This sauce is poured into an inverted cone of radius 4.8 cm. Find the height of the cone.

Discussion

830.	Select the appropriate alternative.(1) In ∆ABC and ∆PQR, in a one to one correspondence ABQR=BCPR=CAPQ then(A) ∆PQR ~ ∆ABC(B) ∆PQR ~ ∆CAB(C) ∆CBA ~ ∆PQR(D) ∆BCA ~ ∆PQR(2) If in ∆DEF and ∆PQR, ∠D ≅ ∠Q, ∠R ≅ ∠E then which of the following statements is false?(A) EFPR=DFPQ (B) DEPQ=EFRP(C) DEQR=DFPQ (D) EFRP=DEQR(3) In ∆ABC and ∆DEF ∠B = ∠E, ∠F = ∠C and AB = 3DE then which of the statements regarding the two triangles is true ?(A)The triangles are not congruent and not similar(B) The triangles are similar but not congruent.(C) The triangles are congruent and similar.(D) None of the statements above is true.(4) ∆ABC and ∆DEF are equilateral triangles, A (∆ABC) : A (∆DEF) = 1 : 2If AB = 4 then what is length of DE?(A) 22(B) 4(C) 8(D) 42(5) In the given figure, seg XY \|\| seg BC, then which of the following statements is true?(A) ABAC=AXAY (B) AXXB=AYAC(C) AXYC=AYXB (D) ABYC=ACXB
Answer» Select the appropriate alternative. (1) In ∆ABC and ∆PQR, in a one to one correspondence $\frac{AB}{QR} = \frac{BC}{PR} = \frac{CA}{PQ}$ then (A) ∆PQR ~ ∆ABC (B) ∆PQR ~ ∆CAB (C) ∆CBA ~ ∆PQR (D) ∆BCA ~ ∆PQR (2) If in ∆DEF and ∆PQR, ∠D ≅ ∠Q, ∠R ≅ ∠E then which of the following statements is false? (A) $\frac{EF}{PR} = \frac{DF}{PQ}$ (B) $\frac{DE}{PQ} = \frac{EF}{RP}$ (C) $\frac{DE}{QR} = \frac{DF}{PQ}$ (D) $\frac{EF}{RP} = \frac{DE}{QR}$ (3) In ∆ABC and ∆DEF ∠B = ∠E, ∠F = ∠C and AB = 3DE then which of the statements regarding the two triangles is true ? (A)The triangles are not congruent and not similar (B) The triangles are similar but not congruent. (C) The triangles are congruent and similar. (D) None of the statements above is true. (4) ∆ABC and ∆DEF are equilateral triangles, A (∆ABC) : A (∆DEF) = 1 : 2 If AB = 4 then what is length of DE? (A) $2 \sqrt{2}$ (B) 4 (C) 8 (D) $4 \sqrt{2}$ (5) In the given figure, seg XY \|\| seg BC, then which of the following statements is true? (A) $\frac{AB}{AC} = \frac{AX}{AY}$ (B) $\frac{AX}{XB} = \frac{AY}{AC}$ (C) $\frac{AX}{YC} = \frac{AY}{XB}$ (D) $\frac{AB}{YC} = \frac{AC}{XB}$

Discussion

831.	P, Q and R are partners sharing profits and losses in the ratio of 3 : 3 : 2 respectively. Their respective capitals are in their profit-sharing proportions. On 1st April, 2018, the total capital of the firm and the balance of General Reserve are ₹ 80,000 and ₹ 20,000 respectively. During the year 2018-19, the firm made a profit of ₹ 28,000 before charging interest on capital 5%. The drawings of the partners are P—₹ 8,000; Q—₹ 7,000; and R—₹ 5,000. On 31st March, 2019, their liabilities were ₹ 18,000.On this date, they decided to dissolve the firm. The assets realised ₹ 1,08,600 and realisation expenses amounted to ₹ 1,800.Prepare necessary Ledger Accounts to close the books of the firm.
Answer» P, Q and R are partners sharing profits and losses in the ratio of 3 : 3 : 2 respectively. Their respective capitals are in their profit-sharing proportions. On 1st April, 2018, the total capital of the firm and the balance of General Reserve are ₹ 80,000 and ₹ 20,000 respectively. During the year 2018-19, the firm made a profit of ₹ 28,000 before charging interest on capital 5%. The drawings of the partners are P $—$ ₹ 8,000; Q $—$ ₹ 7,000; and R $—$ ₹ 5,000. On 31st March, 2019, their liabilities were ₹ 18,000. On this date, they decided to dissolve the firm. The assets realised ₹ 1,08,600 and realisation expenses amounted to ₹ 1,800. Prepare necessary Ledger Accounts to close the books of the firm.

Discussion

832.	Prove that √sec θ−1sec θ+1+√sec θ+1sec θ−1=2 cosec θ [3 MARKS]
Answer» Prove that $\sqrt{\frac{s e c θ - 1}{s e c θ + 1}} + \sqrt{\frac{s e c θ + 1}{s e c θ - 1}} = 2 c o s e c θ$ [3 MARKS]

Discussion

833.	If TP and TQ are two tangents to a circle with center O such that ∠POQ=110o, then ∠PTQ will be .
Answer» $If TP and TQ are two tangents to a circle with center O such that ∠ P O Q = 110^{o}, then ∠ P T Q will be$ .

Discussion

834.	Anil started a business with Rs. 52,000 and after 4 months B joined him with Rs. 39,000. At the end of the year, out of the total profits B received total Rs. 20,000 including 25% of the profits as commission for managing the business. What amount did A receive?
Answer» Anil started a business with Rs. 52,000 and after 4 months B joined him with Rs. 39,000. At the end of the year, out of the total profits B received total Rs. 20,000 including 25% of the profits as commission for managing the business. What amount did A receive?

Discussion

835.	Mohan & Sohan are visiting a particular shop in the same week (Mon to Fri). They are equally likely to visit the shop on any of the days. What is the probability that both will visit the shop on
Answer» Mohan & Sohan are visiting a particular shop in the same week (Mon to Fri). They are equally likely to visit the shop on any of the days. What is the probability that both will visit the shop on

835.

Mohan & Sohan are visiting a particular shop in the same week (Mon to Fri). They are equally likely to visit the shop on any of the days. What is the probability that both will visit the shop on

Answer»

Mohan & Sohan are visiting a particular shop in the same week (Mon to Fri).

They are equally likely to visit the shop on any of the days. What is the probability that both will visit the shop on

Discussion

836.	If x + 2 is a factor of x2 + ax + 2b and a + b = 4, then(a) a= 1, b = 3(b) a = 3, b = 1(c) a = −1, b = 5(d) a = 5, b = −1
Answer» If x + 2 is a factor of x² + ax + 2b and a + b = 4, then (a) a= 1, b = 3 (b) a = 3, b = 1 (c) a = −1, b = 5 (d) a = 5, b = −1

Discussion

837.	2arc sin(1/2) + 3arc tan(-1) +2arc cos(-1/2)=?
Answer» 2arc sin(1/2) + 3arc tan(-1) +2arc cos(-1/2)=?

Discussion

838.

The following balances were extracted from the books of Mr. Din Dayal as at 31st March, 2019: Particulars ₹ Particulars ₹ Stock at the beginning 41,000 Purchases 2,20,000 Rent 9,600 Sales 2,80,000 Salary 20,000 Returns (Dr.) 6,000 Bad-Debts 400 Returns (Cr.) 2,000 Provision for Doubtful Debts 3,000 Carriage Inward 3,500 Travelling Expenses 1,400 Carriage Outward 500 Insurance Premium 1,800 Capital 1,75,000 Proprietor's Withdrawals 4,000 Loan (Cr.) 20,000 Telephone Charges 7,300 Debtors 40,000 Printing and Advertising 5,000 Creditors 27,000 Commission (Cr.) 6,000 Investments 5,000 Rent from Sublet 4,800 Interest on Investments 600 Land and Building 1,40,000 Furniture 10,000 Cash 2,900 Prepare Trading and Profit & Loss Account for the year and a Balance Sheet as at 31st March, 2019, after taking into account the following:(1) Stock was valued at ₹ 75,000 on 31st March, 2019. You are informed that a fire occurred on 28th March, 2019 in the godown and stock of the value of ₹ 10,000 was destroyed. Insurance Company admitted a claim of 75%.(2) One-third of the commission received is in respect of work to be done next year.(3) Create a provision of 5% for Doubtful Debts.(4) 50% of Printing and Advertising is to be carried forward as a charge in the following year.(5) ₹ 900 is due for interest on loan.(6) Provide for Manager's Commission at 10% on Net Profit before charging such commission.

Answer» The following balances were extracted from the books of Mr. Din Dayal as at 31st March, 2019:

Particulars	₹	Particulars	₹
Stock at the beginning	41,000	Purchases	2,20,000
Rent	9,600	Sales	2,80,000
Salary	20,000	Returns (Dr.)	6,000
Bad-Debts	400	Returns (Cr.)	2,000
Provision for Doubtful Debts	3,000	Carriage Inward	3,500
Travelling Expenses	1,400	Carriage Outward	500
Insurance Premium	1,800	Capital	1,75,000
Proprietor's Withdrawals	4,000	Loan (Cr.)	20,000
Telephone Charges	7,300	Debtors	40,000
Printing and Advertising	5,000	Creditors	27,000
Commission (Cr.)	6,000	Investments	5,000
Rent from Sublet	4,800	Interest on Investments	600
Land and Building	1,40,000
Furniture	10,000
Cash	2,900

Prepare Trading and Profit & Loss Account for the year and a Balance Sheet as at 31st March, 2019, after taking into account the following:

(1) Stock was valued at ₹ 75,000 on 31st March, 2019. You are informed that a fire occurred on 28th March, 2019 in the godown and stock of the value of ₹ 10,000 was destroyed. Insurance Company admitted a claim of 75%.

(2) One-third of the commission received is in respect of work to be done next year.

(3) Create a provision of 5% for Doubtful Debts.

(4) 50% of Printing and Advertising is to be carried forward as a charge in the following year.

(5) ₹ 900 is due for interest on loan.

(6) Provide for Manager's Commission at 10% on Net Profit before charging such commission.

Discussion

839.	Savitri had to make a model of a cylindrical kaleidoscope for her science project. She wanted to use chart paper to make the curved surface of the kaleidoscope. What would be the area of chart paper required by her, if she wanted to make a kaleidoscope of length 25 cm with a 3.5 cm radius? You may take π = 227
Answer» Savitri had to make a model of a cylindrical kaleidoscope for her science project. She wanted to use chart paper to make the curved surface of the kaleidoscope. What would be the area of chart paper required by her, if she wanted to make a kaleidoscope of length 25 cm with a 3.5 cm radius? You may take π = $\frac{22}{7}$

Discussion

840.	If x-3x-3≥0, then x belongs to the interval ___________.
Answer» If $\frac{x - 3}{\|x - 3\|} \geq 0,$ then x belongs to the interval ___________.

Discussion

841.	In the given figure, E is any point on median AD of a ΔABC. Show that ar (ABE) = ar (ACE) [2 MARKS]
Answer» In the given figure, E is any point on median AD of a ΔABC. Show that ar (ABE) = ar (ACE) [2 MARKS]

841.

In the given figure, E is any point on median AD of a ΔABC. Show that ar (ABE) = ar (ACE) [2 MARKS]

Answer»

In the given figure, E is any point on median AD of a ΔABC. Show that ar (ABE) = ar (ACE) [2 MARKS]

Discussion

842.	In Fig. 2, a circle of radius 7 cm is inscribed in a square. Find the area of the shaded regionUse π=227.
Answer» In Fig. 2, a circle of radius 7 cm is inscribed in a square. Find the area of the shaded region $(U s e π = \frac{22}{7}) .$

Discussion

843.	1192 - 1112 is:
Answer» 119² - 111² is:

Discussion

844.	A and B are points on the line x + y = a lying on the coordinate axis. If AB = 5 √2, find the coordinates of A and B, given that A and B are equidistant from the origin.
Answer» A and B are points on the line x + y = a lying on the coordinate axis. If AB = 5 $\sqrt{2}$ , find the coordinates of A and B, given that A and B are equidistant from the origin.

Discussion

845.	A jar contains 24 marbles of which some are green and others are blue. If a marble is drawn randomly from the jar, the probability that it is green is 23. Find the probability of drawing a blue marble from the jar.
Answer» A jar contains 24 marbles of which some are green and others are blue. If a marble is drawn randomly from the jar, the probability that it is green is $\frac{2}{3}$ . Find the probability of drawing a blue marble from the jar.

Discussion

846.	Question 4Draw a histogram to represent the following grouped frequency distributionAge(in years)Number of teachers20−241025−292830−343235−394840−445045−493550−5412
Answer» Question 4 Draw a histogram to represent the following grouped frequency distribution $\begin{matrix} Age(in years) & Number of teachers 20 - 24 & 10 25 - 29 & 28 30 - 34 & 32 35 - 39 & 48 40 - 44 & 50 45 - 49 & 35 50 - 54 & 12 \end{matrix}$

Discussion

847.	What should be added to the polynomial x2 − 5x + 4, so that 3 is the zero of the resulting polynomial?(a) 1(b) 2(c) 4(d) 5
Answer» What should be added to the polynomial x² − 5x + 4, so that 3 is the zero of the resulting polynomial? (a) 1 (b) 2 (c) 4 (d) 5

Discussion

848.	All face cards of diamonds are removed from the deck of 52 cards. One card is drawn from the remaining cards. The probability that the card drawn is diamond is
Answer» All face cards of diamonds are removed from the deck of 52 cards. One card is drawn from the remaining cards. The probability that the card drawn is diamond is

Discussion

849.	4. If inΔ ABC r1=r2+r3+r then prove that triangle is right angle triangle
Answer» 4. If inΔ ABC r1=r2+r3+r then prove that triangle is right angle triangle

Discussion

850.	Question 21 (iii)Find the sum:a−ba+b+3a−2ba+b+5a−3ba+b+⋯to 11 terms
Answer» Question 21 (iii) Find the sum: $\frac{a - b}{a + b} + \frac{3 a - 2 b}{a + b} + \frac{5 a - 3 b}{a + b} + \dots t o 11 t e r m s$

Discussion

Explore topic-wise InterviewSolutions in .

(i) What is the Range for Probability of any event?(ii) What is impossible event?

Find the inverse of each of the following matrices by using elementary row transformations:2-3532-411-2

10. Find the equation of the line passing through (2,3) and parallel to the line joining the points (2,-2) and (6,4).

11. If sec theta cos alpha=root 2 and tan theta cot alpha=root 3, then find the values of tan theta and tan alpha that satisfy the equations.

{104 . The circle }x^2+y^2-4x-4y+4=0 is inscribed in a triangle which has two of its sides }} along the coordinate axes. The locus of the circumcentre of the triangle is }{x+y-xy+k(x^2+y^2)^{1/2}=0. Then }k=}{ 2) }1

32. A semi-circular sheet of metal diameter 28cm is bent to form an open conical cup. Find the capacity of cup.

In the given figure, ABC is a triangle and PQ is a straight line meeting AB in P and AC in Q. If AP = 1 cm, PB = 3 cm, AQ = 1.5 cm, QC = 4.5 cm, prove that area of ΔAPQ is 116 of the area of ΔABC.

The probabilities of a student getting grade A, B, C, and D are 0.2, 0.3, 0.15 and 0.35 respectively. Then what is the probability that a student gets at least a C grade?

define radius of gyration. is it a cons†an t quantity

If the volume of a hemisphere is four times its total surface area, then find its radius(in cm)?18

In the given figure, PA and PB are two tangents from an external point P to a circle with centre O. If ∠PBA = 65∘ , find ∠OAB and ∠APB

If the mean of the following data is 8, find the value of p. x35791113f6815p84

In △ ABC, ∠ACB=90∘,CD⊥AB. Prove that BC2AC2=BDAD

The list of numbers 5, - 2, -9, -16 ... is ___.

One says, “give me hundred, friend! I shall then become twice as rich as you” The other replies, “If you give me ten, I shall be six times as rich as you”. Tell me what is the amount of their respective capital?

Prove that cosθ+sin(270∘+θ)−sin(270∘−θ)+cos(180∘+θ)

If x2−y2=18 and x−y=3, then 4xy= _____.27

Find the polynomial whose sum of its zeroes is −85 and the products of the zeroes is 75

25. A tower stands at the centre of a circular. A and B are the points on the boundary of the park such that AB(=a) subtends an angle of 60 degree at the foot of the tower and the angle of elevation of the top of tower from A orB is 30 degree. Find height of tower

In the figure ∠B=90∘, D and E trisect BC, Prove that 8AE2=3AC2+5AD2 [4 MARKS]

Question 8 Solve the equation -4 + (-1) + 2 + . . . . . + x = 437.

Question 18 Find the number of revolutions made by a circular wheel of area 1.54 m2 in rolling a distance of 176 m.

A card is drawn at random from a pack of 52 playing cards. The probability of getting a face card is

A path of width 3.5 m runs around a semi-circular grassy plot whose perimeter is 72 m. Find the area of the path. (Use π=227)

Find angle BOC in the given figure if AOB = 30 degrees and AC is the diameter of the given circle.

If 5θ and 4θ are acute angles satisfying sin 5θ = cos 4θ, then 2 sin 3θ − 3 tan 3θ is equal to(a) 1(b) 0(c) −1(d) 1+3

2xcube -xy square -ycube........factorize

A building (toy) is in the form of a cylinder surmounted by a hemispherical dome. The base diameter of the dome is equal to 1/3 of the total height of the building. If the base radius of the cylinder is 6 cm, then the volume of the building is

A hemispherical bowl of diameter 7.2 cm is filled completely with chocolate sauce. This sauce is poured into an inverted cone of radius 4.8 cm. Find the height of the cone.

Prove that √sec θ−1sec θ+1+√sec θ+1sec θ−1=2 cosec θ [3 MARKS]

If TP and TQ are two tangents to a circle with center O such that ∠POQ=110o, then ∠PTQ will be .

Anil started a business with Rs. 52,000 and after 4 months B joined him with Rs. 39,000. At the end of the year, out of the total profits B received total Rs. 20,000 including 25% of the profits as commission for managing the business. What amount did A receive?

Mohan &amp; Sohan are visiting a particular shop in the same week (Mon to Fri). They are equally likely to visit the shop on any of the days. What is the probability that both will visit the shop on

If x + 2 is a factor of x2 + ax + 2b and a + b = 4, then(a) a= 1, b = 3(b) a = 3, b = 1(c) a = −1, b = 5(d) a = 5, b = −1

2arc sin(1/2) + 3arc tan(-1) +2arc cos(-1/2)=?

If x-3x-3≥0, then x belongs to the interval ___________.

In the given figure, E is any point on median AD of a ΔABC. Show that ar (ABE) = ar (ACE) [2 MARKS]

In Fig. 2, a circle of radius 7 cm is inscribed in a square. Find the area of the shaded regionUse π=227.

1192 - 1112 is:

A and B are points on the line x + y = a lying on the coordinate axis. If AB = 5 √2, find the coordinates of A and B, given that A and B are equidistant from the origin.

A jar contains 24 marbles of which some are green and others are blue. If a marble is drawn randomly from the jar, the probability that it is green is 23. Find the probability of drawing a blue marble from the jar.

Question 4Draw a histogram to represent the following grouped frequency distributionAge(in years)Number of teachers20−241025−292830−343235−394840−445045−493550−5412

What should be added to the polynomial x2 − 5x + 4, so that 3 is the zero of the resulting polynomial?(a) 1(b) 2(c) 4(d) 5

All face cards of diamonds are removed from the deck of 52 cards. One card is drawn from the remaining cards. The probability that the card drawn is diamond is

4. If inΔ ABC r1=r2+r3+r then prove that triangle is right angle triangle

Question 21 (iii)Find the sum:a−ba+b+3a−2ba+b+5a−3ba+b+⋯to 11 terms

Mohan & Sohan are visiting a particular shop in the same week (Mon to Fri). They are equally likely to visit the shop on any of the days. What is the probability that both will visit the shop on