32581 + Interview Questions in Mathematics Page 281 InterviewSolution

14001.	In Fig. 7.140, ∠AB=90∘ and BD⊥AC. If AB = 5.7 cm, BD = 3.8 cm and CD=5.4 cm, find BC.
Answer» In Fig. 7.140, $∠ A B = 90^{\circ}$ and $B D ⊥ A C$ . If AB = 5.7 cm, BD = 3.8 cm and CD=5.4 cm, find BC.

14001.

In Fig. 7.140, ∠AB=90∘ and BD⊥AC. If AB = 5.7 cm, BD = 3.8 cm and CD=5.4 cm, find BC.

Answer»

In Fig. 7.140, $∠ A B = 90^{\circ}$ and $B D ⊥ A C$ . If AB = 5.7 cm, BD = 3.8 cm and CD=5.4 cm, find BC.

14002.	Which of the following should be the LAST sentence after rearrangement?
Answer» Which of the following should be the LAST sentence after rearrangement?

Discussion

14003.	In the adjoining figure,ABCD is a trapezium in which AB\|\|DC;AB=7 cm;AD=BC=5 cm and the distance between AB and DC is 4 cm.Find the length of DC and hence,find the area of trap,ABCD.
Answer» In the adjoining figure,ABCD is a trapezium in which AB\|\|DC;AB=7 cm;AD=BC=5 cm and the distance between AB and DC is 4 cm.Find the length of DC and hence,find the area of trap,ABCD.

14003.

In the adjoining figure,ABCD is a trapezium in which AB||DC;AB=7 cm;AD=BC=5 cm and the distance between AB and DC is 4 cm.Find the length of DC and hence,find the area of trap,ABCD.

Answer»

In the adjoining figure,ABCD is a trapezium in which AB||DC;AB=7 cm;AD=BC=5 cm and the distance between AB and DC is 4 cm.Find the length of DC and hence,find the area of trap,ABCD.

Discussion

14004.	The following data give the number of boys of a particular age in a class of 40 students. Age (in years)151617181920Frequency(fi)3891163 Calculate the mean ager of the students.
Answer» The following data give the number of boys of a particular age in a class of 40 students. $\begin{matrix} Age (in years) & 15 & 16 & 17 & 18 & 19 & 20 Frequency (f_{i}) & 3 & 8 & 9 & 11 & 6 & 3 \end{matrix}$ Calculate the mean ager of the students.

Discussion

14005.	a) A shopkeeper sells an item at the price of Rs 810 including sales tax of 8%. What should a customer pay for the same item if the sales tax is reduced to 6%? b) The price of TV set inclusive of sales tax of 9% is Rs 13,407. Find its marked price. If the sales tax is increased to 13%. how much more does the customer pay for the TV? [6 MARKS]
Answer» a) A shopkeeper sells an item at the price of Rs 810 including sales tax of 8%. What should a customer pay for the same item if the sales tax is reduced to 6%? b) The price of TV set inclusive of sales tax of 9% is Rs 13,407. Find its marked price. If the sales tax is increased to 13%. how much more does the customer pay for the TV? [6 MARKS]

Discussion

14006.	The sum of two number a and b is 15, and the sum of their reciprocals 1a and 1b is 3/10. Find the numbers a and b.
Answer» The sum of two number a and b is 15, and the sum of their reciprocals $\frac{1}{a} and \frac{1}{b}$ is 3/10. Find the numbers a and b.

Discussion

14007.	Three equal cubes are placed adjacently in a row. Find the ratio of the total surface area of the resulting cuboid to that of the sum of the surface areas of three cubes.
Answer» Three equal cubes are placed adjacently in a row. Find the ratio of the total surface area of the resulting cuboid to that of the sum of the surface areas of three cubes.

Discussion

14008.	Question 27Find the sum of first 17 terms of an AP whose 4th and 9th terms are – 15 and –30, respectively.
Answer» Question 27 Find the sum of first 17 terms of an AP whose $4^{t h}$ and $9^{t h}$ terms are – 15 and –30, respectively.

Discussion

14009.	In the given figure, a balloon is descending at a constant speed of 10 m/s as shown in the dotted lines. A person standing on top of a tower is observing the trajectory. Find the time taken by the balloon to reach the ground. (in seconds) ___
Answer» In the given figure, a balloon is descending at a constant speed of 10 m/s as shown in the dotted lines. A person standing on top of a tower is observing the trajectory. Find the time taken by the balloon to reach the ground. (in seconds) ___

14009.

In the given figure, a balloon is descending at a constant speed of 10 m/s as shown in the dotted lines. A person standing on top of a tower is observing the trajectory. Find the time taken by the balloon to reach the ground. (in seconds) ___

Answer»

In the given figure, a balloon is descending at a constant speed of 10 m/s as shown in the dotted lines. A person standing on top of a tower is observing the trajectory. Find the time taken by the balloon to reach the ground. (in seconds) ___

Discussion

14010.	Question 73On throwing a die once, the probability of occurence of an even number is 12.
Answer» Question 73 On throwing a die once, the probability of occurence of an even number is $\frac{1}{2}$ .

14010.

Question 73On throwing a die once, the probability of occurence of an even number is 12.

Answer»

Question 73

On throwing a die once, the probability of occurence of an even number is $\frac{1}{2}$ .

Discussion

14011.	In fig., DE \|\| BC. If AD = x, DB = x - 2, AE = x + 2 and EC = x - 1, find the value of x.
Answer» In fig., DE \|\| BC. If AD = x, DB = x - 2, AE = x + 2 and EC = x - 1, find the value of x.

14011.

In fig., DE || BC. If AD = x, DB = x - 2, AE = x + 2 and EC = x - 1, find the value of x.

Answer»

In fig., DE || BC. If AD = x, DB = x - 2, AE = x + 2 and EC = x - 1, find the value of x.

Discussion

14012.	Question 47 The product of two fraction =Product of their denominatorsProduct of their numerators
Answer» Question 47 The product of two fraction $= \frac{P r o d u c t o f t h e i r d e n o m i n a t o r s}{P r o d u c t o f t h e i r n u m e r a t o r s}$

14012.

Question 47 The product of two fraction =Product of their denominatorsProduct of their numerators

Answer»

Question 47

The product of two fraction $= \frac{P r o d u c t o f t h e i r d e n o m i n a t o r s}{P r o d u c t o f t h e i r n u m e r a t o r s}$

Discussion

14013.	The ordered pairs (2,7),(4,8)and (5,9) are among 9 elements of the set A× B.Determine the other elements of A×
Answer» The ordered pairs (2,7),(4,8)and (5,9) are among 9 elements of the set A× B.Determine the other elements of A×

Discussion

14014.	If A=[10234264], then fourth element of second column of AT = ___
Answer» If $A = [\begin{matrix} 1 & 0 & 2 & 3 4 & 2 & 6 & 4 \end{matrix}]$ , then fourth element of second column of $A^{T}$ = ___

Discussion

14015.	The lengths of the diagonals of a rhombus are 16 cm and 12 cm. Then the length of the side of the rhombus is __________.
Answer» The lengths of the diagonals of a rhombus are 16 cm and 12 cm. Then the length of the side of the rhombus is __________.

Discussion

14016.	what is difference among ; zeroes , roots , solutions of polynomial
Answer» what is difference among ; zeroes , roots , solutions of polynomial

Discussion

14017.	If the radius of a circle is diminished by 10%, then its area is diminished by(a) 10%(b) 19%(c) 20%(d) 36%
Answer» If the radius of a circle is diminished by 10%, then its area is diminished by (a) 10% (b) 19% (c) 20% (d) 36%

Discussion

14018.	Find the sum of the following series in G.P: 10 terms of the series 1+3^(1/2)+3+.......
Answer» Find the sum of the following series in G.P: 10 terms of the series 1+3^(1/2)+3+.......

Discussion

14019.	Find the zeros of the following quadratic polynomials and verify the relationship between the zeros and the coeffients : 5x2−4−8x
Answer» Find the zeros of the following quadratic polynomials and verify the relationship between the zeros and the coeffients : $5 x^{2} - 4 - 8 x$

14019.

Find the zeros of the following quadratic polynomials and verify the relationship between the zeros and the coeffients : 5x2−4−8x

Answer»

Find the zeros of the following quadratic polynomials and verify the relationship between the zeros and the coeffients :

$5 x^{2} - 4 - 8 x$

Discussion

14020.	A toy is in the form of a cone mounted on a hemisphere of radius 3.5 cm. If the total height of the toy is 15.5 cm, then its total surface area is
Answer» A toy is in the form of a cone mounted on a hemisphere of radius 3.5 cm. If the total height of the toy is 15.5 cm, then its total surface area is

Discussion

14021.	The perimeter of a sector of circle with radius 5.7 m is 27.2 m. The length of the arc of sector (in m) is _______.
Answer» The perimeter of a sector of circle with radius 5.7 m is 27.2 m. The length of the arc of sector (in m) is _______.

Discussion

14022.	Star Ltd. took over the assets of ₹ 6,60,000 and liabilities of ₹ 80,000 of Moon Ltd. for ₹ 6,00,000. Give necessary Journal entries in the books of Star Ltd. assuming that:Case (a): The purchase consideration was payable 10% in cash and the balance in 5,400; 12% Debentures of ₹ 100 each.Case (b): The purchase consideration was payable 10% in cash and the balance in 4,500; 12% Debentures of ₹ 100 each issued at 20% premium.
Answer» Star Ltd. took over the assets of ₹ 6,60,000 and liabilities of ₹ 80,000 of Moon Ltd. for ₹ 6,00,000. Give necessary Journal entries in the books of Star Ltd. assuming that: Case (a): The purchase consideration was payable 10% in cash and the balance in 5,400; 12% Debentures of ₹ 100 each. Case (b): The purchase consideration was payable 10% in cash and the balance in 4,500; 12% Debentures of ₹ 100 each issued at 20% premium.

Discussion

14023.	In each of the following, one of the six trigonometric ratios is given. Find the values of the other trigonometric ratios.(i) sin A=23(ii) cos A=45(iii) tan θ = 11(iv) sin θ=1115(v) tan α=512(vi) sin θ=32(vii) cos θ=725(viii) tan θ=815(ix) cot θ=125(x) sec θ=135(xi) cosec θ=10(xii) cos θ=1215
Answer» In each of the following, one of the six trigonometric ratios is given. Find the values of the other trigonometric ratios. (i) $\sin A = \frac{2}{3}$ (ii) $\cos A = \frac{4}{5}$ (iii) tan θ = 11 (iv) $\sin θ = \frac{11}{15}$ (v) $\tan α = \frac{5}{12}$ (vi) $\sin θ = \frac{\sqrt{3}}{2}$ (vii) $\cos θ = \frac{7}{25}$ (viii) $\tan θ = \frac{8}{15}$ (ix) $\cot θ = \frac{12}{5}$ (x) $\sec θ = \frac{13}{5}$ (xi) $cosec θ = \sqrt{10}$ (xii) $\cos θ = \frac{12}{15}$

Discussion

14024.	Which of the following is the sketch of the graph y = (\|cosx\|cosx)
Answer» Which of the following is the sketch of the graph $y = (\frac{\| c o s x \|}{c o s x})$

Discussion

14025.	A farmer prepares a rectangular vegetable garden of area 180 sq metres. With 39 metres of barbed wire, he can fence the three sides of the garden, leaving one of the longer sides unfenced. Find the dimensions of the garden.
Answer» A farmer prepares a rectangular vegetable garden of area 180 sq metres. With 39 metres of barbed wire, he can fence the three sides of the garden, leaving one of the longer sides unfenced. Find the dimensions of the garden.

Discussion

14026.	Write the exponent of 2 in the price factorization of 144.
Answer» Write the exponent of 2 in the price factorization of 144.

Discussion

14027.	Using quadratic formula solve the following quadratic equation: p2x2+(p2−q2)x−q2=0,p≠0
Answer» Using quadratic formula solve the following quadratic equation: $p^{2} x^{2} + (p^{2} - q^{2}) x - q^{2} = 0, p \neq 0$

Discussion

14028.	A polynomial p(x) when divided by x - 2 leaves a remainder 12. P(x) = x^3+2x^2+x-6. Find all its zeroes.
Answer» A polynomial p(x) when divided by x - 2 leaves a remainder 12. P(x) = x^3+2x^2+x-6. Find all its zeroes.

14028.

A polynomial p(x) when divided by x - 2 leaves a remainder 12. P(x) = x^3+2x^2+x-6. Find all its zeroes.

Answer»

A polynomial p(x) when divided by x - 2 leaves a remainder 12.

P(x) = x^3+2x^2+x-6.

Find all its zeroes.

Discussion

14029.	What are co terminal angle?
Answer» What are co terminal angle?

Discussion

14030.	Question 4(a)Simplify : 3x (4x-5) +3 and find values for (i) x=3 (ii) x= 12
Answer» Question 4(a) Simplify : 3x (4x-5) +3 and find values for (i) x=3 (ii) x= $\frac{1}{2}$

Discussion

14031.

From the following balances, as on 31st March, 2019, prepare Trading and Profit and Loss Account and Balance Sheet: ₹ ₹ Capital Account 1,00,000 Returns Outward 5,000 Plant and Machinery 40,000 Rent 4,000 Sundry Debtors 24,000 Sales 1,64,000 Sundry Creditors 12,000 Manufacturing Expenses 8,000 Life Insurance Premium 12,000 Trade Expenses 7,000 Purchases 1,05,000 Bad Debts 2,000 Wages 50,000 Carriage 1,500 Bank 10,000 Bills Payable 7,000 Repairs 500 Returns Inward 4,000 Stock (1st April, 2018) 20,000 Closing Stock on 31st March, 2019 was valued at ₹ 14,500.

Answer» From the following balances, as on 31st March, 2019, prepare Trading and Profit and Loss Account and Balance Sheet:

	₹		₹
Capital Account	1,00,000	Returns Outward	5,000
Plant and Machinery	40,000	Rent	4,000
Sundry Debtors	24,000	Sales	1,64,000
Sundry Creditors	12,000	Manufacturing Expenses	8,000
Life Insurance Premium	12,000	Trade Expenses	7,000
Purchases	1,05,000	Bad Debts	2,000
Wages	50,000	Carriage	1,500
Bank	10,000	Bills Payable	7,000
Repairs	500	Returns Inward	4,000
Stock (1st April, 2018)	20,000

Closing Stock on 31st March, 2019 was valued at ₹ 14,500.

Discussion

14032.	Find the square of 93.
Answer» Find the square of 93.

Discussion

14033.	If the equations x^2 + bx +ca = 0 and x^2 + cx + ab = 0 have a non-zero common root, prove that a+b+c = 0 and their other root satisfy x^2 + ax + bc = 0
Answer» If the equations x^2 + bx +ca = 0 and x^2 + cx + ab = 0 have a non-zero common root, prove that a+b+c = 0 and their other root satisfy x^2 + ax + bc = 0

Discussion

14034.	Prove the following identities:y+zzyzz+xxyxx+y=4xyz
Answer» Prove the following identities: $\|\begin{matrix} y + z & z & y \\ z & z + x & x \\ y & x & x + y \end{matrix}\| = 4 x y z$

Discussion

14035.	The position vector of the point which divides the join of points 2a→-3b→ and a→+b→ in the ratio 3:1 is(a) 128a→-2b→ (b) 147a→-8b→ (c) 34a→ (d) 54a→
Answer» The position vector of the point which divides the join of points $2 \vec{a} - 3 \vec{b} and \vec{a} + \vec{b}$ in the ratio 3:1 is $(a) \frac{1}{2} (8 \vec{a} - 2 \vec{b}) (b) \frac{1}{4} (7 \vec{a} - 8 \vec{b}) (c) \frac{3}{4} \vec{a} (d) \frac{5}{4} \vec{a}$

Discussion

14036.	Determine the value of k so that the following linear equations have no solution:(3k + 1) x + 3y − 2 = 0(k2 + 1) x + (k − 2) y − 5 = 0
Answer» Determine the value of k so that the following linear equations have no solution: (3k + 1) x + 3y − 2 = 0 (k² + 1) x + (k − 2) y − 5 = 0

Discussion

14037.	Quadratic polynomials with rational coefficients having √3 as a zero are given by ________.
Answer» Quadratic polynomials with rational coefficients having $\sqrt{3}$ as a zero are given by ________.

Discussion

14038.	A bucket open at the top, and made up of a metal sheet is in the form of a frustum of a cone. The depth of the bucket is 24 cm and the diameters of its upper and lower circular ends are 30 cm and 10 cm respectively. Find the cost of metal sheet used in it at the rate of Rs. 10 per 100 cm2 .(Use π = 3.14).
Answer» A bucket open at the top, and made up of a metal sheet is in the form of a frustum of a cone. The depth of the bucket is 24 cm and the diameters of its upper and lower circular ends are 30 cm and 10 cm respectively. Find the cost of metal sheet used in it at the rate of Rs. 10 per 100 cm² . (Use π = 3.14).

Discussion

14039.	The area of the sector of a circle of radius 10.5 cm is 69.3 cm2. Find the central angle of the sector.
Answer» The area of the sector of a circle of radius 10.5 cm is 69.3 cm². Find the central angle of the sector.

Discussion

14040.	Question 5The following table gives the distribution of the life time of 400 neon lamps:Life time (in hours)Number of lamps1500−2000142000−2500562500−3000603000−3500863500−4000744000−4500624500−500048Find the median life time of a lamp.
Answer» Question 5 The following table gives the distribution of the life time of 400 neon lamps: $\begin{matrix} L i f e t i m e (i n h o u r s) & N u m b e r o f l a m p s 1500 - 2000 & 14 2000 - 2500 & 56 2500 - 3000 & 60 3000 - 3500 & 86 3500 - 4000 & 74 4000 - 4500 & 62 4500 - 5000 & 48 \end{matrix}$ Find the median life time of a lamp.

14040.

Question 5The following table gives the distribution of the life time of 400 neon lamps:Life time (in hours)Number of lamps1500−2000142000−2500562500−3000603000−3500863500−4000744000−4500624500−500048Find the median life time of a lamp.

Answer»

Question 5

The following table gives the distribution of the life time of 400 neon lamps:

$\begin{matrix} L i f e t i m e (i n h o u r s) & N u m b e r o f l a m p s 1500 - 2000 & 14 2000 - 2500 & 56 2500 - 3000 & 60 3000 - 3500 & 86 3500 - 4000 & 74 4000 - 4500 & 62 4500 - 5000 & 48 \end{matrix}$

Find the median life time of a lamp.

Discussion

14041.	Solve the following systems of equations:2x+3y=135x-4y=-2
Answer» Solve the following systems of equations: $\frac{2}{x} + \frac{3}{y} = 13 \frac{5}{x} - \frac{4}{y} = - 2$

Discussion

14042.	What is one to one function or injection
Answer» What is one to one function or injection

Discussion

14043.	There is a grouped data distribution for which mean is to be found by step deviation method. For this purpose, the below table is constructed. Fill in the blanks Class IntervalNumber of Frequency(fi)Class mark(xi)di=xi−aui=dih0−1004050−200D......100−20039150B.....E.....200−3003425000300−400303501001400−50045450C.....F......TotalA.∑fi=...... The A, B, C, D, E and F respectively are
Answer» There is a grouped data distribution for which mean is to be found by step deviation method. For this purpose, the below table is constructed. Fill in the blanks $\begin{matrix} C l a s s I n t e r v a l & N u m b e r o f F r e q u e n c y (f_{i}) & C l a s s m a r k (x_{i}) & d_{i} = x_{i} - a & u_{i} = \frac{d_{i}}{h} 0 - 100 & 40 & 50 & - 200 & D . . . . . . 100 - 200 & 39 & 150 & B . . . . . & E . . . . . 200 - 300 & 34 & 250 & 0 & 0 300 - 400 & 30 & 350 & 100 & 1 400 - 500 & 45 & 450 & C . . . . . & F . . . . . . T o t a l & A . \sum f_{i} = . . . . . . \end{matrix}$ The A, B, C, D, E and F respectively are

14043.

There is a grouped data distribution for which mean is to be found by step deviation method. For this purpose, the below table is constructed. Fill in the blanks Class IntervalNumber of Frequency(fi)Class mark(xi)di=xi−aui=dih0−1004050−200D......100−20039150B.....E.....200−3003425000300−400303501001400−50045450C.....F......TotalA.∑fi=...... The A, B, C, D, E and F respectively are

Answer»

There is a grouped data distribution for which mean is to be found by step deviation method. For this purpose, the below table is constructed. Fill in the blanks

$\begin{matrix} C l a s s I n t e r v a l & N u m b e r o f F r e q u e n c y (f_{i}) & C l a s s m a r k (x_{i}) & d_{i} = x_{i} - a & u_{i} = \frac{d_{i}}{h} 0 - 100 & 40 & 50 & - 200 & D . . . . . . 100 - 200 & 39 & 150 & B . . . . . & E . . . . . 200 - 300 & 34 & 250 & 0 & 0 300 - 400 & 30 & 350 & 100 & 1 400 - 500 & 45 & 450 & C . . . . . & F . . . . . . T o t a l & A . \sum f_{i} = . . . . . . \end{matrix}$

The A, B, C, D, E and F respectively are

Discussion

14044.	What length of solid cylinder 2 cm in diameter must be taken to recast into a hollow cylinder of external diameter 20 cm, 0.25 cm thick and 15 cm long?
Answer» What length of solid cylinder 2 cm in diameter must be taken to recast into a hollow cylinder of external diameter 20 cm, 0.25 cm thick and 15 cm long?

Discussion

14045.	The median of the following observations 11, 12, 14, ( – 2), ( + 4), ( + 9), 32, 38, 47 arranged in ascending order is 24. Find the value of
Answer» The median of the following observations 11, 12, 14, ( – 2), ( + 4), ( + 9), 32, 38, 47 arranged in ascending order is 24. Find the value of

Discussion

14046.	In the given figure, BC is parallel to DE. Area of triangle ABC = 25 cm2, Area trapezium BCED = 24 cm2 and DE = 14 cm. Calculate the length of BC. Also, find the area of triangle BCD.
Answer» In the given figure, BC is parallel to DE. Area of triangle ABC = 25 $c m^{2}$ , Area trapezium BCED = 24 $c m^{2}$ and DE = 14 cm. Calculate the length of BC. Also, find the area of triangle BCD.

14046.

In the given figure, BC is parallel to DE. Area of triangle ABC = 25 cm2, Area trapezium BCED = 24 cm2 and DE = 14 cm. Calculate the length of BC. Also, find the area of triangle BCD.

Answer»

In the given figure, BC is parallel to DE. Area of triangle ABC = 25 $c m^{2}$ , Area trapezium BCED = 24 $c m^{2}$ and DE = 14 cm. Calculate the length of BC. Also, find the area of triangle BCD.

Discussion

14047.	Question 4Which term of the A.P3,8,13,18, … is 78?
Answer» Question 4 Which term of the A.P $3, 8, 13, 18, \dots$ is 78?

Discussion

14048.	Question 1 (ii)Use Euclid's division algorithm to find the HCF of:(ii) 196 and 38220
Answer» Question 1 (ii) Use Euclid's division algorithm to find the HCF of: (ii) 196 and 38220

Discussion

14049.	The shape of the cross section of a canal is a trapezium. If the canal is 10 m wide at the top, 6 m wide at the bottom and the area of its cross section is 640 m2, find the depth of the canal.
Answer» The shape of the cross section of a canal is a trapezium. If the canal is 10 m wide at the top, 6 m wide at the bottom and the area of its cross section is 640 $m^{2}$ , find the depth of the canal.

Discussion

14050.	If a→,b,→c→ are three vectors such that a→+b→+c→=0→ and a→=2,b→=3,c→=5, then the value of a→·b→+b→·c→+·c→·a→ is(a) 0 (b) 1 (c) -19 (d) 38
Answer» If $\vec{a}, \vec{b,} \vec{c}$ are three vectors such that $\vec{a} + \vec{b} + \vec{c} = \vec{0} and \|\vec{a}\| = 2, \|\vec{b}\| = 3, \|\vec{c}\| = 5,$ then the value of $\vec{a} \cdot \vec{b} + \vec{b} \cdot \vec{c} + \cdot \vec{c} \cdot \vec{a} is$ (a) 0 (b) 1 (c) -19 (d) 38

Discussion

Explore topic-wise InterviewSolutions in .

In Fig. 7.140, ∠AB=90∘ and BD⊥AC. If AB = 5.7 cm, BD = 3.8 cm and CD=5.4 cm, find BC.

Which of the following should be the LAST sentence after rearrangement?

In the adjoining figure,ABCD is a trapezium in which AB||DC;AB=7 cm;AD=BC=5 cm and the distance between AB and DC is 4 cm.Find the length of DC and hence,find the area of trap,ABCD.

The following data give the number of boys of a particular age in a class of 40 students. Age (in years)151617181920Frequency(fi)3891163 Calculate the mean ager of the students.

The sum of two number a and b is 15, and the sum of their reciprocals 1a and 1b is 3/10. Find the numbers a and b.

Three equal cubes are placed adjacently in a row. Find the ratio of the total surface area of the resulting cuboid to that of the sum of the surface areas of three cubes.

Question 27Find the sum of first 17 terms of an AP whose 4th and 9th terms are – 15 and –30, respectively.

In the given figure, a balloon is descending at a constant speed of 10 m/s as shown in the dotted lines. A person standing on top of a tower is observing the trajectory. Find the time taken by the balloon to reach the ground. (in seconds) ___

Question 73On throwing a die once, the probability of occurence of an even number is 12.

In fig., DE || BC. If AD = x, DB = x - 2, AE = x + 2 and EC = x - 1, find the value of x.

Question 47 The product of two fraction =Product of their denominatorsProduct of their numerators

The ordered pairs (2,7),(4,8)and (5,9) are among 9 elements of the set A× B.Determine the other elements of A×

If A=[10234264], then fourth element of second column of AT = ___

The lengths of the diagonals of a rhombus are 16 cm and 12 cm. Then the length of the side of the rhombus is __________.

what is difference among ; zeroes , roots , solutions of polynomial

If the radius of a circle is diminished by 10%, then its area is diminished by(a) 10%(b) 19%(c) 20%(d) 36%

Find the sum of the following series in G.P: 10 terms of the series 1+3^(1/2)+3+.......

Find the zeros of the following quadratic polynomials and verify the relationship between the zeros and the coeffients : 5x2−4−8x

A toy is in the form of a cone mounted on a hemisphere of radius 3.5 cm. If the total height of the toy is 15.5 cm, then its total surface area is

The perimeter of a sector of circle with radius 5.7 m is 27.2 m. The length of the arc of sector (in m) is _______.

Which of the following is the sketch of the graph y = (|cosx|cosx)

A farmer prepares a rectangular vegetable garden of area 180 sq metres. With 39 metres of barbed wire, he can fence the three sides of the garden, leaving one of the longer sides unfenced. Find the dimensions of the garden.

Write the exponent of 2 in the price factorization of 144.

Using quadratic formula solve the following quadratic equation: p2x2+(p2−q2)x−q2=0,p≠0

A polynomial p(x) when divided by x - 2 leaves a remainder 12. P(x) = x^3+2x^2+x-6. Find all its zeroes.

What are co terminal angle?

Question 4(a)Simplify : 3x (4x-5) +3 and find values for (i) x=3 (ii) x= 12

Find the square of 93.

If the equations x^2 + bx +ca = 0 and x^2 + cx + ab = 0 have a non-zero common root, prove that a+b+c = 0 and their other root satisfy x^2 + ax + bc = 0

Prove the following identities:y+zzyzz+xxyxx+y=4xyz

The position vector of the point which divides the join of points 2a→-3b→ and a→+b→ in the ratio 3:1 is(a) 128a→-2b→ (b) 147a→-8b→ (c) 34a→ (d) 54a→

Determine the value of k so that the following linear equations have no solution:(3k + 1) x + 3y − 2 = 0(k2 + 1) x + (k − 2) y − 5 = 0

Quadratic polynomials with rational coefficients having √3 as a zero are given by ________.

The area of the sector of a circle of radius 10.5 cm is 69.3 cm2. Find the central angle of the sector.

Question 5The following table gives the distribution of the life time of 400 neon lamps:Life time (in hours)Number of lamps1500−2000142000−2500562500−3000603000−3500863500−4000744000−4500624500−500048Find the median life time of a lamp.

Solve the following systems of equations:2x+3y=135x-4y=-2

What is one to one function or injection

What length of solid cylinder 2 cm in diameter must be taken to recast into a hollow cylinder of external diameter 20 cm, 0.25 cm thick and 15 cm long?

The median of the following observations 11, 12, 14, ( – 2), ( + 4), ( + 9), 32, 38, 47 arranged in ascending order is 24. Find the value of

In the given figure, BC is parallel to DE. Area of triangle ABC = 25 cm2, Area trapezium BCED = 24 cm2 and DE = 14 cm. Calculate the length of BC. Also, find the area of triangle BCD.

Question 4Which term of the A.P3,8,13,18, … is 78?

Question 1 (ii)Use Euclid's division algorithm to find the HCF of:(ii) 196 and 38220

The shape of the cross section of a canal is a trapezium. If the canal is 10 m wide at the top, 6 m wide at the bottom and the area of its cross section is 640 m2, find the depth of the canal.

If a→,b,→c→ are three vectors such that a→+b→+c→=0→ and a→=2,b→=3,c→=5, then the value of a→·b→+b→·c→+·c→·a→ is(a) 0 (b) 1 (c) -19 (d) 38