32581 + Interview Questions in Mathematics Page 65 InterviewSolution

3201.	The value of sin2 30o - cos2 30o is :
Answer» The value of sin² 30^o - cos² 30^o is :

Discussion

3202.	If a1, a2, a3, ....., an, ..... is an A.P. such that a18 – a14 = 32, then its common difference is __________.
Answer» If a₁, a₂, a₃, ....., a_n, ..... is an A.P. such that a₁₈ – a₁₄ = 32, then its common difference is __________.

Discussion

3203.	Degree of the algebraic expression 4x+5x+2 is ______.
Answer» Degree of the algebraic expression 4x+5x+2 is ______.

Discussion

3204.	Draw a triangle ABC in which AB = 5 cm, BC = 6 cm and ∠ ABC = 60∘. Then, construct a triangle whose sides are 57 times the corresponding sides of Δ ABC. Justify your construction.
Answer» Draw a triangle ABC in which AB = 5 cm, BC = 6 cm and $∠$ ABC = $60^{\circ}$ . Then, construct a triangle whose sides are $\frac{5}{7}$ times the corresponding sides of $Δ$ ABC. Justify your construction.

Discussion

3205.	A TV tower stands vertically on a bank of canal. From a point on other bank directly opposite the tower, the angle of elevation of the top of the tower is 60°. From another point 20 m away from this point on the line joining this point to the foot of the tower, the angle of elevation of the top of the tower is 30°. Find the height of the tower and the width of the canal.
Answer» A TV tower stands vertically on a bank of canal. From a point on other bank directly opposite the tower, the angle of elevation of the top of the tower is 60°. From another point 20 m away from this point on the line joining this point to the foot of the tower, the angle of elevation of the top of the tower is 30°. Find the height of the tower and the width of the canal.

Discussion

3206.	The given table shows the Marks obtained by students in Mathematics.MarksNo. of Students0−10310−20720−301230−401540−502050−60960−70870−801680−901490−1006Using the table determine the Lower Quartile by drawing an ogive curve.
Answer» The given table shows the Marks obtained by students in Mathematics. $\begin{matrix} Marks & No. of Students 0 - 10 & 3 10 - 20 & 7 20 - 30 & 12 30 - 40 & 15 40 - 50 & 20 50 - 60 & 9 60 - 70 & 8 70 - 80 & 16 80 - 90 & 14 90 - 100 & 6 \end{matrix}$ Using the table determine the Lower Quartile by drawing an ogive curve.

3206.

The given table shows the Marks obtained by students in Mathematics.MarksNo. of Students0−10310−20720−301230−401540−502050−60960−70870−801680−901490−1006Using the table determine the Lower Quartile by drawing an ogive curve.

Answer»

The given table shows the Marks obtained by students in Mathematics.

$\begin{matrix} Marks & No. of Students 0 - 10 & 3 10 - 20 & 7 20 - 30 & 12 30 - 40 & 15 40 - 50 & 20 50 - 60 & 9 60 - 70 & 8 70 - 80 & 16 80 - 90 & 14 90 - 100 & 6 \end{matrix}$

Using the table determine the Lower Quartile by drawing an ogive curve.

Discussion

3207.	A function is described as:For the function, its range will be
Answer» A function is described as: For the function, its range will be

Discussion

3208.	What is the simplified form of the given expression?x3y + 4x2y2 + 3xy3 + 7x2y2 + 3x3 + 4y2 + 6xy + 7x3y + 8y2
Answer» What is the simplified form of the given expression? $x^{3} y + 4 x^{2} y^{2} + 3 x y^{3} + 7 x^{2} y^{2} + 3 x^{3} + 4 y^{2} + 6 x y + 7 x^{3} y + 8 y^{2}$

Discussion

3209.	If √a>√b>√c>√d , where a, b, c and d are consecutive natural numbers , then which of the following is correct?(i) √a-√b > √c-√d(ii) √c-√d > √a-√b(iii) √a-√c > √b-√d(iv) √c-√d = √a-√bExplain.
Answer» If √a>√b>√c>√d , where a, b, c and d are consecutive natural numbers , then which of the following is correct? (i) √a-√b > √c-√d (ii) √c-√d > √a-√b (iii) √a-√c > √b-√d (iv) √c-√d = √a-√b Explain.

Discussion

3210.	A hemispherical bowl of internal diameter 36cm contains a liquid. This liquid is to be filled in cylindrical bottles of radius 3cm and height 6cm. How many bottles are required to empty the bowl. ( Is it needed to convert volume into litres)
Answer» A hemispherical bowl of internal diameter 36cm contains a liquid. This liquid is to be filled in cylindrical bottles of radius 3cm and height 6cm. How many bottles are required to empty the bowl. ( Is it needed to convert volume into litres)

Discussion

3211.	If sin ( θ + 24 ) = cos θ , where θ + 24 is a acute angle . Find the value of θ .
Answer» If sin ( θ + 24 ) = cos θ , where θ + 24 is a acute angle . Find the value of θ .

Discussion

3212.	What is the difference between secant and diameter ?
Answer» What is the difference between secant and diameter ?

Discussion

3213.	Find the nature of the roots of the following quadratic equations. If the real roots exist, find them: 2x2−6x+3=0
Answer» Find the nature of the roots of the following quadratic equations. If the real roots exist, find them: $2 x^{2} - 6 x + 3 = 0$

Discussion

3214.	Question 160 Quadrilateral EFGH is a rectangle in which J is the point of intersection of the diagonals. Find the value of x, if JF = 8x + 4 and EG = 24x - 8.
Answer» Question 160 Quadrilateral EFGH is a rectangle in which J is the point of intersection of the diagonals. Find the value of x, if JF = 8x + 4 and EG = 24x - 8.

Discussion

3215.	Question 17 Find the 20th term from the last term of the A.P. 3, 8, 13, …, 253.
Answer» Question 17 Find the $20^{t h}$ term from the last term of the A.P. 3, 8, 13, …, 253.

Discussion

3216.	In the given figure, QR is a common tangent to the given circle, touching externally at the point T. The tangent at T meets QR at P. If PT = 3.8 cm then the length of QR is [CBSE 2014](a) 1.9 cm(b) 3.8 cm(c) 5.7 cm(d) 7.6 cm
Answer» In the given figure, QR is a common tangent to the given circle, touching externally at the point T. The tangent at T meets QR at P. If PT = 3.8 cm then the length of QR is [CBSE 2014] (a) 1.9 cm (b) 3.8 cm (c) 5.7 cm (d) 7.6 cm

Discussion

3217.	If cos θ=513, find the value of sin2 θ-cos2 θ2 sin θ cos θ×1tan2 θ.
Answer» If $\cos θ = \frac{5}{13}$ , find the value of $\frac{\sin^{2} θ - \cos^{2} θ}{2 \sin θ \cos θ} \times \frac{1}{\tan^{2} θ}$ .

Discussion

3218.	Find the mode of the following data. xifi10101415187219259
Answer» Find the mode of the following data. $\begin{matrix} x_{i} & f_{i} 10 & 10 14 & 15 18 & 7 21 & 9 25 & 9 \end{matrix}$

Discussion

3219.	For the following distribution :Class: 0-5 5-10 10-15 15-20 20-25Frequency: 10 15 12 20 9the sum of the lower limits of the median and modal class is (a) 15 (b) 25 (c) 30 (d) 35
Answer» For the following distribution : Class: 0-5 5-10 10-15 15-20 20-25 Frequency: 10 15 12 20 9 the sum of the lower limits of the median and modal class is (a) 15 (b) 25 (c) 30 (d) 35

Discussion

3220.	In the given figure if DE \|\| BC, then find EC.
Answer» In the given figure if DE \|\| BC, then find EC.

Discussion

3221.	Choose the correct answer in each of the following questions:If an denotes the nth term of the AP 3, 8, 13, 18, ... then what is the value of a30-a20?(a) 40 (b) 36 (c) 50 (d) 56
Answer» Choose the correct answer in each of the following questions: If a_n denotes the nth term of the AP 3, 8, 13, 18, ... then what is the value of $(a_{30} - a_{20})$ ? (a) 40 (b) 36 (c) 50 (d) 56

Discussion

3222.	The radii of the ends of the frustum of a cone are r1 and r2 cm and If h cm is the height of the frustum, then the volume of the frustum of the cone in cm3 is _________.
Answer» The radii of the ends of the frustum of a cone are r₁ and r₂cm and If h cm is the height of the frustum, then the volume of the frustum of the cone in cm³is _________.

Discussion

3223.	A boat goes 30 km upstream and 44 km downstream in 10 hours. It can go 40 km upstream and 55 km downstream in 13 hours. Find the speed of the stream and that of the boat in still water.
Answer» A boat goes 30 km upstream and 44 km downstream in 10 hours. It can go 40 km upstream and 55 km downstream in 13 hours. Find the speed of the stream and that of the boat in still water.

Discussion

3224.	Question 5 The following table gives the distribution of the life time of 400 neon lamps: Life time (in hours)Number of lamps1500−2000142000−2500562500−3000603000−3500863500−4000744000−4500624500−500048 Find 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.

3224.

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

3225.

Find the mean of each of the following frequency distributions : Class interval: 10−30 30−50 50−70 70−90 90−110 110−130 Frequency: 5 8 12 20 3 2

Answer» Find the mean of each of the following frequency distributions :

Class interval:	10−30	30−50	50−70	70−90	90−110	110−130
Frequency:	5	8	12	20	3	2

Discussion

3226.	The given distribution shows the number of runs scored by some top batsmen of the world in one-day international cricket matches. Runs scoredNumber of bastsmanRuns scoredNumber of bastsman3000−400047000−800064000−5000188000−900035000−600099000−1000016000−7000710000−110001 Find the mode of the data.
Answer» The given distribution shows the number of runs scored by some top batsmen of the world in one-day international cricket matches. $\begin{matrix} Runs scored & Number of bastsman & Runs scored & Number of bastsman 3000 - 4000 & 4 & 7000 - 8000 & 6 4000 - 5000 & 18 & 8000 - 9000 & 3 5000 - 6000 & 9 & 9000 - 10000 & 1 6000 - 7000 & 7 & 10000 - 11000 & 1 \end{matrix}$ Find the mode of the data.

Discussion

3227.	Write the next day’s entry in Walter’s diary. Make up information, in order to make your entry interesting.
Answer» Write the next day’s entry in Walter’s diary. Make up information, in order to make your entry interesting.

Discussion

3228.	The height of an equilateral triangle is 6 cm. Find its area. [Take 3 = 1.73]
Answer» The height of an equilateral triangle is 6 cm. Find its area. [Take $\sqrt{3}$ = 1.73]

Discussion

3229.	The product of 3 consecutive numbers, when the first number is even is divisible by ___
Answer» The product of $3$ consecutive numbers, when the first number is even is divisible by ___

Discussion

3230.	A and B are two points on the x-axis and y-axis respectively. P(2, -3) is the mid point of AB. Find the (i) co-ordinates of A and B (ii) slope of line AB (iii) equation of line AB.
Answer» A and B are two points on the x-axis and y-axis respectively. P(2, -3) is the mid point of AB. Find the (i) co-ordinates of A and B (ii) slope of line AB (iii) equation of line AB.

3230.

A and B are two points on the x-axis and y-axis respectively. P(2, -3) is the mid point of AB. Find the (i) co-ordinates of A and B (ii) slope of line AB (iii) equation of line AB.

Answer»

A and B are two points on the x-axis and y-axis respectively. P(2, -3) is the mid point of AB. Find the

(i) co-ordinates of A and B

(ii) slope of line AB

(iii) equation of line AB.

Discussion

3231.	Determine the AP whose third term is 16 and the 7th term exceeds the 5th term by 12.
Answer» Determine the AP whose third term is 16 and the $7^{t h}$ term exceeds the $5^{t h}$ term by 12.

Discussion

3232.	N positive integers are multiplied together . What is the probability that last digit of the number is 5?
Answer» N positive integers are multiplied together . What is the probability that last digit of the number is 5?

Discussion

3233.

A retail Trader has not kept proper books of accounts. Ascertain his profit or loss for the year ending 31st March, 2017, and prepare a final statement of affairs from the following information: 1st April, 2016 31st March, 2017 ₹ ₹ Cash Balance 3,500 4,100 Bank Balance Dr. 6,000 Cr. 15,000 Stock 22,000 36,400 Sundry Debtors 18,800 34,500 Sundry Creditors 12,100 8,000 Loan from X – 10,000 Bills Receivable 4,000 – Fixed Assets 40,000 60,000 He withdrew from the business ₹ 1,500 per month for his personal use and ₹ 8,000 for giving a personal loan to his brother. He also used a house for his personal purposes, the rent of which at the rate of ₹ 900 per month and electricity charges at an average rate of ₹ 250 per month were paid from the business account.He had received a lottery prize of ₹ 25,000, out of which he invested half the amount in business.He has not paid two months' salary to his clerk ₹ 1,200 per month, but insurance premium ₹ 600 per annum was paid on 1st October, 2016 to run for one year.Loan from X was taken on 1st July, 2016 on which interest was unpaid 18% p.a.Fixed assets are to be depreciated 10% p.a.

Answer» A retail Trader has not kept proper books of accounts. Ascertain his profit or loss for the year ending 31st March, 2017, and prepare a final statement of affairs from the following information:


	1st April, 2016	31st March, 2017
	₹	₹
Cash Balance	3,500	4,100
Bank Balance	Dr. 6,000	Cr. 15,000
Stock	22,000	36,400
Sundry Debtors	18,800	34,500
Sundry Creditors	12,100	8,000
Loan from X	–	10,000
Bills Receivable	4,000	–
Fixed Assets	40,000	60,000

He withdrew from the business ₹ 1,500 per month for his personal use and ₹ 8,000 for giving a personal loan to his brother. He also used a house for his personal purposes, the rent of which at the rate of ₹ 900 per month and electricity charges at an average rate of ₹ 250 per month were paid from the business account.

He had received a lottery prize of ₹ 25,000, out of which he invested half the amount in business.

He has not paid two months' salary to his clerk ₹ 1,200 per month, but insurance premium ₹ 600 per annum was paid on 1st October, 2016 to run for one year.

Loan from X was taken on 1st July, 2016 on which interest was unpaid 18% p.a.

Fixed assets are to be depreciated 10% p.a.

Discussion

3234.	The sum of all positive integers n for which 13+23....+(2n)312+22+...n2 is also an integer is.
Answer» The sum of all positive integers n for which $\frac{1^{3} + 2^{3} . . . . + (2 n)^{3}}{1^{2} + 2^{2} + . . . n^{2}}$ is also an integer is.

Discussion

3235.	(x-2y)^3 - (x+2y)^3
Answer» (x-2y)^3 - (x+2y)^3

Discussion

3236.	In the following diagram, AB is a floor-board; PQRS is a cubical box with each edge = 1 m and ∠B=60∘. Calculate the length of the board AB.
Answer» In the following diagram, AB is a floor-board; PQRS is a cubical box with each edge = 1 m and $∠ B = 60^{\circ}$ . Calculate the length of the board AB.

3236.

In the following diagram, AB is a floor-board; PQRS is a cubical box with each edge = 1 m and ∠B=60∘. Calculate the length of the board AB.

Answer»

In the following diagram, AB is a floor-board; PQRS is a cubical box with each edge = 1 m and $∠ B = 60^{\circ}$ . Calculate the length of the board AB.

Discussion

3237.	A quadratic polynomial, the sum of whose zeroes is 0 and one zero is 3, is(a) x2 − 9(b) x2 + 9(c) x2 + 3(d) x2 − 3
Answer» A quadratic polynomial, the sum of whose zeroes is 0 and one zero is 3, is (a) x² − 9 (b) x² + 9 (c) x² + 3 (d) x² − 3

Discussion

3238.	The age of the employees in a startup company is shown below. AgeNo. of Employees18−263026−347034−425042−503050−581058−6610 Find the modal age of the employees of the company.
Answer» The age of the employees in a startup company is shown below. $\begin{matrix} Age & No. of Employees 18 - 26 & 30 26 - 34 & 70 34 - 42 & 50 42 - 50 & 30 50 - 58 & 10 58 - 66 & 10 \end{matrix}$ Find the modal age of the employees of the company.

Discussion

3239.	Four cyclists start cycling around simultaneously with speeds of 9 m/s, 15 m/s, 25 m/s, and 33 m/s in the same direction. After how much time will they meet for the first time if the length of the track is 500 metres?
Answer» Four cyclists start cycling around simultaneously with speeds of 9 m/s, 15 m/s, 25 m/s, and 33 m/s in the same direction. After how much time will they meet for the first time if the length of the track is 500 metres?

Discussion

3240.	Match the following solid objects with the expressions of their volume.
Answer» Match the following solid objects with the expressions of their volume.

Discussion

3241.	In the given figure, PT touches a circle whose centre is O at R. Diameter SQ produced meets PT at P. If ∠SPR=x∘ and ∠QRP=ycirc, then which of the following statements relate x and y?
Answer» In the given figure, PT touches a circle whose centre is O at R. Diameter SQ produced meets PT at P. If $∠ S P R = x^{\circ}$ and $∠ Q R P = y^{c i r c}$ , then which of the following statements relate x and y?

Discussion

3242.	A linear equation in two variables has _____________
Answer» A linear equation in two variables has _____________

Discussion

3243.	State whether the given statement is true or false. Justify your answer The points A(3,1), B(12,-2) and C(0,2) cannot be vertices of a triangle.
Answer» State whether the given statement is true or false. Justify your answer The points A(3,1), B(12,-2) and C(0,2) cannot be vertices of a triangle.

Discussion

3244.	In any ΔABC, prove that. a(sin B−sin C)+b (sin C−sin A)+c (sin A−sin B)=0
Answer» In any $Δ A B C$ , prove that. $a (s i n B - s i n C) + b (s i n C - s i n A) + c (s i n A - s i n B) = 0$

3244.

In any ΔABC, prove that. a(sin B−sin C)+b (sin C−sin A)+c (sin A−sin B)=0

Answer»

In any $Δ A B C$ , prove that.

$a (s i n B - s i n C) + b (s i n C - s i n A) + c (s i n A - s i n B) = 0$

Discussion

3245.	Determine the ratio in which a line 2x + y – 4 = 0 divides another line segment joining points A(2, – 2) and B(3, 7).
Answer» Determine the ratio in which a line 2x + y – 4 = 0 divides another line segment joining points A(2, – 2) and B(3, 7).

Discussion

3246.	In the arithmetic progression given below, find the common difference. 1, a, b, c, 9
Answer» In the arithmetic progression given below, find the common difference. 1, a, b, c, 9

Discussion

3247.	To divide AB in the ratio 5:1, after some stages, we draw an arc with centre at A6, repeat the same with equal radius at A5. Then mark the first arc (A6 and A5) at C1 and mark the same for second arc (A5 and A4) at C2. This is done in order to:
Answer» To divide AB in the ratio 5:1, after some stages, we draw an arc with centre at $A_{6}$ , repeat the same with equal radius at $A_{5}$ . Then mark the first arc ( $A_{6}$ and $A_{5}$ ) at $C_{1}$ and mark the same for second arc ( $A_{5}$ and $A_{4}$ ) at $C_{2}$ . This is done in order to:

3247.

To divide AB in the ratio 5:1, after some stages, we draw an arc with centre at A6, repeat the same with equal radius at A5. Then mark the first arc (A6 and A5) at C1 and mark the same for second arc (A5 and A4) at C2. This is done in order to:

Answer»

To divide AB in the ratio 5:1, after some stages, we draw an arc with centre at $A_{6}$ , repeat the same with equal radius at $A_{5}$ . Then mark the first arc ( $A_{6}$ and $A_{5}$ ) at $C_{1}$ and mark the same for second arc ( $A_{5}$ and $A_{4}$ ) at $C_{2}$ . This is done in order to:

Discussion

3248.	Volumes of two spheres are in the ratio 64 ; 27 . The ratio of their surface areas is (a) 3 : 4 (b) 4 : 3 (c) 9 : 16 (d) 16 : 9
Answer» Volumes of two spheres are in the ratio 64 ; 27 . The ratio of their surface areas is (a) 3 : 4 (b) 4 : 3 (c) 9 : 16 (d) 16 : 9

Discussion

3249.	If A(−1,8), B(4,−2) and C(−5,−3) are the vertices of a triangle, then the equation of the altitude through (−1,8) is given as ax+b=y. Find a+b.26
Answer» If A $(- 1, 8)$ , B $(4, - 2)$ and C $(- 5, - 3)$ are the vertices of a triangle, then the equation of the altitude through $(- 1, 8)$ is given as $a x + b = y$ . Find $a + b$ . 26

Discussion

3250.	The monthly incomes of Aryan and Babban are in the ratio 3 : 4 and their monthly expenditures are in the ratio 5 : 7. If each saves Rs 15,000 per month, find their monthly incomes using matrix method. This problem reflects which value?
Answer» The monthly incomes of Aryan and Babban are in the ratio 3 : 4 and their monthly expenditures are in the ratio 5 : 7. If each saves Rs 15,000 per month, find their monthly incomes using matrix method. This problem reflects which value?

Discussion

Explore topic-wise InterviewSolutions in .

The value of sin2 30o - cos2 30o is :

If a1, a2, a3, ....., an, ..... is an A.P. such that a18 – a14 = 32, then its common difference is __________.

Degree of the algebraic expression 4x+5x+2 is ______.

Draw a triangle ABC in which AB = 5 cm, BC = 6 cm and ∠ ABC = 60∘. Then, construct a triangle whose sides are 57 times the corresponding sides of Δ ABC. Justify your construction.

The given table shows the Marks obtained by students in Mathematics.MarksNo. of Students0−10310−20720−301230−401540−502050−60960−70870−801680−901490−1006Using the table determine the Lower Quartile by drawing an ogive curve.

A function is described as:For the function, its range will be

What is the simplified form of the given expression?x3y + 4x2y2 + 3xy3 + 7x2y2 + 3x3 + 4y2 + 6xy + 7x3y + 8y2

If √a>√b>√c>√d , where a, b, c and d are consecutive natural numbers , then which of the following is correct?(i) √a-√b > √c-√d(ii) √c-√d > √a-√b(iii) √a-√c > √b-√d(iv) √c-√d = √a-√bExplain.

A hemispherical bowl of internal diameter 36cm contains a liquid. This liquid is to be filled in cylindrical bottles of radius 3cm and height 6cm. How many bottles are required to empty the bowl. ( Is it needed to convert volume into litres)

If sin ( θ + 24 ) = cos θ , where θ + 24 is a acute angle . Find the value of θ .

What is the difference between secant and diameter ?

Find the nature of the roots of the following quadratic equations. If the real roots exist, find them: 2x2−6x+3=0

Question 160 Quadrilateral EFGH is a rectangle in which J is the point of intersection of the diagonals. Find the value of x, if JF = 8x + 4 and EG = 24x - 8.

Question 17 Find the 20th term from the last term of the A.P. 3, 8, 13, …, 253.

In the given figure, QR is a common tangent to the given circle, touching externally at the point T. The tangent at T meets QR at P. If PT = 3.8 cm then the length of QR is [CBSE 2014](a) 1.9 cm(b) 3.8 cm(c) 5.7 cm(d) 7.6 cm

If cos θ=513, find the value of sin2 θ-cos2 θ2 sin θ cos θ×1tan2 θ.

Find the mode of the following data. xifi10101415187219259

For the following distribution :Class: 0-5 5-10 10-15 15-20 20-25Frequency: 10 15 12 20 9the sum of the lower limits of the median and modal class is (a) 15 (b) 25 (c) 30 (d) 35

In the given figure if DE || BC, then find EC.

Choose the correct answer in each of the following questions:If an denotes the nth term of the AP 3, 8, 13, 18, ... then what is the value of a30-a20?(a) 40 (b) 36 (c) 50 (d) 56

The radii of the ends of the frustum of a cone are r1 and r2 cm and If h cm is the height of the frustum, then the volume of the frustum of the cone in cm3 is _________.

A boat goes 30 km upstream and 44 km downstream in 10 hours. It can go 40 km upstream and 55 km downstream in 13 hours. Find the speed of the stream and that of the boat in still water.

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

Find the mean of each of the following frequency distributions : Class interval: 10−30 30−50 50−70 70−90 90−110 110−130 Frequency: 5 8 12 20 3 2

Write the next day’s entry in Walter’s diary. Make up information, in order to make your entry interesting.

The height of an equilateral triangle is 6 cm. Find its area. [Take 3 = 1.73]

The product of 3 consecutive numbers, when the first number is even is divisible by ___

A and B are two points on the x-axis and y-axis respectively. P(2, -3) is the mid point of AB. Find the (i) co-ordinates of A and B (ii) slope of line AB (iii) equation of line AB.

Determine the AP whose third term is 16 and the 7th term exceeds the 5th term by 12.

N positive integers are multiplied together . What is the probability that last digit of the number is 5?

The sum of all positive integers n for which 13+23....+(2n)312+22+...n2 is also an integer is.

(x-2y)^3 - (x+2y)^3

In the following diagram, AB is a floor-board; PQRS is a cubical box with each edge = 1 m and ∠B=60∘. Calculate the length of the board AB.

A quadratic polynomial, the sum of whose zeroes is 0 and one zero is 3, is(a) x2 − 9(b) x2 + 9(c) x2 + 3(d) x2 − 3

The age of the employees in a startup company is shown below. AgeNo. of Employees18−263026−347034−425042−503050−581058−6610 Find the modal age of the employees of the company.

Four cyclists start cycling around simultaneously with speeds of 9 m/s, 15 m/s, 25 m/s, and 33 m/s in the same direction. After how much time will they meet for the first time if the length of the track is 500 metres?

Match the following solid objects with the expressions of their volume.

In the given figure, PT touches a circle whose centre is O at R. Diameter SQ produced meets PT at P. If ∠SPR=x∘ and ∠QRP=ycirc, then which of the following statements relate x and y?

A linear equation in two variables has _____________

State whether the given statement is true or false. Justify your answer The points A(3,1), B(12,-2) and C(0,2) cannot be vertices of a triangle.

In any ΔABC, prove that. a(sin B−sin C)+b (sin C−sin A)+c (sin A−sin B)=0

Determine the ratio in which a line 2x + y – 4 = 0 divides another line segment joining points A(2, – 2) and B(3, 7).

In the arithmetic progression given below, find the common difference. 1, a, b, c, 9

To divide AB in the ratio 5:1, after some stages, we draw an arc with centre at A6, repeat the same with equal radius at A5. Then mark the first arc (A6 and A5) at C1 and mark the same for second arc (A5 and A4) at C2. This is done in order to:

Volumes of two spheres are in the ratio 64 ; 27 . The ratio of their surface areas is (a) 3 : 4 (b) 4 : 3 (c) 9 : 16 (d) 16 : 9

If A(−1,8), B(4,−2) and C(−5,−3) are the vertices of a triangle, then the equation of the altitude through (−1,8) is given as ax+b=y. Find a+b.26

The monthly incomes of Aryan and Babban are in the ratio 3 : 4 and their monthly expenditures are in the ratio 5 : 7. If each saves Rs 15,000 per month, find their monthly incomes using matrix method. This problem reflects which value?