32581 + Interview Questions in Mathematics Page 18 InterviewSolution

851.	(a) Find the first term of G.P. in which S6 = 1365 and r = 4(b) Find the common ratio of a G.P. in which S2 = 6 and a = 2
Answer» (a) Find the first term of G.P. in which S₆ = 1365 and r = 4 (b) Find the common ratio of a G.P. in which S₂ = 6 and a = 2

851.

(a) Find the first term of G.P. in which S6 = 1365 and r = 4(b) Find the common ratio of a G.P. in which S2 = 6 and a = 2

Answer»

(a) Find the first term of G.P. in which S₆ = 1365 and r = 4

(b) Find the common ratio of a G.P. in which S₂ = 6 and a = 2

852.	The following table gives the daily income of 50 workers of a factory: Daily income(in Rs.)100−120120−140140−160160−180180−200Number of workers12148610 Find the mean, mode and median of the above data.
Answer» The following table gives the daily income of 50 workers of a factory: $\begin{matrix} Daily income(in Rs.) & 100 - 120 & 120 - 140 & 140 - 160 & 160 - 180 & 180 - 200 Number of workers & 12 & 14 & 8 & 6 & 10 \end{matrix}$ Find the mean, mode and median of the above data.

Discussion

853.	Question 7 (ii)In the below figure, altitudes AD and CE of ΔABC intersect each other at the point P. Show that(ii) ΔABD∼ΔCBE
Answer» Question 7 (ii) In the below figure, altitudes AD and CE of $Δ A B C$ intersect each other at the point P. Show that (ii) $Δ A B D \sim Δ C B E$

Discussion

854.	An open metal bucket is in the shape of a frustum of a cone, mounted on a hollow cylindrical base made of the same metallic sheet. The diameters of the two circular ends of the bucket are 45 cm and 25 cm, the total vertical height of the bucket is 40 cm and that of the cylindrical base is 6 cm. Find the area of the metallic sheet used to make the bucket. Also, find the volume of water the bucket can hold, in litres.
Answer» An open metal bucket is in the shape of a frustum of a cone, mounted on a hollow cylindrical base made of the same metallic sheet. The diameters of the two circular ends of the bucket are 45 cm and 25 cm, the total vertical height of the bucket is 40 cm and that of the cylindrical base is 6 cm. Find the area of the metallic sheet used to make the bucket. Also, find the volume of water the bucket can hold, in litres.

Discussion

855.	Find the mean, median and mode of the following data: Class0−5050−100100−150150−200200−250250−300300−350Frequency2356531
Answer» Find the mean, median and mode of the following data: $\begin{matrix} Class & 0 - 50 & 50 - 100 & 100 - 150 & 150 - 200 & 200 - 250 & 250 - 300 & 300 - 350 Frequency & 2 & 3 & 5 & 6 & 5 & 3 & 1 \end{matrix}$

Discussion

856.	Decide whether following sequence is an A.P., if so find the 20th term of the progression.–12, –5, 2, 9, 16, 23, 30,...
Answer» Decide whether following sequence is an A.P., if so find the 20^th term of the progression. –12, –5, 2, 9, 16, 23, 30,...

Discussion

857.

The following table gives production yield in kg. per hectare of wheat of 150 farms in a village. Calculate the mean, median and mode values. Production yield (kg. per hectare) 50 – 53 53 – 56 56 – 59 59 – 62 62 – 65 65 – 68 68 – 71 71 – 74 74 – 77 Number of farms 3 8 14 30 36 28 16 10 5

Answer»

The following table gives production yield in kg. per hectare of wheat of 150 farms in a village. Calculate the mean, median and mode values.

Production yield (kg. per hectare)	50 – 53	53 – 56	56 – 59	59 – 62	62 – 65	65 – 68	68 – 71	71 – 74	74 – 77
Number of farms	3	8	14	30	36	28	16	10	5

Discussion

858.	The hypotenuse of a right triangle is 310 cm. If the smaller leg is tripled and the longer leg doubled, new hypotenuse wll be 95 cm. How long are the legs of the triangle?
Answer» The hypotenuse of a right triangle is $3 \sqrt{10} cm$ . If the smaller leg is tripled and the longer leg doubled, new hypotenuse wll be $9 \sqrt{5} cm$ . How long are the legs of the triangle?

Discussion

859.	Differences between tan theta and theta
Answer» Differences between tan theta and theta

Discussion

860.	If the cost of 48 bags of paddy is Rs 16,800, then cost of 36 bags of paddy is Rs__________
Answer» If the cost of 48 bags of paddy is Rs 16,800, then cost of 36 bags of paddy is Rs__________

Discussion

861.	Use Euclid's division lemma to show that the square of any positive integer is either of the form 3m or 3m +1 for some interger m.
Answer» Use Euclid's division lemma to show that the square of any positive integer is either of the form 3m or 3m +1 for some interger m.

Discussion

862.	Tangents drawn from an external point to a circle subtend ________ angles to the centre.
Answer» Tangents drawn from an external point to a circle subtend ________ angles to the centre.

Discussion

863.	In which of the following situations, the sequence of numbers formed will form an A.P.?(i) The cost of digging a well for the first metre is Rs 150 and rises by Rs 20 for each succeeding metre.(ii) The amount of air present in the cylinder when a vacuum pump removes each time 14 of their remaining in the cylinder.Q
Answer» In which of the following situations, the sequence of numbers formed will form an A.P.? (i) The cost of digging a well for the first metre is Rs 150 and rises by Rs 20 for each succeeding metre. (ii) The amount of air present in the cylinder when a vacuum pump removes each time $\frac{1}{4}$ of their remaining in the cylinder. Q

Discussion

864.	Find, in terms of π, the length of the arc that subtends an angle of 30° at the centre of a circle of radius 4 cm.
Answer» Find, in terms of π, the length of the arc that subtends an angle of 30° at the centre of a circle of radius 4 cm.

Discussion

865.	A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to 1 cm and the height of the cone is equal to its radius. Find the volume of the solid in terms of π.
Answer» A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to 1 cm and the height of the cone is equal to its radius. Find the volume of the solid in terms of $π$ .

Discussion

866.	1.Sin+co26 Cos
Answer» 1.Sin+co26 Cos

Discussion

867.	Which of the following is true for the histogram ?
Answer» Which of the following is true for the histogram ?

867.

Which of the following is true for the histogram ?

Answer»

Which of the following is true for the histogram ?

Discussion

868.	In v−t graph shown in fig. the displacement of the body in 4 seconds will be, if it starts from origin.
Answer» In $v - t$ graph shown in fig. the displacement of the body in $4$ seconds will be, if it starts from origin.

Discussion

869.	In three line segments OA, OB and OC points L, M, N respectively are so chosen that LM \|\| AB and MN \|\| BC but neither of L, M, N nor of A, B, C are collinear. Show that LN \|\| AC.
Answer» In three line segments OA, OB and OC points L, M, N respectively are so chosen that LM \|\| AB and MN \|\| BC but neither of L, M, N nor of A, B, C are collinear. Show that LN \|\| AC.

Discussion

870.	Let A be a set containing n elements. Which of the following conditions is always satisfied by n?
Answer» Let A be a set containing n elements. Which of the following conditions is always satisfied by n?

Discussion

871.	The depth of a hemispherical water tank is 2.1 m at the centre. Find the capacity of the water tank in litres.
Answer» The depth of a hemispherical water tank is 2.1 m at the centre. Find the capacity of the water tank in litres.

Discussion

872.	A statue, 1.6 m tall, stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60∘ and from the same point the angle of elevation of the top of the pedestal is 45∘. Find the height of the pedestal.
Answer» A statue, 1.6 m tall, stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is $60^{\circ}$ and from the same point the angle of elevation of the top of the pedestal is $45^{\circ}$ . Find the height of the pedestal.

Discussion

873.	From the given table find the Median : Variable123456789Frequency5781291015222
Answer» From the given table find the Median : $\begin{matrix} Variable & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 Frequency & 5 & 7 & 8 & 12 & 9 & 10 & 15 & 2 & 22 \end{matrix}$

873.

From the given table find the Median : Variable123456789Frequency5781291015222

Answer»

From the given table find the Median :

$\begin{matrix} Variable & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 Frequency & 5 & 7 & 8 & 12 & 9 & 10 & 15 & 2 & 22 \end{matrix}$

Discussion

874.	Natural numbers which end in 1 or 6, written in order. Can you describe this sequence in any other way?
Answer» Natural numbers which end in 1 or 6, written in order. Can you describe this sequence in any other way?

Discussion

875.	If cosec θ = 2x and cot θ=2x, find the value of 2x2-1x2.
Answer» If cosec θ = 2x and $\cot θ = \frac{2}{x}$ , find the value of $2 (x^{2} - \frac{1}{x^{2}})$ .

Discussion

876.	On heating a uniform metallic cylinder lengthncrea.ses by 3% The aroa of cross-sector of itsbase wil increase by
Answer» On heating a uniform metallic cylinder lengthncrea.ses by 3% The aroa of cross-sector of itsbase wil increase by

Discussion

877.	If p, q are real and p ≠ q, then show that the roots of the equation (p − q) x2 + 5(p + q) x − 2(p − q) = 0 are real and unequal.
Answer» If p, q are real and p ≠ q, then show that the roots of the equation (p − q) x² + 5(p + q) x − 2(p − q) = 0 are real and unequal.

Discussion

878.	In the board exams, when we find the HCF in 2 numbers, do we have to do the devision or just directly write the statements like this (225= 135 × 1 + 9) ? Will they cut marks if you don't do devision ?
Answer» In the board exams, when we find the HCF in 2 numbers, do we have to do the devision or just directly write the statements like this (225= 135 × 1 + 9) ? Will they cut marks if you don't do devision ?

Discussion

879.	If the mean of frequency distribution is 8.1 and Σfixi = 132 + 5k, Σfi = 20, then k =(a) 3(b) 4(c) 5(d) 6
Answer» If the mean of frequency distribution is 8.1 and Σf_ix_i = 132 + 5k, Σf_i = 20, then k = (a) 3 (b) 4 (c) 5 (d) 6

Discussion

880.	Find the area of the triangle formed by joining the mid-point of the sides of the triangle whose vertices are (0,–1), (2, 1) and (0, 3). Find the ratio of area of the triangle formed to the area of the given triangle
Answer» Find the area of the triangle formed by joining the mid-point of the sides of the triangle whose vertices are (0,–1), (2, 1) and (0, 3). Find the ratio of area of the triangle formed to the area of the given triangle

Discussion

881.	Find a quadratic polynomial with the given number as the sum and the product of its zeroes respectively √2 , 1/3
Answer» Find a quadratic polynomial with the given number as the sum and the product of its zeroes respectively √2 , 1/3

881.

Find a quadratic polynomial with the given number as the sum and the product of its zeroes respectively √2 , 1/3

Answer»

Find a quadratic polynomial with the given number as the sum and the product of its zeroes respectively

√2 , 1/3

Discussion

882.	The equation of the horizontal line passing through the point (4,-7) is
Answer» The equation of the horizontal line passing through the point (4,-7) is

Discussion

883.	Mettez les verbes suivants aux temps convenables.
Answer» Mettez les verbes suivants aux temps convenables.

Discussion

884.	Star Ltd. is registered with capital of ₹ 50,00,000 divided into 50,000 equity shares of ₹ 100 each, The Company issued 25,000 equity shares for subscription. Subscription was received for 23,750 shares and all the due amount was duly received, except the first and final call of ₹ 20 per share on 600 shares. Show the 'Share Capital' in the Balance Sheet of the company.
Answer» Star Ltd. is registered with capital of ₹ 50,00,000 divided into 50,000 equity shares of ₹ 100 each, The Company issued 25,000 equity shares for subscription. Subscription was received for 23,750 shares and all the due amount was duly received, except the first and final call of ₹ 20 per share on 600 shares. Show the 'Share Capital' in the Balance Sheet of the company.

Discussion

885.	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

886.	In a circle of radius 10 cm, an arc subtends an angle of 108° at the centre. what is the area of the sector in terms of π?
Answer» In a circle of radius 10 cm, an arc subtends an angle of 108° at the centre. what is the area of the sector in terms of π?

Discussion

887.	The number of solid spheres, each of diameter 6 cm that could be moulded to form a solid metal cylinder of height 45 cm and diameter 4 cm, is(a) 3(b) 4(c) 5(d) 6
Answer» The number of solid spheres, each of diameter 6 cm that could be moulded to form a solid metal cylinder of height 45 cm and diameter 4 cm, is (a) 3 (b) 4 (c) 5 (d) 6

Discussion

888.	The mean ¯x of a grouped data is given by:
Answer» The mean $¯ x$ of a grouped data is given by:

Discussion

889.	How many outcomes will have no heads in a toss of multiples coins as given below? 1 coin - outcome(s) 2 coins - outcome(s) 3 coins - outcome(s)
Answer» How many outcomes will have no heads in a toss of multiples coins as given below? 1 coin - outcome(s) 2 coins - outcome(s) 3 coins - outcome(s)

889.

How many outcomes will have no heads in a toss of multiples coins as given below? 1 coin - outcome(s) 2 coins - outcome(s) 3 coins - outcome(s)

Answer»

How many outcomes will have no heads in a toss of multiples coins as given below?

1 coin - outcome(s)

2 coins - outcome(s)

3 coins - outcome(s)

Discussion

890.	Construct a ∆ABC in which base AB = 5 cm, ∠A = 30° and AC – BC = 2.5 cm. Justify your construction.
Answer» Construct a ∆ABC in which base AB = 5 cm, ∠A = 30° and AC – BC = 2.5 cm. Justify your construction.

Discussion

891.	…, −4,−3,−2,−1 In which order the above integers are arranged in? ___
Answer» …, $- 4, - 3, - 2, - 1$ In which order the above integers are arranged in? ___

891.

…, −4,−3,−2,−1 In which order the above integers are arranged in? ___

Answer»

…, $- 4, - 3, - 2, - 1$

In which order the above integers are arranged in?

___

Discussion

892.	In the given fig. the circle touch the lines at X, Y, Z, B, C and D. If PQ = 8 cm, QA = 9 cm and PA = 7 cm, then the length PX, AZ and QY are respectively.
Answer» In the given fig. the circle touch the lines at X, Y, Z, B, C and D. If PQ = 8 cm, QA = 9 cm and PA = 7 cm, then the length PX, AZ and QY are respectively.

892.

In the given fig. the circle touch the lines at X, Y, Z, B, C and D. If PQ = 8 cm, QA = 9 cm and PA = 7 cm, then the length PX, AZ and QY are respectively.

Answer»

In the given fig. the circle touch the lines at X, Y, Z, B, C and D. If PQ = 8 cm, QA = 9 cm and PA = 7 cm, then the length PX, AZ and QY are respectively.

Discussion

893.	Kamal and Kapil are partners having fixed capitals of ₹ 5,00,000 each as on 31st March, 2018. Kamal introduced further capital of ₹ 1,00,000 on 1st October, 2018 whereas Kapil withdrew ₹ 1,00,000 on 1st October, 2018 out of capital.Interest on capital is to be allowed 10% p.a.The firm earned net profit of ₹ 6,00,000 for the year ended 31st March 2019.Pass the Journal entry for interest on capital and prepare Profit and Loss Appropriation Account.
Answer» Kamal and Kapil are partners having fixed capitals of ₹ 5,00,000 each as on 31st March, 2018. Kamal introduced further capital of ₹ 1,00,000 on 1st October, 2018 whereas Kapil withdrew ₹ 1,00,000 on 1st October, 2018 out of capital. Interest on capital is to be allowed 10% p.a. The firm earned net profit of ₹ 6,00,000 for the year ended 31st March 2019. Pass the Journal entry for interest on capital and prepare Profit and Loss Appropriation Account.

Discussion

894.	Does the line joining (2, 3) and (3, 1) pass through the point (5, 6)? What about (5, −9)?
Answer» Does the line joining (2, 3) and (3, 1) pass through the point (5, 6)? What about (5, −9)?

Discussion

895.	Ramesh’s salary in February 2008 is Rs. 10,000. If he’s promised an increase of Rs. 1000 every year, what would be his salary in Feb 2011?
Answer» Ramesh’s salary in February 2008 is Rs. 10,000. If he’s promised an increase of Rs. 1000 every year, what would be his salary in Feb 2011?

Discussion

896.	The output (X) of the logic circuit shown in the figure will be-
Answer» The output $(X)$ of the logic circuit shown in the figure will be-

Discussion

897.	Find four consecutive terms in an A.P. whose sum is 12 and sum of 3rd and 4th term is 14.(Assume the four consecutive terms in A.P. are a – d, a, a + d, a +2d)
Answer» Find four consecutive terms in an A.P. whose sum is 12 and sum of 3^rd and 4^th term is 14. (Assume the four consecutive terms in A.P. are a – d, a, a + d, a +2d)

Discussion

898.	Find the value of d²x/dx²:(1) y=cos3xsin4x(2) y=xe^(1/X)
Answer» Find the value of d²x/dx²: (1) y=cos3xsin4x (2) y=xe^(1/X)

Discussion

899.	The sum of the third and the seventh terms of an A.P is 6 and their product is 8. Find the sum of first sixteen terms of the A.P.
Answer» The sum of the third and the seventh terms of an A.P is 6 and their product is 8. Find the sum of first sixteen terms of the A.P.

Discussion

900.	A light post standing at point P on a circular path of radius ‘x’ subtends an angle θ at some point Q on the path and PQ subtends an angle of 45º at any other point on the path.What is height of the light post ?
Answer» A light post standing at point P on a circular path of radius ‘x’ subtends an angle $θ$ at some point Q on the path and PQ subtends an angle of 45º at any other point on the path. What is height of the light post ?

Discussion

Explore topic-wise InterviewSolutions in .

(a) Find the first term of G.P. in which S6 = 1365 and r = 4(b) Find the common ratio of a G.P. in which S2 = 6 and a = 2

The following table gives the daily income of 50 workers of a factory: Daily income(in Rs.)100−120120−140140−160160−180180−200Number of workers12148610 Find the mean, mode and median of the above data.

Question 7 (ii)In the below figure, altitudes AD and CE of ΔABC intersect each other at the point P. Show that(ii) ΔABD∼ΔCBE

Find the mean, median and mode of the following data: Class0−5050−100100−150150−200200−250250−300300−350Frequency2356531

Decide whether following sequence is an A.P., if so find the 20th term of the progression.–12, –5, 2, 9, 16, 23, 30,...

The hypotenuse of a right triangle is 310 cm. If the smaller leg is tripled and the longer leg doubled, new hypotenuse wll be 95 cm. How long are the legs of the triangle?

Differences between tan theta and theta

If the cost of 48 bags of paddy is Rs 16,800, then cost of 36 bags of paddy is Rs__________

Use Euclid's division lemma to show that the square of any positive integer is either of the form 3m or 3m +1 for some interger m.

Tangents drawn from an external point to a circle subtend ________ angles to the centre.

Find, in terms of π, the length of the arc that subtends an angle of 30° at the centre of a circle of radius 4 cm.

A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to 1 cm and the height of the cone is equal to its radius. Find the volume of the solid in terms of π.

1.Sin+co26 Cos

Which of the following is true for the histogram ?

In v−t graph shown in fig. the displacement of the body in 4 seconds will be, if it starts from origin.

In three line segments OA, OB and OC points L, M, N respectively are so chosen that LM || AB and MN || BC but neither of L, M, N nor of A, B, C are collinear. Show that LN || AC.

Let A be a set containing n elements. Which of the following conditions is always satisfied by n?

The depth of a hemispherical water tank is 2.1 m at the centre. Find the capacity of the water tank in litres.

A statue, 1.6 m tall, stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60∘ and from the same point the angle of elevation of the top of the pedestal is 45∘. Find the height of the pedestal.

From the given table find the Median : Variable123456789Frequency5781291015222

Natural numbers which end in 1 or 6, written in order. Can you describe this sequence in any other way?

If cosec θ = 2x and cot θ=2x, find the value of 2x2-1x2.

On heating a uniform metallic cylinder lengthncrea.ses by 3% The aroa of cross-sector of itsbase wil increase by

If p, q are real and p ≠ q, then show that the roots of the equation (p − q) x2 + 5(p + q) x − 2(p − q) = 0 are real and unequal.

In the board exams, when we find the HCF in 2 numbers, do we have to do the devision or just directly write the statements like this (225= 135 × 1 + 9) ? Will they cut marks if you don't do devision ?

If the mean of frequency distribution is 8.1 and Σfixi = 132 + 5k, Σfi = 20, then k =(a) 3(b) 4(c) 5(d) 6

Find the area of the triangle formed by joining the mid-point of the sides of the triangle whose vertices are (0,–1), (2, 1) and (0, 3). Find the ratio of area of the triangle formed to the area of the given triangle

Find a quadratic polynomial with the given number as the sum and the product of its zeroes respectively √2 , 1/3

The equation of the horizontal line passing through the point (4,-7) is

Mettez les verbes suivants aux temps convenables.

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

In a circle of radius 10 cm, an arc subtends an angle of 108° at the centre. what is the area of the sector in terms of π?

The number of solid spheres, each of diameter 6 cm that could be moulded to form a solid metal cylinder of height 45 cm and diameter 4 cm, is(a) 3(b) 4(c) 5(d) 6

The mean ¯x of a grouped data is given by:

How many outcomes will have no heads in a toss of multiples coins as given below? 1 coin - outcome(s) 2 coins - outcome(s) 3 coins - outcome(s)

Construct a ∆ABC in which base AB = 5 cm, ∠A = 30° and AC – BC = 2.5 cm. Justify your construction.

…, −4,−3,−2,−1 In which order the above integers are arranged in? ___

In the given fig. the circle touch the lines at X, Y, Z, B, C and D. If PQ = 8 cm, QA = 9 cm and PA = 7 cm, then the length PX, AZ and QY are respectively.

Does the line joining (2, 3) and (3, 1) pass through the point (5, 6)? What about (5, −9)?

Ramesh’s salary in February 2008 is Rs. 10,000. If he’s promised an increase of Rs. 1000 every year, what would be his salary in Feb 2011?

The output (X) of the logic circuit shown in the figure will be-

Find four consecutive terms in an A.P. whose sum is 12 and sum of 3rd and 4th term is 14.(Assume the four consecutive terms in A.P. are a – d, a, a + d, a +2d)

Find the value of d²x/dx²:(1) y=cos3xsin4x(2) y=xe^(1/X)

The sum of the third and the seventh terms of an A.P is 6 and their product is 8. Find the sum of first sixteen terms of the A.P.

A light post standing at point P on a circular path of radius ‘x’ subtends an angle θ at some point Q on the path and PQ subtends an angle of 45º at any other point on the path.What is height of the light post ?