32581 + Interview Questions in Mathematics Page 265 InterviewSolution

13201.	What is the equation of the line joining the points (1, 3) and (2, 7)? Prove that if (x, y) is a point on this line, so is the point (x + 1, y + 4).
Answer» What is the equation of the line joining the points (1, 3) and (2, 7)? Prove that if (x, y) is a point on this line, so is the point (x + 1, y + 4).

Discussion

13202.	Manish opens a Recurring Deposit Account with the Bank of Rajasthan and deposits ₹600 per month for 20 months. Calculate the maturity value of this account, if the bank pays interest at the rate of 10% per annum.
Answer» Manish opens a Recurring Deposit Account with the Bank of Rajasthan and deposits ₹600 per month for 20 months. Calculate the maturity value of this account, if the bank pays interest at the rate of 10% per annum.

Discussion

13203.	If α and β are the zeroes of the polynomial x2+4x−77, then the quadratic polynomial whose zeroes are 1α and 1β can be equal to
Answer» If $α and β$ are the zeroes of the polynomial $x^{2} + 4 x - 77,$ then the quadratic polynomial whose zeroes are $\frac{1}{α}$ and $\frac{1}{β}$ can be equal to

Discussion

13204.	What is units place in 99
Answer» What is units place in 9⁹

Discussion

13205.	Which of the following correctly represents the HCF and LCM of 4500 and 10584?
Answer» Which of the following correctly represents the HCF and LCM of 4500 and 10584?

Discussion

13206.	Th sum of the first 30 terms of the arithmetic sequence 10, 18, 26... is ___.
Answer» Th sum of the first 30 terms of the arithmetic sequence 10, 18, 26... is ___.

Discussion

13207.	Which of the following statements are true ? (i) All cubes are cuboids. (ii) All cuboids are cubes. (iii) A cube has 6 faces, 8 vertices and 12 edges. (iv) A cube has 8 faces, 12 vertices and 6 edges.
Answer» Which of the following statements are true ? (i) All cubes are cuboids. (ii) All cuboids are cubes. (iii) A cube has 6 faces, 8 vertices and 12 edges. (iv) A cube has 8 faces, 12 vertices and 6 edges.

Discussion

13208.	Write the set builder form A = {-1, 1}.
Answer» Write the set builder form A = {-1, 1}.

Discussion

13209.	A store room in the form of a cuboid has measures 42 m×35 m×21 m. How many cuboidal boxes can be stored in it if the volume of one box is 0.7 m3?
Answer» A store room in the form of a cuboid has measures $42 m \times 35 m \times 21 m$ . How many cuboidal boxes can be stored in it if the volume of one box is $0.7 m^{3}$ ?

Discussion

13210.	Question 37The curved surface area of a cylinder which exactly fits in a cube of side b is ___
Answer» Question 37 The curved surface area of a cylinder which exactly fits in a cube of side b is ___

13210.

Question 37The curved surface area of a cylinder which exactly fits in a cube of side b is ___

Answer»

Question 37

The curved surface area of a cylinder which exactly fits in a cube of side b is ___

Discussion

13211.	A particle is projected from the ground at some anglewith the horizontal and it passes through points(4 m, 6 m) and (6 m, 4 m) in the xy plane. Therange of the particle is(1) 16 m(3) 10 m(2) 7.6 m(4) 3.8 m
Answer» A particle is projected from the ground at some anglewith the horizontal and it passes through points(4 m, 6 m) and (6 m, 4 m) in the xy plane. Therange of the particle is(1) 16 m(3) 10 m(2) 7.6 m(4) 3.8 m

Discussion

13212.	Draw a circle with centre O and radius 3.5 cm. Take point P at a distance 5.7 cm from the centre. Draw tangents to the circle from point P.
Answer» Draw a circle with centre O and radius 3.5 cm. Take point P at a distance 5.7 cm from the centre. Draw tangents to the circle from point P.

Discussion

13213.	The length of the plot in meters is 1 more than twice its breadth and the area of a rectangle plot is 528 m2. Which of the following quadratic equations represents the given situation:
Answer» The length of the plot in meters is 1 more than twice its breadth and the area of a rectangle plot is 528 m². Which of the following quadratic equations represents the given situation:

Discussion

13214.	A lead pencil consists of a cylinder of wood with a solid cylinder of graphite filled in the interior.The diameter of the pencil is 7 mm and the diameter of the graphite is 1 mm.If the length of the pencil is 14 cm, find the volume of the wood and that of the graphite.[Assume π=227]
Answer» A lead pencil consists of a cylinder of wood with a solid cylinder of graphite filled in the interior.The diameter of the pencil is 7 mm and the diameter of the graphite is 1 mm.If the length of the pencil is 14 cm, find the volume of the wood and that of the graphite. $[A s s u m e π = \frac{22}{7}]$

Discussion

13215.	In △ABC, AB=3 cm, AC=4 cm and AD is the bisector of ∠A. Then, BD:DC is0.25
Answer» In $△ A B C, A B = 3 c m, A C = 4 c m$ and AD is the bisector of $∠$ A. Then, $B D : D C$ is 0.25

Discussion

13216.	P(x) be any polynomial. When it is divided by (x−17) and (x−71) , then the remainders are 71 and 17 respectively. Find remainder, when P(x) is divided by(x−17)(x−71).
Answer» P(x) be any polynomial. When it is divided by $(x - 17)$ and $(x - 71)$ , then the remainders are 71 and 17 respectively. Find remainder, when $P (x)$ is divided by $(x - 17) (x - 71)$ .

Discussion

13217.	Solve and find x and y:- 1/2(x+2y) +5/4(3x-2y)=-3/2 -------(i) 5/4(x+2y) - 3/5(3x-2y)=61/60 ---------(ii)
Answer» Solve and find x and y:- 1/2(x+2y) +5/4(3x-2y)=-3/2 -------(i) 5/4(x+2y) - 3/5(3x-2y)=61/60 ---------(ii)

13217.

Solve and find x and y:- 1/2(x+2y) +5/4(3x-2y)=-3/2 -------(i) 5/4(x+2y) - 3/5(3x-2y)=61/60 ---------(ii)

Answer»

Solve and find x and y:-

1/2(x+2y) +5/4(3x-2y)=-3/2 -------(i)

5/4(x+2y) - 3/5(3x-2y)=61/60 ---------(ii)

Discussion

13218.	Find the median of the following data. Class interval100−120120−140140−160160−180180−200Frequency10138712
Answer» Find the median of the following data. $\begin{matrix} C l a s s i n t e r v a l & 100 - 120 & 120 - 140 & 140 - 160 & 160 - 180 & 180 - 200 F r e q u e n c y & 10 & 13 & 8 & 7 & 12 \end{matrix}$

Discussion

13219.	Find the value(s) of k for which the points (3k−1,k−2),(k,k−7) and (k−1,−k−2) are collinear.
Answer» Find the value(s) of $k$ for which the points $(3 k - 1, k - 2), (k, k - 7)$ and $(k - 1, - k - 2)$ are collinear.

Discussion

13220.	Three cubes of a metal whose edges are in the ratios 3 : 4 : 5 are melted and converted into a single cube whose diagonal is 123 cm . Find the edges of the three cubes.
Answer» Three cubes of a metal whose edges are in the ratios 3 : 4 : 5 are melted and converted into a single cube whose diagonal is $12 \sqrt{3}$ cm . Find the edges of the three cubes.

Discussion

13221.	For the following A.Ps, write the first term and the common difference.3, 1, - 1, - 3 …
Answer» For the following A.Ps, write the first term and the common difference. 3, 1, - 1, - 3 …

Discussion

13222.	For two numbers 96 and 404, the HCF is 4. What is the LCM of the two numbers?9696
Answer» For two numbers 96 and 404, the HCF is 4. What is the LCM of the two numbers? 9696

Discussion

13223.	The length of an arc of a circle, subtending an angle of 54∘ at the centre is 16.5 cm. Calculate the radius, circumference and area of the circle.
Answer» The length of an arc of a circle, subtending an angle of $54^{\circ}$ at the centre is 16.5 cm. Calculate the radius, circumference and area of the circle.

Discussion

13224.	a housewife used to spend rupees 120 per month on the purchase of wheat at prevailing price. when the price Rose by rupees 2 per kg she found that the same amount should purchase 2 kg less. Find the new price per kg of the wheat.
Answer» a housewife used to spend rupees 120 per month on the purchase of wheat at prevailing price. when the price Rose by rupees 2 per kg she found that the same amount should purchase 2 kg less. Find the new price per kg of the wheat.

Discussion

13225.	If the standard deviation of first n natural numbers is 2, then n = ________________.
Answer» If the standard deviation of first n natural numbers is 2, then n = ________________.

Discussion

13226.	if m is slope of one of lines represented by ax^2+2hxy+by^2=0 then (h+bm)^2=h^2+abh^2-ab(a+b)^2(a-b)^2
Answer» if m is slope of one of lines represented by ax^2+2hxy+by^2=0 then (h+bm)^2= h^2+ab h^2-ab (a+b)^2 (a-b)^2

Discussion

13227.	A drinking glass is in the shape of a frustum of a cone of height 14 cm. The diameters of its two circular ends are 4 cm and 2 cm. Find the capacity of the glass(in cm3).
Answer» A drinking glass is in the shape of a frustum of a cone of height 14 cm. The diameters of its two circular ends are 4 cm and 2 cm. Find the capacity of the glass(in $c m^{3}$ ).

Discussion

13228.	Question 7 (ii)Solve the following pair of linear equations.(ii) ax + by = c bx + ay = 1 + c
Answer» Question 7 (ii) Solve the following pair of linear equations. (ii) ax + by = c bx + ay = 1 + c

Discussion

13229.	Find the single discount equivalent to two successive discounts 30% and 20%.
Answer» Find the single discount equivalent to two successive discounts 30% and 20%.

Discussion

13230.	79 If 13-x-10=8+5 then the value of x
Answer» 79 If 13-x-10=8+5 then the value of x

Discussion

13231.	The centre of a circle is (3, 4) and it passes through the point (2, 5). What is its radius?
Answer» The centre of a circle is (3, 4) and it passes through the point (2, 5). What is its radius?

Discussion

13232.	The base of a 15 cm tall container completely filled with water appears to be raised by 3.75 cm. Calculate the RI of water.
Answer» The base of a 15 cm tall container completely filled with water appears to be raised by 3.75 cm. Calculate the RI of water.

Discussion

13233.	If two zeroes of the polynomial x3 + x2 − 9x − 9 are 3 and −3, then its third zero is(a) −1(b) 1(c) −9(d) 9
Answer» If two zeroes of the polynomial x³ + x² − 9x − 9 are 3 and −3, then its third zero is (a) −1 (b) 1 (c) −9 (d) 9

Discussion

13234.	Null set should written in list form nd set builder form
Answer» Null set should written in list form nd set builder form

Discussion

13235.	A rhombus of side 18 cm has one of its angles as 135∘, then the area of the rhombus will be equal to
Answer» A rhombus of side 18 cm has one of its angles as $135^{\circ}$ , then the area of the rhombus will be equal to

13235.

A rhombus of side 18 cm has one of its angles as 135∘, then the area of the rhombus will be equal to

Answer»

A rhombus of side 18 cm has one of its angles as $135^{\circ}$ , then the area of the rhombus will be equal to

Discussion

13236.	Solve the following system of linear equations in three variables. x−2y+z=0 9x−8y+3z=0 2x+3y+5z=36
Answer» Solve the following system of linear equations in three variables. $x - 2 y + z = 0$ $9 x - 8 y + 3 z = 0$ $2 x + 3 y + 5 z = 36$

Discussion

13237.	Vinod sold goods to Darbara Singh for ₹ 1,000 on 1st January, 2019. He drew on the latter a bill for the amount payable 3 months after date.He discounted the bill with his bank for ₹ 990 on 4th January, 2019. On maturity, the bill is duly met. Make the Journal entries in the books of Vinod and Darbara Singh.
Answer» Vinod sold goods to Darbara Singh for ₹ 1,000 on 1st January, 2019. He drew on the latter a bill for the amount payable 3 months after date.He discounted the bill with his bank for ₹ 990 on 4th January, 2019. On maturity, the bill is duly met. Make the Journal entries in the books of Vinod and Darbara Singh.

Discussion

13238.	4 years ago a father was 6 times as old is Sun 10 years later the father will be two and a half Times as old as his son determine the present age of father and the son
Answer» 4 years ago a father was 6 times as old is Sun 10 years later the father will be two and a half Times as old as his son determine the present age of father and the son

Discussion

13239.	Suppose you drop a die at random on the rectangular region shown in the given figure. What is the probability that it will land inside the circle with diameter 1 m?
Answer» Suppose you drop a die at random on the rectangular region shown in the given figure. What is the probability that it will land inside the circle with diameter 1 m?

13239.

Suppose you drop a die at random on the rectangular region shown in the given figure. What is the probability that it will land inside the circle with diameter 1 m?

Answer»

Suppose you drop a die at random on the rectangular region shown in the given figure. What is the probability that it will land inside the circle with diameter 1 m?

Discussion

13240.	If the vertices of a triangle are (-4,0), (4,0) and (0,3), the triangle is a/an _______.
Answer» If the vertices of a triangle are (-4,0), (4,0) and (0,3), the triangle is a/an _______.

Discussion

13241.	if tan theta=1/2 and tan pi=1/3 then the value of theta+pi
Answer» if tan theta=1/2 and tan pi=1/3 then the value of theta+pi

Discussion

13242.	If the points A(1,-2) , B(2,3) , C(-3,2) and D(-4,-3) are the vertices of a parallelogram ABCD, then taking AB as the base, find the height of the parallelogram.
Answer» If the points A(1,-2) , B(2,3) , C(-3,2) and D(-4,-3) are the vertices of a parallelogram ABCD, then taking AB as the base, find the height of the parallelogram.

Discussion

13243.	The area of a circle is 38.5 cm2. Its circumference is
Answer» The area of a circle is $38.5 {cm}^{2}$ . Its circumference is

Discussion

13244.	Anita buys a new salt cellar in the shape of a cylinder topped by a hemisphere as shown below. The cylinder has a diameter of 6 cm and a height of 10 cm. She pours the salt into the salt cellar, so that it takes up half the total volume of the cellar. Find the depth of the salt, marked with x in the diagram
Answer» Anita buys a new salt cellar in the shape of a cylinder topped by a hemisphere as shown below. The cylinder has a diameter of 6 cm and a height of 10 cm. She pours the salt into the salt cellar, so that it takes up half the total volume of the cellar. Find the depth of the salt, marked with x in the diagram

Discussion

13245.	If one zero of the polynomial x2−4x+1 is 2+√3, then find the other zero.
Answer» If one zero of the polynomial $x^{2} - 4 x + 1 i s 2 + \sqrt{3}$ , then find the other zero.

Discussion

13246.	If the points A(2,k),B(3,4) and C(7,9) are co-linear, then the value of k = .
Answer» If the points A(2,k),B(3,4) and C(7,9) are co-linear, then the value of k = .

Discussion

13247.	The equation of the circle having (4,−1) and (2,−1) as the endpoints of its diameter is
Answer» The equation of the circle having $(4, - 1)$ and $(2, - 1)$ as the endpoints of its diameter is

Discussion

13248.	The value of x for which vectors →a=2^i+x^j and →b=^i+2^j are parallel, is equal to
Answer» The value of $x$ for which vectors $\to a = 2^i + x^j$ and $\to b =^i + 2^j$ are parallel, is equal to

Discussion

13249.	A train covers a distance of 300 km at a uniform speed. If the speed of the train is increased by 5 km/hour, it takes 2 hours less in the journey. Find the original speed of the train.
Answer» A train covers a distance of 300 km at a uniform speed. If the speed of the train is increased by 5 km/hour, it takes 2 hours less in the journey. Find the original speed of the train.

Discussion

13250.

The following distribution gives the state-wise teacher-student ratio in higher secondary schools of India. Find the mode and mean of this data. Interpret, the two measures: Number of students per Teacher Number of States/U.T Number of students per Teacher Number of State/ U.T 15−20 20−25 25−30 30−35 3 8 9 10 35−40 40−45 45−50 50−55 3 0 0 2

Answer» The following distribution gives the state-wise teacher-student ratio in higher secondary schools of India. Find the mode and mean of this data. Interpret, the two measures:

Number of students per Teacher	Number of States/U.T	Number of students per Teacher	Number of State/ U.T
15−20 20−25 25−30 30−35	3 8 9 10	35−40 40−45 45−50 50−55	3 0 0 2

Discussion

Explore topic-wise InterviewSolutions in .

What is the equation of the line joining the points (1, 3) and (2, 7)? Prove that if (x, y) is a point on this line, so is the point (x + 1, y + 4).

Manish opens a Recurring Deposit Account with the Bank of Rajasthan and deposits ₹600 per month for 20 months. Calculate the maturity value of this account, if the bank pays interest at the rate of 10% per annum.

If α and β are the zeroes of the polynomial x2+4x−77, then the quadratic polynomial whose zeroes are 1α and 1β can be equal to

What is units place in 99

Which of the following correctly represents the HCF and LCM of 4500 and 10584?

Th sum of the first 30 terms of the arithmetic sequence 10, 18, 26... is ___.

Which of the following statements are true ? (i) All cubes are cuboids. (ii) All cuboids are cubes. (iii) A cube has 6 faces, 8 vertices and 12 edges. (iv) A cube has 8 faces, 12 vertices and 6 edges.

Write the set builder form A = {-1, 1}.

A store room in the form of a cuboid has measures 42 m×35 m×21 m. How many cuboidal boxes can be stored in it if the volume of one box is 0.7 m3?

Question 37The curved surface area of a cylinder which exactly fits in a cube of side b is ___

A particle is projected from the ground at some anglewith the horizontal and it passes through points(4 m, 6 m) and (6 m, 4 m) in the xy plane. Therange of the particle is(1) 16 m(3) 10 m(2) 7.6 m(4) 3.8 m

Draw a circle with centre O and radius 3.5 cm. Take point P at a distance 5.7 cm from the centre. Draw tangents to the circle from point P.

The length of the plot in meters is 1 more than twice its breadth and the area of a rectangle plot is 528 m2. Which of the following quadratic equations represents the given situation:

A lead pencil consists of a cylinder of wood with a solid cylinder of graphite filled in the interior.The diameter of the pencil is 7 mm and the diameter of the graphite is 1 mm.If the length of the pencil is 14 cm, find the volume of the wood and that of the graphite.[Assume π=227]

In △ABC, AB=3 cm, AC=4 cm and AD is the bisector of ∠A. Then, BD:DC is0.25

P(x) be any polynomial. When it is divided by (x−17) and (x−71) , then the remainders are 71 and 17 respectively. Find remainder, when P(x) is divided by(x−17)(x−71).

Solve and find x and y:- 1/2(x+2y) +5/4(3x-2y)=-3/2 -------(i) 5/4(x+2y) - 3/5(3x-2y)=61/60 ---------(ii)

Find the median of the following data. Class interval100−120120−140140−160160−180180−200Frequency10138712

Find the value(s) of k for which the points (3k−1,k−2),(k,k−7) and (k−1,−k−2) are collinear.

Three cubes of a metal whose edges are in the ratios 3 : 4 : 5 are melted and converted into a single cube whose diagonal is 123 cm . Find the edges of the three cubes.

For the following A.Ps, write the first term and the common difference.3, 1, - 1, - 3 …

For two numbers 96 and 404, the HCF is 4. What is the LCM of the two numbers?9696

The length of an arc of a circle, subtending an angle of 54∘ at the centre is 16.5 cm. Calculate the radius, circumference and area of the circle.

a housewife used to spend rupees 120 per month on the purchase of wheat at prevailing price. when the price Rose by rupees 2 per kg she found that the same amount should purchase 2 kg less. Find the new price per kg of the wheat.

If the standard deviation of first n natural numbers is 2, then n = ________________.

if m is slope of one of lines represented by ax^2+2hxy+by^2=0 then (h+bm)^2=h^2+abh^2-ab(a+b)^2(a-b)^2

A drinking glass is in the shape of a frustum of a cone of height 14 cm. The diameters of its two circular ends are 4 cm and 2 cm. Find the capacity of the glass(in cm3).

Question 7 (ii)Solve the following pair of linear equations.(ii) ax + by = c bx + ay = 1 + c

Find the single discount equivalent to two successive discounts 30% and 20%.

79 If 13-x-10=8+5 then the value of x

The centre of a circle is (3, 4) and it passes through the point (2, 5). What is its radius?

The base of a 15 cm tall container completely filled with water appears to be raised by 3.75 cm. Calculate the RI of water.

If two zeroes of the polynomial x3 + x2 − 9x − 9 are 3 and −3, then its third zero is(a) −1(b) 1(c) −9(d) 9

Null set should written in list form nd set builder form

A rhombus of side 18 cm has one of its angles as 135∘, then the area of the rhombus will be equal to

Solve the following system of linear equations in three variables. x−2y+z=0 9x−8y+3z=0 2x+3y+5z=36

4 years ago a father was 6 times as old is Sun 10 years later the father will be two and a half Times as old as his son determine the present age of father and the son

Suppose you drop a die at random on the rectangular region shown in the given figure. What is the probability that it will land inside the circle with diameter 1 m?

If the vertices of a triangle are (-4,0), (4,0) and (0,3), the triangle is a/an _______.

if tan theta=1/2 and tan pi=1/3 then the value of theta+pi

If the points A(1,-2) , B(2,3) , C(-3,2) and D(-4,-3) are the vertices of a parallelogram ABCD, then taking AB as the base, find the height of the parallelogram.

The area of a circle is 38.5 cm2. Its circumference is

If one zero of the polynomial x2−4x+1 is 2+√3, then find the other zero.

If the points A(2,k),B(3,4) and C(7,9) are co-linear, then the value of k = .

The equation of the circle having (4,−1) and (2,−1) as the endpoints of its diameter is

The value of x for which vectors →a=2^i+x^j and →b=^i+2^j are parallel, is equal to

A train covers a distance of 300 km at a uniform speed. If the speed of the train is increased by 5 km/hour, it takes 2 hours less in the journey. Find the original speed of the train.