24740 + Interview Questions in Mathematics Page 18 InterviewSolution

851.	Draw a line segment AB and by ruler and compasses, obtain a line segment of length 34 (AB).
Answer» Draw a line segment AB and by ruler and compasses, obtain a line segment of length $\frac{3}{4}$ (AB).

Discussion

852.	how to take out zeroes of the polynomial f(x)=2x(power3) -9x(power2)+x+12
Answer» how to take out zeroes of the polynomial f(x)=2x(power3) -9x(power2)+x+12

Discussion

853.	pq form of the number 0.123¯¯¯¯¯¯¯¯456, where p and q are integers and q≠0, is ____
Answer» $\frac{p}{q}$ form of the number $0.123 ¯ ¯¯¯¯¯¯ ¯ 456$ , where p and q are integers and $q \neq 0$ , is ____

Discussion

854.	If two polynomials p(x) = x3 + ax2 – 8x + 10 and q(x) = x2 + 8x + b are divided by (x + 3), the remainder are 7 and 18 respectively, then the remainder when (x2 + bx + a) is divided by (x – 1) is
Answer» If two polynomials p(x) = x3 + ax2 – 8x + 10 and q(x) = x2 + 8x + b are divided by (x + 3), the remainder are 7 and 18 respectively, then the remainder when (x2 + bx + a) is divided by (x – 1) is

Discussion

855.	ntThe st line x/a+y/b=1 passes through the point of intersection of the st line7x+9y=3 and 2y-x+7=0 and makes and angle 90 degree wiyh the st .line 5x-6y+15=0.Find the values of a and b.n ntn
Answer» ntThe st line x/a+y/b=1 passes through the point of intersection of the st line7x+9y=3 and 2y-x+7=0 and makes and angle 90 degree wiyh the st .line 5x-6y+15=0.Find the values of a and b.n ntn

Discussion

856.	Number of circles that can be drawn through three non-collinear points is(a) 1(b) 0(c) 2(d) 3
Answer» Number of circles that can be drawn through three non-collinear points is (a) 1 (b) 0 (c) 2 (d) 3

Discussion

857.	If A={1,2}, B={3,4} and C={5,6}, then A∪(B∪C) = ___.
Answer» If $A = {1, 2},$ $B = {3, 4}$ and $C = {5, 6},$ then $A \cup (B \cup C)$ = ___.

Discussion

858.	At the Carnival, Carla sold 2 soft toys. Cosmo sold 4 times as many as Carla. How many soft toys Cosmo sold?
Answer» At the Carnival, Carla sold 2 soft toys. Cosmo sold 4 times as many as Carla. How many soft toys Cosmo sold?

Discussion

859.	Examine whether x + 2 is a factor of x3+3x2+5x+6 and 2x + 4.
Answer» Examine whether x + 2 is a factor of $x^{3} + 3 x^{2} + 5 x + 6$ and 2x + 4.

Discussion

860.	Write the names of pairs of congruent line segments. (Use a divider to find them.)(i) ...........................(ii) ...........................(iii) ...........................(iv) ...........................
Answer» Write the names of pairs of congruent line segments. (Use a divider to find them.) (i) ........................... (ii) ........................... (iii) ........................... (iv) ...........................

Discussion

861.	Factorise: 24x2−41x+12
Answer» Factorise: $24 x^{2} - 41 x + 12$

Discussion

862.	The total surface area of a hollow metal cylinder, open at both ends of external radius 8 cm and height 10 cm is 338 p cm2. Taking r to be inner radius, obtain an equation in r and use it to obtain the thickness of the metal in the cylinder.
Answer» The total surface area of a hollow metal cylinder, open at both ends of external radius 8 cm and height 10 cm is 338 p cm². Taking r to be inner radius, obtain an equation in r and use it to obtain the thickness of the metal in the cylinder.

Discussion

863.	A class contains 60 boys and 40 girls. A student is selected at random and what is the probability of that selected student is a girl?
Answer» A class contains 60 boys and 40 girls. A student is selected at random and what is the probability of that selected student is a girl?

Discussion

864.	In a society 6 children out of 28 did not participate in the campaign save energy find the probability that a child selected at random participated in the campaign and did not participate in the campaign which values of children are depicted here
Answer» In a society 6 children out of 28 did not participate in the campaign save energy find the probability that a child selected at random participated in the campaign and did not participate in the campaign which values of children are depicted here

Discussion

865.	A cone and a hemisphere have equal bases and equal volumes the ratio of their heights is(a) 1 : 2(b) 2 : 1(c) 4 : 1(d) 2 : 1
Answer» A cone and a hemisphere have equal bases and equal volumes the ratio of their heights is (a) 1 : 2 (b) 2 : 1 (c) 4 : 1 (d) $\sqrt{2}$ : 1

Discussion

866.	State True or False.Daigonals of Parallelogram are bisecet each other.
Answer» State True or False. Daigonals of Parallelogram are bisecet each other.

Discussion

867.	Draw ΔABC with AB = 4 cm, BC = 5 cm and CA = 6 cm. Draw an isosceles triangle of the same area with one side as AB itself.
Answer» Draw ΔABC with AB = 4 cm, BC = 5 cm and CA = 6 cm. Draw an isosceles triangle of the same area with one side as AB itself.

Discussion

868.	You have been asked to plot graphs of the following equations:Equation 1: 3x+2y=1Equation 2: y−2x=2Fill the following tables (find p, q, r, s) which you will use to plot the graphs:Equation 1:x05ypqEquation 2:xrsy05
Answer» You have been asked to plot graphs of the following equations: Equation 1: $3 x + 2 y = 1$ Equation 2: $y - 2 x = 2$ Fill the following tables (find p, q, r, s) which you will use to plot the graphs: Equation 1: $\begin{matrix} x & 0 & 5 y & p & q \end{matrix}$ Equation 2: $\begin{matrix} x & r & s y & 0 & 5 \end{matrix}$

Discussion

869.	In a parallelogram ABCD, points M and N have been taken on opposite sides AB and CD respectively such that AM = CN. Show that AC and MN bisect each other.
Answer» In a parallelogram ABCD, points M and N have been taken on opposite sides AB and CD respectively such that AM = CN. Show that AC and MN bisect each other.

Discussion

870.	Peter throws two different dice together and finds the product of the two numbers obtained. Rina throws a die and squares the number obtained. Who has the better chance to get the number 25? [CBSE 2017]
Answer» Peter throws two different dice together and finds the product of the two numbers obtained. Rina throws a die and squares the number obtained. Who has the better chance to get the number 25? [CBSE 2017]

Discussion

871.	A game consists of tossing a one rupee coin 3 times and noting its outcome each time. Hanif wins if all the tosses give the same result, i.e., three heads or three tails and loses otherwise. Calculate the probability that Hanif will lose the game.
Answer» A game consists of tossing a one rupee coin 3 times and noting its outcome each time. Hanif wins if all the tosses give the same result, i.e., three heads or three tails and loses otherwise. Calculate the probability that Hanif will lose the game.

Discussion

872.	A cylindrical bucket with base radius 15 cm is filled with water up to a height of 20 cm.A heavy iron spherical ball of radius 9 cm is dropped into the bucket to submerge completely in the water.Find the increase in the level of water.
Answer» A cylindrical bucket with base radius 15 cm is filled with water up to a height of 20 cm.A heavy iron spherical ball of radius 9 cm is dropped into the bucket to submerge completely in the water.Find the increase in the level of water.

Discussion

873.	If x=1+log 2−log 5, y=2 log 3 and z=log a−log 5; find the value of a, if x+y=2z.
Answer» If $x = 1 + l o g 2 - l o g 5, y = 2 l o g 3$ and $z = l o g a - l o g 5$ ; find the value of a, if $x + y = 2 z$ .

Discussion

874.	If the area of a circle with radius r is equal to the curved surface area of cone with radius r1 and slant height l then the value of r1 in terms of r and l is:
Answer» If the area of a circle with radius r is equal to the curved surface area of cone with radius $r_{1}$ and slant height l then the value of $r_{1}$ in terms of r and l is:

Discussion

875.	In figure, A, B and C are three points on a circle with centre O such that ∠BOC = 30∘ and ∠AOB = 60∘. If D is a point on the circle other than the arc ABC, find ∠ADC.
Answer» In figure, A, B and C are three points on a circle with centre O such that $∠$ BOC = $30^{\circ}$ and $∠$ AOB = $60^{\circ}$ . If D is a point on the circle other than the arc ABC, find $∠$ ADC.

875.

In figure, A, B and C are three points on a circle with centre O such that ∠BOC = 30∘ and ∠AOB = 60∘. If D is a point on the circle other than the arc ABC, find ∠ADC.

Answer»

In figure, A, B and C are three points on a circle with centre O such that $∠$ BOC = $30^{\circ}$ and $∠$ AOB = $60^{\circ}$ . If D is a point on the circle other than the arc ABC, find $∠$ ADC.

Discussion

876.	Construct ¯¯¯¯¯¯¯¯AB of length 7.8 cm. From this cut off ¯¯¯¯¯¯¯¯AC of length 4.7 cm. Measure ¯¯¯¯¯¯¯¯BC.
Answer» Construct $¯ ¯¯¯¯¯¯ ¯ A B$ of length 7.8 cm. From this cut off $¯ ¯¯¯¯¯¯ ¯ A C$ of length 4.7 cm. Measure $¯ ¯¯¯¯¯¯ ¯ B C$ .

Discussion

877.	Express 2.36 (36 is reccuring) +0.23 (23 is reccuring) as a fraction in the simplest form.
Answer» Express 2.36 (36 is reccuring) +0.23 (23 is reccuring) as a fraction in the simplest form.

Discussion

878.	In the given figure,, if ∠DAB = 60∘ , ∠ABD = 50∘ , then ∠ACB = _________
Answer» In the given figure,, if ∠DAB = 60∘ , ∠ABD = 50∘ , then ∠ACB = _________

Discussion

879.	Which of the following are the factors of x2−5x+6?
Answer» Which of the following are the factors of $x^{2} - 5 x + 6 ?$

Discussion

880.	Question 17Which of the following is a factor of (x+y)3–(x3+y3)?A) x2+y2+2xyB) x2+y2–xyC) xy2D) 3xy
Answer» Question 17 Which of the following is a factor of $(x + y)^{3} - (x^{3} + y^{3})$ ? A) $x^{2} + y^{2} + 2 x y$ B) $x^{2} + y^{2} - x y$ C) $x y^{2}$ D) $3 x y$

Discussion

881.	The ten's place of a two digit number is three times the unit digit .The sum of the number and the unit digit is 32 .Find the number.
Answer» The ten's place of a two digit number is three times the unit digit .The sum of the number and the unit digit is 32 .Find the number.

Discussion

882.	A solid metal cylinder of base radius 15 centimetres and height 32 centimetres is melted down and recast into a cylinder of base radius 20 centimetres. What is the height of this cylinder?
Answer» A solid metal cylinder of base radius 15 centimetres and height 32 centimetres is melted down and recast into a cylinder of base radius 20 centimetres. What is the height of this cylinder?

882.

A solid metal cylinder of base radius 15 centimetres and height 32 centimetres is melted down and recast into a cylinder of base radius 20 centimetres. What is the height of this cylinder?

Answer»

A solid metal cylinder of base radius 15 centimetres and height 32 centimetres is melted down and recast into a cylinder of base radius 20 centimetres. What is the height of this cylinder?

Discussion

883.	Find two irrational numbers between 0.5 and 0.55
Answer» Find two irrational numbers between 0.5 and 0.55

Discussion

884.	Choose the correct ascending order of angles for the triangle with side lengths as AB = 50 ft, BC = 44 ft, and AC = 29 ft.
Answer» Choose the correct ascending order of angles for the triangle with side lengths as AB = 50 ft, BC = 44 ft, and AC = 29 ft.

Discussion

885.	In a class, there are 30 badminton players and 40 cricket players. The total strength of the class is 50. Find the number of players who play only badminton (assume every student plays at least one of the games).
Answer» In a class, there are 30 badminton players and 40 cricket players. The total strength of the class is 50. Find the number of players who play only badminton (assume every student plays at least one of the games).

Discussion

886.	Solve the following equations.(i) x - 2 = 7 (ii) y + 3 = 10 (iii) 6 = z + 2
Answer» Solve the following equations. (i) x - 2 = 7 (ii) y + 3 = 10 (iii) 6 = z + 2

Discussion

887.	Determine the average value of function y=Asin²x in the range x=0tox=π.
Answer» Determine the average value of function $y = A s i n ² x$ in the range $x = 0 t o x = π$ .

Discussion

888.	If logx y=100 and log2 x=10, then the value of y is
Answer» If $l o g_{x} y = 100$ and $l o g_{2} x = 10$ , then the value of y is

Discussion

889.	If APB and CQD are two parallel lines then the bisectors of ∠APQ, ∠BPQ, ∠CQP and ∠PQD enclose a (a) square (b) rhombus (c) rectangle (d) kite
Answer» If $A P B$ and $C Q D$ are two parallel lines then the bisectors of $∠ A P Q, ∠ B P Q, ∠ C Q P a n d ∠ P Q D$ enclose a (a) square (b) rhombus (c) rectangle (d) kite

889.

If APB and CQD are two parallel lines then the bisectors of ∠APQ, ∠BPQ, ∠CQP and ∠PQD enclose a (a) square (b) rhombus (c) rectangle (d) kite

Answer»

If $A P B$ and $C Q D$ are two parallel lines then the bisectors of $∠ A P Q, ∠ B P Q, ∠ C Q P a n d ∠ P Q D$ enclose a

(a) square

(b) rhombus

(c) rectangle

(d) kite

Discussion

890.

The following tables gives the quantity of goods (in crore tonnes) Year 1950-51 1960-61 1965-66 1970-71 1980-81 1982-83 Quantity of Goods (in crore tonnes) 9 16 20 20 22 26 Represent this information with the help of a bar graph.Explain through the bar graph if the quantity of goods carried by the Indian Railways in 1965-66 is more than double the quantity of goods carried in the year 1950-51.

Answer» The following tables gives the quantity of goods (in crore tonnes)

Year	1950-51	1960-61	1965-66	1970-71	1980-81	1982-83
Quantity of Goods (in crore tonnes)	9	16	20	20	22	26

Represent this information with the help of a bar graph.

Explain through the bar graph if the quantity of goods carried by the Indian Railways in 1965-66 is more than double the quantity of goods carried in the year 1950-51.

Discussion

891.	If Sin P=5/13, then find the value of tanP.
Answer» If Sin P=5/13, then find the value of tanP.

Discussion

892.	Question 20Volumes of two spheres are in the ratio 64 : 27 , then the ratio of their surface area is(A) 3 : 4(B) 4 : 3(C) 9 : 16(D) 16 : 9
Answer» Question 20 Volumes of two spheres are in the ratio 64 : 27 , then the ratio of their surface area is (A) 3 : 4 (B) 4 : 3 (C) 9 : 16 (D) 16 : 9

Discussion

893.	Each Equation is followed by the values of the variable. Decide whether these values are the solutions of that equation.(i) x−4=3,x=−1,7,−7(ii) 3−y=4,y=−1,1,2
Answer» Each Equation is followed by the values of the variable. Decide whether these values are the solutions of that equation. $(i) x - 4 = 3, x = - 1, 7, - 7$ $(ii) 3 - y = 4, y = - 1, 1, 2$

Discussion

894.	18. the area bounded by the circles xx+yy=rr ,r=1,2 and the rays given by 2xx-3xy-2yy=0, y>0 is
Answer» 18. the area bounded by the circles xx+yy=rr ,r=1,2 and the rays given by 2xx-3xy-2yy=0, y>0 is

Discussion

895.	28.Show that the points A (3, 5) B(6,0) ,C(-1,3) and D(-2,2) are the vertices of square ABCD??
Answer» 28.Show that the points A (3, 5) B(6,0) ,C(-1,3) and D(-2,2) are the vertices of square ABCD??

Discussion

896.	The angles of a quadrilateral are in ratio 1 : 3 : 7 :9 find the measure of each angle.
Answer» The angles of a quadrilateral are in ratio 1 : 3 : 7 :9 find the measure of each angle.

Discussion

897.	The given figure shows a right angled triangle ABC and an equilateral triangle BCD. Find the area of the shaded portion.
Answer» The given figure shows a right angled triangle ABC and an equilateral triangle BCD. Find the area of the shaded portion.

897.

The given figure shows a right angled triangle ABC and an equilateral triangle BCD. Find the area of the shaded portion.

Answer»

The given figure shows a right angled triangle ABC and an equilateral triangle BCD. Find the area of the shaded portion.

Discussion

898.	Which of the following represents a circle of triangular numbers?
Answer» Which of the following represents a circle of triangular numbers?

Discussion

899.	A,B and C are three collinear points such that A lies between B and C. Name all the line segments determined by these points and write the relation between them.
Answer» A,B and C are three collinear points such that A lies between B and C. Name all the line segments determined by these points and write the relation between them.

899.

A,B and C are three collinear points such that A lies between B and C. Name all the line segments determined by these points and write the relation between them.

Answer»

A,B and C are three collinear points such that A lies between B and C.

Name all the line segments determined by these points and write the relation between them.

Discussion

900.

Given, ΔABC∼ΔPQR. Find the values of y and z.

Answer»

Given, $Δ A B C \sim Δ P Q R$ .

Find the values of y and z.

Discussion

Explore topic-wise InterviewSolutions in .

Draw a line segment AB and by ruler and compasses, obtain a line segment of length 34 (AB).

how to take out zeroes of the polynomial f(x)=2x(power3) -9x(power2)+x+12

pq form of the number 0.123¯¯¯¯¯¯¯¯456, where p and q are integers and q≠0, is ____

If two polynomials p(x) = x3 + ax2 – 8x + 10 and q(x) = x2 + 8x + b are divided by (x + 3), the remainder are 7 and 18 respectively, then the remainder when (x2 + bx + a) is divided by (x – 1) is

ntThe st line x/a+y/b=1 passes through the point of intersection of the st line7x+9y=3 and 2y-x+7=0 and makes and angle 90 degree wiyh the st .line 5x-6y+15=0.Find the values of a and b.n ntn

Number of circles that can be drawn through three non-collinear points is(a) 1(b) 0(c) 2(d) 3

If A={1,2}, B={3,4} and C={5,6}, then A∪(B∪C) = ___.

At the Carnival, Carla sold 2 soft toys. Cosmo sold 4 times as many as Carla. How many soft toys Cosmo sold?

Examine whether x + 2 is a factor of x3+3x2+5x+6 and 2x + 4.

Write the names of pairs of congruent line segments. (Use a divider to find them.)(i) ...........................(ii) ...........................(iii) ...........................(iv) ...........................

Factorise: 24x2−41x+12

The total surface area of a hollow metal cylinder, open at both ends of external radius 8 cm and height 10 cm is 338 p cm2. Taking r to be inner radius, obtain an equation in r and use it to obtain the thickness of the metal in the cylinder.

A class contains 60 boys and 40 girls. A student is selected at random and what is the probability of that selected student is a girl?

In a society 6 children out of 28 did not participate in the campaign save energy find the probability that a child selected at random participated in the campaign and did not participate in the campaign which values of children are depicted here

A cone and a hemisphere have equal bases and equal volumes the ratio of their heights is(a) 1 : 2(b) 2 : 1(c) 4 : 1(d) 2 : 1

State True or False.Daigonals of Parallelogram are bisecet each other.

Draw ΔABC with AB = 4 cm, BC = 5 cm and CA = 6 cm. Draw an isosceles triangle of the same area with one side as AB itself.

You have been asked to plot graphs of the following equations:Equation 1: 3x+2y=1Equation 2: y−2x=2Fill the following tables (find p, q, r, s) which you will use to plot the graphs:Equation 1:x05ypqEquation 2:xrsy05

In a parallelogram ABCD, points M and N have been taken on opposite sides AB and CD respectively such that AM = CN. Show that AC and MN bisect each other.

Peter throws two different dice together and finds the product of the two numbers obtained. Rina throws a die and squares the number obtained. Who has the better chance to get the number 25? [CBSE 2017]

A game consists of tossing a one rupee coin 3 times and noting its outcome each time. Hanif wins if all the tosses give the same result, i.e., three heads or three tails and loses otherwise. Calculate the probability that Hanif will lose the game.

A cylindrical bucket with base radius 15 cm is filled with water up to a height of 20 cm.A heavy iron spherical ball of radius 9 cm is dropped into the bucket to submerge completely in the water.Find the increase in the level of water.

If x=1+log 2−log 5, y=2 log 3 and z=log a−log 5; find the value of a, if x+y=2z.

If the area of a circle with radius r is equal to the curved surface area of cone with radius r1 and slant height l then the value of r1 in terms of r and l is:

In figure, A, B and C are three points on a circle with centre O such that ∠BOC = 30∘ and ∠AOB = 60∘. If D is a point on the circle other than the arc ABC, find ∠ADC.

Construct ¯¯¯¯¯¯¯¯AB of length 7.8 cm. From this cut off ¯¯¯¯¯¯¯¯AC of length 4.7 cm. Measure ¯¯¯¯¯¯¯¯BC.

Express 2.36 (36 is reccuring) +0.23 (23 is reccuring) as a fraction in the simplest form.

In the given figure,, if ∠DAB = 60∘ , ∠ABD = 50∘ , then ∠ACB = _________

Which of the following are the factors of x2−5x+6?

Question 17Which of the following is a factor of (x+y)3–(x3+y3)?A) x2+y2+2xyB) x2+y2–xyC) xy2​​​​​​​D) 3xy

The ten's place of a two digit number is three times the unit digit .The sum of the number and the unit digit is 32 .Find the number.

A solid metal cylinder of base radius 15 centimetres and height 32 centimetres is melted down and recast into a cylinder of base radius 20 centimetres. What is the height of this cylinder?

Find two irrational numbers between 0.5 and 0.55

Choose the correct ascending order of angles for the triangle with side lengths as AB = 50 ft, BC = 44 ft, and AC = 29 ft.

In a class, there are 30 badminton players and 40 cricket players. The total strength of the class is 50. Find the number of players who play only badminton (assume every student plays at least one of the games).

Solve the following equations.(i) x - 2 = 7 (ii) y + 3 = 10 (iii) 6 = z + 2

Determine the average value of function y=Asin²x in the range x=0tox=π.

If logx y=100 and log2 x=10, then the value of y is

If APB and CQD are two parallel lines then the bisectors of ∠APQ, ∠BPQ, ∠CQP and ∠PQD enclose a (a) square (b) rhombus (c) rectangle (d) kite

If Sin P=5/13, then find the value of tanP.

Question 20Volumes of two spheres are in the ratio 64 : 27 , then the ratio of their surface area is(A) 3 : 4(B) 4 : 3(C) 9 : 16(D) 16 : 9

Each Equation is followed by the values of the variable. Decide whether these values are the solutions of that equation.(i) x−4=3,x=−1,7,−7(ii) 3−y=4,y=−1,1,2

18. the area bounded by the circles xx+yy=rr ,r=1,2 and the rays given by 2xx-3xy-2yy=0, y>0 is

28.Show that the points A (3, 5) B(6,0) ,C(-1,3) and D(-2,2) are the vertices of square ABCD??

The angles of a quadrilateral are in ratio 1 : 3 : 7 :9 find the measure of each angle.

The given figure shows a right angled triangle ABC and an equilateral triangle BCD. Find the area of the shaded portion.

Which of the following represents a circle of triangular numbers?

A,B and C are three collinear points such that A lies between B and C. Name all the line segments determined by these points and write the relation between them.

Given, ΔABC∼ΔPQR. Find the values of y and z.

Question 17Which of the following is a factor of (x+y)3–(x3+y3)?A) x2+y2+2xyB) x2+y2–xyC) xy2D) 3xy