32581 + Interview Questions in Mathematics Page 143 InterviewSolution

7101.	If the difference between the circumference and radius of a circle is 37 cm, then using π = 227, the circumference (in cm) of the circle is(a) 154(b) 44(c) 14(d) 7
Answer» If the difference between the circumference and radius of a circle is 37 cm, then using π = $\frac{22}{7}$ , the circumference (in cm) of the circle is (a) 154 (b) 44 (c) 14 (d) 7

Discussion

7102.	The angle of elevation of the top of a tower at a point on the ground is 30º. What will be the angle of elevation, if the height of the tower is tripled? [CBSE 2015]
Answer» The angle of elevation of the top of a tower at a point on the ground is 30º. What will be the angle of elevation, if the height of the tower is tripled? [CBSE 2015]

Discussion

7103.	If P={x:x∈N,10<x<16},Q={y:y is an even number between 8 and 20}, thenP−Q=
Answer» $If P = {x : x \in N, 10 < x < 16},$ $Q = {y : y is an even number between 8 and 20},$ then $P - Q =$

Discussion

7104.	Question 2 (iii)Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.0,√5
Answer» Question 2 (iii) Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively. $0, \sqrt{5}$

7104.

Question 2 (iii)Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.0,√5

Answer»

Question 2 (iii)

Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.

$0, \sqrt{5}$

Discussion

7105.	In a ΔPQR,PS⊥QR. If QS:SP:SR=9:12:16, then the value of ∠PQR is always equal to
Answer» In a $Δ P Q R, P S ⊥ Q R .$ If $Q S : S P : S R = 9 : 12 : 16,$ then the value of $∠ P Q R$ is always equal to

Discussion

7106.	Solve the following quadratic equations by factorization:x-3x+3-x+3x-3=487, x≠3, x≠-3
Answer» Solve the following quadratic equations by factorization: $\frac{x - 3}{x + 3} - \frac{x + 3}{x - 3} = \frac{48}{7}, x \neq 3, x \neq - 3$

Discussion

7107.	If ΔABC and ΔPQR are to be congruent, name one additional pair of corresponding parts. Which criterion did you use?
Answer» If $Δ A B C$ and $Δ P Q R$ are to be congruent, name one additional pair of corresponding parts. Which criterion did you use?

Discussion

7108.	If x=1(2−√3), then find the value of (x3−2x2−7x+5).
Answer» If $x = \frac{1}{(2 - \sqrt{3}),}$ then find the value of $(x^{3} - 2 x^{2} - 7 x + 5)$ .

Discussion

7109.	Mode of the data15, 14, 19, 20, 14, 15, 19, 14, 15, 20, 14, 19, 15, 15, 17 is
Answer» Mode of the data 15, 14, 19, 20, 14, 15, 19, 14, 15, 20, 14, 19, 15, 15, 17 is

Discussion

7110.	Two APs have the same common difference. If the first terms of these APs be 3 and 8 respectively, find the difference between the sums of their first 50 terms. [CBSE 2011]
Answer» Two APs have the same common difference. If the first terms of these APs be 3 and 8 respectively, find the difference between the sums of their first 50 terms. [CBSE 2011]

Discussion

7111.	A bag contains 5 black, 7red and 3 white balls. A ball is drawn from the bag at random. Find the probability that the ball drawn is :(i) red(ii) black or white(iii) not black
Answer» A bag contains 5 black, 7red and 3 white balls. A ball is drawn from the bag at random. Find the probability that the ball drawn is : (i) red (ii) black or white (iii) not black

Discussion

7112.	Sachin wants to make a pet house for his dog with length, breadth and height of 3m, 2m and 1m respectively. What is the area of walls inside the pet house that has to be painted? [3 MARKS]
Answer» Sachin wants to make a pet house for his dog with length, breadth and height of 3m, 2m and 1m respectively. What is the area of walls inside the pet house that has to be painted? [3 MARKS]

Discussion

7113.	Find the solution set for the following inequation:x+52<−52+5x; xϵR
Answer» Find the solution set for the following inequation: $x + \frac{5}{2} < - \frac{5}{2} + 5 x$ ; $x ϵ R$

Discussion

7114.	Question 3 (iii) In the following APs, find the missing term in the boxes. (iii) 5,□,□,912
Answer» Question 3 (iii) In the following APs, find the missing term in the boxes. (iii) $5, □, □, 9 \frac{1}{2}$

Discussion

7115.

The table given below shows the weekly expenditures on food of some households in a locality. Weekly expenditure (in ₹) Number of households 100−200 5 200−300 6 300−400 11 400−500 13 500−600 5 600−700 4 700−800 3 800−900 2 Draw a 'less than type ogive' and a 'more than type ogive' for this distribution.

Answer» The table given below shows the weekly expenditures on food of some households in a locality.

Weekly expenditure (in ₹)	Number of households
100−200	5
200−300	6
300−400	11
400−500	13
500−600	5
600−700	4
700−800	3
800−900	2

Draw a 'less than type ogive' and a 'more than type ogive' for this distribution.

Discussion

7116.	From a solid cylinder of height 14 cm and base diameter 7 cm, two equal conical holes each of radius 2.1 cm and height 4 cm are cut off. Find the volume of the remaining solid.
Answer» From a solid cylinder of height 14 cm and base diameter 7 cm, two equal conical holes each of radius 2.1 cm and height 4 cm are cut off. Find the volume of the remaining solid.

Discussion

7117.	Construct a regular hexagon of side 4 cm. Construct a circle circumscribing the hexagon and measure its circumradius.
Answer» Construct a regular hexagon of side 4 cm. Construct a circle circumscribing the hexagon and measure its circumradius.

Discussion

7118.	A dice is rolled once. What is the probability of getting a four?
Answer» A dice is rolled once. What is the probability of getting a four?

Discussion

7119.	If the straight lines x=1+s,y=−3−λs,z=1+λs and x=t2,y=1+t,z=2−t with parameters s and t respectively are coplanar, then the value of (3λ2+2λ+1)=
Answer» If the straight lines $x = 1 + s, y = - 3 - λ s, z = 1 + λ s$ and $x = \frac{t}{2}, y = 1 + t, z = 2 - t$ with parameters $s$ and $t$ respectively are coplanar, then the value of $(3 λ^{2} + 2 λ + 1) =$

Discussion

7120.	If p^2 -3p-1=0,find p^2+1/p^2
Answer» If p^2 -3p-1=0,find p^2+1/p^2

Discussion

7121.	Draw the graphs of the following equations on the same graph paper:2x+y=22x+y=6Find the coordinates of the vertices of the trapezium formed by these lines. Also, find the area of the trapezium so formed.
Answer» Draw the graphs of the following equations on the same graph paper: $2 x + y = 2 2 x + y = 6$ Find the coordinates of the vertices of the trapezium formed by these lines. Also, find the area of the trapezium so formed.

Discussion

7122.	The area of a triangle with vertices A(5, 0), B(8, 0) and C(8, 4) in square units is (a) 20 (b) 12 (c) 6 (d) 16
Answer» The area of a triangle with vertices A(5, 0), B(8, 0) and C(8, 4) in square units is (a) 20 (b) 12 (c) 6 (d) 16

7122.

The area of a triangle with vertices A(5, 0), B(8, 0) and C(8, 4) in square units is (a) 20 (b) 12 (c) 6 (d) 16

Answer»

The area of a triangle with vertices A(5, 0), B(8, 0) and C(8, 4) in square units is

(a) 20 (b) 12 (c) 6 (d) 16

Discussion

7123.	Mark the correct alternative in each of the following:If x-1>5, then(a) x∈(-4, 6)(b) x∈[-4, 6](c) x∈(-∞, -4) ∪ (6, ∞)(d) x∈(-∞, -4) ∪ [6. ∞)
Answer» Mark the correct alternative in each of the following: If $\|x - 1\|$ $>$ 5, then (a) x $\in$ ( $-$ 4, 6) (b) x $\in$ [ $-$ 4, 6] (c) x $\in$ ( $-$ $\infty$ , $-$ 4) $\cup$ (6, $\infty$ ) (d) x $\in$ ( $-$ $\infty$ , $-$ 4) $\cup$ [6. $\infty$ )

Discussion

7124.	A metal place has a bore (inner diameter) of 5 cm.The pipe is 5 mm thick all around.Find the weight,in kilogram,of 2 meters of the pipe if 1 cm3 of the metal weighs 7.7 g.
Answer» A metal place has a bore (inner diameter) of 5 cm.The pipe is 5 mm thick all around.Find the weight,in kilogram,of 2 meters of the pipe if $1 c m^{3}$ of the metal weighs 7.7 g.

Discussion

7125.	If the system of equations has infinitely many solutions, then2x+3y=72ax+a+by=28(a) a = 2b(b) b = 2a(c) a + 2b = 0(d) 2a + b = 0
Answer» If the system of equations has infinitely many solutions, then $2 x + 3 y = 7 2 a x + (a + b) y = 28$ (a) a = 2b (b) b = 2a (c) a + 2b = 0 (d) 2a + b = 0

Discussion

7126.	If 8 tan x = 15, then sin x − cos x is equal to(a) 817(b) 177(c) 117(d) 717
Answer» If 8 tan x = 15, then sin x − cos x is equal to (a) $\frac{8}{17}$ (b) $\frac{17}{7}$ (c) $\frac{1}{17}$ (d) $\frac{7}{17}$

Discussion

7127.	Question 10 To draw a histogram to represent the frequency distribution. Class interval5−1010−1515−2525−4545−75Frequency61210815 The adjusted frequency for the class 25 - 45 is: A) 6 B) 5 C) 3 D) 2
Answer» Question 10 To draw a histogram to represent the frequency distribution. $\begin{matrix} Class interval & 5 - 10 & 10 - 15 & 15 - 25 & 25 - 45 & 45 - 75 Frequency & 6 & 12 & 10 & 8 & 15 \end{matrix}$ The adjusted frequency for the class 25 - 45 is: A) 6 B) 5 C) 3 D) 2

Discussion

7128.	A book has pages numbered from 1 to 85. What is the probability that the sum of the digits on the page is 8 if a page is chosen at random?
Answer» A book has pages numbered from 1 to 85. What is the probability that the sum of the digits on the page is 8 if a page is chosen at random?

Discussion

7129.	Find the degree of the polynomial -3x + 1,
Answer» Find the degree of the polynomial -3x + 1,

Discussion

7130.	The volume of a right circular cylinder with its height equal to the radius is 2517 cm3. Find the height of the cylinder.
Answer» The volume of a right circular cylinder with its height equal to the radius is $25 \frac{1}{7}$ cm³. Find the height of the cylinder.

Discussion

7131.	In the first proof reading of a book containing 300 pages the following distribution of misprints was obtained: No. of misprints per page (x) : 0 1 2 3 4 5 No. of pages (f ) : 154 95 36 9 5 1 Find the average number of misprints per page.
Answer» In the first proof reading of a book containing 300 pages the following distribution of misprints was obtained: No. of misprints per page (x) : 0 1 2 3 4 5 No. of pages (f ) : 154 95 36 9 5 1 Find the average number of misprints per page.

Discussion

7132.	Factories (1) 4x2 - 12x +9, x2+y-xy-y ,
Answer» Factories (1) 4x² - 12x +9, x²+y-xy-y ,

Discussion

7133.	A milk container of height 16 cm is made of metal sheet in the form of a frustum of a cone with radii of its lower and upper ends as 8 cm and 20 cm respectively . Find the cost of milk at the rate of ₹44 per litre which the container can hold.
Answer» A milk container of height 16 cm is made of metal sheet in the form of a frustum of a cone with radii of its lower and upper ends as 8 cm and 20 cm respectively . Find the cost of milk at the rate of ₹44 per litre which the container can hold.

Discussion

7134.	Distance of a point Q(x,y) from y-axis is
Answer» Distance of a point Q(x,y) from y-axis is

Discussion

7135.	If sin4A = cos (A - 30)
Answer» If sin4A = cos (A - 30)

Discussion

7136.	In the Figure 6, find the area of the shaded region, if ABCD is a square of side 14 cm and APD and BPC are semicircles.
Answer» In the Figure 6, find the area of the shaded region, if ABCD is a square of side 14 cm and APD and BPC are semicircles.

Discussion

7137.	Question 3Curved surface area of a cone is 308 cm2 and its slant height is 14 cm. Find(i) radius of the base.(ii) total surface area of the cone. [Assume π=227]
Answer» Question 3 Curved surface area of a cone is $308 c m^{2}$ and its slant height is 14 cm. Find (i) radius of the base. (ii) total surface area of the cone. $[A s s u m e π = \frac{22}{7}]$

Discussion

7138.	Question 12Is it true to say that if in two triangles, an angle of one triangle is equal to an angle of another triangle and two sides of one triangle are proportional to the two sides of the other triangle, then the triangles are similar? Give reasons for your answer.
Answer» Question 12 Is it true to say that if in two triangles, an angle of one triangle is equal to an angle of another triangle and two sides of one triangle are proportional to the two sides of the other triangle, then the triangles are similar? Give reasons for your answer.

Discussion

7139.	In the given figure, △ABC is right-angled at A. Semicircles are drawn on AB, AC and BC as diameters. It is given that AB = 3 cm and AC = 4 cm. Find the area of the shaded region.
Answer» In the given figure, $△ A B C$ is right-angled at A. Semicircles are drawn on AB, AC and BC as diameters. It is given that AB = 3 cm and AC = 4 cm. Find the area of the shaded region.

7139.

In the given figure, △ABC is right-angled at A. Semicircles are drawn on AB, AC and BC as diameters. It is given that AB = 3 cm and AC = 4 cm. Find the area of the shaded region.

Answer»

In the given figure, $△ A B C$ is right-angled at A. Semicircles are drawn on AB, AC and BC as diameters. It is given that AB = 3 cm and AC = 4 cm. Find the area of the shaded region.

Discussion

7140.	What is the value of 45 degrees if the value of 180 degrees is equal to pi?
Answer» What is the value of 45 degrees if the value of 180 degrees is equal to pi?

Discussion

7141.	If the system of equations has infinitely many solutions, then2x + 3y = 7(a + b)x + (2a − b)y = 21(a) a = 1, b = 5(b) a = 5, b = 1(c) a = −1, b = 5(d) a = 5, b = −1
Answer» If the system of equations has infinitely many solutions, then 2x + 3y = 7 (a + b)x + (2a − b)y = 21 (a) a = 1, b = 5 (b) a = 5, b = 1 (c) a = −1, b = 5 (d) a = 5, b = −1

Discussion

7142.	Using Euclid's division algorithm, find the largest number that divides 1251, 9377 and 15628 leaving remainders 1, 2 and 3 respectively.
Answer» Using Euclid's division algorithm, find the largest number that divides 1251, 9377 and 15628 leaving remainders 1, 2 and 3 respectively.

Discussion

7143.	what is pseudo electronic configuratio
Answer» what is pseudo electronic configuratio

Discussion

7144.	If 12x+17y=53 and 17x+12y=63 then find the value of (x+y).
Answer» If $12 x + 17 y = 53$ and $17 x + 12 y = 63$ then find the value of (x+y).

Discussion

7145.	The value of a for which the lines 2x+y−1=0ax+3y−3=03x+2y−2=0 are concurrent:
Answer» The value of $a$ for which the lines $2 x + y - 1 = 0 a x + 3 y - 3 = 0 3 x + 2 y - 2 = 0$ are concurrent:

Discussion

7146.	A cone of maximum size is carved out from a solid cube of edge 14 cm. The total surface area of the remaining solid left after the cone is carved out is
Answer» A cone of maximum size is carved out from a solid cube of edge 14 cm. The total surface area of the remaining solid left after the cone is carved out is

Discussion

7147.	Find the mode of the given data. Class Frequency 0−52005−1025010−1522515−2030020−2527518.75
Answer» Find the mode of the given data. $\begin{matrix} C l a s s & F r e q u e n c y 0 - 5 & 200 5 - 10 & 250 10 - 15 & 225 15 - 20 & 300 20 - 25 & 275 \end{matrix}$ 18.75

Discussion

7148.	Find x if log10(x+1)+log10(x−1)=log1011+2log103
Answer» $Find x if$ $l o g_{10} (x + 1) + l o g_{10} (x - 1) = l o g_{10} 11 + 2 l o g_{10} 3$

7148.

Find x if log10(x+1)+log10(x−1)=log1011+2log103

Answer»

$Find x if$ $l o g_{10} (x + 1) + l o g_{10} (x - 1) = l o g_{10} 11 + 2 l o g_{10} 3$

Discussion

7149.	At which point does the linear equation 6x + 5y = 9 cut the x-axis?
Answer» At which point does the linear equation 6x + 5y = 9 cut the x-axis?

Discussion

7150.	The sequence of squares of odd natural numbers is ___
Answer» The sequence of squares of odd natural numbers is ___

Discussion

Explore topic-wise InterviewSolutions in .

If the difference between the circumference and radius of a circle is 37 cm, then using π = 227, the circumference (in cm) of the circle is(a) 154(b) 44(c) 14(d) 7

The angle of elevation of the top of a tower at a point on the ground is 30º. What will be the angle of elevation, if the height of the tower is tripled? [CBSE 2015]

If P={x:x∈N,10&lt;x&lt;16},Q={y:y is an even number between 8 and 20}, thenP−Q=

Question 2 (iii)Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.0,√5

In a ΔPQR,PS⊥QR. If QS:SP:SR=9:12:16, then the value of ∠PQR is always equal to

Solve the following quadratic equations by factorization:x-3x+3-x+3x-3=487, x≠3, x≠-3

If ΔABC and ΔPQR are to be congruent, name one additional pair of corresponding parts. Which criterion did you use?

If x=1(2−√3), then find the value of (x3−2x2−7x+5).

Mode of the data15, 14, 19, 20, 14, 15, 19, 14, 15, 20, 14, 19, 15, 15, 17 is

Two APs have the same common difference. If the first terms of these APs be 3 and 8 respectively, find the difference between the sums of their first 50 terms. [CBSE 2011]

A bag contains 5 black, 7red and 3 white balls. A ball is drawn from the bag at random. Find the probability that the ball drawn is :(i) red(ii) black or white(iii) not black

Sachin wants to make a pet house for his dog with length, breadth and height of 3m, 2m and 1m respectively. What is the area of walls inside the pet house that has to be painted? [3 MARKS]

Find the solution set for the following inequation:x+52&lt;−52+5x; xϵR

Question 3 (iii) In the following APs, find the missing term in the boxes. (iii) 5,□,□,912

From a solid cylinder of height 14 cm and base diameter 7 cm, two equal conical holes each of radius 2.1 cm and height 4 cm are cut off. Find the volume of the remaining solid.

Construct a regular hexagon of side 4 cm. Construct a circle circumscribing the hexagon and measure its circumradius.

A dice is rolled once. What is the probability of getting a four?

If the straight lines x=1+s,y=−3−λs,z=1+λs and x=t2,y=1+t,z=2−t with parameters s and t respectively are coplanar, then the value of (3λ2+2λ+1)=

If p^2 -3p-1=0,find p^2+1/p^2

Draw the graphs of the following equations on the same graph paper:2x+y=22x+y=6Find the coordinates of the vertices of the trapezium formed by these lines. Also, find the area of the trapezium so formed.

The area of a triangle with vertices A(5, 0), B(8, 0) and C(8, 4) in square units is (a) 20 (b) 12 (c) 6 (d) 16

Mark the correct alternative in each of the following:If x-1&gt;5, then(a) x∈(-4, 6)(b) x∈[-4, 6](c) x∈(-∞, -4) ∪ (6, ∞)(d) x∈(-∞, -4) ∪ [6. ∞)

A metal place has a bore (inner diameter) of 5 cm.The pipe is 5 mm thick all around.Find the weight,in kilogram,of 2 meters of the pipe if 1 cm3 of the metal weighs 7.7 g.

If the system of equations has infinitely many solutions, then2x+3y=72ax+a+by=28(a) a = 2b(b) b = 2a(c) a + 2b = 0(d) 2a + b = 0

If 8 tan x = 15, then sin x − cos x is equal to(a) 817(b) 177(c) 117(d) 717

Question 10 To draw a histogram to represent the frequency distribution. Class interval5−1010−1515−2525−4545−75Frequency61210815 The adjusted frequency for the class 25 - 45 is: A) 6 B) 5 C) 3 D) 2

A book has pages numbered from 1 to 85. What is the probability that the sum of the digits on the page is 8 if a page is chosen at random?

Find the degree of the polynomial -3x + 1,

The volume of a right circular cylinder with its height equal to the radius is 2517 cm3. Find the height of the cylinder.

In the first proof reading of a book containing 300 pages the following distribution of misprints was obtained: No. of misprints per page (x) : 0 1 2 3 4 5 No. of pages (f ) : 154 95 36 9 5 1 Find the average number of misprints per page.

Factories (1) 4​​​​​x2 - 12x +9, x​​​​​​2+y-xy-y , ​​​​​​

A milk container of height 16 cm is made of metal sheet in the form of a frustum of a cone with radii of its lower and upper ends as 8 cm and 20 cm respectively . Find the cost of milk at the rate of ₹44 per litre which the container can hold.

Distance of a point Q(x,y) from y-axis is

If sin4A = cos (A - 30)

In the Figure 6, find the area of the shaded region, if ABCD is a square of side 14 cm and APD and BPC are semicircles.

Question 3Curved surface area of a cone is 308 cm2 and its slant height is 14 cm. Find(i) radius of the base.(ii) total surface area of the cone. [Assume π=227]

Question 12Is it true to say that if in two triangles, an angle of one triangle is equal to an angle of another triangle and two sides of one triangle are proportional to the two sides of the other triangle, then the triangles are similar? Give reasons for your answer.

In the given figure, △ABC is right-angled at A. Semicircles are drawn on AB, AC and BC as diameters. It is given that AB = 3 cm and AC = 4 cm. Find the area of the shaded region.

What is the value of 45 degrees if the value of 180 degrees is equal to pi?

If the system of equations has infinitely many solutions, then2x + 3y = 7(a + b)x + (2a − b)y = 21(a) a = 1, b = 5(b) a = 5, b = 1(c) a = −1, b = 5(d) a = 5, b = −1

Using Euclid's division algorithm, find the largest number that divides 1251, 9377 and 15628 leaving remainders 1, 2 and 3 respectively.

what is pseudo electronic configuratio

If 12x+17y=53 and 17x+12y=63 then find the value of (x+y).

The value of a for which the lines 2x+y−1=0ax+3y−3=03x+2y−2=0 are concurrent:

A cone of maximum size is carved out from a solid cube of edge 14 cm. The total surface area of the remaining solid left after the cone is carved out is

Find the mode of the given data. Class Frequency 0−52005−1025010−1522515−2030020−2527518.75

Find x if log10(x+1)+log10(x−1)=log1011+2log103

At which point does the linear equation 6x + 5y = 9 cut the x-axis?

The sequence of squares of odd natural numbers is ___

If P={x:x∈N,10<x<16},Q={y:y is an even number between 8 and 20}, thenP−Q=

Find the solution set for the following inequation:x+52<−52+5x; xϵR

Mark the correct alternative in each of the following:If x-1>5, then(a) x∈(-4, 6)(b) x∈[-4, 6](c) x∈(-∞, -4) ∪ (6, ∞)(d) x∈(-∞, -4) ∪ [6. ∞)

Factories (1) 4x2 - 12x +9, x2+y-xy-y ,