32581 + Interview Questions in Mathematics Page 61 InterviewSolution

3001.	Find the sum of first n natural numbers.
Answer» Find the sum of first $n$ natural numbers.

Discussion

3002.	Which of the following mathematical statement represents inequation
Answer» Which of the following mathematical statement represents inequation

Discussion

3003.	The line joining P(−4,5) and Q(3,2) intersect the y-axis at point R .PM and QN are perpendicular to P and Q on the x- axis. Find:(1) the ratio PR:RQ.(2) the coordinate of R.(3) the area of the quadrilateral PMNQ.
Answer» The line joining $P (- 4, 5)$ and $Q (3, 2)$ intersect the $y$ -axis at point $R$ . $P M$ and $Q N$ are perpendicular to $P$ and $Q$ on the $x$ - axis. Find: (1) the ratio $P R : R Q$ . (2) the coordinate of $R$ . (3) the area of the quadrilateral $P M N Q$ .

3003.

The line joining P(−4,5) and Q(3,2) intersect the y-axis at point R .PM and QN are perpendicular to P and Q on the x- axis. Find:(1) the ratio PR:RQ.(2) the coordinate of R.(3) the area of the quadrilateral PMNQ.

Answer»

The line joining $P (- 4, 5)$ and $Q (3, 2)$ intersect the $y$ -axis at point $R$ . $P M$ and $Q N$ are perpendicular to $P$ and $Q$ on the $x$ - axis. Find:

(1) the ratio $P R : R Q$ .

(2) the coordinate of $R$ .

(3) the area of the quadrilateral $P M N Q$ .

Discussion

3004.	Choose the correct answer of the following question:If a l.5-m-tall girl stands at a distance of 3 m from a lamp post and casts a shadow of length 4.5 m on the ground, then the height of the lamp post is(a) 1.5 m (b) 2 m (c) 2.5 m (d) 2.8 m
Answer» Choose the correct answer of the following question: If a l.5-m-tall girl stands at a distance of 3 m from a lamp post and casts a shadow of length 4.5 m on the ground, then the height of the lamp post is (a) 1.5 m (b) 2 m (c) 2.5 m (d) 2.8 m

Discussion

3005.	Given below is a cumulative frequency table: MarksNumber of studentsBelow 1017Below 2022Below 3029Below 4037Below 5050Below 6060 Extract a frequency table from the above.
Answer» Given below is a cumulative frequency table: $\begin{matrix} Marks & Number of students Below 10 & 17 Below 20 & 22 Below 30 & 29 Below 40 & 37 Below 50 & 50 Below 60 & 60 \end{matrix}$ Extract a frequency table from the above.

Discussion

3006.	Find the sign of a, b and c in the below graph of polynomial f(x)=ax2+b.
Answer» Find the sign of a, b and c in the below graph of polynomial $f (x) = a x^{2} + b$ .

Discussion

3007.	Solve the following quadratic equation by factorization. 48x2−13x−1=0
Answer» Solve the following quadratic equation by factorization. $48 x^{2} - 13 x - 1 = 0$

Discussion

3008.	Question 1Find the coordinates of the point which divides the join of (- 1, 7) and (4, - 3) in the ratio 2:3.
Answer» Question 1 Find the coordinates of the point which divides the join of (- 1, 7) and (4, - 3) in the ratio 2:3.

Discussion

3009.	Solve the following quadratic equations by factorization:3x+1+4x-1=294x-1; x≠1, -1, 14
Answer» Solve the following quadratic equations by factorization: $\frac{3}{x + 1} + \frac{4}{x - 1} = \frac{29}{4 x - 1}; x \neq 1, - 1, \frac{1}{4}$

Discussion

3010.	State the type of the conditional clause in the sentence. If you attend the class regularly, you will learn many new things.
Answer» State the type of the conditional clause in the sentence. If you attend the class regularly, you will learn many new things.

Discussion

3011.	1. A positive integer is divided by 63, we get the remainder as 25. The remainder when the same number is divided by 9 is equal .
Answer» 1. A positive integer is divided by 63, we get the remainder as 25. The remainder when the same number is divided by 9 is equal .

Discussion

3012.	3.If the point P(x,y) is equidistant from the points A(5,1) and B(1,5) then prove that x-y= 0
Answer» 3.If the point P(x,y) is equidistant from the points A(5,1) and B(1,5) then prove that x-y= 0

Discussion

3013.	Very-Short and Short-Answer QuestionsIf the sum of first n terms is (3n2 + 5n), find its common difference.
Answer» Very-Short and Short-Answer Questions If the sum of first n terms is (3n² + 5n), find its common difference.

Discussion

3014.	If the graph of f(x)=3x2+6ax+6c touches the x-axis, then which of the following is always correct?
Answer» If the graph of $f (x) = 3 x^{2} + 6 a x + 6 c$ touches the $x$ -axis, then which of the following is always correct?

Discussion

3015.	In triangles ABC and DEF, AB = FD and ∠A = ∠D. The two triangles will be congruent by SAS axiom, if __________.
Answer» In triangles ABC and DEF, AB = FD and ∠A = ∠D. The two triangles will be congruent by SAS axiom, if __________.

Discussion

3016.	If the nth term of two AP's 63, 65, 67 .... and 3, 10, 17, .... is equal, then find the value of 'n'.
Answer» If the n $^{t h}$ term of two AP's 63, 65, 67 .... and 3, 10, 17, .... is equal, then find the value of 'n'.

Discussion

3017.	What are the roots of the quadratic equation (x+2)2-16 = 0?
Answer» What are the roots of the quadratic equation $(x + 2)^{2}$ -16 = 0?

Discussion

3018.	Question 20 When a die is thrown, the probability of getting an odd number less than 3 is (a) 16 (b) 13 (c) 12 (d) 0
Answer» Question 20 When a die is thrown, the probability of getting an odd number less than 3 is (a) $\frac{1}{6}$ (b) $\frac{1}{3}$ (c) $\frac{1}{2}$ (d) 0

Discussion

3019.	12.The product and difference of inner and outer radiusof a hemi-spherical shell are 12 cm2 and 1 cmrespectively. The sum of inner and outer surfaceareas of the shell i equal to
Answer» 12.The product and difference of inner and outer radiusof a hemi-spherical shell are 12 cm2 and 1 cmrespectively. The sum of inner and outer surfaceareas of the shell i equal to

Discussion

3020.	37. A 6m tall tower is placed on the top of a building, it throws a shadow of 23m on the ground then angle of elevation of the sun is
Answer» 37. A 6m tall tower is placed on the top of a building, it throws a shadow of 23m on the ground then angle of elevation of the sun is

Discussion

3021.	In the adjoining figure, PQ \|\| BC, then what could be the values of AP & PB respectively
Answer» In the adjoining figure, PQ \|\| BC, then what could be the values of AP & PB respectively

Discussion

3022.	Question 3 (ix) In an AP: (ix) Given a = 3, n = 8, S = 192, find d.
Answer» Question 3 (ix) In an AP: (ix) Given a = 3, n = 8, S = 192, find d.

Discussion

3023.	Find:(i) Is 68 a term of the A.P. 7, 10, 13, ...?(ii) Is 302 a term of the A.P. 3, 8, 13, ...?(iii) Is − 150 a term of the A.P. 11, 8, 5, 2, ...?
Answer» Find: (i) Is 68 a term of the A.P. 7, 10, 13, ...? (ii) Is 302 a term of the A.P. 3, 8, 13, ...? (iii) Is − 150 a term of the A.P. 11, 8, 5, 2, ...?

Discussion

3024.	Find the roots of the quadratic equation, 3x2 – 5x + 2 = 0, using quadratic formula.
Answer» Find the roots of the quadratic equation, 3x² – 5x + 2 = 0, using quadratic formula.

Discussion

3025.	From the top of a 7 m high building, the angle of elevation of the top of a cable tower is 60∘ and the angle of depression of its foot is 45∘. Determine the height of the tower.
Answer» From the top of a 7 m high building, the angle of elevation of the top of a cable tower is $60^{\circ}$ and the angle of depression of its foot is $45^{\circ}$ . Determine the height of the tower.

Discussion

3026.

100 surnames were randomly picked up from a local telephone directly and the frequency distribution of the number of letters in the English alphabets in the surnames was obtained as follows: Number of letters: 1−4 4−7 7−10 10−13 13−16 16−19 Number of surnames: 6 30 40 16 4 4 Determine the median number of letters in the surnames. Find the mean number of letters in the surnames. Also, fund the modal size of the surnames.

Answer» 100 surnames were randomly picked up from a local telephone directly and the frequency distribution of the number of letters in the English alphabets in the surnames was obtained as follows:

Number of letters:	1−4	4−7	7−10	10−13	13−16	16−19
Number of surnames:	6	30	40	16	4	4

Determine the median number of letters in the surnames. Find the mean number of letters in the surnames. Also, fund the modal size of the surnames.

Discussion

3027.	If B=[−102341],C=[−123210], then 3C−4B is
Answer» If $B = [\begin{matrix} - 1 & 0 & 2 3 & 4 & 1 \end{matrix}], C = [\begin{matrix} - 1 & 2 & 3 2 & 1 & 0 \end{matrix}],$ then $3 C - 4 B$ is

Discussion

3028.	Question 5S and T are point on sides PR and QR of ΔPQR such that ∠P=∠RTS. Show that ΔRPQ∼ΔRTS.
Answer» Question 5 S and T are point on sides PR and QR of $Δ P Q R$ such that $∠ P = ∠ R T S$ . Show that $Δ R P Q \sim Δ R T S$ .

Discussion

3029.	The area of a circle inscribed in an equilateral triangle is 154 cm2. Find the perimeter of the triangle. [Use π=227 and √3=1.73]
Answer» The area of a circle inscribed in an equilateral triangle is $154 c m^{2}$ . Find the perimeter of the triangle. [Use $π = \frac{22}{7}$ and $\sqrt{3} = 1.73$ ]

Discussion

3030.	Show that any positive odd integer is of the form , or , or , where q is some integer.
Answer» Show that any positive odd integer is of the form , or , or , where q is some integer.

Discussion

3031.	genral value of θ satisfuing the equation †an^2θ+sec2θ=
Answer» genral value of θ satisfuing the equation †an^2θ+sec2θ=

Discussion

3032.	on dividing a polynomial3x3+4x2+5x−13 by a g(X) the quotient and the remainder were (3x+10) and (16x-43) find g(x)
Answer» on dividing a polynomial $3 x^{3} + 4 x^{2} + 5 x - 13$ by a g(X) the quotient and the remainder were (3x+10) and (16x-43) find g(x)

Discussion

3033.	If one root the equation 2x2 + kx + 4 = 0 is 2, then the other root is(a) 6(b) −6(c) −1(d) 1
Answer» If one root the equation 2x² + kx + 4 = 0 is 2, then the other root is (a) 6 (b) −6 (c) −1 (d) 1

Discussion

3034.	Specific volume of a cylindrical virus particle is 6.02×10^-2 cc/gm whose radius and length are 7Å and 10Å respectively. Find molecular weight of virus.
Answer» Specific volume of a cylindrical virus particle is 6.02×10^-2 cc/gm whose radius and length are 7Å and 10Å respectively. Find molecular weight of virus.

Discussion

3035.	If A=⎡⎢⎣a000b000c⎤⎥⎦, then An=
Answer» If $A = ⎡ ⎢ ⎣ \begin{matrix} a & 0 & 0 0 & b & 0 0 & 0 & c \end{matrix} ⎤ ⎥ ⎦$ , then $A^{n} =$

Discussion

3036.	In the given figure, AB is a chord of length 16 cm of a circle of radius 10 cm. The tangents at A and B intersect at a point P. Find the length of PA.
Answer» In the given figure, AB is a chord of length 16 cm of a circle of radius 10 cm. The tangents at A and B intersect at a point P. Find the length of PA.

Discussion

3037.	On rolling a pair of dice, what is the probability of getting the same number on both the dice?
Answer» On rolling a pair of dice, what is the probability of getting the same number on both the dice?

Discussion

3038.	In a hotel, four rooms are available. Six persons are to be accommodated in these four rooms in such a way that each of these rooms contains at least one person and at most two persons. Then the number of all possible ways in which this can be done is
Answer» In a hotel, four rooms are available. Six persons are to be accommodated in these four rooms in such a way that each of these rooms contains at least one person and at most two persons. Then the number of all possible ways in which this can be done is

Discussion

3039.	Find the maximum value of 5−(2x2−8x+6).
Answer» Find the maximum value of $5^{- (2 x^{2} - 8 x + 6)} .$

Discussion

3040.	State AAA similarity criterion.
Answer» State AAA similarity criterion.

Discussion

3041.	Deepthi and Shruthi are friends. Find the probability that both of them have the same birthdays. (Ignore a leap year)
Answer» Deepthi and Shruthi are friends. Find the probability that both of them have the same birthdays. (Ignore a leap year)

Discussion

3042.	ABCD is a parallelogram. If the radius of the circle passing through all the vertices of the parallelogram is 4 cm, then find length of AC.
Answer» ABCD is a parallelogram. If the radius of the circle passing through all the vertices of the parallelogram is 4 cm, then find length of AC.

Discussion

3043.	Ramesh travels 760km to his home partly by train and partly by car . He takes 8 hours if he travels 160km by train and the rest by car .he takes 12 minutes more if he travels 240km by train and the rest by car . Find the speed of the train and car respectively.
Answer» Ramesh travels 760km to his home partly by train and partly by car . He takes 8 hours if he travels 160km by train and the rest by car .he takes 12 minutes more if he travels 240km by train and the rest by car . Find the speed of the train and car respectively.

Discussion

3044.	62.Find the circumradius of the circle circumscribed get the triangle formed by vertices A (-a,0),B (0,b)and (a, 0)
Answer» 62.Find the circumradius of the circle circumscribed get the triangle formed by vertices A (-a,0),B (0,b)and (a, 0)

Discussion

3045.	Find the coordinates of the image of the point (5,−3) under (i) reflection in the x- axis (ii) reflection in the y- axis and (iii) reflection in the origin.
Answer» Find the coordinates of the image of the point $(5, - 3)$ under (i) reflection in the x- axis (ii) reflection in the y- axis and (iii) reflection in the origin.

Discussion

3046.	∆ABC is a right triangle such that AB = AC and bisector of angle C intersects the side AB at D. Prove that AC + AD = BC.
Answer» ∆ABC is a right triangle such that AB = AC and bisector of angle C intersects the side AB at D. Prove that AC + AD = BC.

Discussion

3047.	Question 24A coin is tossed two times. Find the probability of getting at most one head.
Answer» Question 24 A coin is tossed two times. Find the probability of getting at most one head.

Discussion

3048.	A solid rectangular block of dimensions 4.4 m, 2.6 m and 1 m is cast into a hollow cylindrical pipe of internal radius 30 cm and thickness5 cm. Find the length of the pipe.
Answer» A solid rectangular block of dimensions 4.4 m, 2.6 m and 1 m is cast into a hollow cylindrical pipe of internal radius 30 cm and thickness 5 cm. Find the length of the pipe.

Discussion

3049.	The solution of equation cos^2theta - 2cos theta = 4sin theta - sin2theta where theta belongs to 0 to pi is
Answer» The solution of equation cos^2theta - 2cos theta = 4sin theta - sin2theta where theta belongs to 0 to pi is

Discussion

3050.	Question 1 (iii) Which of the following pairs of linear equations has unique solution, no solution or infinitely many solutions? In case there is a unique solution, find it by using cross multiplication method. 3x - 5y = 20 ; 6x - 10y =40
Answer» Question 1 (iii) Which of the following pairs of linear equations has unique solution, no solution or infinitely many solutions? In case there is a unique solution, find it by using cross multiplication method. 3x - 5y = 20 ; 6x - 10y =40

Discussion

Explore topic-wise InterviewSolutions in .

Find the sum of first n natural numbers.

Which of the following mathematical statement represents inequation

The line joining P(−4,5) and Q(3,2) intersect the y-axis at point R .PM and QN are perpendicular to P and Q on the x- axis. Find:(1) the ratio PR:RQ.(2) the coordinate of R.(3) the area of the quadrilateral PMNQ.

Choose the correct answer of the following question:If a l.5-m-tall girl stands at a distance of 3 m from a lamp post and casts a shadow of length 4.5 m on the ground, then the height of the lamp post is(a) 1.5 m (b) 2 m (c) 2.5 m (d) 2.8 m

Given below is a cumulative frequency table: MarksNumber of studentsBelow 1017Below 2022Below 3029Below 4037Below 5050Below 6060 Extract a frequency table from the above.

Find the sign of a, b and c in the below graph of polynomial f(x)=ax2+b.

Solve the following quadratic equation by factorization. 48x2−13x−1=0

Question 1Find the coordinates of the point which divides the join of (- 1, 7) and (4, - 3) in the ratio 2:3.

Solve the following quadratic equations by factorization:3x+1+4x-1=294x-1; x≠1, -1, 14

State the type of the conditional clause in the sentence. If you attend the class regularly, you will learn many new things.

1. A positive integer is divided by 63, we get the remainder as 25. The remainder when the same number is divided by 9 is equal .

3.If the point P(x,y) is equidistant from the points A(5,1) and B(1,5) then prove that x-y= 0

Very-Short and Short-Answer QuestionsIf the sum of first n terms is (3n2 + 5n), find its common difference.

If the graph of f(x)=3x2+6ax+6c touches the x-axis, then which of the following is always correct?

In triangles ABC and DEF, AB = FD and ∠A = ∠D. The two triangles will be congruent by SAS axiom, if __________.

If the nth term of two AP's 63, 65, 67 .... and 3, 10, 17, .... is equal, then find the value of 'n'.

What are the roots of the quadratic equation (x+2)2-16 = 0?

Question 20 When a die is thrown, the probability of getting an odd number less than 3 is (a) 16 (b) 13 (c) 12 (d) 0

12.The product and difference of inner and outer radiusof a hemi-spherical shell are 12 cm2 and 1 cmrespectively. The sum of inner and outer surfaceareas of the shell i equal to

37. A 6m tall tower is placed on the top of a building, it throws a shadow of 23m on the ground then angle of elevation of the sun is

In the adjoining figure, PQ || BC, then what could be the values of AP &amp; PB respectively

Question 3 (ix) In an AP: (ix) Given a = 3, n = 8, S = 192, find d.

Find:(i) Is 68 a term of the A.P. 7, 10, 13, ...?(ii) Is 302 a term of the A.P. 3, 8, 13, ...?(iii) Is − 150 a term of the A.P. 11, 8, 5, 2, ...?

Find the roots of the quadratic equation, 3x2 – 5x + 2 = 0, using quadratic formula.

From the top of a 7 m high building, the angle of elevation of the top of a cable tower is 60∘ and the angle of depression of its foot is 45∘. Determine the height of the tower.

If B=[−102341],C=[−123210], then 3C−4B is

Question 5S and T are point on sides PR and QR of ΔPQR such that ∠P=∠RTS. Show that ΔRPQ∼ΔRTS.

The area of a circle inscribed in an equilateral triangle is 154 cm2. Find the perimeter of the triangle. [Use π=227 and √3=1.73]

Show that any positive odd integer is of the form , or , or , where q is some integer.

genral value of θ satisfuing the equation †an^2θ+sec2θ=

on dividing a polynomial3x3+4x2+5x−13 by a g(X) the quotient and the remainder were (3x+10) and (16x-43) find g(x)

If one root the equation 2x2 + kx + 4 = 0 is 2, then the other root is(a) 6(b) −6(c) −1(d) 1

Specific volume of a cylindrical virus particle is 6.02×10^-2 cc/gm whose radius and length are 7Å and 10Å respectively. Find molecular weight of virus.

If A=⎡⎢⎣a000b000c⎤⎥⎦, then An=

In the given figure, AB is a chord of length 16 cm of a circle of radius 10 cm. The tangents at A and B intersect at a point P. Find the length of PA.

On rolling a pair of dice, what is the probability of getting the same number on both the dice?

In a hotel, four rooms are available. Six persons are to be accommodated in these four rooms in such a way that each of these rooms contains at least one person and at most two persons. Then the number of all possible ways in which this can be done is

Find the maximum value of 5−(2x2−8x+6).

State AAA similarity criterion.

Deepthi and Shruthi are friends. Find the probability that both of them have the same birthdays. (Ignore a leap year)

ABCD is a parallelogram. If the radius of the circle passing through all the vertices of the parallelogram is 4 cm, then find length of AC.

Ramesh travels 760km to his home partly by train and partly by car . He takes 8 hours if he travels 160km by train and the rest by car .he takes 12 minutes more if he travels 240km by train and the rest by car . Find the speed of the train and car respectively.

62.Find the circumradius of the circle circumscribed get the triangle formed by vertices A (-a,0),B (0,b)and (a, 0)

Find the coordinates of the image of the point (5,−3) under (i) reflection in the x- axis (ii) reflection in the y- axis and (iii) reflection in the origin.

∆ABC is a right triangle such that AB = AC and bisector of angle C intersects the side AB at D. Prove that AC + AD = BC.

Question 24A coin is tossed two times. Find the probability of getting at most one head.

A solid rectangular block of dimensions 4.4 m, 2.6 m and 1 m is cast into a hollow cylindrical pipe of internal radius 30 cm and thickness​5 cm. Find the length of the pipe.

The solution of equation cos^2theta - 2cos theta = 4sin theta - sin2theta where theta belongs to 0 to pi is

Question 1 (iii) Which of the following pairs of linear equations has unique solution, no solution or infinitely many solutions? In case there is a unique solution, find it by using cross multiplication method. 3x - 5y = 20 ; 6x - 10y =40

In the adjoining figure, PQ || BC, then what could be the values of AP & PB respectively

A solid rectangular block of dimensions 4.4 m, 2.6 m and 1 m is cast into a hollow cylindrical pipe of internal radius 30 cm and thickness5 cm. Find the length of the pipe.