32581 + Interview Questions in Mathematics Page 4 InterviewSolution

151.	A circle of radius 3 cm with centre O is drawn circumscribing a ΔABC. Find OA + OB + OC.
Answer» A circle of radius 3 cm with centre O is drawn circumscribing a $Δ$ ABC. Find OA + OB + OC.

Discussion

152.	Which of the following equations are quadratic?
Answer» Which of the following equations are quadratic?

Discussion

153.	Divide polynomial 3x3−8x2+x+7 by x−3 using synthetic method and write the quotient and remainder.
Answer» Divide polynomial $3 x^{3} - 8 x^{2} + x + 7$ by $x - 3$ using synthetic method and write the quotient and remainder.

Discussion

154.	used euclid's division Lemma to show that cube of any positive integer is either of form 9M 9M + 1 or 9 M + 8 for some integer m
Answer» used euclid's division Lemma to show that cube of any positive integer is either of form 9M 9M + 1 or 9 M + 8 for some integer m

Discussion

155.	From the given data, find the average speed of Jack (in km/hr).
Answer» From the given data, find the average speed of Jack (in km/hr).

155.

From the given data, find the average speed of Jack (in km/hr).

Answer»

From the given data, find the average speed of Jack (in km/hr).

Discussion

156.	Find the value of k for which the roots of 9x2+8kx+16=0 are real and equal.
Answer» Find the value of k for which the roots of $9 x^{2} + 8 k x + 16 = 0$ are real and equal.

Discussion

157.	Solve the following quadratic equation by factorization. 9x2−3x−2=0
Answer» Solve the following quadratic equation by factorization. $9 x^{2} - 3 x - 2 = 0$

Discussion

158.	VERIFY THAT LHS = RHS (tanA1-cotA)+(cotA1+tana)=1+tanA+cotA
Answer» VERIFY THAT LHS = RHS (tanA1-cotA)+(cotA1+tana)=1+tanA+cotA

Discussion

159.	Solve each of the following systems of equations by the method of cross-multiplication: ax+by=a+b2 3x+5y=4
Answer» Solve each of the following systems of equations by the method of cross-multiplication: $a x + b y = \frac{a + b}{2}$ $3 x + 5 y = 4$

159.

Solve each of the following systems of equations by the method of cross-multiplication: ax+by=a+b2 3x+5y=4

Answer»

Solve each of the following systems of equations by the method of cross-multiplication:

$a x + b y = \frac{a + b}{2}$

$3 x + 5 y = 4$

Discussion

160.	The centroidal co - ordinate ¯x for the shaded area will be m. The outer boundary of the shaded area is that of a circle having a radius of 1 m. 0.16928
Answer» The centroidal co - ordinate $¯ x$ for the shaded area will be m. The outer boundary of the shaded area is that of a circle having a radius of 1 m. 0.16928

Discussion

161.	Using factor theorem, show that g(x) is a factor of p(x), whenpx=3x3+x2-20x+12,gx=3x-2
Answer» Using factor theorem, show that g(x) is a factor of p(x), when $p (x) = 3 x^{3} + x^{2} - 20 x + 12, g (x) = 3 x - 2$

Discussion

162.	tan theta =1-cos phi/sin phi then find the value tan3theta
Answer» tan theta =1-cos phi/sin phi then find the value tan3theta

Discussion

163.	In a factory there are 7xy+3yz-5zx workers. 8xy+4yz+8zx workers come in the first shift, -5xy-2yz+3zx workers in the second shift and the rest come in the third shift. How many workers come in the third shift?
Answer» In a factory there are 7xy+3yz-5zx workers. 8xy+4yz+8zx workers come in the first shift, -5xy-2yz+3zx workers in the second shift and the rest come in the third shift. How many workers come in the third shift?

Discussion

164.	The value of 0.2¯ in the form pq, where p and q are integers and q ≠ 0, is(a) 15 (b) 29(c) 25(d) 18
Answer» The value of $0 . \bar{2}$ in the form $\frac{p}{q}$ , where p and q are integers and q ≠ 0, is (a) $\frac{1}{5}$ (b) $\frac{2}{9}$ (c) $\frac{2}{5}$ (d) $\frac{1}{8}$

Discussion

165.	Question 5At one end A of a diameter AB of a circle of radius 5 cm, tangent XAY is drawn to the circle. The length of the chord CD parallel to XY and at a distance 8 cm from A, is(A) 4 cm(B) 5 cm(C) 6 cm(D) 8 cm
Answer» Question 5 At one end A of a diameter AB of a circle of radius 5 cm, tangent XAY is drawn to the circle. The length of the chord CD parallel to XY and at a distance 8 cm from A, is (A) 4 cm (B) 5 cm (C) 6 cm (D) 8 cm

Discussion

166.	Solve the given inequality and show the graph of the solution on number line: 3(1 – x) < 2 (x + 4)
Answer» Solve the given inequality and show the graph of the solution on number line: 3(1 – x) < 2 (x + 4)

Discussion

167.	Question 5The largest number which divides 70 and 125, leaving remainders 5 and 8 respectively, isA) 13B) 65C) 875D) 1750
Answer» Question 5 The largest number which divides 70 and 125, leaving remainders 5 and 8 respectively, is A) 13 B) 65 C) 875 D) 1750

Discussion

168.	If A=[2141],B=[3423] and C=[3−4−23], then the value of tr(A)+tr(ABC2)+tr(A(BC)24)+tr(A(BC)38)+...∞ is
Answer» If $A = [\begin{matrix} 2 & 1 4 & 1 \end{matrix}], B = [\begin{matrix} 3 & 4 2 & 3 \end{matrix}] and C = [\begin{matrix} 3 & - 4 - 2 & 3 \end{matrix}],$ then the value of $t r (A) + t r (\frac{A B C}{2}) + t r (\frac{A (B C)^{2}}{4}) + t r (\frac{A (B C)^{3}}{8}) + . . . \infty$ is

Discussion

169.	What is the locus of a Circle
Answer» What is the locus of a Circle

Discussion

170.	Find the value of ‘k’ if (x−1) is a factor of P(x) = 4x3 + x2 – 3x + k.
Answer» Find the value of ‘k’ if $(x - 1)$ is a factor of P(x) = 4 $x^{3}$ + $x^{2}$ – 3x + k.

Discussion

171.	Question 23Two dice are numbered 1,2,3,4,5,6 and 1,1,2,2,3,3, respectively. They are thrown and the sum of the numbers on them is noted. Find the probability of getting each sum from 2 to 9, separately.
Answer» Question 23 Two dice are numbered 1,2,3,4,5,6 and 1,1,2,2,3,3, respectively. They are thrown and the sum of the numbers on them is noted. Find the probability of getting each sum from 2 to 9, separately.

Discussion

172.	One hectare = ________m2. (Enter a numeric value) ___
Answer» One hectare = ________ $m^{2}$ . (Enter a numeric value) ___

Discussion

173.	How tio determine the conic sections(in matrix form ) if determinent is known(proof)
Answer» How tio determine the conic sections(in matrix form ) if determinent is known(proof)

Discussion

174.	Which of the following is a factor of (x + y)3 – (x3 + y3)?(a) x2 + y2 + 2xy(b) x2 + y2 – xy(c) xy2(d) 3xy
Answer» Which of the following is a factor of (x + y)³ – (x³+ y³)? (a) x²+ y² + 2xy (b) x²+ y² – xy (c) xy² (d) 3xy

Discussion

175.	Find the sum of the first 15 multiples of 8.
Answer» Find the sum of the first 15 multiples of 8.

Discussion

176.	Q1) What is the shape of \lbrack NiCl2(PMe3)2\rbrack
Answer» Q1) What is the shape of \lbrack NiCl2(PMe3)2\rbrack

Discussion

177.	The G.C.D. of 1.08, 0.36 and 0.9 is
Answer» The G.C.D. of 1.08, 0.36 and 0.9 is

Discussion

178.	In the given figure, PA and PB are the tangents to a circle with centre O. Show that the points A, O, B, P are concyclic.
Answer» In the given figure, PA and PB are the tangents to a circle with centre O. Show that the points A, O, B, P are concyclic.

Discussion

179.	If polynomial p(x) is divided by (x−a) and the remainder is zero, then (x−a) is called __ of polynomial p(x)
Answer» If polynomial p( $x$ ) is divided by ( $x - a$ ) and the remainder is zero, then ( $x - a$ ) is called __ of polynomial p( $x$ )

Discussion

180.	Which of the following is not true for a point P on the circle?
Answer» Which of the following is not true for a point P on the circle?

Discussion

181.	Question 77 In figure, what is the ratio of the areas of a) shaded portion I to shaded portion II? b) Shaded portion II to shaded portion III? c) The shaded portion I and II taken together and shaded portion III?
Answer» Question 77 In figure, what is the ratio of the areas of a) shaded portion I to shaded portion II? b) Shaded portion II to shaded portion III? c) The shaded portion I and II taken together and shaded portion III?

181.

Question 77 In figure, what is the ratio of the areas of a) shaded portion I to shaded portion II? b) Shaded portion II to shaded portion III? c) The shaded portion I and II taken together and shaded portion III?

Answer»

Question 77

In figure, what is the ratio of the areas of

a) shaded portion I to shaded portion II?

b) Shaded portion II to shaded portion III?

c) The shaded portion I and II taken together and shaded portion III?

Discussion

182.	P and Q invested ₹700 and ₹500 respectively. If the loss incurred after one year is ₹132, find the loss incurred by A and B.
Answer» P and Q invested ₹700 and ₹500 respectively. If the loss incurred after one year is ₹132, find the loss incurred by A and B.

Discussion

183.	How to find HCF Of 3 numbers using Euclids Division Lemma
Answer» How to find HCF Of 3 numbers using Euclids Division Lemma

Discussion

184.	Number of terms of the AP. 21, 18, 15, that must be added to get the sum equal to zero is(1) 12(3) 14(2) 13(4) 15
Answer» Number of terms of the AP. 21, 18, 15, that must be added to get the sum equal to zero is (1) 12 (3) 14 (2) 13 (4) 15

Discussion

185.	The least number which leaves a remainder of 3 when divided by 2, 5, 7, 10 and 15 is
Answer» The least number which leaves a remainder of 3 when divided by 2, 5, 7, 10 and 15 is

Discussion

186.	199 students were asked how many hours they exercise each week.The following table shows the data : Time(t hours)No. of students0−5125−101510−152315−203020−254025−303530−352535−4020Find the Median of the data.
Answer» 199 students were asked how many hours they exercise each week. The following table shows the data : $\begin{matrix} Time(t hours) & No. of students 0 - 5 & 12 5 - 10 & 15 10 - 15 & 23 15 - 20 & 30 20 - 25 & 40 25 - 30 & 35 30 - 35 & 25 35 - 40 & 20 \end{matrix}$ Find the Median of the data.

186.

199 students were asked how many hours they exercise each week.The following table shows the data : Time(t hours)No. of students0−5125−101510−152315−203020−254025−303530−352535−4020Find the Median of the data.

Answer»

199 students were asked how many hours they exercise each week.

The following table shows the data :

$\begin{matrix} Time(t hours) & No. of students 0 - 5 & 12 5 - 10 & 15 10 - 15 & 23 15 - 20 & 30 20 - 25 & 40 25 - 30 & 35 30 - 35 & 25 35 - 40 & 20 \end{matrix}$

Find the Median of the data.

Discussion

187.	Find the probability of the events given when a die is thrown, list the outcomes of an event of getting:(a) a prime number (b) not a prime number
Answer» Find the probability of the events given when a die is thrown, list the outcomes of an event of getting: (a) a prime number (b) not a prime number

Discussion

188.	Question 3 (ii)Find the LCM and HCF of 17, 23 and 29 by applying the prime factorization method.
Answer» Question 3 (ii) Find the LCM and HCF of 17, 23 and 29 by applying the prime factorization method.

Discussion

189.	Mr. Rahul Vyas gets Rs 6455 at the end of one year at the rate of 14% per annum in a recurring deposit account. Find the monthly installment.
Answer» Mr. Rahul Vyas gets Rs 6455 at the end of one year at the rate of 14% per annum in a recurring deposit account. Find the monthly installment.

Discussion

190.	In a hot water heating system, there is a cylindrical pipe of length 28 m and diameter 5 cm. Find the total radiating surface of the system.[Assume π=227]
Answer» In a hot water heating system, there is a cylindrical pipe of length 28 m and diameter 5 cm. Find the total radiating surface of the system. $[A s s u m e π = \frac{22}{7}]$

Discussion

191.	Which of the following fractions is greater than 811?
Answer» Which of the following fractions is greater than $\frac{8}{11}$ ?

Discussion

192.	Mark the correct alternative in each of the following:A die is thrown once. The probability of getting a prime number is(a) 23 (b) 13 (c) 12 (d) 16 [CBSE 2013]
Answer» Mark the correct alternative in each of the following: A die is thrown once. The probability of getting a prime number is (a) $\frac{2}{3}$ (b) $\frac{1}{3}$ (c) $\frac{1}{2}$ (d) $\frac{1}{6}$ [CBSE 2013]

Discussion

193.	If α, β and gamma are zeroes of the polynomial x^3 + ax + b, then the value of α^3 + β^3 + gamma^3 is
Answer» If α, β and gamma are zeroes of the polynomial x^3 + ax + b, then the value of α^3 + β^3 + gamma^3 is

Discussion

194.	If the ratio of sum of the first m and n terms of an A.P. is m^2: n^2, show that the ratio of its m^{th} and n^{th} terms is (2m 1):(2n-1).
Answer» If the ratio of sum of the first m and n terms of an A.P. is m^2: n^2, show that the ratio of its m^{th} and n^{th} terms is (2m 1):(2n-1).

Discussion

195.	If f is a function satisfying such that , find the value of n .
Answer» If f is a function satisfying such that , find the value of n .

Discussion

196.	If the perimeter of a quadrant of a circle is 25 cm, then the radius of the circle is
Answer» If the perimeter of a quadrant of a circle is $25 cm$ , then the radius of the circle is

Discussion

197.	A peacock is sitting on the top of a tree. It observes a serpent on the ground making an angle of depression of 30∘. The peacock with the speed of 400 m/min catches the serpent in 15 seconds. Find the height of the tree.
Answer» A peacock is sitting on the top of a tree. It observes a serpent on the ground making an angle of depression of $30^{\circ}$ . The peacock with the speed of 400 m/min catches the serpent in 15 seconds. Find the height of the tree.

Discussion

198.	In a science lab, some chemicals should be preserved under 2 degree Celsius. Which of the following graph shows the inequality for the above situation?
Answer» In a science lab, some chemicals should be preserved under 2 degree Celsius. Which of the following graph shows the inequality for the above situation?

Discussion

199.	On Diwali, Ted’s mom made a colorful rangoli as shown in the figure. The bigger square measured 30 cm by 30 cm and the smaller square measured 15 cm by 15 cm. What was the area of the orange colored part?
Answer» On Diwali, Ted’s mom made a colorful rangoli as shown in the figure. The bigger square measured 30 cm by 30 cm and the smaller square measured 15 cm by 15 cm. What was the area of the orange colored part?

199.

On Diwali, Ted’s mom made a colorful rangoli as shown in the figure. The bigger square measured 30 cm by 30 cm and the smaller square measured 15 cm by 15 cm. What was the area of the orange colored part?

Answer»

On Diwali, Ted’s mom made a colorful rangoli as shown in the figure. The bigger square measured 30 cm by 30 cm and the smaller square measured 15 cm by 15 cm. What was the area of the orange colored part?

Discussion

200.	If a letter is chosen at random from the word ''ASSASSINATION'', then probability that the letter is vowel, is
Answer» If a letter is chosen at random from the word ''ASSASSINATION'', then probability that the letter is vowel, is

Discussion

Explore topic-wise InterviewSolutions in .

A circle of radius 3 cm with centre O is drawn circumscribing a ΔABC. Find OA + OB + OC.

Which of the following equations are quadratic?

Divide polynomial 3x3−8x2+x+7 by x−3 using synthetic method and write the quotient and remainder.

used euclid's division Lemma to show that cube of any positive integer is either of form 9M 9M + 1 or 9 M + 8 for some integer m

From the given data, find the average speed of Jack (in km/hr).

Find the value of k for which the roots of 9x2+8kx+16=0 are real and equal.

Solve the following quadratic equation by factorization. 9x2−3x−2=0

VERIFY THAT LHS = RHS (tanA1-cotA)+(cotA1+tana)=1+tanA+cotA

Solve each of the following systems of equations by the method of cross-multiplication: ax+by=a+b2 3x+5y=4

The centroidal co - ordinate ¯x for the shaded area will be m. The outer boundary of the shaded area is that of a circle having a radius of 1 m. 0.16928

Using factor theorem, show that g(x) is a factor of p(x), whenpx=3x3+x2-20x+12,gx=3x-2

tan theta =1-cos phi/sin phi then find the value tan3theta

In a factory there are 7xy+3yz-5zx workers. 8xy+4yz+8zx workers come in the first shift, -5xy-2yz+3zx workers in the second shift and the rest come in the third shift. How many workers come in the third shift?

The value of 0.2¯ in the form pq, where p and q are integers and q ≠ 0, is(a) 15 (b) 29(c) 25(d) 18

Question 5At one end A of a diameter AB of a circle of radius 5 cm, tangent XAY is drawn to the circle. The length of the chord CD parallel to XY and at a distance 8 cm from A, is(A) 4 cm(B) 5 cm(C) 6 cm(D) 8 cm

Solve the given inequality and show the graph of the solution on number line: 3(1 – x) &lt; 2 (x + 4)

Question 5The largest number which divides 70 and 125, leaving remainders 5 and 8 respectively, isA) 13B) 65C) 875D) 1750

If A=[2141],B=[3423] and C=[3−4−23], then the value of tr(A)+tr(ABC2)+tr(A(BC)24)+tr(A(BC)38)+...∞ is

What is the locus of a Circle

Find the value of ‘k’ if (x−1) is a factor of P(x) = 4x3 + x2 – 3x + k.

Question 23Two dice are numbered 1,2,3,4,5,6 and 1,1,2,2,3,3, respectively. They are thrown and the sum of the numbers on them is noted. Find the probability of getting each sum from 2 to 9, separately.

One hectare = ________m2. (Enter a numeric value) ___

How tio determine the conic sections(in matrix form ) if determinent is known(proof)

Which of the following is a factor of (x + y)3 – (x3 + y3)?(a) x2 + y2 + 2xy(b) x2 + y2 – xy(c) xy2(d) 3xy

Find the sum of the first 15 multiples of 8.

Q1) What is the shape of \lbrack NiCl2(PMe3)2\rbrack

The G.C.D. of 1.08, 0.36 and 0.9 is

In the given figure, PA and PB are the tangents to a circle with centre O. Show that the points A, O, B, P are concyclic.

If polynomial p(x) is divided by (x−a) and the remainder is zero, then (x−a) is called __ of polynomial p(x)

Which of the following is not true for a point P on the circle?

Question 77 In figure, what is the ratio of the areas of a) shaded portion I to shaded portion II? b) Shaded portion II to shaded portion III? c) The shaded portion I and II taken together and shaded portion III?

P and Q invested ₹700 and ₹500 respectively. If the loss incurred after one year is ₹132, find the loss incurred by A and B.

How to find HCF Of 3 numbers using Euclids Division Lemma

Number of terms of the AP. 21, 18, 15, that must be added to get the sum equal to zero is(1) 12(3) 14(2) 13(4) 15

The least number which leaves a remainder of 3 when divided by 2, 5, 7, 10 and 15 is

199 students were asked how many hours they exercise each week.The following table shows the data : Time(t hours)No. of students0−5125−101510−152315−203020−254025−303530−352535−4020Find the Median of the data.

Find the probability of the events given when a die is thrown, list the outcomes of an event of getting:(a) a prime number (b) not a prime number

Question 3 (ii)Find the LCM and HCF of 17, 23 and 29 by applying the prime factorization method.

Mr. Rahul Vyas gets Rs 6455 at the end of one year at the rate of 14% per annum in a recurring deposit account. Find the monthly installment.

In a hot water heating system, there is a cylindrical pipe of length 28 m and diameter 5 cm. Find the total radiating surface of the system.[Assume π=227]

Which of the following fractions is greater than 811?

Mark the correct alternative in each of the following:A die is thrown once. The probability of getting a prime number is(a) 23 (b) 13 (c) 12 (d) 16 [CBSE 2013]

If α, β and gamma are zeroes of the polynomial x^3 + ax + b, then the value of α^3 + β^3 + gamma^3 is

If the ratio of sum of the first m and n terms of an A.P. is m^2: n^2, show that the ratio of its m^{th} and n^{th} terms is (2m 1):(2n-1).

If f is a function satisfying such that , find the value of n .

If the perimeter of a quadrant of a circle is 25 cm, then the radius of the circle is

A peacock is sitting on the top of a tree. It observes a serpent on the ground making an angle of depression of 30∘. The peacock with the speed of 400 m/min catches the serpent in 15 seconds. Find the height of the tree.

In a science lab, some chemicals should be preserved under 2 degree Celsius. Which of the following graph shows the inequality for the above situation?

On Diwali, Ted’s mom made a colorful rangoli as shown in the figure. The bigger square measured 30 cm by 30 cm and the smaller square measured 15 cm by 15 cm. What was the area of the orange colored part?

If a letter is chosen at random from the word ''ASSASSINATION'', then probability that the letter is vowel, is

Solve the given inequality and show the graph of the solution on number line: 3(1 – x) < 2 (x + 4)

One hectare = ______m2. (Enter a numeric value) _