32581 + Interview Questions in Mathematics

1.	Question 8 Show that 0.142857142857……=17
Answer» Question 8 Show that $0.142857142857 \dots \dots = \frac{1}{7}$

Discussion

2.	Using slopes, show that the vertices (-2, -1), (4, 0), (3, 3) and (-3, 2) are the vertices of a parallelogram.
Answer» Using slopes, show that the vertices (-2, -1), (4, 0), (3, 3) and (-3, 2) are the vertices of a parallelogram.

Discussion

3.	P (–10, 2) and Q (–5, –1) are the vertices of a parallelogram PQRS. The coordinates of the point where the diagonals intersect are (–3, 2). Find the coordinates of R and S.
Answer» P (–10, 2) and Q (–5, –1) are the vertices of a parallelogram PQRS. The coordinates of the point where the diagonals intersect are (–3, 2). Find the coordinates of R and S.

Discussion

4.	Question 15 Check whether p(x) is a multiple of g(x) or not: (i) p(x)=x3–5x2+4x–3, g(x)=x–2 (ii) p(x)=2x3–11x2–4x+5, g(x)=2x+1
Answer» Question 15 Check whether p(x) is a multiple of g(x) or not: (i) $p (x) = x^{3} - 5 x^{2} + 4 x - 3, g (x) = x - 2$ (ii) $p (x) = 2 x^{3} - 11 x^{2} - 4 x + 5, g (x) = 2 x + 1$

Discussion

5.	If a die is thrown, what is the probability of getting a multiple of 3?
Answer» If a die is thrown, what is the probability of getting a multiple of 3?

Discussion

6.	The graph obtained by plotting y=x2 is in the shape of a ___ .
Answer» The graph obtained by plotting $y = x^{2}$ is in the shape of a ___ .

Discussion

7.	Let c1& c2 be the centers and r1& r2 be the radius of two circles. Then Cases Conditions p. 1.\|r1−r2\|< c1c2< r1+r2 q. 2. \|r1−r2\|=c1c2 r. 3.c1c2< \|r1+r2\| s. 4. r1+r2< c1r2 t. 5. r1+r2=c1r2
Answer» Let $c_{1} & c_{2}$ be the centers and $r_{1} & r_{2}$ be the radius of two circles. Then Cases Conditions p. 1. $\| r_{1} - r_{2} \| < c_{1} c_{2} < r_{1} + r_{2}$ q. 2. $\| r_{1} - r_{2} \| = c_{1} c_{2}$ r. 3. $c_{1} c_{2} < \| r_{1} + r_{2} \|$ s. 4. $r_{1} + r_{2} < c_{1} r_{2}$ t. 5. $r_{1} + r_{2} = c_{1} r_{2}$

7.

Let c1& c2 be the centers and r1& r2 be the radius of two circles. Then Cases Conditions p. 1.|r1−r2|< c1c2< r1+r2 q. 2. |r1−r2|=c1c2 r. 3.c1c2< |r1+r2| s. 4. r1+r2< c1r2 t. 5. r1+r2=c1r2

Answer»

Let $c_{1} & c_{2}$ be the centers and $r_{1} & r_{2}$ be the radius of two circles. Then

Cases Conditions

p. 1. $| r_{1} - r_{2} | < c_{1} c_{2} < r_{1} + r_{2}$

q. 2. $| r_{1} - r_{2} | = c_{1} c_{2}$

r. 3. $c_{1} c_{2} < | r_{1} + r_{2} |$

s.

4. $r_{1} + r_{2} < c_{1} r_{2}$

t. 5. $r_{1} + r_{2} = c_{1} r_{2}$

Discussion

8.	If sin−1x=θ+β and sin−1y=θ−β then 1+xy is equal to
Answer» If $s i n^{- 1} x = θ + β$ and $s i n^{- 1} y = θ - β$ then 1+xy is equal to

Discussion

9.	In Fig 7.60, AD bisects ∠ A, AB = 12 cm, AC = 420 cm and BD = 5 cm determine CD.
Answer» In Fig 7.60, AD bisects $∠$ A, AB = 12 cm, AC = 420 cm and BD = 5 cm determine CD.

9.

In Fig 7.60, AD bisects ∠ A, AB = 12 cm, AC = 420 cm and BD = 5 cm determine CD.

Answer»

In Fig 7.60, AD bisects $∠$ A, AB = 12 cm, AC = 420 cm and BD = 5 cm determine CD.

Discussion

10.	The mid-point of the line segment AB where cordinates of A are (−2,x2) and coordinates of B are (x4,2) is
Answer» The mid-point of the line segment $A B$ where cordinates of $A$ are $(- 2, \frac{x}{2})$ and coordinates of B are $(\frac{x}{4}, 2)$ is

Discussion

11.	The compound ratio of 2 : 3, 3 : 5, 5 : 1, and 4 : 3 is:
Answer» The compound ratio of 2 : 3, 3 : 5, 5 : 1, and 4 : 3 is:

Discussion

12.	In the figure given below, if BC ∥ EF and FG ∥ CD. AEAB =
Answer» In the figure given below, if BC $∥$ EF and FG $∥$ CD. $\frac{A E}{A B}$ =

12.

In the figure given below, if BC ∥ EF and FG ∥ CD. AEAB =

Answer»

In the figure given below, if BC $∥$ EF and FG $∥$ CD. $\frac{A E}{A B}$ =

Discussion

13.	From the figure, the value of cosec A + cot A is :
Answer» From the figure, the value of cosec A + cot A is :

13.

From the figure, the value of cosec A + cot A is :

Answer»

From the figure, the value of cosec A + cot A is :

Discussion

14.	What is the ratio ACBC for the following construction method: A ray is extended from A and 30 arcs of equal lengths are cut, cutting the ray at A1,A2.......A30. A line is drawn from A30 to B and a line parallel to A30B is drawn, passing through the point A17.
Answer» What is the ratio $\frac{A C}{B C}$ for the following construction method: A ray is extended from A and 30 arcs of equal lengths are cut, cutting the ray at $A_{1}, A_{2} . . . . . . . A_{30}$ . A line is drawn from $A_{30}$ to B and a line parallel to $A_{30} B$ is drawn, passing through the point $A_{17}$ .

Discussion

15.	Question 1(v) Find the roots of the following quadratic equations by factorization: (v)100x2−20x+1=0
Answer» Question 1(v) Find the roots of the following quadratic equations by factorization: $(v) 100 x^{2} - 20 x + 1 = 0$

Discussion

16.	If the 10th term of an A.P. is 52 amd the 17th term is 20 more than the 13th term, find the A.P.
Answer» If the $10^{t h}$ term of an A.P. is 52 amd the $17^{t h}$ term is 20 more than the $13^{t h}$ term, find the A.P.

Discussion

17.	Draw a circle of radius 3 cm. Mark a point P at a distance of 5 cm from the centre of the circle. Draw two tangents PA and PB to the given circle and measure the length of each tangent.
Answer» Draw a circle of radius 3 cm. Mark a point P at a distance of 5 cm from the centre of the circle. Draw two tangents PA and PB to the given circle and measure the length of each tangent.

Discussion

18.	Find GCD of 765 and 65
Answer» Find GCD of 765 and 65

Discussion

19.	If A is a square matrix of order 2 such that A2=0, then
Answer» If A is a square matrix of order 2 such that $A^{2} = 0$ , then

Discussion

20.	An electric pole is 10 m high. If the shadow is 17.32 metres in length,find the elevation of sun
Answer» An electric pole is 10 m high. If the shadow is 17.32 metres in length,find the elevation of sun

Discussion

21.	Which of the following operations can be performed on a variable?
Answer» Which of the following operations can be performed on a variable?

Discussion

22.	When x4+x3−2x2+x+1 is divided by x−1, the remainder is 2 and the quotient is q(x). Find q(x).
Answer» When $x^{4} + x^{3} - 2 x^{2} + x + 1$ is divided by $x - 1$ , the remainder is 2 and the quotient is q(x). Find q(x).

Discussion

23.	A person standing at some distance from a tower sees the top of the tower, making an angle of elevation of 50∘. When he moves 10 m towards the tower the angle of elevation changes to 70∘. The height of the tower is [tan 70∘=2.74 ,tan 50∘=1.2]
Answer» A person standing at some distance from a tower sees the top of the tower, making an angle of elevation of $50^{\circ}$ . When he moves 10 m towards the tower the angle of elevation changes to $70^{\circ}$ . The height of the tower is $[t a n 70^{\circ} = 2.74, t a n 50^{\circ} = 1.2]$

23.

A person standing at some distance from a tower sees the top of the tower, making an angle of elevation of 50∘. When he moves 10 m towards the tower the angle of elevation changes to 70∘. The height of the tower is [tan 70∘=2.74 ,tan 50∘=1.2]

Answer»

A person standing at some distance from a tower sees the top of the tower, making an angle of elevation of $50^{\circ}$ . When he moves 10 m towards the tower the angle of elevation changes to $70^{\circ}$ . The height of the tower is

$[t a n 70^{\circ} = 2.74, t a n 50^{\circ} = 1.2]$

Discussion

24.	Find the greatest number of 4 digit which is divisible by both 8 and 11
Answer» Find the greatest number of 4 digit which is divisible by both 8 and 11

Discussion

25.	A number x is selected at random from the numbers 1, 4, 9, 16 and another number y is selected at random from the numbers 1, 2, 3, 4. Find the probability that the value of xy is more than 16.
Answer» A number x is selected at random from the numbers 1, 4, 9, 16 and another number y is selected at random from the numbers 1, 2, 3, 4. Find the probability that the value of xy is more than 16.

Discussion

26.	If 1 is a zero of the polynomial p(x), then which of the following is correct?
Answer» If 1 is a zero of the polynomial p(x), then which of the following is correct?

Discussion

27.	the TSA of cylinder is 924cm2.If the CSA is 2/3 of the TSA,find the radius and height.
Answer» the TSA of cylinder is 924cm².If the CSA is 2/3 of the TSA,find the radius and height.

Discussion

28.	The points (K, 3), (2, -4) and (-k + 1, -2) are collinear. Find K.
Answer» The points (K, 3), (2, -4) and (-k + 1, -2) are collinear. Find K.

Discussion

29.	What the probability that a leap year selected randomly will have 53 Sundays?
Answer» What the probability that a leap year selected randomly will have 53 Sundays?

Discussion

30.	You are given just a compass and a ruler which does not show any measurement on it. You see a circle on the cartesian coordinate plane. Call this circle ‘C’. You are required to construct a circle (call this circle ‘D’) concentric to circle C and with radius which is √2 times the radius of C. You do not have the value of ‘r’, the radius of C. Study the following steps carefully. Remember that the only thing you can do with the ruler provided is just draw a straight line. What is the first step to construct the circle ‘D’?
Answer» You are given just a compass and a ruler which does not show any measurement on it. You see a circle on the cartesian coordinate plane. Call this circle ‘C’. You are required to construct a circle (call this circle ‘D’) concentric to circle C and with radius which is $\sqrt{2}$ times the radius of C. You do not have the value of ‘r’, the radius of C. Study the following steps carefully. Remember that the only thing you can do with the ruler provided is just draw a straight line. What is the first step to construct the circle ‘D’?

Discussion

31.	what are the values of remainder r, when a positive integer a is divided by 3???
Answer» what are the values of remainder r, when a positive integer a is divided by 3???

Discussion

32.	In Fig., a circle with centre O is inscribed in a quadrilateral ABCD such that, it touches the sides BC, AB, AD and CD at points P,Q,R and S respectively, If AB = 29 cm, AD = 23 cm, DB=90∘ and DS = 5 cm, then the radius of the circle (in cm.) is :
Answer» In Fig., a circle with centre O is inscribed in a quadrilateral ABCD such that, it touches the sides BC, AB, AD and CD at points P,Q,R and S respectively, If AB = 29 cm, AD = 23 cm, $D B = 90^{\circ}$ and DS = 5 cm, then the radius of the circle (in cm.) is :

32.

In Fig., a circle with centre O is inscribed in a quadrilateral ABCD such that, it touches the sides BC, AB, AD and CD at points P,Q,R and S respectively, If AB = 29 cm, AD = 23 cm, DB=90∘ and DS = 5 cm, then the radius of the circle (in cm.) is :

Answer»

In Fig., a circle with centre O is inscribed in a quadrilateral ABCD such that, it touches the sides BC, AB, AD and CD at points P,Q,R and S respectively, If AB = 29 cm, AD = 23 cm, $D B = 90^{\circ}$ and DS = 5 cm, then the radius of the circle (in cm.) is :

Discussion

33.	A marble of radius 15 cm correctly fits under a cone. The slant height of the cone is eqal to the diameter of its base. What is the height (in cm) of the cone?
Answer» A marble of radius 15 cm correctly fits under a cone. The slant height of the cone is eqal to the diameter of its base. What is the height (in cm) of the cone?

Discussion

34.	Range Frequency Cumulative frequency 0−105(b)10−20(a)820−302(c)30−406(d) Fill in the missing slots and find the value of (a)+(b)+(c)+(d).
Answer» $\begin{matrix} R a n g e & F r e q u e n c y & C u m u l a t i v e f r e q u e n c y 0 - 10 & 5 & (b) 10 - 20 & (a) & 8 20 - 30 & 2 & (c) 30 - 40 & 6 & (d) \end{matrix}$ Fill in the missing slots and find the value of $(a) + (b) + (c) + (d)$ .

34.

Range Frequency Cumulative frequency 0−105(b)10−20(a)820−302(c)30−406(d) Fill in the missing slots and find the value of (a)+(b)+(c)+(d).

Answer»

$\begin{matrix} R a n g e & F r e q u e n c y & C u m u l a t i v e f r e q u e n c y 0 - 10 & 5 & (b) 10 - 20 & (a) & 8 20 - 30 & 2 & (c) 30 - 40 & 6 & (d) \end{matrix}$

Fill in the missing slots and find the value of $(a) + (b) + (c) + (d)$ .

Discussion

35.	Which all of the following are pythagoras triplet
Answer» Which all of the following are pythagoras triplet

Discussion

36.	A single die is rolled. Find the probability of the sum of the five visible faces being greater than or equal to 19. [3 MARKS]
Answer» A single die is rolled. Find the probability of the sum of the five visible faces being greater than or equal to 19. [3 MARKS]

Discussion

37.	If R is the outer radius of a hollow cylinder, r its inner radius, and h its height, then its volume (in cu. units) is:
Answer» If R is the outer radius of a hollow cylinder, r its inner radius, and h its height, then its volume (in cu. units) is:

Discussion

38.	Question 7 The zeroes of the quadratic polynomial x2+99x+127 are (A) both positive (B) both negative (C) one positive and one negative (D) both equal
Answer» Question 7 The zeroes of the quadratic polynomial $x^{2} + 99 x + 127$ are (A) both positive (B) both negative (C) one positive and one negative (D) both equal

Discussion

39.	Pick the incorrect statement from the below options based on the folllowing information: The list of numbers 5, - 2, -9, -16 ...
Answer» Pick the incorrect statement from the below options based on the folllowing information: The list of numbers 5, - 2, -9, -16 ...

Discussion

40.	In a Δ ABC, P and Q are points on sides AB and AC respectively, such that PQ \|\| BC. If 2.4 cm, AQ =2 cm, QC = 3cm and BC =6cm, Finnd AB and PQ.
Answer» In a $Δ A B C$ , P and Q are points on sides AB and AC respectively, such that PQ \|\| BC. If 2.4 cm, AQ =2 cm, QC = 3cm and BC =6cm, Finnd AB and PQ.

Discussion

41.	For a rectangular field of area 3 sq. units, the length is one unit more than twice the breadth ‘x′. The quadratic equation representing the situation is:
Answer» For a rectangular field of area 3 sq. units, the length is one unit more than twice the breadth $‘ x^{'}$ . The quadratic equation representing the situation is:

Discussion

42.	The sums of first n terms of three arithmetic progressions are S1, S2 and S3 respectively. The first term of each A.P. is 1 and their common difference are 1, 2 and 3 respectively. Prove that S1+S3=2S2.
Answer» The sums of first n terms of three arithmetic progressions are $S_{1}, S_{2}$ and $S_{3}$ respectively. The first term of each A.P. is 1 and their common difference are 1, 2 and 3 respectively. Prove that $S_{1} + S_{3} = 2 S_{2}$ .

Discussion

43.	Divide 20 into two parts such that three times the square of one part exceeds the other part by 10.
Answer» Divide 20 into two parts such that three times the square of one part exceeds the other part by 10.

Discussion

44.	Discriminant of the equation ax2+bx+c=0 is given by
Answer» Discriminant of the equation $a x^{2} + b x + c = 0$ is given by

Discussion

45.	Using Pythagoras theorem determine the length of AD in terms of b and shown an Fig. 7.221
Answer» Using Pythagoras theorem determine the length of AD in terms of b and shown an Fig. 7.221

45.

Using Pythagoras theorem determine the length of AD in terms of b and shown an Fig. 7.221

Answer»

Using Pythagoras theorem determine the length of AD in terms of b and shown an Fig. 7.221

Discussion

46.	Which of the following equations have x = 7, y = 3 as solution?
Answer» Which of the following equations have x = 7, y = 3 as solution?

Discussion

47.	Question 3 Find the area of a sector of a circle of radius 28 cm and central angle 45∘.
Answer» Question 3 Find the area of a sector of a circle of radius 28 cm and central angle $45^{\circ}$ .

Discussion

48.	The sum of the first 100 natural numbers is greater than the sum of the even numbers between 1 and 100 by _____.
Answer» The sum of the first 100 natural numbers is greater than the sum of the even numbers between 1 and 100 by _____.

Discussion

49.	Brokerage is always calculated on ___ value of shares.
Answer» Brokerage is always calculated on ___ value of shares.

Discussion

50.	Question 1 (vii) Find the zeroes of the following polynomials by factorization method and verify the relations between the zeroes and the coefficient of the polynomials (vii) 2s2−(1+2√2)s+√2
Answer» Question 1 (vii) Find the zeroes of the following polynomials by factorization method and verify the relations between the zeroes and the coefficient of the polynomials (vii) $2 s^{2} - (1 + 2 \sqrt{2}) s + \sqrt{2}$

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Question 8 Show that 0.142857142857……=17

Using slopes, show that the vertices (-2, -1), (4, 0), (3, 3) and (-3, 2) are the vertices of a parallelogram.

P (–10, 2) and Q (–5, –1) are the vertices of a parallelogram PQRS. The coordinates of the point where the diagonals intersect are (–3, 2). Find the coordinates of R and S.

Question 15 Check whether p(x) is a multiple of g(x) or not: (i) p(x)=x3–5x2+4x–3, g(x)=x–2 (ii) p(x)=2x3–11x2–4x+5, g(x)=2x+1

If a die is thrown, what is the probability of getting a multiple of 3?

The graph obtained by plotting y=x2 is in the shape of a ___ .

Let c1&amp; c2 be the centers and r1&amp; r2 be the radius of two circles. Then Cases Conditions p. 1.|r1−r2|&lt; c1c2&lt; r1+r2 q. 2. |r1−r2|=c1c2 r. 3.c1c2&lt; |r1+r2| s. 4. r1+r2&lt; c1r2 t. 5. r1+r2=c1r2

If sin−1x=θ+β and sin−1y=θ−β then 1+xy is equal to

In Fig 7.60, AD bisects ∠ A, AB = 12 cm, AC = 420 cm and BD = 5 cm determine CD.

The mid-point of the line segment AB where cordinates of A are (−2,x2) and coordinates of B are (x4,2) is

The compound ratio of 2 : 3, 3 : 5, 5 : 1, and 4 : 3 is:

In the figure given below, if BC ∥ EF and FG ∥ CD. AEAB =

From the figure, the value of cosec A + cot A is :

What is the ratio ACBC for the following construction method: A ray is extended from A and 30 arcs of equal lengths are cut, cutting the ray at A1,A2.......A30. A line is drawn from A30 to B and a line parallel to A30B is drawn, passing through the point A17.

Question 1(v) Find the roots of the following quadratic equations by factorization: (v)100x2−20x+1=0

If the 10th term of an A.P. is 52 amd the 17th term is 20 more than the 13th term, find the A.P.

Draw a circle of radius 3 cm. Mark a point P at a distance of 5 cm from the centre of the circle. Draw two tangents PA and PB to the given circle and measure the length of each tangent.

Find GCD of 765 and 65

If A is a square matrix of order 2 such that A2=0, then

An electric pole is 10 m high. If the shadow is 17.32 metres in length,find the elevation of sun

Which of the following operations can be performed on a variable?

When x4+x3−2x2+x+1 is divided by x−1, the remainder is 2 and the quotient is q(x). Find q(x).

A person standing at some distance from a tower sees the top of the tower, making an angle of elevation of 50∘. When he moves 10 m towards the tower the angle of elevation changes to 70∘. The height of the tower is [tan 70∘=2.74 ,tan 50∘=1.2]

Find the greatest number of 4 digit which is divisible by both 8 and 11

A number x is selected at random from the numbers 1, 4, 9, 16 and another number y is selected at random from the numbers 1, 2, 3, 4. Find the probability that the value of xy is more than 16.

If 1 is a zero of the polynomial p(x), then which of the following is correct?

the TSA of cylinder is 924cm2.If the CSA is 2/3 of the TSA,find the radius and height.

The points (K, 3), (2, -4) and (-k + 1, -2) are collinear. Find K.

What the probability that a leap year selected randomly will have 53 Sundays?

what are the values of remainder r, when a positive integer a is divided by 3???

In Fig., a circle with centre O is inscribed in a quadrilateral ABCD such that, it touches the sides BC, AB, AD and CD at points P,Q,R and S respectively, If AB = 29 cm, AD = 23 cm, DB=90∘ and DS = 5 cm, then the radius of the circle (in cm.) is :

A marble of radius 15 cm correctly fits under a cone. The slant height of the cone is eqal to the diameter of its base. What is the height (in cm) of the cone?

Range Frequency Cumulative frequency 0−105(b)10−20(a)820−302(c)30−406(d) Fill in the missing slots and find the value of (a)+(b)+(c)+(d).

Which all of the following are pythagoras triplet

A single die is rolled. Find the probability of the sum of the five visible faces being greater than or equal to 19. [3 MARKS]

If R is the outer radius of a hollow cylinder, r its inner radius, and h its height, then its volume (in cu. units) is:

Question 7 The zeroes of the quadratic polynomial x2+99x+127 are (A) both positive (B) both negative (C) one positive and one negative (D) both equal

Pick the incorrect statement from the below options based on the folllowing information: The list of numbers 5, - 2, -9, -16 ...

In a Δ ABC, P and Q are points on sides AB and AC respectively, such that PQ || BC. If 2.4 cm, AQ =2 cm, QC = 3cm and BC =6cm, Finnd AB and PQ.

For a rectangular field of area 3 sq. units, the length is one unit more than twice the breadth ‘x′. The quadratic equation representing the situation is:

The sums of first n terms of three arithmetic progressions are S1, S2 and S3 respectively. The first term of each A.P. is 1 and their common difference are 1, 2 and 3 respectively. Prove that S1+S3=2S2.

Divide 20 into two parts such that three times the square of one part exceeds the other part by 10.

Discriminant of the equation ax2+bx+c=0 is given by

Using Pythagoras theorem determine the length of AD in terms of b and shown an Fig. 7.221

Which of the following equations have x = 7, y = 3 as solution?

Question 3 Find the area of a sector of a circle of radius 28 cm and central angle 45∘.

The sum of the first 100 natural numbers is greater than the sum of the even numbers between 1 and 100 by _____.

Brokerage is always calculated on ___ value of shares.

Question 1 (vii) Find the zeroes of the following polynomials by factorization method and verify the relations between the zeroes and the coefficient of the polynomials (vii) 2s2−(1+2√2)s+√2

Let c1& c2 be the centers and r1& r2 be the radius of two circles. Then Cases Conditions p. 1.|r1−r2|< c1c2< r1+r2 q. 2. |r1−r2|=c1c2 r. 3.c1c2< |r1+r2| s. 4. r1+r2< c1r2 t. 5. r1+r2=c1r2