32581 + Interview Questions in Mathematics

1.	How many zeroes do the polynomials P1(x)=x3+x2+x+1 and P2(x)=x2+1 have in common?
Answer» How many zeroes do the polynomials $P_{1} (x) = x^{3} + x^{2} + x + 1$ and $P_{2} (x) = x^{2} + 1$ have in common?

Discussion

2.	Find the dependent pair of linear equations from the following.
Answer» Find the dependent pair of linear equations from the following.

Discussion

3.	Find the value of sin2θ+cos2θ at θ=30∘ & 60∘ ?
Answer» $F i n d t h e v a l u e o f s i n^{2} θ + c o s^{2} θ a t θ = 30^{\circ} & 60^{\circ} ?$

Discussion

4.	Given the linear equation x - 2y - 6 = 0,write another linear equation in these two variables, such that the geometrical representation of the pair so formed is: (i) coincident lines (ii) intersection lines
Answer» Given the linear equation x - 2y - 6 = 0,write another linear equation in these two variables, such that the geometrical representation of the pair so formed is: (i) coincident lines (ii) intersection lines

Discussion

5.	If (x+a) is a factor of (2x2+2ax+5x+10), find the value of a.
Answer» If (x+a) is a factor of $(2 x^{2} + 2 a x + 5 x + 10)$ , find the value of a.

Discussion

6.	By actual division , shows that x2−3 is a factor of 2x4+3x3−2x2−9x−12.
Answer» By actual division , shows that $x^{2} - 3$ is a factor of $2 x^{4} + 3 x^{3} - 2 x^{2} - 9 x - 12.$

Discussion

7.	A boy scored the following marks in various tests during a term, each test being marked out of 20. 15,17,16,7,10,12,14,16,19,12,16. The median marks are
Answer» A boy scored the following marks in various tests during a term, each test being marked out of $20$ . $15, 17, 16, 7, 10, 12, 14, 16, 19, 12, 16$ . The median marks are

7.

A boy scored the following marks in various tests during a term, each test being marked out of 20. 15,17,16,7,10,12,14,16,19,12,16. The median marks are

Answer»

A boy scored the following marks in various tests during a term, each test being marked out of $20$ .

$15, 17, 16, 7, 10, 12, 14, 16, 19, 12, 16$ . The median marks are

Discussion

8.	The monthly income of a group of 320 employees in a company is as follows : Monthly income (in Rs.1000) 6 – 7 7 – 8 8 – 9 9 – 10 10 – 11 11 – 12 12 – 13 Number of employees 20 45 65 95 60 30 5 Draw an ogive for the given distribution taking 2cm = Rs.1000 on one axis & 2cm = 50 employees on the other axis. Using the graph determine:
Answer» The monthly income of a group of 320 employees in a company is as follows : Monthly income (in Rs.1000) 6 – 7 7 – 8 8 – 9 9 – 10 10 – 11 11 – 12 12 – 13 Number of employees 20 45 65 95 60 30 5 Draw an ogive for the given distribution taking 2cm = Rs.1000 on one axis & 2cm = 50 employees on the other axis. Using the graph determine:

8.

The monthly income of a group of 320 employees in a company is as follows : Monthly income (in Rs.1000) 6 – 7 7 – 8 8 – 9 9 – 10 10 – 11 11 – 12 12 – 13 Number of employees 20 45 65 95 60 30 5 Draw an ogive for the given distribution taking 2cm = Rs.1000 on one axis & 2cm = 50 employees on the other axis. Using the graph determine:

Answer»

The monthly income of a group of 320 employees in a company is as follows :

Monthly income (in Rs.1000) 6 – 7 7 – 8 8 – 9 9 – 10 10 – 11 11 – 12 12 – 13

Number of employees 20 45 65 95 60 30 5

Draw an ogive for the given distribution taking 2cm = Rs.1000 on one axis & 2cm = 50 employees on the other axis. Using the graph determine:

Discussion

9.	In triangle ABC,D is a point on AB and E is a point on AC such that DE\|\|BC. If ADAB=AEx, Then x is _______.
Answer» In triangle $A B C, D$ is a point on $A B$ and $E$ is a point on $A C$ such that $D E \| \| B C$ . If $\frac{A D}{A B} = \frac{A E}{x}$ , Then $x$ is _______.

Discussion

10.	Find the equation of a circle, the end points of one of whose diameters are A (2, -3) and B(-3, 5).
Answer» Find the equation of a circle, the end points of one of whose diameters are A (2, -3) and B(-3, 5).

Discussion

11.	HCF of 42 hand 72 is 6 then their LCM is___?
Answer» HCF of 42 hand 72 is 6 then their LCM is___?

Discussion

12.	Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion. (i) 238 (ii) 125441 (iii) 3550 (iv) 77210 (v) 12922×57×717 (vi) 98710500
Answer» Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion. (i) $\frac{23}{8}$ (ii) $\frac{125}{441}$ (iii) $\frac{35}{50}$ (iv) $\frac{77}{210}$ (v) $\frac{129}{2^{2} \times 5^{7} \times 7^{17}}$ (vi) $\frac{987}{10500}$

Discussion

13.	If 3 cot θ=2, show that 4sinθ−3cosθ(2sinθ+6cosθ)=13.
Answer» If 3 cot $θ = 2$ , show that $\frac{4 s i n θ - 3 c o s θ}{(2 s i n θ + 6 c o s θ)} = \frac{1}{3}$ .

Discussion

14.	Fint the roots of the following quadratic equations (if they exist) by the method of completing the square. 2x2+x+4=0
Answer» Fint the roots of the following quadratic equations (if they exist) by the method of completing the square. $2 x^{2} + x + 4 = 0$

Discussion

15.	A hollow sphere of internal and external diameters 4 cm and 8 cm respectively is melted into a cone of base diameter 8 cm. Calculate the height of the cone.
Answer» A hollow sphere of internal and external diameters 4 cm and 8 cm respectively is melted into a cone of base diameter 8 cm. Calculate the height of the cone.

Discussion

16.	In the adjacent figure O is the centre of the bigger circle and AC is its diameter. Another circle with AB as diameter is drawn. If AC = 54 cm and BC = 10 cm find the area of the shaded region in cm2. __
Answer» In the adjacent figure O is the centre of the bigger circle and AC is its diameter. Another circle with AB as diameter is drawn. If AC = 54 cm and BC = 10 cm find the area of the shaded region in $c m^{2}$ . __

16.

In the adjacent figure O is the centre of the bigger circle and AC is its diameter. Another circle with AB as diameter is drawn. If AC = 54 cm and BC = 10 cm find the area of the shaded region in cm2. __

Answer»

In the adjacent figure O is the centre of the bigger circle and AC is its diameter. Another circle with AB as diameter is drawn. If AC = 54 cm and BC = 10 cm find the area of the shaded region in $c m^{2}$ .

__

Discussion

17.	A marksman is equally likely to hit or miss his target. How many times must he fire to have a 90% chance to hit the target at least once?
Answer» A marksman is equally likely to hit or miss his target. How many times must he fire to have a $90 %$ chance to hit the target at least once?

Discussion

18.	Question 200 Construct a parallelogram when one of its side is 4 cm and its two diagonals are 5.6 cm and 7 cm. Measure the other side.
Answer» Question 200 Construct a parallelogram when one of its side is 4 cm and its two diagonals are 5.6 cm and 7 cm. Measure the other side.

Discussion

19.	Find a point on x+y = 8 , 2 units from the x axis.
Answer» Find a point on x+y = 8 , 2 units from the x axis.

Discussion

20.	Question 58 State whether the following statement is True or False. On the basis of the given figure, the length of a rectangle in the net of a cylinder is same as the circumference of circles in its net.
Answer» Question 58 State whether the following statement is True or False. On the basis of the given figure, the length of a rectangle in the net of a cylinder is same as the circumference of circles in its net.

Discussion

21.	The 4th term of an AP is 11. the sum of the 5th and 7th terms of this AP is 34. Find its common difference.
Answer» The 4th term of an AP is 11. the sum of the 5th and 7th terms of this AP is 34. Find its common difference.

Discussion

22.	Which term of the AP 72, 63, 54,... is 0 ? (a) 8th (b) 9th (c) 10th (d) 11th
Answer» Which term of the AP 72, 63, 54,... is 0 ? (a) 8th (b) 9th (c) 10th (d) 11th

Discussion

23.	Find the sum of all multiples of 7 between 300 and 700
Answer» Find the sum of all multiples of 7 between 300 and 700

Discussion

24.	If one of the zero of x2-3kx+4k is twice the other. Find the value of k.
Answer» If one of the zero of x²-3kx+4k is twice the other. Find the value of k.

Discussion

25.	Ryan is a wrestler trying to make weight. He currently weighs 200 lbs. If he cuts 2 lbs. per week, how many weeks will it take him to weigh less than 175 lbs.?
Answer» Ryan is a wrestler trying to make weight. He currently weighs 200 lbs. If he cuts 2 lbs. per week, how many weeks will it take him to weigh less than 175 lbs.?

Discussion

26.	Find 3 consecutive terms in GP whose sum is 13 and sum of whose square is 91?
Answer» Find 3 consecutive terms in GP whose sum is 13 and sum of whose square is 91?

Discussion

27.	Question 37 State whether the following statement is true (T) or false (F). The number of boys and girls in a class are in the ratio 5:4. If the number of boys is 9 more than the number of girls, then number of boys is 9.
Answer» Question 37 State whether the following statement is true (T) or false (F). The number of boys and girls in a class are in the ratio 5:4. If the number of boys is 9 more than the number of girls, then number of boys is 9.

27.

Question 37 State whether the following statement is true (T) or false (F). The number of boys and girls in a class are in the ratio 5:4. If the number of boys is 9 more than the number of girls, then number of boys is 9.

Answer»

Question 37

State whether the following statement is true (T) or false (F).

The number of boys and girls in a class are in the ratio 5:4. If the number of boys is 9 more than the number of girls, then number of boys is 9.

Discussion

28.	The third term of an A.P is 1/5 an the fifth term is 1/3. Show that the sum to 15 terms of the A.P is 8.
Answer» The third term of an A.P is 1/5 an the fifth term is 1/3. Show that the sum to 15 terms of the A.P is 8.

Discussion

29.	Sides of two similar triangles are in the ratio of 4: 9. Areas of these triangles are in the ratio?
Answer» Sides of two similar triangles are in the ratio of 4: 9. Areas of these triangles are in the ratio?

Discussion

30.	The value of cos 45∘ is
Answer» The value of $cos$ $45^{\circ}$ is

Discussion

31.	Dear sir/madam, Can you please explain to this question from AP If s(m)=n, s(n)=m prove that s(m+n)=-(m+n)
Answer» Dear sir/madam, Can you please explain to this question from AP If s(m)=n, s(n)=m prove that s(m+n)=-(m+n)

31.

Dear sir/madam, Can you please explain to this question from AP If s(m)=n, s(n)=m prove that s(m+n)=-(m+n)

Answer»

Dear sir/madam,

Can you please explain to this question from AP

If s(m)=n, s(n)=m prove that s(m+n)=-(m+n)

Discussion

32.	Question 1 Write whether every positive integer can be of the form 4q + 2, where q is an integer. Justify your answer.
Answer» Question 1 Write whether every positive integer can be of the form 4q + 2, where q is an integer. Justify your answer.

Discussion

33.	Consider A = {1, 2, 3, 4} and B = {2, 3, 5, 9}. Is the relation f = {(1, 2), (2, 3), (3, 3), (3, 5)} a function from A to B?
Answer» Consider A = {1, 2, 3, 4} and B = {2, 3, 5, 9}. Is the relation f = {(1, 2), (2, 3), (3, 3), (3, 5)} a function from A to B?

Discussion

34.	Use Venn diagrams to verify De Morgan’s law of complementation (A∪B)’ = A’ ∩ B’
Answer» Use Venn diagrams to verify De Morgan’s law of complementation (A $\cup$ B)’ = A’ $\cap$ B’

Discussion

35.	What is the difference in the revenues (in crore) of the company for the two years 2008 and 2009, if the revenue of the company in the year 2009 was 432 crore.___
Answer» What is the difference in the revenues (in crore) of the company for the two years 2008 and 2009, if the revenue of the company in the year 2009 was 432 crore.___

Discussion

36.	The roots of the following quadratic equation: x2=15 are:
Answer» The roots of the following quadratic equation: $x^{2} = 15$ are:

Discussion

37.	In the sum fo first n terms of an A.P. is cn2 then the sum of squares of these n terms is
Answer» In the sum fo first n terms of an A.P. is $c n^{2}$ then the sum of squares of these n terms is

Discussion

38.	The horizontal distance between two towers is 140 m. The angle of elevation of the top of the first tower when seen from the top of the second tower is 30o. If the height of the second tower is 60 m then, the height of the first tower is
Answer» The horizontal distance between two towers is 140 m. The angle of elevation of the top of the first tower when seen from the top of the second tower is 30^o. If the height of the second tower is 60 m then, the height of the first tower is

Discussion

39.	Joseph bought two varieties of rice, costing 6 cents per ounce and 8 cents per ounce each, and mixed them in some ratio. Then he sold the mixture at 10 cents per ounce, making a profit of 50 percent. What was the ratio of the mixture?
Answer» Joseph bought two varieties of rice, costing 6 cents per ounce and 8 cents per ounce each, and mixed them in some ratio. Then he sold the mixture at 10 cents per ounce, making a profit of 50 percent. What was the ratio of the mixture?

Discussion

40.	If the points (, y), (, b) & ( – , y – ) are collinear, find bx = ?
Answer» If the points (, y), (, b) & ( – , y – ) are collinear, find bx = ?

Discussion

41.	The square of (2x -1) is equal to 5. If one of the values of x satisfying the given relation is 1−√52, what is the value of x ?
Answer» The square of (2 $x$ -1) is equal to 5. If one of the values of $x$ satisfying the given relation is $\frac{1 - \sqrt{5}}{2}$ , what is the value of $x$ ?

Discussion

42.	Illustrate the set {x:−3≤x<0 or x>2; x∈R} on a real number line.
Answer» Illustrate the set ${x : - 3 \leq x < 0 o r x > 2; x \in R}$ on a real number line.

Discussion

43.	Exponential growth of plants is expressed with equation, Wt=Woert. In this equation 'e' represents
Answer» Exponential growth of plants is expressed with equation, $W_{t} = W_{o} e^{r t}$ . In this equation 'e' represents

Discussion

44.	The points A(-1, -2), B(4,3), C(2,5) and D(-3,0) form a ___
Answer» The points A(-1, -2), B(4,3), C(2,5) and D(-3,0) form a ___

Discussion

45.	If f(x) = \|x\| + \|x - 1\| + \|x - 2\|, then
Answer» If f(x) = \|x\| + \|x - 1\| + \|x - 2\|, then

Discussion

46.	A (1, -5), B (2, 2) and C (-2, 4) are the vertices of triangle ABC. Find the equations of : (i) the median of the triangle through A. (ii) the altitude of the triangle through B. (iii) the line through C and parallel to AB.
Answer» A (1, -5), B (2, 2) and C (-2, 4) are the vertices of triangle ABC. Find the equations of : (i) the median of the triangle through A. (ii) the altitude of the triangle through B. (iii) the line through C and parallel to AB.

46.

A (1, -5), B (2, 2) and C (-2, 4) are the vertices of triangle ABC. Find the equations of : (i) the median of the triangle through A. (ii) the altitude of the triangle through B. (iii) the line through C and parallel to AB.

Answer»

A (1, -5), B (2, 2) and C (-2, 4) are the vertices of triangle ABC. Find the equations of :

(i) the median of the triangle through A.

(ii) the altitude of the triangle through B.

(iii) the line through C and parallel to AB.

Discussion

47.	The distance and displacement respectively covered by a man on reaching point C from point A as shown in the figure is
Answer» The distance and displacement respectively covered by a man on reaching point $C$ from point $A$ as shown in the figure is

Discussion

48.	A two digit number is such that the product of the digits is 16. When 54 is subtracted from the number, the digits are interchanged find the number.
Answer» A two digit number is such that the product of the digits is 16. When 54 is subtracted from the number, the digits are interchanged find the number.

Discussion

49.	Explain fundamental theorem of arithmetic and decimal expansion of rational numbers
Answer» Explain fundamental theorem of arithmetic and decimal expansion of rational numbers

Discussion

50.	In the given figure, a circle inscribed in a triangle ABC touches the sides AB, BC and CA at points D, E and F respectively. If AB = 14 cm, BC = 8 cm and CA = 12 cm. Find the lengths AD, BE and CF.
Answer» In the given figure, a circle inscribed in a triangle ABC touches the sides AB, BC and CA at points D, E and F respectively. If AB = 14 cm, BC = 8 cm and CA = 12 cm. Find the lengths AD, BE and CF.

50.

In the given figure, a circle inscribed in a triangle ABC touches the sides AB, BC and CA at points D, E and F respectively. If AB = 14 cm, BC = 8 cm and CA = 12 cm. Find the lengths AD, BE and CF.

Answer»

In the given figure, a circle inscribed in a triangle ABC touches the sides AB, BC and CA at points D, E and F respectively. If AB = 14 cm, BC = 8 cm and CA = 12 cm. Find the lengths AD, BE and CF.

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

How many zeroes do the polynomials P1(x)=x3+x2+x+1 and P2(x)=x2+1 have in common?

Find the dependent pair of linear equations from the following.

Find the value of sin2θ+cos2θ at θ=30∘ &amp; 60∘ ?

Given the linear equation x - 2y - 6 = 0,write another linear equation in these two variables, such that the geometrical representation of the pair so formed is: (i) coincident lines (ii) intersection lines

If (x+a) is a factor of (2x2+2ax+5x+10), find the value of a.

By actual division , shows that x2−3 is a factor of 2x4+3x3−2x2−9x−12.

A boy scored the following marks in various tests during a term, each test being marked out of 20. 15,17,16,7,10,12,14,16,19,12,16. The median marks are

In triangle ABC,D is a point on AB and E is a point on AC such that DE||BC. If ADAB=AEx, Then x is _______.

Find the equation of a circle, the end points of one of whose diameters are A (2, -3) and B(-3, 5).

HCF of 42 hand 72 is 6 then their LCM is___?

Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion. (i) 238 (ii) 125441 (iii) 3550 (iv) 77210 (v) 12922×57×717 (vi) 98710500

If 3 cot θ=2, show that 4sinθ−3cosθ(2sinθ+6cosθ)=13.

Fint the roots of the following quadratic equations (if they exist) by the method of completing the square. 2x2+x+4=0

A hollow sphere of internal and external diameters 4 cm and 8 cm respectively is melted into a cone of base diameter 8 cm. Calculate the height of the cone.

In the adjacent figure O is the centre of the bigger circle and AC is its diameter. Another circle with AB as diameter is drawn. If AC = 54 cm and BC = 10 cm find the area of the shaded region in cm2. __

A marksman is equally likely to hit or miss his target. How many times must he fire to have a 90% chance to hit the target at least once?

Question 200 Construct a parallelogram when one of its side is 4 cm and its two diagonals are 5.6 cm and 7 cm. Measure the other side.

Find a point on x+y = 8 , 2 units from the x axis.

Question 58 State whether the following statement is True or False. On the basis of the given figure, the length of a rectangle in the net of a cylinder is same as the circumference of circles in its net.

The 4th term of an AP is 11. the sum of the 5th and 7th terms of this AP is 34. Find its common difference.

Which term of the AP 72, 63, 54,... is 0 ? (a) 8th (b) 9th (c) 10th (d) 11th

Find the sum of all multiples of 7 between 300 and 700

If one of the zero of x2-3kx+4k is twice the other. Find the value of k.

Ryan is a wrestler trying to make weight. He currently weighs 200 lbs. If he cuts 2 lbs. per week, how many weeks will it take him to weigh less than 175 lbs.?

Find 3 consecutive terms in GP whose sum is 13 and sum of whose square is 91?

Question 37 State whether the following statement is true (T) or false (F). The number of boys and girls in a class are in the ratio 5:4. If the number of boys is 9 more than the number of girls, then number of boys is 9.

The third term of an A.P is 1/5 an the fifth term is 1/3. Show that the sum to 15 terms of the A.P is 8.

Sides of two similar triangles are in the ratio of 4: 9. Areas of these triangles are in the ratio?

The value of cos 45∘ is

Dear sir/madam, Can you please explain to this question from AP If s(m)=n, s(n)=m prove that s(m+n)=-(m+n)

Question 1 Write whether every positive integer can be of the form 4q + 2, where q is an integer. Justify your answer.

Consider A = {1, 2, 3, 4} and B = {2, 3, 5, 9}. Is the relation f = {(1, 2), (2, 3), (3, 3), (3, 5)} a function from A to B?

Use Venn diagrams to verify De Morgan’s law of complementation (A∪B)’ = A’ ∩ B’

What is the difference in the revenues (in crore) of the company for the two years 2008 and 2009, if the revenue of the company in the year 2009 was 432 crore.___

The roots of the following quadratic equation: x2=15 are:

In the sum fo first n terms of an A.P. is cn2 then the sum of squares of these n terms is

The horizontal distance between two towers is 140 m. The angle of elevation of the top of the first tower when seen from the top of the second tower is 30o. If the height of the second tower is 60 m then, the height of the first tower is

Joseph bought two varieties of rice, costing 6 cents per ounce and 8 cents per ounce each, and mixed them in some ratio. Then he sold the mixture at 10 cents per ounce, making a profit of 50 percent. What was the ratio of the mixture?

If the points (, y), (, b) &amp; ( – , y – ) are collinear, find bx = ?

The square of (2x -1) is equal to 5. If one of the values of x satisfying the given relation is 1−√52, what is the value of x ?

Illustrate the set {x:−3≤x&lt;0 or x&gt;2; x∈R} on a real number line.

Exponential growth of plants is expressed with equation, Wt=Woert. In this equation 'e' represents

The points A(-1, -2), B(4,3), C(2,5) and D(-3,0) form a ___

If f(x) = |x| + |x - 1| + |x - 2|, then

A (1, -5), B (2, 2) and C (-2, 4) are the vertices of triangle ABC. Find the equations of : (i) the median of the triangle through A. (ii) the altitude of the triangle through B. (iii) the line through C and parallel to AB.

The distance and displacement respectively covered by a man on reaching point C from point A as shown in the figure is

A two digit number is such that the product of the digits is 16. When 54 is subtracted from the number, the digits are interchanged find the number.

Explain fundamental theorem of arithmetic and decimal expansion of rational numbers

In the given figure, a circle inscribed in a triangle ABC touches the sides AB, BC and CA at points D, E and F respectively. If AB = 14 cm, BC = 8 cm and CA = 12 cm. Find the lengths AD, BE and CF.

Find the value of sin2θ+cos2θ at θ=30∘ & 60∘ ?

If the points (, y), (, b) & ( – , y – ) are collinear, find bx = ?

Illustrate the set {x:−3≤x<0 or x>2; x∈R} on a real number line.