32581 + Interview Questions in Mathematics

1.	Solve each of the following given systems of equations graphically and find the vertices and area of the triangle formed by these lines and the x-axis: x−y−5=0,3x+5y−15=0.
Answer» Solve each of the following given systems of equations graphically and find the vertices and area of the triangle formed by these lines and the x-axis: $x - y - 5 = 0, 3 x + 5 y - 15 = 0.$

Discussion

2.	If the numbers a, 9, b, 25 form an AP, find a and b.
Answer» If the numbers a, 9, b, 25 form an AP, find a and b.

Discussion

3.	The length of the minute hand of a clock is 14cm. The area swept by the minute hand between 3: 20 and 3: 45 is __ .
Answer» The length of the minute hand of a clock is 14cm. The area swept by the minute hand between 3: 20 and 3: 45 is __ .

Discussion

4.	find the ratio in which line segment joining a (1, - 5) and b (-4,5) is divided by the x axis also find the coordinates of the point of division
Answer» find the ratio in which line segment joining a (1, - 5) and b (-4,5) is divided by the x axis also find the coordinates of the point of division

Discussion

5.	A, B, C, D are 4 non collinear points in a plane such that ∠ ACB =∠ ADB, then how many circle(s) can be drawn passing through all 4 points.
Answer» A, B, C, D are 4 non collinear points in a plane such that $∠$ ACB $= ∠$ ADB, then how many circle(s) can be drawn passing through all 4 points.

Discussion

6.	1m is inscribed in a square as shown below, find the perimeter of the square.
Answer» 1m is inscribed in a square as shown below, find the perimeter of the square.

6.

1m is inscribed in a square as shown below, find the perimeter of the square.

Answer»

1m is inscribed in a square as shown below, find the perimeter of the square.

Discussion

7.	The value of p for which the points L(1,5), M(p,1) and N(4,11) are collinear is
Answer» The value of p for which the points L(1,5), M(p,1) and N(4,11) are collinear is

Discussion

8.	The slant height of the frustum of a cone is 6 cm and the perimeter of its circular ends are 20 cm and 8 cm. Its curved surface area is
Answer» The slant height of the frustum of a cone is 6 cm and the perimeter of its circular ends are 20 cm and 8 cm. Its curved surface area is

Discussion

9.	Question 3 If x′is are the mid-points of the calss intervals of grouped data, f′is are the corresponding frequencies and ¯x is the mean, then ∑(fixi−¯x) is equal to (a) 0 (b) -1 (c) 1 (d) 2
Answer» Question 3 If $x_{i}^{'} s$ are the mid-points of the calss intervals of grouped data, $f_{i}^{'} s$ are the corresponding frequencies and $¯ x$ is the mean, then $\sum (f_{i} x_{i} - ¯ x)$ is equal to (a) 0 (b) -1 (c) 1 (d) 2

Discussion

10.	In which type of account, deposits are made regularly on monthly basis for future requirements?
Answer» In which type of account, deposits are made regularly on monthly basis for future requirements?

Discussion

11.	The remainder when the polynomial 1+x2+x4+x6+….+x22 is divided by 1+x+x2+x3+….+x11 is
Answer» The remainder when the polynomial $1 + x^{2} + x^{4} + x^{6} + \dots . + x^{22}$ is divided by $1 + x + x^{2} + x^{3} + \dots . + x^{11}$ is

Discussion

12.	The line L has intercepts a and b on the coordinate axes. When keeping the origin fixed, the coordinate axes are rotated through a fixed angle, then the same line has intercepts p and q on the rotated axes. Then (I.I.T. 1990)
Answer» The line L has intercepts a and b on the coordinate axes. When keeping the origin fixed, the coordinate axes are rotated through a fixed angle, then the same line has intercepts p and q on the rotated axes. Then (I.I.T. 1990)

Discussion

13.	If 2 cos(A + B) = 1, and 2 sin(A –B) = 1 then the values of A and B are
Answer» If 2 cos(A + B) = 1, and 2 sin(A –B) = 1 then the values of A and B are

Discussion

14.	A chord of a circle of radius 14 cm makes a right angle at the center. Find the areas of the minor and major segments of the circle.
Answer» A chord of a circle of radius $14 c m$ makes a right angle at the center. Find the areas of the minor and major segments of the circle.

Discussion

15.	A box contains 12 balls of which some are red in colour . If 6 more red balls are put in the box and a ball is drawn at random , the probability of drawing a red ball doubles than what it was before . Find the number of red balls in the box .
Answer» A box contains 12 balls of which some are red in colour . If 6 more red balls are put in the box and a ball is drawn at random , the probability of drawing a red ball doubles than what it was before . Find the number of red balls in the box .

Discussion

16.	In △ABC, the medians BE and CF intersect at G. AG is a line when extended meets BC in D. If GD is 1.5 cm, then AD is equal to
Answer» In $△$ ABC, the medians BE and CF intersect at G. AG is a line when extended meets BC in D. If GD is 1.5 cm, then AD is equal to

16.

In △ABC, the medians BE and CF intersect at G. AG is a line when extended meets BC in D. If GD is 1.5 cm, then AD is equal to

Answer»

In $△$ ABC, the medians BE and CF intersect at G. AG is a line when extended meets BC in D. If GD is 1.5 cm, then AD is equal to

Discussion

17.	Raghu had to make a cylindrical tube with an aluminium cover. What is the area of the aluminium sheet he needs to cover the tube if the tube has a length of 1m and base radius 3.5cm? (Take π=22/7)
Answer» Raghu had to make a cylindrical tube with an aluminium cover. What is the area of the aluminium sheet he needs to cover the tube if the tube has a length of 1m and base radius 3.5cm? (Take π=22/7)

Discussion

18.	ABC is an isosceles triangle right-angled at B. Similar triangles ACD and ABE are constructed on sides AC and AB. Find the ratio between the areas of △ ABE and △ACD.
Answer» ABC is an isosceles triangle right-angled at B. Similar triangles ACD and ABE are constructed on sides AC and AB. Find the ratio between the areas of $△$ ABE and $△$ ACD.

Discussion

19.	A metallic sphere of radius 4.2 cm is melted and recast into the shape of a cylinder of radius 6 cm. Find the height of the cylinder (in cm). ___
Answer» A metallic sphere of radius 4.2 cm is melted and recast into the shape of a cylinder of radius 6 cm. Find the height of the cylinder (in cm). ___

Discussion

20.	Construct a 3×3 matrix whose elements aij are given by aij=0 if i≠j and aij=−8 if i=j.
Answer» Construct a $3 \times 3$ matrix whose elements $a_{i j}$ are given by $a_{i j} = 0$ if $i \neq j$ and $a_{i j} = - 8$ if $i = j$ .

Discussion

21.	Identify which among the pieces given below will not be required to complete the triangular pattern shown below.
Answer» Identify which among the pieces given below will not be required to complete the triangular pattern shown below.

21.

Identify which among the pieces given below will not be required to complete the triangular pattern shown below.

Answer»

Identify which among the pieces given below will not be required to complete the triangular pattern shown below.

Discussion

22.	Two vertices of a triangle are (3, –5) and (–7, 4). If its centroid is (2, –1). Find the third vertex.
Answer» Two vertices of a triangle are (3, –5) and (–7, 4). If its centroid is (2, –1). Find the third vertex.

Discussion

23.	The solution set for the following inequation is: −x3≤x2−113<16, xϵR
Answer» The solution set for the following inequation is: $- \frac{x}{3} \leq \frac{x}{2} - 1 \frac{1}{3} < \frac{1}{6}, x ϵ R$

Discussion

24.	The surface area of a cube is equal to the surface area of a sphere. The ratio of their volumes will be
Answer» The surface area of a cube is equal to the surface area of a sphere. The ratio of their volumes will be

Discussion

25.	If the radius of a circle is increased by 40%.What will be its increase in area?
Answer» If the radius of a circle is increased by 40%.What will be its increase in area?

Discussion

26.	The value of cos 1° cos2° cos 3° ...........cos 180° is
Answer» The value of cos 1° cos2° cos 3° ...........cos 180° is

Discussion

27.	The heights (in cm) of students of a class is tabulated below. HeightNumber of students150−1544155−1593160−1642165−1691170−1742175−1792180−1844185−1902 The cumulative frequency for the class interval 179.5 - 184.5 is ?
Answer» The heights (in cm) of students of a class is tabulated below. $\begin{matrix} Height & Number of students 150 - 154 & 4 155 - 159 & 3 160 - 164 & 2 165 - 169 & 1 170 - 174 & 2 175 - 179 & 2 180 - 184 & 4 185 - 190 & 2 \end{matrix}$ The cumulative frequency for the class interval 179.5 - 184.5 is ?

Discussion

28.	If two-third of a number is multiplied by three-fourth of the same number, the result is 338. Then, the number is what!?
Answer» If two-third of a number is multiplied by three-fourth of the same number, the result is 338. Then, the number is what!?

Discussion

29.	A die is thrown once. Find the probability of getting a number that is either composite or prime.
Answer» A die is thrown once. Find the probability of getting a number that is either composite or prime.

Discussion

30.	A letter of English alphabet is chosen at random. Determine the probability that the chosen letter is consonant.
Answer» A letter of English alphabet is chosen at random. Determine the probability that the chosen letter is consonant.

Discussion

31.	A student performs a titration with different burettes and finds titre values of 25.2 mL, 25.25 mL, and 25.0 mL. The number of significant figures in the average titre value is ___
Answer» A student performs a titration with different burettes and finds titre values of 25.2 mL, 25.25 mL, and 25.0 mL. The number of significant figures in the average titre value is ___

Discussion

32.	ABC and DBC are two triangles on the same base BC. If AD intersects BC at O, prove that area(ABC)area(DBC)=AODO.
Answer» ABC and DBC are two triangles on the same base BC. If AD intersects BC at O, prove that $\frac{a r e a (A B C)}{a r e a (D B C)} = \frac{A O}{D O}$ .

Discussion

33.	A polynomial of degree 6 is divided by a polynomial of degree 2 if the divisor is the factor of the dividend find the degree of the remainder
Answer» A polynomial of degree 6 is divided by a polynomial of degree 2 if the divisor is the factor of the dividend find the degree of the remainder

Discussion

34.	The product of two consecutive integers is 56. Find the integers.
Answer» The product of two consecutive integers is 56. Find the integers.

Discussion

35.	Express the GCD as a linear combination for the following For some x and y 1. 72 and 24 2. 48 and 18 3.252 and 198 4. 216 and 126 5. 657 and 963
Answer» Express the GCD as a linear combination for the following For some x and y 1. 72 and 24 2. 48 and 18 3.252 and 198 4. 216 and 126 5. 657 and 963

35.

Express the GCD as a linear combination for the following For some x and y 1. 72 and 24 2. 48 and 18 3.252 and 198 4. 216 and 126 5. 657 and 963

Answer»

Express the GCD as a linear combination for the following

For some x and y

1. 72 and 24

2. 48 and 18

3.252 and 198

4. 216 and 126

5. 657 and 963

Discussion

36.	Write the decimal expansion : 0.234234234.......as a rational number
Answer» Write the decimal expansion : 0.234234234.......as a rational number

Discussion

37.	In a class of 60, where the number of girls is twice the number of boys, Kamal is ranked 17th from the top. If there are 9 girls ahead of Kamal, how many boys are ranked after him?
Answer» In a class of 60, where the number of girls is twice the number of boys, Kamal is ranked 17th from the top. If there are 9 girls ahead of Kamal, how many boys are ranked after him?

Discussion

38.	If Sn denotes the sum of first n terms of an A.P., prove that S12=3(S8−S4)
Answer» If $S_{n}$ denotes the sum of first n terms of an A.P., prove that $S_{12} = 3 (S_{8} - S_{4})$

Discussion

39.	The cost of a machine is supposed to depreciate each year by 12% of the year . If the machine is valued at Rupees 44000 at the beginning of 2008 find its value: 1. At the end of 2009 2. At the beginning of 2007
Answer» The cost of a machine is supposed to depreciate each year by 12% of the year . If the machine is valued at Rupees 44000 at the beginning of 2008 find its value: 1. At the end of 2009 2. At the beginning of 2007

Discussion

40.	The event A but not B is represented by
Answer» The event A but not B is represented by

Discussion

41.	Spherical marbles of diameter 1.4 cm are dropped into cylindrical beaker containing some water & are fully submerged. The diameter of the beaker is 7 cm. Find how many marbles have been dropped in it if the water rises by 5.6 cm.
Answer» Spherical marbles of diameter 1.4 cm are dropped into cylindrical beaker containing some water & are fully submerged. The diameter of the beaker is 7 cm. Find how many marbles have been dropped in it if the water rises by 5.6 cm.

41.

Spherical marbles of diameter 1.4 cm are dropped into cylindrical beaker containing some water & are fully submerged. The diameter of the beaker is 7 cm. Find how many marbles have been dropped in it if the water rises by 5.6 cm.

Answer»

Spherical marbles of diameter 1.4 cm are dropped into cylindrical beaker containing some water & are fully submerged. The diameter of the beaker is 7 cm. Find how many marbles have been dropped in it if the water rises by 5.6 cm.

Discussion

42.	If tan 2A = cot (A - 18o), then the value of A is
Answer» If tan 2A = cot (A - 18^o), then the value of A is

Discussion

43.	Find the third vertex of a triangle, if its two vertices are (-1, 4) and (5, 2) and mid-point of one side is (0, 3). [4 MARKS]
Answer» Find the third vertex of a triangle, if its two vertices are (-1, 4) and (5, 2) and mid-point of one side is (0, 3). [4 MARKS]

Discussion

44.	If secA = x+1x,prove that secA×tanA=2x or 12×.
Answer» If secA = $x + \frac{1}{x}$ ,prove that secA×tanA=2x or $\frac{1}{2}$ ×.

Discussion

45.	A dice is thrown twice. What is the probability that the same number will come up either time ?
Answer» A dice is thrown twice. What is the probability that the same number will come up either time ?

Discussion

46.	AB & CD are 2 perpendicular diameters of a circle with centre O. If AB = 16 cm, calculate the area & perimeter of the shaded part. (π = 3.14)
Answer» AB & CD are 2 perpendicular diameters of a circle with centre O. If AB = 16 cm, calculate the area & perimeter of the shaded part. (π = 3.14)

46.

AB & CD are 2 perpendicular diameters of a circle with centre O. If AB = 16 cm, calculate the area & perimeter of the shaded part. (π = 3.14)

Answer»

AB & CD are 2 perpendicular diameters of a circle with centre O. If AB = 16 cm, calculate the area & perimeter of the shaded part. (π = 3.14)

Discussion

47.	If 2θ+45o and 30o−θ are acuter angles, find the degree measure of θsatisfying sin (2θ+45o) = (30o−θ)
Answer» If $2 θ + 45^{o}$ and $30^{o} - θ$ are acuter angles, find the degree measure of $θ$ satisfying sin $(2 θ + 45^{o})$ = $(30^{o} - θ)$

47.

If 2θ+45o and 30o−θ are acuter angles, find the degree measure of θsatisfying sin (2θ+45o) = (30o−θ)

Answer»

If $2 θ + 45^{o}$ and $30^{o} - θ$ are acuter angles, find the degree measure of $θ$ satisfying

sin $(2 θ + 45^{o})$ = $(30^{o} - θ)$

Discussion

48.	An army contingent of 616 members is to march behind an army band of 32 members in parade. The two groups are to march in the same number of columns. What is the maxiumum number of columns in which they can march?
Answer» An army contingent of 616 members is to march behind an army band of 32 members in parade. The two groups are to march in the same number of columns. What is the maxiumum number of columns in which they can march?

Discussion

49.	What is multiplied to term x2 in the following polynomial? 2+x2+x __
Answer» What is multiplied to term $x^{2}$ in the following polynomial? $2 + x^{2} + x$ __

49.

What is multiplied to term x2 in the following polynomial? 2+x2+x __

Answer»

What is multiplied to term $x^{2}$ in the following polynomial?

$2 + x^{2} + x$

__

Discussion

50.	Find all the common zeroes of the polynomials x3+5x2−9x−45 and x3+8x2+15x.
Answer» Find all the common zeroes of the polynomials $x^{3} + 5 x^{2} - 9 x - 45$ and $x^{3} + 8 x^{2} + 15 x$ .

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Solve each of the following given systems of equations graphically and find the vertices and area of the triangle formed by these lines and the x-axis: x−y−5=0,3x+5y−15=0.

If the numbers a, 9, b, 25 form an AP, find a and b.

The length of the minute hand of a clock is 14cm. The area swept by the minute hand between 3: 20 and 3: 45 is __ .

find the ratio in which line segment joining a (1, - 5) and b (-4,5) is divided by the x axis also find the coordinates of the point of division

A, B, C, D are 4 non collinear points in a plane such that ∠ ACB =∠ ADB, then how many circle(s) can be drawn passing through all 4 points.

1m is inscribed in a square as shown below, find the perimeter of the square.

The value of p for which the points L(1,5), M(p,1) and N(4,11) are collinear is

The slant height of the frustum of a cone is 6 cm and the perimeter of its circular ends are 20 cm and 8 cm. Its curved surface area is

Question 3 If x′is are the mid-points of the calss intervals of grouped data, f′is are the corresponding frequencies and ¯x is the mean, then ∑(fixi−¯x) is equal to (a) 0 (b) -1 (c) 1 (d) 2

In which type of account, deposits are made regularly on monthly basis for future requirements?

The remainder when the polynomial 1+x2+x4+x6+….+x22 is divided by 1+x+x2+x3+….+x11 is

The line L has intercepts a and b on the coordinate axes. When keeping the origin fixed, the coordinate axes are rotated through a fixed angle, then the same line has intercepts p and q on the rotated axes. Then (I.I.T. 1990)

If 2 cos(A + B) = 1, and 2 sin(A –B) = 1 then the values of A and B are

A chord of a circle of radius 14 cm makes a right angle at the center. Find the areas of the minor and major segments of the circle.

A box contains 12 balls of which some are red in colour . If 6 more red balls are put in the box and a ball is drawn at random , the probability of drawing a red ball doubles than what it was before . Find the number of red balls in the box .

In △ABC, the medians BE and CF intersect at G. AG is a line when extended meets BC in D. If GD is 1.5 cm, then AD is equal to

Raghu had to make a cylindrical tube with an aluminium cover. What is the area of the aluminium sheet he needs to cover the tube if the tube has a length of 1m and base radius 3.5cm? (Take π=22/7)

ABC is an isosceles triangle right-angled at B. Similar triangles ACD and ABE are constructed on sides AC and AB. Find the ratio between the areas of △ ABE and △ACD.

A metallic sphere of radius 4.2 cm is melted and recast into the shape of a cylinder of radius 6 cm. Find the height of the cylinder (in cm). ___

Construct a 3×3 matrix whose elements aij are given by aij=0 if i≠j and aij=−8 if i=j.

Identify which among the pieces given below will not be required to complete the triangular pattern shown below.

Two vertices of a triangle are (3, –5) and (–7, 4). If its centroid is (2, –1). Find the third vertex.

The solution set for the following inequation is: −x3≤x2−113&lt;16, xϵR

The surface area of a cube is equal to the surface area of a sphere. The ratio of their volumes will be

If the radius of a circle is increased by 40%.What will be its increase in area?

The value of cos 1° cos2° cos 3° ...........cos 180° is

The heights (in cm) of students of a class is tabulated below. HeightNumber of students150−1544155−1593160−1642165−1691170−1742175−1792180−1844185−1902 The cumulative frequency for the class interval 179.5 - 184.5 is ?

If two-third of a number is multiplied by three-fourth of the same number, the result is 338. Then, the number is what!?

A die is thrown once. Find the probability of getting a number that is either composite or prime.

A letter of English alphabet is chosen at random. Determine the probability that the chosen letter is consonant.

A student performs a titration with different burettes and finds titre values of 25.2 mL, 25.25 mL, and 25.0 mL. The number of significant figures in the average titre value is ___

ABC and DBC are two triangles on the same base BC. If AD intersects BC at O, prove that area(ABC)area(DBC)=AODO.

A polynomial of degree 6 is divided by a polynomial of degree 2 if the divisor is the factor of the dividend find the degree of the remainder

The product of two consecutive integers is 56. Find the integers.

Express the GCD as a linear combination for the following For some x and y 1. 72 and 24 2. 48 and 18 3.252 and 198 4. 216 and 126 5. 657 and 963

Write the decimal expansion : 0.234234234.......as a rational number

In a class of 60, where the number of girls is twice the number of boys, Kamal is ranked 17th from the top. If there are 9 girls ahead of Kamal, how many boys are ranked after him?

If Sn denotes the sum of first n terms of an A.P., prove that S12=3(S8−S4)

The cost of a machine is supposed to depreciate each year by 12% of the year . If the machine is valued at Rupees 44000 at the beginning of 2008 find its value: 1. At the end of 2009 2. At the beginning of 2007

The event A but not B is represented by

Spherical marbles of diameter 1.4 cm are dropped into cylindrical beaker containing some water &amp; are fully submerged. The diameter of the beaker is 7 cm. Find how many marbles have been dropped in it if the water rises by 5.6 cm.

If tan 2A = cot (A - 18o), then the value of A is

Find the third vertex of a triangle, if its two vertices are (-1, 4) and (5, 2) and mid-point of one side is (0, 3). [4 MARKS]

If secA = x+1x,prove that secA×tanA=2x or 12×.

A dice is thrown twice. What is the probability that the same number will come up either time ?

AB &amp; CD are 2 perpendicular diameters of a circle with centre O. If AB = 16 cm, calculate the area &amp; perimeter of the shaded part. (π = 3.14)

If 2θ+45o and 30o−θ are acuter angles, find the degree measure of θsatisfying sin (2θ+45o) = (30o−θ)

An army contingent of 616 members is to march behind an army band of 32 members in parade. The two groups are to march in the same number of columns. What is the maxiumum number of columns in which they can march?

What is multiplied to term x2 in the following polynomial? 2+x2+x __

Find all the common zeroes of the polynomials x3+5x2−9x−45 and x3+8x2+15x.

The solution set for the following inequation is: −x3≤x2−113<16, xϵR

Spherical marbles of diameter 1.4 cm are dropped into cylindrical beaker containing some water & are fully submerged. The diameter of the beaker is 7 cm. Find how many marbles have been dropped in it if the water rises by 5.6 cm.

AB & CD are 2 perpendicular diameters of a circle with centre O. If AB = 16 cm, calculate the area & perimeter of the shaded part. (π = 3.14)