32581 + Interview Questions in Mathematics

1.	IF and event cannot occur then its probability is (a) 1 (b) 12 (c) 34 (d) 0
Answer» IF and event cannot occur then its probability is (a) 1 (b) $\frac{1}{2}$ (c) $\frac{3}{4}$ (d) 0

Discussion

2.	What is the area of the triangle formed by the points O (0, 0), A (6, 0) and B (0, 4)?
Answer» What is the area of the triangle formed by the points O (0, 0), A (6, 0) and B (0, 4)?

Discussion

3.	the value of∫_{50}^{40}(1/θ-θ^°)\operatorname dθ where θ^°=30 (a cons†an t ) is
Answer» the value of∫_{50}^{40}(1/θ-θ^°)\operatorname dθ where θ^°=30 (a cons†an t ) is

Discussion

4.	If sec 2A=cosec(A−42∘), where 2A is an acute angle, find the value of A.
Answer» If $s e c 2 A = c o s e c (A - 42^{\circ})$ , where 2A is an acute angle, find the value of A.

Discussion

5.	The sum of the first n terms of an AP whose first term is 8 and the common difference is 20 is equal to the sum of the first 2n terms of another AP, whose first term is - 30 and the common difference is 8. find n?
Answer» The sum of the first n terms of an AP whose first term is 8 and the common difference is 20 is equal to the sum of the first 2n terms of another AP, whose first term is - 30 and the common difference is 8. find n?

Discussion

6.	Find the sum of first 20 terms of the sequence whose nth term is an=An+B.
Answer» Find the sum of first 20 terms of the sequence whose nth term is $a_{n} = A n + B$ .

Discussion

7.	Solve the following systems of equations graphically:x + y = 42x − 3y = 3
Answer» Solve the following systems of equations graphically: x + y = 4 2x − 3y = 3

Discussion

8.	A fraction becomes 1/3 when 2 is subtracted from the numerator and it becomes 1/2 when 1 is subtracted from the denominator. Find the fraction.
Answer» A fraction becomes 1/3 when 2 is subtracted from the numerator and it becomes 1/2 when 1 is subtracted from the denominator. Find the fraction.

Discussion

9.	find 3 solutions of the equation 2x+3y=6
Answer» find 3 solutions of the equation 2x+3y=6

Discussion

10.	Determine the greatest 3-digit number exactly divisible by 8, 10 and 12.
Answer» Determine the greatest 3-digit number exactly divisible by 8, 10 and 12.

Discussion

11.	On dividing 3x3+x2+2x+5 by a polynomial g(x), the quotient and remainder are (3x-5) and (9x+10) respectively. Find g(x).
Answer» On dividing $3 x^{3} + x^{2} + 2 x + 5$ by a polynomial g(x), the quotient and remainder are (3x-5) and (9x+10) respectively. Find g(x).

Discussion

12.	i) find the value of a = [{x}] + [{-x}] +{[x]} + {[-x]} + {x} + {-x}ii) solve the equation 2x = [x] + {x
Answer» i) find the value of a = [{x}] + [{-x}] +{[x]} + {[-x]} + {x} + {-x} ii) solve the equation 2x = [x] + {x

Discussion

13.	Solve the following quadratic equations by factorization:3x2 − 14x − 5 = 0
Answer» Solve the following quadratic equations by factorization: 3x² − 14x − 5 = 0

Discussion

14.	ABCD is a cyclic quadrilateral finds the angles of the cyclic quadrilateral.
Answer» ABCD is a cyclic quadrilateral finds the angles of the cyclic quadrilateral.

14.

ABCD is a cyclic quadrilateral finds the angles of the cyclic quadrilateral.

Answer»

ABCD is a cyclic quadrilateral finds the angles of the cyclic quadrilateral.

Discussion

15.	Simplify: (x3+2x2+3x)÷2x
Answer» Simplify: $(x^{3} + 2 x^{2} + 3 x) \div 2 x$

Discussion

16.	An arc of length 15 cm subtends an angle of 45∘ at the centre of a circle. Find in terms of π, the radius of the circle.
Answer» An arc of length 15 cm subtends an angle of $45^{\circ}$ at the centre of a circle. Find in terms of $π$ , the radius of the circle.

Discussion

17.	A conical tomb is made up of bricks of a front surface area of 5 sq. m. The slant height and radius of the tomb are measured to be 25 m and 7 m respectively. The approximate number of bricks used to construct the tomb are ___ (Take π=227)
Answer» A conical tomb is made up of bricks of a front surface area of $5$ sq. m. The slant height and radius of the tomb are measured to be $25 m$ and $7 m$ respectively. The approximate number of bricks used to construct the tomb are ___ $(Take π = \frac{22}{7})$

Discussion

18.	Let A={a,e,i,o,u} and B={a,i,u}. Show that A∪B=A
Answer» Let $A = {a, e, i, o, u}$ and $B = {a, i, u}$ . Show that $A \cup B = A$

Discussion

19.	A number x is chosen at random from the numbers -3, -2, -1, 0, 1, 2, 3, the probability that \|x\| < 2 is
Answer» A number x is chosen at random from the numbers -3, -2, -1, 0, 1, 2, 3, the probability that \|x\| < 2 is

Discussion

20.	The value of sin 70°sin 110° is _____________.
Answer» The value of $\frac{\sin 70 °}{\sin 110 °}$ is _____________.

Discussion

21.	Identify the number sequence from the following pattern taking only the smallest square as a unit square.
Answer» Identify the number sequence from the following pattern taking only the smallest square as a unit square.

Discussion

22.	Determine k so that (3k − 2), (4k − 6) and (k + 2) are three consecutive terms of an AP. [CBSE 2009C]
Answer» Determine k so that (3k − 2), (4k − 6) and (k + 2) are three consecutive terms of an AP. [CBSE 2009C]

Discussion

23.	A metallic bucket, open at the top, of height 24 cm is in the form of the frustum of a cone, the radii of whose lower and upper circular ends are 7 cm and 14 cm, respectively. Find(i) the volume of water which can completely fill the bucket;(ii) the area of the metal sheet used to make the bucket. [CBSE 2014]
Answer» A metallic bucket, open at the top, of height 24 cm is in the form of the frustum of a cone, the radii of whose lower and upper circular ends are 7 cm and 14 cm, respectively. Find (i) the volume of water which can completely fill the bucket; (ii) the area of the metal sheet used to make the bucket. [CBSE 2014]

Discussion

24.	draw a circle of radius 6cm.from a point 10 cm away from its centre,construct the pair of tangents to the circle and measure their lengths.
Answer» draw a circle of radius 6cm.from a point 10 cm away from its centre,construct the pair of tangents to the circle and measure their lengths.

Discussion

25.	In parallelogram ABCD, A(-5,2), B(1,3) and D(-2,10). Then the coordinates of C is
Answer» In parallelogram ABCD, A(-5,2), B(1,3) and D(-2,10). Then the coordinates of C is

25.

In parallelogram ABCD, A(-5,2), B(1,3) and D(-2,10). Then the coordinates of C is

Answer»

In parallelogram ABCD, A(-5,2), B(1,3) and D(-2,10). Then the coordinates of C is

Discussion

26.	Factorize: (i) x3+3x2+3x−7 (ii) x3−3x2+3x+7 [4 MARKS]
Answer» Factorize: (i) $x^{3} + 3 x^{2} + 3 x - 7$ (ii) $x^{3} - 3 x^{2} + 3 x + 7$ [4 MARKS]

Discussion

27.	A cube has a side 1.2 cm .Its surface area i
Answer» A cube has a side 1.2 cm .Its surface area i

Discussion

28.	68. If right circular cone is seperated into 3 solids of volume V1, V2, V3 by 2 planes which are parallel to base and trisect the altitude .What is the ratio of V1:V2:V3?
Answer» 68. If right circular cone is seperated into 3 solids of volume V1, V2, V3 by 2 planes which are parallel to base and trisect the altitude .What is the ratio of V1:V2:V3?

Discussion

29.	If cos−1(−x)=cos−1x, then the value of x is equal to
Answer» If ${cos}^{- 1} (- x) = {cos}^{- 1} x,$ then the value of $x$ is equal to

Discussion

30.	The first and the last terms of an A.P. are 17 and 350 respectively. If the common difference is 9, how many terms are there and what is their sum?
Answer» The first and the last terms of an A.P. are 17 and 350 respectively. If the common difference is 9, how many terms are there and what is their sum?

Discussion

31.	Following are the lives in hours of 15 pieces of the components of aircraft engine. Find the median:715, 724, 725, 710, 729, 745, 694, 699, 696, 712, 734, 728, 716, 705, 719.
Answer» Following are the lives in hours of 15 pieces of the components of aircraft engine. Find the median: 715, 724, 725, 710, 729, 745, 694, 699, 696, 712, 734, 728, 716, 705, 719.

Discussion

32.	Solve each of the following equations by using the method of completing the square:4x2+43x+3=0
Answer» Solve each of the following equations by using the method of completing the square: $4 x^{2} + 4 \sqrt{3} x + 3 = 0$

Discussion

33.	A hollow metallic cylindrical tube as an internal radius of 3 cm and height 21 cm. The thickness of the metal of the tube is 0.5 cm the tube is melted and cast and were right circular cone of radius 5 cm. Find the height of the cone correct to one decimal place.
Answer» A hollow metallic cylindrical tube as an internal radius of 3 cm and height 21 cm. The thickness of the metal of the tube is 0.5 cm the tube is melted and cast and were right circular cone of radius 5 cm. Find the height of the cone correct to one decimal place.

Discussion

34.	If the line x-23=y-1-5=z+22 lies in the plane x+3y-αz+7=0, then α = _________________.
Answer» If the line $\frac{x - 2}{3} = \frac{y - 1}{- 5} = \frac{z + 2}{2}$ lies in the plane $x + 3 y - α z + 7 = 0, then α$ = _________________.

Discussion

35.	Form a cubic equation whose roots are the cubes of the roots of x³ + 3x² + 2 = 0.
Answer» Form a cubic equation whose roots are the cubes of the roots of x³ + 3x² + 2 = 0.

Discussion

36.	If three consecutive vertices of a parallelogram are (1, −2), (3, 6) and (5, 10), find its fourth vertex.
Answer» If three consecutive vertices of a parallelogram are (1, −2), (3, 6) and (5, 10), find its fourth vertex.

Discussion

37.	Progressive taxes on higher incomes can prevent wealthy people from accumulating
Answer» Progressive taxes on higher incomes can prevent wealthy people from accumulating

Discussion

38.	If a quadratic polynomial f(x) is a square of a linear polynomial, then its two zeros are coincident. (True/False).
Answer» If a quadratic polynomial f(x) is a square of a linear polynomial, then its two zeros are coincident. (True/False).

Discussion

39.	Question 2 (ii) Find the amount of water displaced by a solid spherical ball of diameter: (ii) 0.21 m [Assume π=227]
Answer» Question 2 (ii) Find the amount of water displaced by a solid spherical ball of diameter: (ii) 0.21 m $[A s s u m e π = \frac{22}{7}]$

Discussion

40.	If one of the roots of a quadratic equation is 5 and its constant term is 165. Then the quadratic equation is :
Answer» If one of the roots of a quadratic equation is 5 and its constant term is 165. Then the quadratic equation is :

Discussion

41.	If in an AP the sum of m terms is equal to n end the sum of n terms is equal to m then prove that the sum of (m + n) terms is -(m+n)
Answer» If in an AP the sum of m terms is equal to n end the sum of n terms is equal to m then prove that the sum of (m + n) terms is -(m+n)

Discussion

42.	A man goes 15 metres due west and then 8 metres due north. How far is he from the starting point?
Answer» A man goes 15 metres due west and then 8 metres due north. How far is he from the starting point?

Discussion

43.	The common difference of an arithmetic sequence is −1 and its 4th term is 7. What is its 7th term? And the 11th term?
Answer» The common difference of an arithmetic sequence is −1 and its 4^th term is 7. What is its 7^th term? And the 11^th term?

Discussion

44.	A man completes 30km of a journey at the speed of 6km/hr and remaining 40km of the journey in 5hrs. His average speed for the whole journey is:
Answer» A man completes 30km of a journey at the speed of 6km/hr and remaining 40km of the journey in 5hrs. His average speed for the whole journey is:

Discussion

45.	√−1−√−1−√−1−⋯to ∞ is equal to :
Answer» $\sqrt{- 1 - \sqrt{- 1 - \sqrt{- 1 - \dots to \infty}}}$ is equal to :

Discussion

46.	If first term of an AP is 5, last term is 45 and the sum of the terms is 400, then the number of terms is in the AP is ___.
Answer» If first term of an AP is 5, last term is 45 and the sum of the terms is 400, then the number of terms is in the AP is ___.

Discussion

47.	Which of the following is the graph for identity function?
Answer» Which of the following is the graph for identity function?

Discussion

48.	29. Deepti went to school 216days in full year. If her attendance in90%.Find the number of days on which the school opened
Answer» 29. Deepti went to school 216days in full year. If her attendance in90%.Find the number of days on which the school opened

Discussion

49.	A tree breaks due to a storm and the broken part bends so that the top of the tree touches the ground making an angle 30∘ with it. The distance between the foot of the tree to the point where the top touches the ground is 8m. Find the height of the tree?
Answer» A tree breaks due to a storm and the broken part bends so that the top of the tree touches the ground making an angle $30^{\circ}$ with it. The distance between the foot of the tree to the point where the top touches the ground is 8m. Find the height of the tree?

Discussion

50.	Circular discs 5 mm thickness, are placed one above the other to form a cylinder of curved surface area 462 cm2. Find the number of discs, if the radius is 3.5 cm.
Answer» Circular discs 5 mm thickness, are placed one above the other to form a cylinder of curved surface area 462 $c m^{2}$ . Find the number of discs, if the radius is 3.5 cm.

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

IF and event cannot occur then its probability is (a) 1 (b) 12 (c) 34 (d) 0

What is the area of the triangle formed by the points O (0, 0), A (6, 0) and B (0, 4)?

the value of∫_{50}^{40}(1/θ-θ^°)\operatorname dθ where θ^°=30 (a cons†an t ) is

If sec 2A=cosec(A−42∘), where 2A is an acute angle, find the value of A.

The sum of the first n terms of an AP whose first term is 8 and the common difference is 20 is equal to the sum of the first 2n terms of another AP, whose first term is - 30 and the common difference is 8. find n?

Find the sum of first 20 terms of the sequence whose nth term is an=An+B.

Solve the following systems of equations graphically:x + y = 42x − 3y = 3

A fraction becomes 1/3 when 2 is subtracted from the numerator and it becomes 1/2 when 1 is subtracted from the denominator. Find the fraction.

find 3 solutions of the equation 2x+3y=6

Determine the greatest 3-digit number exactly divisible by 8, 10 and 12.

On dividing 3x3+x2+2x+5 by a polynomial g(x), the quotient and remainder are (3x-5) and (9x+10) respectively. Find g(x).

i) find the value of a = [{x}] + [{-x}] +{[x]} + {[-x]} + {x} + {-x}ii) solve the equation 2x = [x] + {x

Solve the following quadratic equations by factorization:3x2 − 14x − 5 = 0

ABCD is a cyclic quadrilateral finds the angles of the cyclic quadrilateral.

Simplify: (x3+2x2+3x)÷2x

An arc of length 15 cm subtends an angle of 45∘ at the centre of a circle. Find in terms of π, the radius of the circle.

A conical tomb is made up of bricks of a front surface area of 5 sq. m. The slant height and radius of the tomb are measured to be 25 m and 7 m respectively. The approximate number of bricks used to construct the tomb are ___ (Take π=227)

Let A={a,e,i,o,u} and B={a,i,u}. Show that A∪B=A

A number x is chosen at random from the numbers -3, -2, -1, 0, 1, 2, 3, the probability that |x| &lt; 2 is

The value of sin 70°sin 110° is _____________.

Identify the number sequence from the following pattern taking only the smallest square as a unit square.

Determine k so that (3k − 2), (4k − 6) and (k + 2) are three consecutive terms of an AP. [CBSE 2009C]

draw a circle of radius 6cm.from a point 10 cm away from its centre,construct the pair of tangents to the circle and measure their lengths.

In parallelogram ABCD, A(-5,2), B(1,3) and D(-2,10). Then the coordinates of C is

Factorize: (i) x3+3x2+3x−7 (ii) x3−3x2+3x+7 [4 MARKS]

A cube has a side 1.2 cm .Its surface area i

68. If right circular cone is seperated into 3 solids of volume V1, V2, V3 by 2 planes which are parallel to base and trisect the altitude .What is the ratio of V1:V2:V3?

If cos−1(−x)=cos−1x, then the value of x is equal to

The first and the last terms of an A.P. are 17 and 350 respectively. If the common difference is 9, how many terms are there and what is their sum?

Following are the lives in hours of 15 pieces of the components of aircraft engine. Find the median:715, 724, 725, 710, 729, 745, 694, 699, 696, 712, 734, 728, 716, 705, 719.

Solve each of the following equations by using the method of completing the square:4x2+43x+3=0

A hollow metallic cylindrical tube as an internal radius of 3 cm and height 21 cm. The thickness of the metal of the tube is 0.5 cm the tube is melted and cast and were right circular cone of radius 5 cm. Find the height of the cone correct to one decimal place.

If the line x-23=y-1-5=z+22 lies in the plane x+3y-αz+7=0, then α = _________________.

Form a cubic equation whose roots are the cubes of the roots of x³ + 3x² + 2 = 0.

If three consecutive vertices of a parallelogram are (1, −2), (3, 6) and (5, 10), find its fourth vertex.

Progressive taxes on higher incomes can prevent wealthy people from accumulating

If a quadratic polynomial f(x) is a square of a linear polynomial, then its two zeros are coincident. (True/False).

Question 2 (ii) Find the amount of water displaced by a solid spherical ball of diameter: (ii) 0.21 m [Assume π=227]

If one of the roots of a quadratic equation is 5 and its constant term is 165. Then the quadratic equation is :

If in an AP the sum of m terms is equal to n end the sum of n terms is equal to m then prove that the sum of (m + n) terms is -(m+n)

A man goes 15 metres due west and then 8 metres due north. How far is he from the starting point?

The common difference of an arithmetic sequence is −1 and its 4th term is 7. What is its 7th term? And the 11th term?

A man completes 30km of a journey at the speed of 6km/hr and remaining 40km of the journey in 5hrs. His average speed for the whole journey is:

√−1−√−1−√−1−⋯to ∞ is equal to :

If first term of an AP is 5, last term is 45 and the sum of the terms is 400, then the number of terms is in the AP is ___.

Which of the following is the graph for identity function?

29. Deepti went to school 216days in full year. If her attendance in90%.Find the number of days on which the school opened

A tree breaks due to a storm and the broken part bends so that the top of the tree touches the ground making an angle 30∘ with it. The distance between the foot of the tree to the point where the top touches the ground is 8m. Find the height of the tree?

Circular discs 5 mm thickness, are placed one above the other to form a cylinder of curved surface area 462 cm2. Find the number of discs, if the radius is 3.5 cm.

A number x is chosen at random from the numbers -3, -2, -1, 0, 1, 2, 3, the probability that |x| < 2 is