32581 + Interview Questions in Mathematics

1.	A jar contains 24 marbles. Some of these are green and others are blue. If a marble is drawn at random from the jar, the probability that it is green is 23. Find the number of blue marbles in the jar.
Answer» A jar contains 24 marbles. Some of these are green and others are blue. If a marble is drawn at random from the jar, the probability that it is green is $\frac{2}{3}$ . Find the number of blue marbles in the jar.

Discussion

2.	Prove the following trigonometric identities: 1+cos Asin2A=11−cos A
Answer» Prove the following trigonometric identities: $\frac{1 + c o s A}{s i n^{2} A} = \frac{1}{1 - c o s A}$

2.

Prove the following trigonometric identities: 1+cos Asin2A=11−cos A

Answer»

Prove the following trigonometric identities:

$\frac{1 + c o s A}{s i n^{2} A} = \frac{1}{1 - c o s A}$

Discussion

3.	Solve the following systems of equations:11x+15y+23=07x−2y−20=0
Answer» Solve the following systems of equations: $11 x + 15 y + 23 = 0$ $7 x - 2 y - 20 = 0$

3.

Solve the following systems of equations:11x+15y+23=07x−2y−20=0

Answer»

Solve the following systems of equations: $11 x + 15 y + 23 = 0$

$7 x - 2 y - 20 = 0$

Discussion

4.	The value of Cos75°is equal to
Answer» The value of Cos75°is equal to

Discussion

5.	Find the probability that a leap year selected at random will contain 53 Sundays.
Answer» Find the probability that a leap year selected at random will contain 53 Sundays.

Discussion

6.	Prove the following trigonometric identities: (cosec A−sin A)(sec A−cos A)(tan A+cot A)=1
Answer» Prove the following trigonometric identities: $(c o s e c A - s i n A) (s e c A - c o s A) (t a n A + c o t A) = 1$

6.

Prove the following trigonometric identities: (cosec A−sin A)(sec A−cos A)(tan A+cot A)=1

Answer»

Prove the following trigonometric identities:

$(c o s e c A - s i n A) (s e c A - c o s A) (t a n A + c o t A) = 1$

Discussion

7.	If y=12(3x+7) is written in the form ax+by+c=0, which of the following are possible values of a, b and c?
Answer» If $y = \frac{1}{2} (3 x + 7)$ is written in the form $a x + b y + c = 0,$ which of the following are possible values of a, b and c?

Discussion

8.	Find the range of values of x which satisfy −13≤ x2−43< 16, where x ϵ real number.
Answer» Find the range of values of x which satisfy $\frac{- 1}{3} \leq \frac{x}{2} - \frac{4}{3} < \frac{1}{6}$ , where x ϵ real number.

Discussion

9.	Find the value of y for which the expression y2−8 becomes zero.
Answer» Find the value of y for which the expression $y^{2} - 8$ becomes zero.

Discussion

10.	What must be added to f(x)=4x4+2x3−2x2+x−1 so that the resulting polynomial is divisible by g(x)=x2+2x−3 [4 MARKS]
Answer» What must be added to $f (x) = 4 x^{4} + 2 x^{3} - 2 x^{2} + x - 1$ so that the resulting polynomial is divisible by $g (x) = x^{2} + 2 x - 3$ [4 MARKS]

Discussion

11.	What is the next step to find all the roots of a quadratic equation which has been factorized?
Answer» What is the next step to find all the roots of a quadratic equation which has been factorized?

Discussion

12.	On dividing the polynomial f(x)=x3−3x2+x+2 by a polynomial g(x), the quotient q(x) and remainder r(x) are x-2 and -2x+4 respectively. Find the polynomial g(x). [4 MARKS]
Answer» On dividing the polynomial $f (x) = x^{3} - 3 x^{2} + x + 2$ by a polynomial $g (x)$ , the quotient $q (x)$ and remainder $r (x)$ are x-2 and -2x+4 respectively. Find the polynomial $g (x)$ . [4 MARKS]

Discussion

13.	Solve the following pairs of equations by reducing them to a pair of linear equations: 12x+13y=2 13x+12y=136
Answer» Solve the following pairs of equations by reducing them to a pair of linear equations: $\frac{1}{2 x} + \frac{1}{3 y} = 2$ $\frac{1}{3 x} + \frac{1}{2 y} = \frac{13}{6}$

Discussion

14.	A polynomial of degree 2 is called a
Answer» A polynomial of degree 2 is called a

Discussion

15.	The following table gives the literacy rate (in percentage) of 35 cities. Find the mean literacy rate by step deviation method. Literacy rate (in %)No. of cities44−55355−651065−751175−85885−953
Answer» The following table gives the literacy rate (in percentage) of 35 cities. Find the mean literacy rate by step deviation method. $\begin{matrix} Literacy rate (in %) & No. of cities 44 - 55 & 3 55 - 65 & 10 65 - 75 & 11 75 - 85 & 8 85 - 95 & 3 \end{matrix}$

Discussion

16.	The value of θ for which 2cos2θ + sinθ - 2 = 0. 0o < θ ≤90o is:
Answer» The value of θ for which 2cos²θ + sinθ - 2 = 0. 0^o < θ ≤90^o is:

Discussion

17.	The number of beats produced per second by the vibrations x1=A sin(420Ï€t) and x2=A sin(424 Ï€t) is
Answer» The number of beats produced per second by the vibrations x₁=A sin(420Ï€t) and x₂=A sin(424 Ï€t) is

Discussion

18.	Value of sin765o is
Answer» Value of sin765^o is

Discussion

19.	In the figure, the pair of tangents AP and AQ, drawn from an external point A to a circle with centre O, are perpendicular to each other and length of each tangent is 4 cm, then the radius of the circle is
Answer» In the figure, the pair of tangents AP and AQ, drawn from an external point A to a circle with centre O, are perpendicular to each other and length of each tangent is 4 cm, then the radius of the circle is

19.

In the figure, the pair of tangents AP and AQ, drawn from an external point A to a circle with centre O, are perpendicular to each other and length of each tangent is 4 cm, then the radius of the circle is

Answer»

In the figure, the pair of tangents AP and AQ, drawn from an external point A to a circle with centre O, are perpendicular to each other and length of each tangent is 4 cm, then the radius of the circle is

Discussion

20.	Aman has 729 coins. He gives only a part of these coins to his cousin as his birthday gift. This part is the square root of 729. How many coins did his cousin get?
Answer» Aman has 729 coins. He gives only a part of these coins to his cousin as his birthday gift. This part is the square root of 729. How many coins did his cousin get?

Discussion

21.	Divide a line segment AB of any length putting a point C such that ACCB is 3:1.
Answer» Divide a line segment AB of any length putting a point C such that $\frac{A C}{C B}$ is 3:1.

Discussion

22.	Find the sum to n terms of the AP 5, 2, -1, -4, -7, ...
Answer» Find the sum to n terms of the AP 5, 2, -1, -4, -7, ...

Discussion

23.	Question 18 Two numbers are in the ratio 5:6. If 8 is subtracted from each of the numbers, the ratio becomes 4:5, then find the numbers.
Answer» Question 18 Two numbers are in the ratio 5:6. If 8 is subtracted from each of the numbers, the ratio becomes 4:5, then find the numbers.

Discussion

24.	A train travels a distance of 480 km at a uniform speed. If the speed had been 8 km/hr less, then it would have taken 3 hours more to cover the same distance. The speed of the train is ___ kmph.
Answer» A train travels a distance of $480 k m$ at a uniform speed. If the speed had been $8 k m / h r$ less, then it would have taken $3$ hours more to cover the same distance. The speed of the train is ___ kmph.

Discussion

25.	Simplify (cosec θ+cot θ)×(1−cos θ).
Answer» Simplify $(c o s e c θ + c o t θ) \times (1 - c o s θ) .$

Discussion

26.	What is the remainder when 3x2−7x+5 is divided by x -1 ?
Answer» What is the remainder when $3 x^{2} - 7 x + 5$ is divided by x -1 ?

Discussion

27.	One pipe can fill a cistern in 3 hours less than the other. The two pipes together can fill the cistern in 6 hours 40 minutes. Find the time that each pipe will take to fill be cistern.
Answer» One pipe can fill a cistern in 3 hours less than the other. The two pipes together can fill the cistern in 6 hours 40 minutes. Find the time that each pipe will take to fill be cistern.

Discussion

28.	Question 40 Give a possible expression for the length and breadth of the rectangle whose area is given by 4a2+4a−3.
Answer» Question 40 Give a possible expression for the length and breadth of the rectangle whose area is given by $4 a^{2} + 4 a - 3$ .

Discussion

29.	To fill a tank, 30 buckets of water is required. If the capacity of bucket is reduced to two-fifth then how many buckets of water will be required to fill the same tank?
Answer» To fill a tank, 30 buckets of water is required. If the capacity of bucket is reduced to two-fifth then how many buckets of water will be required to fill the same tank?

Discussion

30.	A piece of cloth is required to completely cover a solid object. The solid object is composed of a hemisphere and a cone surmounted on it. If the common radius is 7 m and height of the cone is 1 m, what is the area of cloth required?
Answer» A piece of cloth is required to completely cover a solid object. The solid object is composed of a hemisphere and a cone surmounted on it. If the common radius is 7 m and height of the cone is 1 m, what is the area of cloth required?

Discussion

31.	In ΔABC,AD is the bisector of ∠BAC and I is its incentre .Prove that : AIID=AB+ACBC.
Answer» In $Δ A B C, A D$ is the bisector of $∠ B A C$ and $I$ is its incentre . Prove that : $\frac{A I}{I D} = \frac{A B + A C}{B C}$ .

31.

In ΔABC,AD is the bisector of ∠BAC and I is its incentre .Prove that : AIID=AB+ACBC.

Answer»

In $Δ A B C, A D$ is the bisector of $∠ B A C$ and $I$ is its incentre .

Prove that : $\frac{A I}{I D} = \frac{A B + A C}{B C}$ .

Discussion

32.	The value of cos226∘+cos264∘sin255∘+sin235∘ is: (find out, without using trignometric tables)
Answer» The value of $\frac{c o s^{2} 26^{\circ} + c o s^{2} 64^{\circ}}{s i n^{2} 55^{\circ} + s i n^{2} 35^{\circ}}$ is: (find out, without using trignometric tables)

32.

The value of cos226∘+cos264∘sin255∘+sin235∘ is: (find out, without using trignometric tables)

Answer»

The value of $\frac{c o s^{2} 26^{\circ} + c o s^{2} 64^{\circ}}{s i n^{2} 55^{\circ} + s i n^{2} 35^{\circ}}$ is:

(find out, without using trignometric tables)

Discussion

33.	If AP:PQ = 1:2 and PQ:QB = 4:5, then Q divides line segment AB in the ratio of?
Answer» If AP:PQ = 1:2 and PQ:QB = 4:5, then Q divides line segment AB in the ratio of?

Discussion

34.	102 °F = ___°C
Answer» 102 °F = ___°C

Discussion

35.	From which point shown below can we draw one tangent to the following circle?
Answer» From which point shown below can we draw one tangent to the following circle?

35.

From which point shown below can we draw one tangent to the following circle?

Answer»

From which point shown below can we draw one tangent to the following circle?

Discussion

36.	A chime is made of 3 identical spherical balls of density 363 g/cm3. If mass of each ball is 49 g, then find radius of each ball. Take π=227
Answer» A chime is made of 3 identical spherical balls of density 363 g/ $c m^{3}$ . If mass of each ball is 49 g, then find radius of each ball. Take $π = \frac{22}{7}$

Discussion

37.	Match the following for a square pyramid. Where, a = base edge length, h = slant height and H = height
Answer» $Match the following for a square pyramid.$ Where, a = base edge length, h = slant height and H = height

Discussion

38.	If tan θ =1, then find the value of θ.
Answer» If $t a n θ = 1$ , then find the value of $θ$ .

Discussion

39.	The word finance is used for
Answer» The word finance is used for

Discussion

40.	The molar conductance of NH4OH at 0.01M concentration is 11.3 ohm−1 cm2 mol−1. The degree of dissociation of NH4OH is (molar conductance at infinite dilution is 271.1)
Answer» The molar conductance of $N H_{4} O H$ at 0.01M concentration is 11.3 $o h m^{- 1} c m^{2} m o l^{- 1}$ . The degree of dissociation of $N H_{4} O H$ is (molar conductance at infinite dilution is 271.1)

Discussion

41.	Give an example for a function which is not a sequence.
Answer» Give an example for a function which is not a sequence.

Discussion

42.	If the length of a rectangle is increased by 5 meters and breadth decreased by 3 meters, the area would decrease by 5 square metres. If the length is increased by 3 meters and breadth increased by 2 meters, the area would increase by 50 square metres. What are the length and breadth?
Answer» If the length of a rectangle is increased by 5 meters and breadth decreased by 3 meters, the area would decrease by 5 square metres. If the length is increased by 3 meters and breadth increased by 2 meters, the area would increase by 50 square metres. What are the length and breadth?

Discussion

43.	Find the zeroes of the quadratic polynomial 4s2−4s+1. Also find the sum of the zeroes of the polynomial.
Answer» Find the zeroes of the quadratic polynomial $4 s^{2} - 4 s + 1$ . Also find the sum of the zeroes of the polynomial.

Discussion

44.	If ΔABC∼ΔPQR, identify the pairs of corresponding sides.
Answer» If $Δ ABC \sim Δ PQR$ , identify the pairs of corresponding sides.

Discussion

45.	A vessel is in the shape of cuboid and contains some water,if three identical spheres are immersed then the water level increases by 2 cm.If the area of the base of the cuboid is 160cm2 and height is 12cm then find the radio of the sphere.
Answer» A vessel is in the shape of cuboid and contains some water,if three identical spheres are immersed then the water level increases by 2 cm.If the area of the base of the cuboid is 160cm² and height is 12cm then find the radio of the sphere.

Discussion

46.	Solve the following quadratic equation by factorization method: [2 MARKS] 1x−2+2x−1=6x
Answer» Solve the following quadratic equation by factorization method: [2 MARKS] $\frac{1}{x - 2} + \frac{2}{x - 1} = \frac{6}{x}$

Discussion

47.	Find the sum of all natural numbers between 1 and 100, which are divisible by 2 or 5.
Answer» Find the sum of all natural numbers between 1 and 100, which are divisible by 2 or 5.

Discussion

48.	Draw the graphs representing the equations 4x +3y=24 and 3y=4x + 24 on the same graph paper . Write the Co-ordinate of the point of intersection of these and find the area of the triangle formed by these lines and the X-axis.
Answer» Draw the graphs representing the equations 4x +3y=24 and 3y=4x + 24 on the same graph paper . Write the Co-ordinate of the point of intersection of these and find the area of the triangle formed by these lines and the X-axis.

Discussion

49.	The student of a class are made to stand in rows. If one cent is extra in a row, there would be 2 rows less, and if 1 student is less in a row, there would be 3 rows more. Find the number of student in the class.
Answer» The student of a class are made to stand in rows. If one cent is extra in a row, there would be 2 rows less, and if 1 student is less in a row, there would be 3 rows more. Find the number of student in the class.

Discussion

50.	Column AColumn B(a) sin (90∘−A)(i) cos A(b) tan(90∘−A) (ii) cosec A(c) sec(90∘−A)(iii) cot A
Answer» $\begin{matrix} C o l u m n A & C o l u m n B (a) s i n (90^{\circ} - A) & (i) c o s A (b) t a n (90^{\circ} - A) & (i i) c o s e c A (c) s e c (90^{\circ} - A) & (i i i) c o t A \end{matrix}$

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

A jar contains 24 marbles. Some of these are green and others are blue. If a marble is drawn at random from the jar, the probability that it is green is 23. Find the number of blue marbles in the jar.

Prove the following trigonometric identities: 1+cos Asin2A=11−cos A

Solve the following systems of equations:11x+15y+23=07x−2y−20=0

The value of Cos75°is equal to

Find the probability that a leap year selected at random will contain 53 Sundays.

Prove the following trigonometric identities: (cosec A−sin A)(sec A−cos A)(tan A+cot A)=1

If y=12(3x+7) is written in the form ax+by+c=0, which of the following are possible values of a, b and c?

Find the range of values of x which satisfy −13≤ x2−43&lt; 16, where x ϵ real number.

Find the value of y for which the expression y2−8 becomes zero.

What must be added to f(x)=4x4+2x3−2x2+x−1 so that the resulting polynomial is divisible by g(x)=x2+2x−3 [4 MARKS]

What is the next step to find all the roots of a quadratic equation which has been factorized?

On dividing the polynomial f(x)=x3−3x2+x+2 by a polynomial g(x), the quotient q(x) and remainder r(x) are x-2 and -2x+4 respectively. Find the polynomial g(x). [4 MARKS]

Solve the following pairs of equations by reducing them to a pair of linear equations: 12x+13y=2 13x+12y=136

A polynomial of degree 2 is called a

The following table gives the literacy rate (in percentage) of 35 cities. Find the mean literacy rate by step deviation method. Literacy rate (in %)No. of cities44−55355−651065−751175−85885−953

The value of θ for which 2cos2θ + sinθ - 2 = 0. 0o &lt; θ ≤90o is:

The number of beats produced per second by the vibrations x1=A sin(420Ï€t) and x2=A sin(424 Ï€t) is

Value of sin765o is

In the figure, the pair of tangents AP and AQ, drawn from an external point A to a circle with centre O, are perpendicular to each other and length of each tangent is 4 cm, then the radius of the circle is

Aman has 729 coins. He gives only a part of these coins to his cousin as his birthday gift. This part is the square root of 729. How many coins did his cousin get?

Divide a line segment AB of any length putting a point C such that ACCB is 3:1.

Find the sum to n terms of the AP 5, 2, -1, -4, -7, ...

Question 18 Two numbers are in the ratio 5:6. If 8 is subtracted from each of the numbers, the ratio becomes 4:5, then find the numbers.

A train travels a distance of 480 km at a uniform speed. If the speed had been 8 km/hr less, then it would have taken 3 hours more to cover the same distance. The speed of the train is ___ kmph.

Simplify (cosec θ+cot θ)×(1−cos θ).

What is the remainder when 3x2−7x+5 is divided by x -1 ?

One pipe can fill a cistern in 3 hours less than the other. The two pipes together can fill the cistern in 6 hours 40 minutes. Find the time that each pipe will take to fill be cistern.

Question 40 Give a possible expression for the length and breadth of the rectangle whose area is given by 4a2+4a−3.

To fill a tank, 30 buckets of water is required. If the capacity of bucket is reduced to two-fifth then how many buckets of water will be required to fill the same tank?

A piece of cloth is required to completely cover a solid object. The solid object is composed of a hemisphere and a cone surmounted on it. If the common radius is 7 m and height of the cone is 1 m, what is the area of cloth required?

In ΔABC,AD is the bisector of ∠BAC and I is its incentre .Prove that : AIID=AB+ACBC.

The value of cos226∘+cos264∘sin255∘+sin235∘ is: (find out, without using trignometric tables)

If AP:PQ = 1:2 and PQ:QB = 4:5, then Q divides line segment AB in the ratio of?

102 °F = ___°C

From which point shown below can we draw one tangent to the following circle?

A chime is made of 3 identical spherical balls of density 363 g/cm3. If mass of each ball is 49 g, then find radius of each ball. Take π=227

Match the following for a square pyramid. Where, a = base edge length, h = slant height and H = height

If tan θ =1, then find the value of θ.

The word finance is used for

The molar conductance of NH4OH at 0.01M concentration is 11.3 ohm−1 cm2 mol−1. The degree of dissociation of NH4OH is (molar conductance at infinite dilution is 271.1)

Give an example for a function which is not a sequence.

If the length of a rectangle is increased by 5 meters and breadth decreased by 3 meters, the area would decrease by 5 square metres. If the length is increased by 3 meters and breadth increased by 2 meters, the area would increase by 50 square metres. What are the length and breadth?

Find the zeroes of the quadratic polynomial 4s2−4s+1. Also find the sum of the zeroes of the polynomial.

If ΔABC∼ΔPQR, identify the pairs of corresponding sides.

A vessel is in the shape of cuboid and contains some water,if three identical spheres are immersed then the water level increases by 2 cm.If the area of the base of the cuboid is 160cm2 and height is 12cm then find the radio of the sphere.

Solve the following quadratic equation by factorization method: [2 MARKS] 1x−2+2x−1=6x

Find the sum of all natural numbers between 1 and 100, which are divisible by 2 or 5.

Draw the graphs representing the equations 4x +3y=24 and 3y=4x + 24 on the same graph paper . Write the Co-ordinate of the point of intersection of these and find the area of the triangle formed by these lines and the X-axis.

The student of a class are made to stand in rows. If one cent is extra in a row, there would be 2 rows less, and if 1 student is less in a row, there would be 3 rows more. Find the number of student in the class.

Column AColumn B(a) sin (90∘−A)(i) cos A(b) tan(90∘−A) (ii) cosec A(c) sec(90∘−A)(iii) cot A

Find the range of values of x which satisfy −13≤ x2−43< 16, where x ϵ real number.

The value of θ for which 2cos2θ + sinθ - 2 = 0. 0o < θ ≤90o is: