32581 + Interview Questions in Mathematics

1.	If in an AP S5 is equal to 35 and S4 is equal 22 find the 5th term
Answer» If in an AP S5 is equal to 35 and S4 is equal 22 find the 5th term

Discussion

2.	The values of cosecant of an angle ___ , when the angle varies from 0∘to 90∘.
Answer» The values of cosecant of an angle ___ , when the angle varies from $0^{\circ} to 90^{\circ}$ .

Discussion

3.	8 men and 12 boys can finish a piece of work in 10 days while 6 men and 8 boys can finish it in 14 days.Find the time taken by one man alone , and that by one boy alone to finish the work.
Answer» 8 men and 12 boys can finish a piece of work in 10 days while 6 men and 8 boys can finish it in 14 days.Find the time taken by one man alone , and that by one boy alone to finish the work.

Discussion

4.	Solve the equations y = x + 3 and 3x + y = 17.
Answer» Solve the equations y = x + 3 and 3x + y = 17.

Discussion

5.	Nature of root of x−1x−1=x+42x+2 will be:
Answer» Nature of root of $\frac{x - 1}{x - 1} = \frac{x + 4}{2 x + 2}$ will be:

Discussion

6.	Find the polynomial p(x)=ax+b such that p(1)=2 & p(2)=5.
Answer» $Find the polynomial p (x) = a x + b such that p (1) = 2 & p (2) = 5.$

Discussion

7.	The probability of a person winning a game is 0.8, the probability of him losing a game is x10. The value of x is ___. 2
Answer» The probability of a person winning a game is 0.8, the probability of him losing a game is $\frac{x}{10}$ . The value of $x$ is ___. 2

7.

The probability of a person winning a game is 0.8, the probability of him losing a game is x10. The value of x is ___. 2

Answer»

The probability of a person winning a game is 0.8, the probability of him losing a game is $\frac{x}{10}$ . The value of $x$ is ___.

2

Discussion

8.	What is the condition for the quadratic equation x2+bx+c=0 to have real roots?
Answer» What is the condition for the quadratic equation $x^{2} + b x + c = 0$ to have real roots?

Discussion

9.	Which of the following represents the same A∩(B∪C).
Answer» Which of the following represents the same $A \cap (B \cup C)$ .

Discussion

10.	In the figure, the medians BD & CE of a ∆ ABC meet at G. Find the ratio of GD : GB.
Answer» In the figure, the medians BD & CE of a ∆ ABC meet at G. Find the ratio of GD : GB.

10.

In the figure, the medians BD & CE of a ∆ ABC meet at G. Find the ratio of GD : GB.

Answer»

In the figure, the medians BD & CE of a ∆ ABC meet at G. Find the ratio of GD : GB.

Discussion

11.	AB is a tower, and two objects C and D are located on the ground, on the same side of AB, their angles of depression are 45 and 60 degrees respectively. Find the distance between the two objects, if height of tower is 300m.Give your answer to the nearest metre.
Answer» AB is a tower, and two objects C and D are located on the ground, on the same side of AB, their angles of depression are 45 and 60 degrees respectively. Find the distance between the two objects, if height of tower is 300m.Give your answer to the nearest metre.

Discussion

12.	If X = 5 + 2√6 Find the value of X + 1X
Answer» If X = 5 + 2 $\sqrt{6}$ Find the value of X + $\frac{1}{X}$

12.

If X = 5 + 2√6 Find the value of X + 1X

Answer»

If X = 5 + 2 $\sqrt{6}$ Find the value of X + $\frac{1}{X}$

Discussion

13.	If a and b are two different positive real numbers, then which of the following relations is true
Answer» If a and b are two different positive real numbers, then which of the following relations is true

Discussion

14.	If the integers m and n are chosen at random between 1 and 100, then the probability that a number of the from 7m+7n is divisible by 5, equals
Answer» If the integers m and n are chosen at random between 1 and 100, then the probability that a number of the from $7^{m} + 7^{n}$ is divisible by 5, equals

Discussion

15.	If x=1√3+1 then the value of x+1x is
Answer» If $x = \frac{1}{\sqrt{3} + 1}$ then the value of $x + \frac{1}{x}$ is

Discussion

16.	The zeros of the polynomial x2−√2x−12 are _____
Answer» The zeros of the polynomial $x^{2} - \sqrt{2} x - 12$ are _____

Discussion

17.	For solving each pair of equations, use the method of eliminations by equating coefficients: 5y2−x3=8 y2+5x3=12
Answer» For solving each pair of equations, use the method of eliminations by equating coefficients: $\frac{5 y}{2} - \frac{x}{3} = 8$ $\frac{y}{2} + \frac{5 x}{3} = 12$

17.

For solving each pair of equations, use the method of eliminations by equating coefficients: 5y2−x3=8 y2+5x3=12

Answer»

For solving each pair of equations, use the method of eliminations by equating coefficients:

$\frac{5 y}{2} - \frac{x}{3} = 8$

$\frac{y}{2} + \frac{5 x}{3} = 12$

Discussion

18.	If α,β are the roots of the equation 8x2−3x+27=0, then the value of (α2β)13+(β2α)13 is
Answer» If $α, β$ are the roots of the equation $8 x^{2} - 3 x + 27 = 0$ , then the value of ${(\frac{α^{2}}{β})}^{\frac{1}{3}} + {(\frac{β^{2}}{α})}^{\frac{1}{3}}$ is

Discussion

19.	Question 5 It is true that the distance travelled by a circular wheel of diameter d cm in one revolution is 2πd cm? why?
Answer» Question 5 It is true that the distance travelled by a circular wheel of diameter d cm in one revolution is $2 π d c m$ ? why?

Discussion

20.	Cost of production of each unit of electricity is 3 less than twice the total number of units produced. If the total cost of production is 20, find the number of units of electricity produced?
Answer» Cost of production of each unit of electricity is 3 less than twice the total number of units produced. If the total cost of production is 20, find the number of units of electricity produced?

Discussion

21.	Circles with centres P and Q intersect at points A and B as shown in the figure. CBD is a line segment and EBM is tangent to the circle, with centre Q, at point B. If the circles are congruent; Then, CE = ________
Answer» Circles with centres P and Q intersect at points A and B as shown in the figure. CBD is a line segment and EBM is tangent to the circle, with centre Q, at point B. If the circles are congruent; Then, CE = ________

Discussion

22.	Two circles touch each other internally at a point P. A chord AB of the bigger circle intersects the other circle in C and D. Then, ∠CPA= _______.
Answer» Two circles touch each other internally at a point P. A chord AB of the bigger circle intersects the other circle in C and D. Then, $∠ C P A =$ _______.

22.

Two circles touch each other internally at a point P. A chord AB of the bigger circle intersects the other circle in C and D. Then, ∠CPA= _______.

Answer»

Two circles touch each other internally at a point P. A chord AB of the bigger circle intersects the other circle in C and D. Then, $∠ C P A =$ _______.

Discussion

23.	Refer to the figure: DE is parallel to BC. ADDB = ?
Answer» Refer to the figure: DE is parallel to BC. $\frac{A D}{D B}$ = ?

23.

Refer to the figure: DE is parallel to BC. ADDB = ?

Answer»

Refer to the figure: DE is parallel to BC.

$\frac{A D}{D B}$ = ?

Discussion

24.	are the factors of the polynomial x2+2x−8.
Answer» are the factors of the polynomial $x^{2} + 2 x - 8$ .

Discussion

25.	Draw an isosceles ΔABC in which BC=5.5cm and altitude AL=3 cm. Then construct another triangle whose sides are 34 of the corresponding sides of ΔABC.
Answer» Draw an isosceles $Δ A B C$ in which $B C = 5.5$ cm and altitude $A L = 3$ cm. Then construct another triangle whose sides are $\frac{3}{4}$ of the corresponding sides of $Δ A B C$ .

Discussion

26.	In figure,a tower AB is 20 m high and BC,its shadow in the ground,is 20√3 m long. Find the sun's altitude.
Answer» In figure,a tower AB is 20 m high and BC,its shadow in the ground,is $20 \sqrt{3}$ m long. Find the sun's altitude.

Discussion

27.	The total surface area in m2 of a cuboid with dimensions 26 m×14 m×6.5 m is ___ m2.
Answer» The total surface area in $m^{2}$ of a cuboid with dimensions $26 m \times 14 m \times 6.5 m$ is ___ m $^{2}$ .

27.

The total surface area in m2 of a cuboid with dimensions 26 m×14 m×6.5 m is ___ m2.

Answer»

The total surface area in $m^{2}$ of a cuboid with dimensions $26 m \times 14 m \times 6.5 m$ is

___ m $^{2}$ .

Discussion

28.	If the slope of a line L is (-1/5), then the slope of the line perpendicular to line L is ____________ ___
Answer» If the slope of a line L is (-1/5), then the slope of the line perpendicular to line L is ____________ ___

Discussion

29.	On a map drawn to a scale of 1:50000, a rectangular plot of land ABCD has the following measurements:AB=12cm, BC=16cm and∠A=∠B=∠C=∠D=900Calculate:The length of a diagonal of the plot in km.
Answer» $O n a m a p d r a w n t o a s c a l e o f 1 : 50000, a r e c t a n g u l a r p l o t o f l a n d A B C D h a s t h e f o l l o w i n g m e a s u r e m e n t s : A B = 12 c m, B C = 16 c m a n d ∠ A = ∠ B = ∠ C = ∠ D = 90^{0} C a l c u l a t e : T h e l e n g t h o f a d i a g o n a l o f t h e p l o t i n k m .$

29.

On a map drawn to a scale of 1:50000, a rectangular plot of land ABCD has the following measurements:AB=12cm, BC=16cm and∠A=∠B=∠C=∠D=900Calculate:The length of a diagonal of the plot in km.

Answer»

$O n a m a p d r a w n t o a s c a l e o f 1 : 50000, a r e c t a n g u l a r p l o t o f l a n d A B C D h a s t h e f o l l o w i n g m e a s u r e m e n t s : A B = 12 c m, B C = 16 c m a n d ∠ A = ∠ B = ∠ C = ∠ D = 90^{0} C a l c u l a t e : T h e l e n g t h o f a d i a g o n a l o f t h e p l o t i n k m .$

Discussion

30.	In Fig. 9, is shown a sector OAP of a circle with centre O, containing ∠θ. AB is perpendicular to the radius OA and meets OP produced at B. Prove that the perimeter of shaded region is r[tan θ+sec θ+πθ180−1]
Answer» In Fig. 9, is shown a sector OAP of a circle with centre O, containing $∠ θ$ . AB is perpendicular to the radius OA and meets OP produced at B. Prove that the perimeter of shaded region is $r [t a n θ + s e c θ + \frac{π θ}{180} - 1]$

Discussion

31.	Shadow of a tower standing on a level ground is found to be 40 m longer when the sun's altitude is 30 degree than when it is 60 degree. find the height of the tower
Answer» Shadow of a tower standing on a level ground is found to be 40 m longer when the sun's altitude is 30 degree than when it is 60 degree. find the height of the tower

Discussion

32.	Given below are 2 questions titled A and B and 6 answers numbered from 1 to 6. In each of the options that follow, each question is matched with an answer. Pick the correct match from the options. A - What is the shortest distance between the centre of a circle and tangent drawn to it? B - What is the shortest distance between a point and a line? 1. Radius 2. Secant 3. Perpendicular 4. Chord 5. Arc 6. Tangent
Answer» Given below are 2 questions titled A and B and 6 answers numbered from 1 to 6. In each of the options that follow, each question is matched with an answer. Pick the correct match from the options. A - What is the shortest distance between the centre of a circle and tangent drawn to it? B - What is the shortest distance between a point and a line? 1. Radius 2. Secant 3. Perpendicular 4. Chord 5. Arc 6. Tangent

32.

Given below are 2 questions titled A and B and 6 answers numbered from 1 to 6. In each of the options that follow, each question is matched with an answer. Pick the correct match from the options. A - What is the shortest distance between the centre of a circle and tangent drawn to it? B - What is the shortest distance between a point and a line? 1. Radius 2. Secant 3. Perpendicular 4. Chord 5. Arc 6. Tangent

Answer»

Given below are 2 questions titled A and B and 6 answers numbered from 1 to 6. In each of the options that follow, each question is matched with an answer. Pick the correct match from the options.

A - What is the shortest distance between the centre of a circle and tangent drawn to it?

B - What is the shortest distance between a point and a line?

1. Radius
2. Secant
3. Perpendicular
4. Chord
5. Arc
6. Tangent

Discussion

33.	If P=[√3/21/2−1/2√3/2],A=[1101] and Q=PAPT, then PTQ2005P is
Answer» If $P = [\begin{matrix} \sqrt{3} / 2 & 1 / 2 - 1 / 2 & \sqrt{3} / 2 \end{matrix}], A = [\begin{matrix} 1 & 1 0 & 1 \end{matrix}] and Q = P A P^{T}, then P^{T} Q^{2005} P is$

Discussion

34.	The height of a cone is 30 cm. A small cone is cut off at the top by a plane parallel to the base if it's volume be half of the volume of the given cone.at what height above the base is the section made
Answer» The height of a cone is 30 cm. A small cone is cut off at the top by a plane parallel to the base if it's volume be half of the volume of the given cone.at what height above the base is the section made

Discussion

35.	The point which lies on the perpendicular bisector of line segment joining the points A(-2,-5) and B(2,5)is a) (0,0) b) (0,2) c) (2,0) d) (-2,0)
Answer» The point which lies on the perpendicular bisector of line segment joining the points A(-2,-5) and B(2,5)is a) (0,0) b) (0,2) c) (2,0) d) (-2,0)

35.

The point which lies on the perpendicular bisector of line segment joining the points A(-2,-5) and B(2,5)is a) (0,0) b) (0,2) c) (2,0) d) (-2,0)

Answer»

The point which lies on the perpendicular bisector of line segment joining the points A(-2,-5) and B(2,5)is

a) (0,0) b) (0,2) c) (2,0) d) (-2,0)

Discussion

36.	Find the roots of the equation x+5=2x+10x−6 using the quadratic formula.
Answer» Find the roots of the equation $x + 5 = \frac{2 x + 10}{x - 6}$ using the quadratic formula.

Discussion

37.	Question 1 (ii) Fill in the blanks using the correct word in the given bracket. (ii) All squares are ____.(similar, congruent)
Answer» Question 1 (ii) Fill in the blanks using the correct word in the given bracket. (ii) All squares are ____.(similar, congruent)

Discussion

38.	If cosec A + cot A = x , find the value of cosec A - cot A
Answer» If cosec A + cot A = x , find the value of cosec A - cot A

Discussion

39.	Two AP have the common difference .the difference between their 100th terms is 111,222,333.what is difference between their millionth terms
Answer» Two AP have the common difference .the difference between their 100th terms is 111,222,333.what is difference between their millionth terms

Discussion

40.	A circle of diameter 6 cm makes a sector of angle P∘, what will be the area of the sector?
Answer» A circle of diameter 6 cm makes a sector of angle $P^{\circ}$ , what will be the area of the sector?

Discussion

41.	Two numbers are in the ratio 5:6 and if 4 is subtracted from each, they are reduced to 2:3, then the highest number is
Answer» Two numbers are in the ratio 5:6 and if 4 is subtracted from each, they are reduced to 2:3, then the highest number is

Discussion

42.	Find the values of x and y if : 52+x+1y−4=2 62+x−3y−4=1 Here, x ≠ -2 and y ≠ 4.
Answer» Find the values of $x$ and $y$ if : $\frac{5}{2 + x} + \frac{1}{y - 4} = 2$ $\frac{6}{2 + x} - \frac{3}{y - 4} = 1$ Here, x $\neq$ -2 and y $\neq$ 4.

Discussion

43.	Prove that the lengths of the tangents drawn from an external point to a circle are equal.
Answer» Prove that the lengths of the tangents drawn from an external point to a circle are equal.

Discussion

44.	The total cost to paint all the 4 walls of a room with length, breadth and height as 10 m, 20 m, and 5 m respectively at the rate of Rs. 10 per sq. meter will be:
Answer» The total cost to paint all the 4 walls of a room with length, breadth and height as 10 m, 20 m, and 5 m respectively at the rate of Rs. 10 per sq. meter will be:

Discussion

45.	A boat moves at 11 km/hr in still water and the water stream flows at 9 km/hr. The speed of the boat if it goes along with the water stream is?
Answer» A boat moves at 11 km/hr in still water and the water stream flows at 9 km/hr. The speed of the boat if it goes along with the water stream is?

Discussion

46.	In triangle ABC and triangle XYZ if angle A and angle X are acute angles such that cosA=cosX then show that angle A=angle X
Answer» In triangle ABC and triangle XYZ if angle A and angle X are acute angles such that cosA=cosX then show that angle A=angle X

Discussion

47.	AB is the diameter of a circle of radius 6.5 cm. If the length of chord CA is 5 cm then, the area of ΔABC IS :
Answer» AB is the diameter of a circle of radius 6.5 cm. If the length of chord CA is 5 cm then, the area of ΔABC IS :

Discussion

48.	Total dividend earned is given by _____________
Answer» Total dividend earned is given by _____________

Discussion

49.	The zero of the polynomial that this graph represents is
Answer» The zero of the polynomial that this graph represents is

49.

The zero of the polynomial that this graph represents is

Answer»

The zero of the polynomial that this graph represents is

Discussion

50.	If a square is inscribed in a circle, then the ratio of their areas is
Answer» If a square is inscribed in a circle, then the ratio of their areas is

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

If in an AP S5 is equal to 35 and S4 is equal 22 find the 5th term

The values of cosecant of an angle ___ , when the angle varies from 0∘to 90∘.

8 men and 12 boys can finish a piece of work in 10 days while 6 men and 8 boys can finish it in 14 days.Find the time taken by one man alone , and that by one boy alone to finish the work.

Solve the equations y = x + 3 and 3x + y = 17.

Nature of root of x−1x−1=x+42x+2 will be:

Find the polynomial p(x)=ax+b such that p(1)=2 &amp; p(2)=5.

The probability of a person winning a game is 0.8, the probability of him losing a game is x10. The value of x is ___. 2

What is the condition for the quadratic equation x2+bx+c=0 to have real roots?

Which of the following represents the same A∩(B∪C).

In the figure, the medians BD &amp; CE of a ∆ ABC meet at G. Find the ratio of GD : GB.

AB is a tower, and two objects C and D are located on the ground, on the same side of AB, their angles of depression are 45 and 60 degrees respectively. Find the distance between the two objects, if height of tower is 300m.Give your answer to the nearest metre.

If X = 5 + 2√6 Find the value of X + 1X

If a and b are two different positive real numbers, then which of the following relations is true

If the integers m and n are chosen at random between 1 and 100, then the probability that a number of the from 7m+7n is divisible by 5, equals

If x=1√3+1 then the value of x+1x is

The zeros of the polynomial x2−√2x−12 are _____

For solving each pair of equations, use the method of eliminations by equating coefficients: 5y2−x3=8 y2+5x3=12

If α,β are the roots of the equation 8x2−3x+27=0, then the value of (α2β)13+(β2α)13 is

Question 5 It is true that the distance travelled by a circular wheel of diameter d cm in one revolution is 2πd cm? why?

Cost of production of each unit of electricity is 3 less than twice the total number of units produced. If the total cost of production is 20, find the number of units of electricity produced?

Circles with centres P and Q intersect at points A and B as shown in the figure. CBD is a line segment and EBM is tangent to the circle, with centre Q, at point B. If the circles are congruent; Then, CE = ________

Two circles touch each other internally at a point P. A chord AB of the bigger circle intersects the other circle in C and D. Then, ∠CPA= _______.

Refer to the figure: DE is parallel to BC. ADDB = ?

are the factors of the polynomial x2+2x−8.

Draw an isosceles ΔABC in which BC=5.5cm and altitude AL=3 cm. Then construct another triangle whose sides are 34 of the corresponding sides of ΔABC.

In figure,a tower AB is 20 m high and BC,its shadow in the ground,is 20√3 m long. Find the sun's altitude.

The total surface area in m2 of a cuboid with dimensions 26 m×14 m×6.5 m is ___ m2.

If the slope of a line L is (-1/5), then the slope of the line perpendicular to line L is ____________ ___

On a map drawn to a scale of 1:50000, a rectangular plot of land ABCD has the following measurements:AB=12cm, BC=16cm and∠A=∠B=∠C=∠D=900Calculate:The length of a diagonal of the plot in km.

In Fig. 9, is shown a sector OAP of a circle with centre O, containing ∠θ. AB is perpendicular to the radius OA and meets OP produced at B. Prove that the perimeter of shaded region is r[tan θ+sec θ+πθ180−1]

Shadow of a tower standing on a level ground is found to be 40 m longer when the sun's altitude is 30 degree than when it is 60 degree. find the height of the tower

If P=[√3/21/2−1/2√3/2],A=[1101] and Q=PAPT, then PTQ2005P is

The height of a cone is 30 cm. A small cone is cut off at the top by a plane parallel to the base if it's volume be half of the volume of the given cone.at what height above the base is the section made

The point which lies on the perpendicular bisector of line segment joining the points A(-2,-5) and B(2,5)is a) (0,0) b) (0,2) c) (2,0) d) (-2,0)

Find the roots of the equation x+5=2x+10x−6 using the quadratic formula.

Question 1 (ii) Fill in the blanks using the correct word in the given bracket. (ii) All squares are ____.(similar, congruent)

If cosec A + cot A = x , find the value of cosec A - cot A

Two AP have the common difference .the difference between their 100th terms is 111,222,333.what is difference between their millionth terms

A circle of diameter 6 cm makes a sector of angle P∘, what will be the area of the sector?

Two numbers are in the ratio 5:6 and if 4 is subtracted from each, they are reduced to 2:3, then the highest number is

Find the values of x and y if : 52+x+1y−4=2 62+x−3y−4=1 Here, x ≠ -2 and y ≠ 4.

Prove that the lengths of the tangents drawn from an external point to a circle are equal.

The total cost to paint all the 4 walls of a room with length, breadth and height as 10 m, 20 m, and 5 m respectively at the rate of Rs. 10 per sq. meter will be:

A boat moves at 11 km/hr in still water and the water stream flows at 9 km/hr. The speed of the boat if it goes along with the water stream is?

In triangle ABC and triangle XYZ if angle A and angle X are acute angles such that cosA=cosX then show that angle A=angle X

AB is the diameter of a circle of radius 6.5 cm. If the length of chord CA is 5 cm then, the area of ΔABC IS :

Total dividend earned is given by _____________

The zero of the polynomial that this graph represents is

If a square is inscribed in a circle, then the ratio of their areas is

Find the polynomial p(x)=ax+b such that p(1)=2 & p(2)=5.

In the figure, the medians BD & CE of a ∆ ABC meet at G. Find the ratio of GD : GB.

If the slope of a line L is (-1/5), then the slope of the line perpendicular to line L is __________ _