32581 + Interview Questions in Mathematics

1.	The sum of first 20 natural numbers is ___
Answer» The sum of first 20 natural numbers is ___

Discussion

2.	The ratio of area of the triangles ABD and ADC, where AD is the height is:
Answer» The ratio of area of the triangles ABD and ADC, where AD is the height is:

Discussion

3.	A porous catalyst has an internal surface area of 800 m2 per m3 of bulk material. Fifty percent of the bulk volume consists of the pores (holes), while the other 50% of the volume is made of solid substance. Assume that the pores are cylindrical tubules of uniform diameter, d, and length, l, and that the measured surface area is the total area of the curved surfaces of the tubules. What is the diameter of the pores?
Answer» A porous catalyst has an internal surface area of 800 $m^{2}$ per $m^{3}$ of bulk material. Fifty percent of the bulk volume consists of the pores (holes), while the other 50% of the volume is made of solid substance. Assume that the pores are cylindrical tubules of uniform diameter, d, and length, l, and that the measured surface area is the total area of the curved surfaces of the tubules. What is the diameter of the pores?

Discussion

4.	If the cost of printing a book of 380 pages with 20 lines on each page and on an average 11 words in each line is Rs.19, then the cost of printing a book with 280 pages 22 lines on each page and 10 words in each line is
Answer» If the cost of printing a book of 380 pages with 20 lines on each page and on an average 11 words in each line is Rs.19, then the cost of printing a book with 280 pages 22 lines on each page and 10 words in each line is

Discussion

5.	Question 164(iii) If possible, find a hook-up of prime base number machine that will do the same work as the given stretching machine. Do not use (× 1) machines.
Answer» Question 164(iii) If possible, find a hook-up of prime base number machine that will do the same work as the given stretching machine. Do not use $(\times 1)$ machines.

5.

Question 164(iii) If possible, find a hook-up of prime base number machine that will do the same work as the given stretching machine. Do not use (× 1) machines.

Answer»

Question 164(iii)

If possible, find a hook-up of prime base number machine that will do the same work as the given stretching machine. Do not use
$(\times 1)$ machines.

Discussion

6.	From the top of a light house 100 m high, the angles of depression of two ships are observed as 48∘ and 36∘ respectively. Find the distance between the two ships (in the nearest metre) If : (i) the ships are on the same side of the light house, (ii) the ships are on the opposite sides of the light house.
Answer» From the top of a light house 100 m high, the angles of depression of two ships are observed as $48^{\circ} a n d 36^{\circ}$ respectively. Find the distance between the two ships (in the nearest metre) If : (i) the ships are on the same side of the light house, (ii) the ships are on the opposite sides of the light house.

6.

From the top of a light house 100 m high, the angles of depression of two ships are observed as 48∘ and 36∘ respectively. Find the distance between the two ships (in the nearest metre) If : (i) the ships are on the same side of the light house, (ii) the ships are on the opposite sides of the light house.

Answer»

From the top of a light house 100 m high, the angles of depression of two ships are observed as $48^{\circ} a n d 36^{\circ}$ respectively. Find the distance between the two ships (in the nearest metre) If :

(i) the ships are on the same side of the light house,

(ii) the ships are on the opposite sides of the light house.

Discussion

7.	If an equilateral triangle ABC is drawn as shown below with A(0,0) and a side of 4 units then the other two vertices of the triangle are___
Answer» If an equilateral triangle ABC is drawn as shown below with A(0,0) and a side of 4 units then the other two vertices of the triangle are___

7.

If an equilateral triangle ABC is drawn as shown below with A(0,0) and a side of 4 units then the other two vertices of the triangle are___

Answer»

If an equilateral triangle ABC is drawn as shown below with A(0,0) and a side of 4 units then the other two vertices of the triangle are___

Discussion

8.	For what value of k,the pair of equations 4x-3y=9, 2x+ky=11 has no solution
Answer» For what value of k,the pair of equations 4x-3y=9, 2x+ky=11 has no solution

Discussion

9.	Find the HCF of 52 and 117 and express it in form 52x + 117y.
Answer» Find the HCF of 52 and 117 and express it in form 52x + 117y.

Discussion

10.	State the parts of speech of the underlined words. Air India on Monday announced the addition of a second flight to the India-Sri Lanka sector.
Answer» State the parts of speech of the underlined words. Air India on Monday announced the addition of a second flight to the India-Sri Lanka sector.

10.

State the parts of speech of the underlined words. Air India on Monday announced the addition of a second flight to the India-Sri Lanka sector.

Answer»

State the parts of speech of the underlined words.

Air India on Monday announced the addition of a second flight to the India-Sri Lanka sector.

Discussion

11.	The sum of 1st three terms an AP is 30 and the sum of last three terms is 39.If the 1st term is 9,then find the number of terms in AP
Answer» The sum of 1st three terms an AP is 30 and the sum of last three terms is 39.If the 1st term is 9,then find the number of terms in AP

Discussion

12.	What is the application of probability in real life
Answer» What is the application of probability in real life

Discussion

13.	Which of the following should be the LAST sentence after rearrangement?
Answer» Which of the following should be the LAST sentence after rearrangement?

Discussion

14.	Use Euclid Lemma to show that the cube of any positive integer is of the form 9 m, 9 M + 1 or 9 M + 8
Answer» Use Euclid Lemma to show that the cube of any positive integer is of the form 9 m, 9 M + 1 or 9 M + 8

Discussion

15.	Find the equation of the line passing through the point (2,-5) and making an intercept of -3 on the Y axis.
Answer» Find the equation of the line passing through the point (2,-5) and making an intercept of -3 on the Y axis.

Discussion

16.	An AP consists of 37 terms . The sum of the three middle terms is 22 and the sum of the last three terms is 429 . Find the AP
Answer» An AP consists of 37 terms . The sum of the three middle terms is 22 and the sum of the last three terms is 429 . Find the AP

Discussion

17.	Question 18 The area of a triangle with vertices (a,b+c), (b,c+a) and (c,a+b) is (A) (a+b+c)2 (B) 0 (C) (a+b+c) (D) abc
Answer» Question 18 The area of a triangle with vertices (a,b+c), (b,c+a) and (c,a+b) is (A) $(a + b + c)^{2}$ (B) $0$ (C) $(a + b + c)$ (D) $a b c$

Discussion

18.	An oval-shaped meeting table made of wood has dimensions of its top as 10 m and 6 m. Find the cost of polishing it at Rs. 5.75 per sq.m.
Answer» An oval-shaped meeting table made of wood has dimensions of its top as $10 m$ and $6 m$ . Find the cost of polishing it at $R s . 5.75$ per $s q . m .$

Discussion

19.	In ΔABC,AB=10cm,AC=6cm,∠A=70∘. The length BC is equal to. [cos 70∘=0.34,sin 70∘=0.94]
Answer» In $Δ A B C, A B = 10 c m, A C = 6 c m, ∠ A = 70^{\circ}$ . The length BC is equal to. $[c o s 70^{\circ} = 0.34, s i n 70^{\circ} = 0.94]$

19.

In ΔABC,AB=10cm,AC=6cm,∠A=70∘. The length BC is equal to. [cos 70∘=0.34,sin 70∘=0.94]

Answer»

In $Δ A B C, A B = 10 c m, A C = 6 c m, ∠ A = 70^{\circ}$ . The length BC is equal to. $[c o s 70^{\circ} = 0.34, s i n 70^{\circ} = 0.94]$

Discussion

20.	Simplify:√3+√5
Answer» Simplify:√3+√5

Discussion

21.	Solve the quadratic equation 2x2+ax−a2=0 for x.
Answer» Solve the quadratic equation $2 x^{2} + a x - a^{2} = 0$ for x.

Discussion

22.	A wire is in the shape of a circle of radius 21 cm. It is bent to form a square. The side of the square is:
Answer» A wire is in the shape of a circle of radius 21 cm. It is bent to form a square. The side of the square is:

22.

A wire is in the shape of a circle of radius 21 cm. It is bent to form a square. The side of the square is:

Answer»

A wire is in the shape of a circle of radius 21 cm. It is bent to form a square. The side of the square is:

Discussion

23.	The perimeters of two similar triangles are 25 cm and 15 cm respectively. If one side of first triangle is 9 cm, the corresponding side of the other triangle is
Answer» The perimeters of two similar triangles are 25 cm and 15 cm respectively. If one side of first triangle is 9 cm, the corresponding side of the other triangle is

23.

The perimeters of two similar triangles are 25 cm and 15 cm respectively. If one side of first triangle is 9 cm, the corresponding side of the other triangle is

Answer»

The perimeters of two similar triangles are 25 cm and 15 cm respectively. If one side of first triangle is 9 cm, the corresponding side of the other triangle is

Discussion

24.	If 3rd term of a G.P is 12 and 6th term is 96, then its 7th term will be
Answer» If 3rd term of a G.P is 12 and 6th term is 96, then its 7th term will be

Discussion

25.	The value of 4cot245∘−sec260∘+sin260∘+cos290∘ is
Answer» The value of $4 c o t^{2} 45^{\circ} - s e c^{2} 60^{\circ} + s i n^{2} 60^{\circ} + c o s^{2} 90^{\circ}$ is

Discussion

26.	Question 16 If a circle drawn with origin as the centre, passes through (132,0), then the point which does not lie in the interior of the circle is (A) (−34,1) (B) (2,73,) (C) (5,−12) (D) (−6,52)
Answer» Question 16 If a circle drawn with origin as the centre, passes through $(\frac{13}{2}, 0)$ , then the point which does not lie in the interior of the circle is (A) $(\frac{- 3}{4}, 1)$ (B) $(2, \frac{7}{3},)$ (C) $(5, \frac{- 1}{2})$ (D) $(- 6, \frac{5}{2})$

Discussion

27.	sin (60o + θ) - cos (30o - θ) is equal to (where (60o + θ) and (30o - θ) are both acute angles):
Answer» sin (60^o + θ) - cos (30^o - θ) is equal to (where (60^o + θ) and (30^o - θ) are both acute angles):

Discussion

28.	A boy of height 60 cm is walking away from the base of a building at a speed of 2.2 m/s. If the height of the building is 7.2 m, then find the length of his shadow after 5 seconds.
Answer» A boy of height 60 cm is walking away from the base of a building at a speed of 2.2 m/s. If the height of the building is 7.2 m, then find the length of his shadow after 5 seconds.

Discussion

29.	A contractor plans to install two slides for the children to play in a park. For the children below the age of 5 years, she prefers to have a slide whose top is at a height of 2m and is inclined at an angle of 30∘ to the ground. What should be the length of the slide?
Answer» A contractor plans to install two slides for the children to play in a park. For the children below the age of 5 years, she prefers to have a slide whose top is at a height of 2m and is inclined at an angle of $30^{\circ}$ to the ground. What should be the length of the slide?

Discussion

30.	For two different APs, the ratio of the sums of the first n terms is 7n+14n+27. What is the ratio of the mth terms of the two APs? [4 MARKS]
Answer» For two different APs, the ratio of the sums of the first n terms is $\frac{7 n + 1}{4 n + 27}$ . What is the ratio of the $m^{t h}$ terms of the two APs? [4 MARKS]

Discussion

31.	Sum and the product of zeroes of the polynomial x2 +7x +10 is
Answer» Sum and the product of zeroes of the polynomial x² +7x +10 is

Discussion

32.	Find the factors of x2+18x+80 by splitting the middle term.
Answer» Find the factors of $x^{2} + 18 x + 80$ by splitting the middle term.

Discussion

33.	A company with a share of nominal value of ₹ 150 declares an annual dividend of 15 % . Calculate the annual income of a man who holds 88 shares in the company ?
Answer» A company with a share of nominal value of ₹ 150 declares an annual dividend of 15 % . Calculate the annual income of a man who holds 88 shares in the company ?

Discussion

34.	A conical vessel of radius 6 cm and height 8 cm is completely filled with water. A sphere is lowered into the water and its size is such that when it touches the sides, it is just immersed. What fraction of water overflows?
Answer» A conical vessel of radius 6 cm and height 8 cm is completely filled with water. A sphere is lowered into the water and its size is such that when it touches the sides, it is just immersed. What fraction of water overflows?

Discussion

35.	The linear equation 2x – 5y = x – 2 has
Answer» The linear equation 2x – 5y = x – 2 has

Discussion

36.	Raghu wants to make a closed aluminium cone for his science project. The slant height and radius of the cone should be 10 cm and 7 cm respectively. The area of the aluminium sheet required to make the cone is_____. (Use π=227)
Answer» Raghu wants to make a closed aluminium cone for his science project. The slant height and radius of the cone should be 10 cm and 7 cm respectively. The area of the aluminium sheet required to make the cone is_____. $(U s e π = \frac{22}{7})$

Discussion

37.	Using step - deviation method, calculate the mean marks of the following distribution.Class intervalFrequency50−55555−602060−651065−701070−75975−80680−851285−908
Answer» Using step - deviation method, calculate the mean marks of the following distribution. $\begin{matrix} C l a s s i n t e r v a l & F r e q u e n c y 50 - 55 & 5 55 - 60 & 20 60 - 65 & 10 65 - 70 & 10 70 - 75 & 9 75 - 80 & 6 80 - 85 & 12 85 - 90 & 8 \end{matrix}$

37.

Using step - deviation method, calculate the mean marks of the following distribution.Class intervalFrequency50−55555−602060−651065−701070−75975−80680−851285−908

Answer»

Using step - deviation method, calculate the mean marks of the following distribution.

$\begin{matrix} C l a s s i n t e r v a l & F r e q u e n c y 50 - 55 & 5 55 - 60 & 20 60 - 65 & 10 65 - 70 & 10 70 - 75 & 9 75 - 80 & 6 80 - 85 & 12 85 - 90 & 8 \end{matrix}$

Discussion

38.	The value of the polynomial 5x–4x2+3, when x=−1 is A) −6 B) 6 C) 2 D) −2
Answer» The value of the polynomial $5 x - 4 x^{2} + 3$ , when $x = - 1$ is A) $- 6$ B) $6$ C) $2$ D) $- 2$

Discussion

39.	The value of the polynomial −5x+3 at x=0 is ______.
Answer» The value of the polynomial $- 5 x + 3$ at $x = 0$ is ______.

Discussion

40.	Using trigonometric tables, find the value of sec(51.4)∘.
Answer» Using trigonometric tables, find the value of $s e c (51.4)^{\circ}$ .

Discussion

41.	Is it possible to design a rectangular park of perimeter 80 and area 400 m2? If so find its length and breadth.
Answer» Is it possible to design a rectangular park of perimeter 80 and area 400 $m^{2}$ ? If so find its length and breadth.

Discussion

42.	sin90∘.cos0∘+sin88∘.cos2∘+sin86∘.cos4∘+..........+sin2∘.cos88∘+sin0∘.cos90∘
Answer» $sin 90^{\circ} . cos 0^{\circ} + sin 88^{\circ} . cos 2^{\circ} + sin 86^{\circ} . cos 4^{\circ} + . . . . . . . . . . + sin 2^{\circ} . cos 88^{\circ} + sin 0^{\circ} . cos 90^{\circ}$

Discussion

43.	A right circular cylinder having diameter 12 cm and height 15 cm is full of ice-cream. The ice-cream is to be filled in identical cones of height 12 cm and diameter 6 cm having a hemi-spherical shape on the top. Find the number of cones required.
Answer» A right circular cylinder having diameter 12 cm and height 15 cm is full of ice-cream. The ice-cream is to be filled in identical cones of height 12 cm and diameter 6 cm having a hemi-spherical shape on the top. Find the number of cones required.

Discussion

44.	A quadrilateral ABCD is drawn to circumscribe a circle .If the sum of the length of sides AB + CD = 20 cm then, find the sum of the length of sides AD + BC.
Answer» A quadrilateral ABCD is drawn to circumscribe a circle .If the sum of the length of sides AB + CD = 20 cm then, find the sum of the length of sides AD + BC.

Discussion

45.	Two planes start from a city and fly in opposite directions, one averaging a speed of 40 kmph greater than the second. If they are 3400 km apart from each other in 5 hours, the sum of their average speeds, is
Answer» Two planes start from a city and fly in opposite directions, one averaging a speed of 40 kmph greater than the second. If they are 3400 km apart from each other in 5 hours, the sum of their average speeds, is

Discussion

46.	If three lines are non concurrent and no two of them are parallel, number of circles drawn Touching all the three lines
Answer» If three lines are non concurrent and no two of them are parallel, number of circles drawn Touching all the three lines

Discussion

47.	In fig. 6, find the area of the shaded region, enclosed between two concentric circles of radii 7 cm and 14 cm where ∠AOC=40∘. (Use π=227)
Answer» In fig. 6, find the area of the shaded region, enclosed between two concentric circles of radii 7 cm and 14 cm where $∠ A O C = 40^{\circ}$ . (Use $π = \frac{22}{7}$ )

Discussion

48.	Find the equation of the line passing through the point (-2, 3) and having y – intercept of 5 units.
Answer» Find the equation of the line passing through the point (-2, 3) and having y – intercept of 5 units.

Discussion

49.	Is root3/2 a rational or irrational number.
Answer» Is root3/2 a rational or irrational number.

Discussion

50.	If sin A = 817, find the value of secA cosA + cosecA cosA.
Answer» If sin A = $\frac{8}{17}$ , find the value of secA cosA + cosecA cosA.

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

The sum of first 20 natural numbers is ___

The ratio of area of the triangles ABD and ADC, where AD is the height is:

If the cost of printing a book of 380 pages with 20 lines on each page and on an average 11 words in each line is Rs.19, then the cost of printing a book with 280 pages 22 lines on each page and 10 words in each line is

Question 164(iii) If possible, find a hook-up of prime base number machine that will do the same work as the given stretching machine. Do not use (× 1) machines.

If an equilateral triangle ABC is drawn as shown below with A(0,0) and a side of 4 units then the other two vertices of the triangle are___

For what value of k,the pair of equations 4x-3y=9, 2x+ky=11 has no solution

Find the HCF of 52 and 117 and express it in form 52x + 117y.

State the parts of speech of the underlined words. Air India on Monday announced the addition of a second flight to the India-Sri Lanka sector.

The sum of 1st three terms an AP is 30 and the sum of last three terms is 39.If the 1st term is 9,then find the number of terms in AP

What is the application of probability in real life

Which of the following should be the LAST sentence after rearrangement?

Use Euclid Lemma to show that the cube of any positive integer is of the form 9 m, 9 M + 1 or 9 M + 8

Find the equation of the line passing through the point (2,-5) and making an intercept of -3 on the Y axis.

An AP consists of 37 terms . The sum of the three middle terms is 22 and the sum of the last three terms is 429 . Find the AP

Question 18 The area of a triangle with vertices (a,b+c), (b,c+a) and (c,a+b) is (A) (a+b+c)2 (B) 0 (C) (a+b+c) (D) abc

An oval-shaped meeting table made of wood has dimensions of its top as 10 m and 6 m. Find the cost of polishing it at Rs. 5.75 per sq.m.

In ΔABC,AB=10cm,AC=6cm,∠A=70∘. The length BC is equal to. [cos 70∘=0.34,sin 70∘=0.94]

Simplify:√3+√5

Solve the quadratic equation 2x2+ax−a2=0 for x.

A wire is in the shape of a circle of radius 21 cm. It is bent to form a square. The side of the square is:

The perimeters of two similar triangles are 25 cm and 15 cm respectively. If one side of first triangle is 9 cm, the corresponding side of the other triangle is

If 3rd term of a G.P is 12 and 6th term is 96, then its 7th term will be

The value of 4cot245∘−sec260∘+sin260∘+cos290∘ is

Question 16 If a circle drawn with origin as the centre, passes through (132,0), then the point which does not lie in the interior of the circle is (A) (−34,1) (B) (2,73,) (C) (5,−12) (D) (−6,52)

sin (60o + θ) - cos (30o - θ) is equal to (where (60o + θ) and (30o - θ) are both acute angles):

A boy of height 60 cm is walking away from the base of a building at a speed of 2.2 m/s. If the height of the building is 7.2 m, then find the length of his shadow after 5 seconds.

A contractor plans to install two slides for the children to play in a park. For the children below the age of 5 years, she prefers to have a slide whose top is at a height of 2m and is inclined at an angle of 30∘ to the ground. What should be the length of the slide?

For two different APs, the ratio of the sums of the first n terms is 7n+14n+27. What is the ratio of the mth terms of the two APs? [4 MARKS]

Sum and the product of zeroes of the polynomial x2 +7x +10 is

Find the factors of x2+18x+80 by splitting the middle term.

A company with a share of nominal value of ₹ 150 declares an annual dividend of 15 % . Calculate the annual income of a man who holds 88 shares in the company ?

A conical vessel of radius 6 cm and height 8 cm is completely filled with water. A sphere is lowered into the water and its size is such that when it touches the sides, it is just immersed. What fraction of water overflows?

The linear equation 2x – 5y = x – 2 has

Raghu wants to make a closed aluminium cone for his science project. The slant height and radius of the cone should be 10 cm and 7 cm respectively. The area of the aluminium sheet required to make the cone is_____. (Use π=227)

Using step - deviation method, calculate the mean marks of the following distribution.Class intervalFrequency50−55555−602060−651065−701070−75975−80680−851285−908

The value of the polynomial 5x–4x2+3, when x=−1 is A) −6 B) 6 C) 2 D) −2

The value of the polynomial −5x+3 at x=0 is ______.

Using trigonometric tables, find the value of sec(51.4)∘.

Is it possible to design a rectangular park of perimeter 80 and area 400 m2? If so find its length and breadth.

sin90∘.cos0∘+sin88∘.cos2∘+sin86∘.cos4∘+..........+sin2∘.cos88∘+sin0∘.cos90∘

A right circular cylinder having diameter 12 cm and height 15 cm is full of ice-cream. The ice-cream is to be filled in identical cones of height 12 cm and diameter 6 cm having a hemi-spherical shape on the top. Find the number of cones required.

A quadrilateral ABCD is drawn to circumscribe a circle .If the sum of the length of sides AB + CD = 20 cm then, find the sum of the length of sides AD + BC.

Two planes start from a city and fly in opposite directions, one averaging a speed of 40 kmph greater than the second. If they are 3400 km apart from each other in 5 hours, the sum of their average speeds, is

If three lines are non concurrent and no two of them are parallel, number of circles drawn Touching all the three lines

In fig. 6, find the area of the shaded region, enclosed between two concentric circles of radii 7 cm and 14 cm where ∠AOC=40∘. (Use π=227)

Find the equation of the line passing through the point (-2, 3) and having y – intercept of 5 units.

Is root3/2 a rational or irrational number.

If sin A = 817, find the value of secA cosA + cosecA cosA.