32581 + Interview Questions in Mathematics

1.	Question 22 Three cubes of metal whose edges are 6 cm, 8 cm and 10 cm respectively are melted to form a single cube. The edge of the new cube is (a) 12 cm (b) 24 cm (c) 18 cm (d) 20 cm
Answer» Question 22 Three cubes of metal whose edges are 6 cm, 8 cm and 10 cm respectively are melted to form a single cube. The edge of the new cube is (a) 12 cm (b) 24 cm (c) 18 cm (d) 20 cm

1.

Question 22 Three cubes of metal whose edges are 6 cm, 8 cm and 10 cm respectively are melted to form a single cube. The edge of the new cube is (a) 12 cm (b) 24 cm (c) 18 cm (d) 20 cm

Answer»

Question 22

Three cubes of metal whose edges are 6 cm, 8 cm and 10 cm respectively are melted to form a single cube. The edge of the new cube is
(a) 12 cm (b) 24 cm (c) 18 cm (d) 20 cm

Discussion

2.	The points A(-1, -2), B(4,3), C(2,5) and D(-3,0) in that order form which structure?
Answer» The points A(-1, -2), B(4,3), C(2,5) and D(-3,0) in that order form which structure?

Discussion

3.	If the sum of first n terms of an A.P. be equal to the sum of its first m terms, (m≠n), then the sum of its first (m+n) terms will be
Answer» If the sum of first n terms of an A.P. be equal to the sum of its first m terms, $(m \neq n)$ , then the sum of its first (m+n) terms will be

Discussion

4.	Find the compounded ratio of the duplicate ratio of 3 : 5, the reciprocal ratio of 4 : 25, and the sub-duplicate ratio of 16 : 81.
Answer» Find the compounded ratio of the duplicate ratio of 3 : 5, the reciprocal ratio of 4 : 25, and the sub-duplicate ratio of 16 : 81.

Discussion

5.	If 12th term of an A.P. is - 13 and the sum of the first four terms is 24, what is the sum of first 10 terms ?
Answer» If 12th term of an A.P. is - 13 and the sum of the first four terms is 24, what is the sum of first 10 terms ?

Discussion

6.	Find ddx[√16−x2]
Answer» Find $\frac{d}{d x} [\sqrt{16 - x^{2}}]$

Discussion

7.	Find the point that divides A(2, 4) and B(6, 8) in the ratio a : 1.
Answer» Find the point that divides A(2, 4) and B(6, 8) in the ratio a : 1.

Discussion

8.	A tractor wheel covers a distance of 9.42 m on its 1 complete rotation. Then the radius of the wheel is . Take π=3.14
Answer» A tractor wheel covers a distance of 9.42 m on its 1 complete rotation. Then the radius of the wheel is . Take $π = 3.14$

Discussion

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

Discussion

10.	Show that exactly one of the numbers n,n+2 or n+4 is divisible by 3
Answer» Show that exactly one of the numbers n,n+2 or n+4 is divisible by 3

Discussion

11.	If a1, a2, a3, .... is an A.P. such that a1+ a5 + a10 + a15 + a20 + a24 = 225 then a1 + a2 + a3 + ... + a23 + a24 is equal to
Answer» If $a_{1}$ , $a_{2}$ , $a_{3}$ , .... is an A.P. such that $a_{1}$ + $a_{5}$ + $a_{10}$ + $a_{15}$ + $a_{20}$ + $a_{24}$ = 225 then $a_{1}$ + $a_{2}$ + $a_{3}$ + ... + $a_{23}$ + $a_{24}$ is equal to

Discussion

12.	△PQR, right-angled at Q, if PR = 24cm, QR = 12cm, then find the value of ∠QRP.
Answer» $△ P Q R$ , right-angled at Q, if PR = 24cm, QR = 12cm, then find the value of $∠ Q R P$ .

12.

△PQR, right-angled at Q, if PR = 24cm, QR = 12cm, then find the value of ∠QRP.

Answer»

$△ P Q R$ , right-angled at Q, if PR = 24cm, QR = 12cm, then find the value of $∠ Q R P$ .

Discussion

13.	Ratio of present age of mother and daughter is 8:3 years five yers after ratio of their ages will be 9:3 find their present age
Answer» Ratio of present age of mother and daughter is 8:3 years five yers after ratio of their ages will be 9:3 find their present age

Discussion

14.	SIMPLY : Sin48 Sec42 + Cos48 Cosec42
Answer» SIMPLY : Sin48 Sec42 + Cos48 Cosec42

Discussion

15.	If sin theta +cos theta= root 2 Evaluate. Tan theta +cot theta
Answer» If sin theta +cos theta= root 2 Evaluate. Tan theta +cot theta

15.

If sin theta +cos theta= root 2 Evaluate. Tan theta +cot theta

Answer»

If sin theta +cos theta= root 2

Evaluate. Tan theta +cot theta

Discussion

16.	The condition that one root of ax2 + bx + c = 0 is m times the other is :
Answer» The condition that one root of ax² + bx + c = 0 is m times the other is :

Discussion

17.	Show that only one out of n,n+3,n+6,n+9 is divisible by four
Answer» Show that only one out of n,n+3,n+6,n+9 is divisible by four

Discussion

18.	Find the value of the trigonometric functions of cot (−15π4).
Answer» Find the value of the trigonometric functions of cot $(\frac{- 15 π}{4})$ .

Discussion

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

Discussion

20.	Sum of the digits of a two digit number is 9 . When we interchange the digits, it is found that the resulting new number is greater than the original number by 27 . What is the two digit number ?
Answer» Sum of the digits of a two digit number is 9 . When we interchange the digits, it is found that the resulting new number is greater than the original number by 27 . What is the two digit number ?

Discussion

21.	In a ΔABC, line CD is perpendicular to AB. ∠CAD=45∘ and AB =20 cm. The area of triangle ABC is 40cm2. The length of AC will be equal to
Answer» In a $Δ A B C$ , line CD is perpendicular to AB. $∠ C A D = 45^{\circ}$ and AB =20 cm. The area of triangle ABC is $40 c m^{2}$ . The length of AC will be equal to

Discussion

22.	The remainder when polynomial x3−ax2+6x−a is divided by (x−1) is
Answer» The remainder when polynomial $x^{3} - a x^{2} + 6 x - a$ is divided by $(x - 1)$ is

Discussion

23.	A spherical steel ball is melted to make 8 new identical balls. Then the radius of each new ball is how many times the radius of the original ball?
Answer» A spherical steel ball is melted to make 8 new identical balls. Then the radius of each new ball is how many times the radius of the original ball?

Discussion

24.	If x = 2 is a root of equation x2 + 3x - k = 0 then value of k is
Answer» If x = 2 is a root of equation x² + 3x - k = 0 then value of k is

Discussion

25.	In ∆ABC X is middle point of AC.if XYparallel to AB then prove that Y is middle point of AB
Answer» In ∆ABC X is middle point of AC.if XYparallel to AB then prove that Y is middle point of AB

Discussion

26.	A man buys 400, twenty-rupee shares at a discount of 20% and receives a return of 12% and receives a return of 12% on his money. Calculate : (i) the amount invested by him. (ii) the rate of dividend paid by the company.
Answer» A man buys 400, twenty-rupee shares at a discount of 20% and receives a return of 12% and receives a return of 12% on his money. Calculate : (i) the amount invested by him. (ii) the rate of dividend paid by the company.

26.

A man buys 400, twenty-rupee shares at a discount of 20% and receives a return of 12% and receives a return of 12% on his money. Calculate : (i) the amount invested by him. (ii) the rate of dividend paid by the company.

Answer»

A man buys 400, twenty-rupee shares at a discount of 20% and receives a return of 12% and receives a return of 12% on his money. Calculate :

(i) the amount invested by him.

(ii) the rate of dividend paid by the company.

Discussion

27.	Point A (3, 1) and B (-1,-3) are two vertices of an isosceles Δ ABC with BC = AC. If C is the third vertex and has a y coordinate of 6, what is the x-coordinate of C?
Answer» Point A (3, 1) and B (-1,-3) are two vertices of an isosceles $Δ$ ABC with BC = AC. If C is the third vertex and has a y coordinate of 6, what is the x-coordinate of C?

Discussion

28.	Find the value of k if 8k + 4 = 6k - 2 = 2 k - 7 are three consecutive terms of an AP.
Answer» Find the value of k if 8k + 4 = 6k - 2 = 2 k - 7 are three consecutive terms of an AP.

Discussion

29.	Vivek invests Rs 4,500 in 8% , Rs 10 shares at Rs 15. He sells the shares when the price rises to Rs 30, and invests the proceeds in 12% Rs 100 shares at Rs 125. Calculate : (i) the sale proceeds (ii) the number of Rs 125 shares he buys. (iii) the change in his annual income from dividend.
Answer» Vivek invests Rs 4,500 in 8% , Rs 10 shares at Rs 15. He sells the shares when the price rises to Rs 30, and invests the proceeds in 12% Rs 100 shares at Rs 125. Calculate : (i) the sale proceeds (ii) the number of Rs 125 shares he buys. (iii) the change in his annual income from dividend.

29.

Vivek invests Rs 4,500 in 8% , Rs 10 shares at Rs 15. He sells the shares when the price rises to Rs 30, and invests the proceeds in 12% Rs 100 shares at Rs 125. Calculate : (i) the sale proceeds (ii) the number of Rs 125 shares he buys. (iii) the change in his annual income from dividend.

Answer»

Vivek invests Rs 4,500 in 8% , Rs 10 shares at Rs 15. He sells the shares when the price rises to Rs 30, and invests the proceeds in 12% Rs 100 shares at Rs 125. Calculate :

(i) the sale proceeds

(ii) the number of Rs 125 shares he buys.

(iii) the change in his annual income from dividend.

Discussion

30.	The area of the triangle formed by the line x/a+y/b=1 with the coordinate axes is
Answer» The area of the triangle formed by the line x/a+y/b=1 with the coordinate axes is

Discussion

31.	A solid toy is in the form of a right circular cylinder with a hemispherical shape at one end and a cone at the other end. Their common diameter is 4.2 cm and the heights of the cylindrical and conical portions are 12 cm and 7 cm respectively. The approximate volume of the toy will be
Answer» A solid toy is in the form of a right circular cylinder with a hemispherical shape at one end and a cone at the other end. Their common diameter is $4.2 c m$ and the heights of the cylindrical and conical portions are $12 c m$ and $7 c m$ respectively. The approximate volume of the toy will be

Discussion

32.	From the following frequency distribution, find the median class: Cost of living index1400−15501550−17001700−18501850−2000Number of weeks815218
Answer» From the following frequency distribution, find the median class: $\begin{matrix} Cost of living index & 1400 - 1550 & 1550 - 1700 & 1700 - 1850 & 1850 - 2000 Number of weeks & 8 & 15 & 21 & 8 \end{matrix}$

Discussion

33.	Question 2(i) Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial: t2−3,2t4+3t32t2−9t−12
Answer» Question 2(i) Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial: $t^{2} - 3, 2 t^{4} + 3 t^{3} 2 t^{2} - 9 t - 12$

Discussion

34.	Find whether the following pair of linear equations is consistent or inconsistent: 3x+2y=8 6x−4y=9
Answer» Find whether the following pair of linear equations is consistent or inconsistent: $3 x + 2 y = 8$ $6 x - 4 y = 9$

Discussion

35.	If ΔABC and ΔPQR are two similar triangles shown in the figure. AM and PN are the medians on ΔABC and ΔPQR respectively. The ratio of areas of ΔABC and ΔPQR is 9:25. If AM = PO = 5 cm. Find the value of 3(ON) in cm ___
Answer» If $Δ$ ABC and $Δ$ PQR are two similar triangles shown in the figure. AM and PN are the medians on $Δ$ ABC and $Δ$ PQR respectively. The ratio of areas of $Δ$ ABC and $Δ$ PQR is 9:25. If AM = PO = 5 cm. Find the value of 3(ON) in cm ___

Discussion

36.	The mode and mean are 26.6 and 28.1 respectively in an asymmetrical distribution. Find out the value of median.
Answer» The mode and mean are 26.6 and 28.1 respectively in an asymmetrical distribution. Find out the value of median.

Discussion

37.	Find the middle term of the AP 6,13,20,......,216
Answer» Find the middle term of the AP 6,13,20,......,216

Discussion

38.	If the numerator of a fraction is increased by 2 and denominator is decreased by 1, it becomes 23. If the numerator is increased by 1 and denominator is increased by 2, it becomes 13. Find the fraction.
Answer» If the numerator of a fraction is increased by 2 and denominator is decreased by 1, it becomes $\frac{2}{3}$ . If the numerator is increased by 1 and denominator is increased by 2, it becomes $\frac{1}{3}$ . Find the fraction.

Discussion

39.	In the given figure, PQ is a chord of length 8 cm of a circle with centre O and radius 5 cm. If the tangents to the circle at the points P and Q intersect at 'T', then the length of PT is
Answer» In the given figure, PQ is a chord of length 8 cm of a circle with centre O and radius 5 cm. If the tangents to the circle at the points P and Q intersect at 'T', then the length of PT is

Discussion

40.	Find the mean of the following distribution: Class intervalFrequency0−101010−20620−30830−401240−505 [4 MARKS]
Answer» Find the mean of the following distribution: $\begin{matrix} C l a s s i n t e r v a l & F r e q u e n c y 0 - 10 & 10 10 - 20 & 6 20 - 30 & 8 30 - 40 & 12 40 - 50 & 5 \end{matrix}$ [4 MARKS]

Discussion

41.	The image of a point A(2, 4) that is reflected in the x-axis (Mx), then in the y-axis (My) and finally in the origin is _____
Answer» The image of a point A(2, 4) that is reflected in the x-axis $(M_{x})$ , then in the y-axis $(M_{y})$ and finally in the origin is _____

Discussion

42.	One hundred people line up to board an airplane that can accommodate 100 passengers. Each has a boarding pass with assigned seat. However, the first person to board has lost his boarding pass and takes a random seat. After that, each person takes the assigned seat. What is the probability that the last person to board gets his assigned seat unoccupied?
Answer» One hundred people line up to board an airplane that can accommodate 100 passengers. Each has a boarding pass with assigned seat. However, the first person to board has lost his boarding pass and takes a random seat. After that, each person takes the assigned seat. What is the probability that the last person to board gets his assigned seat unoccupied?

Discussion

43.	The number of solid of solid spheres, each of diameter 6cm that can be made by melting a solid metal cylinder of height 45 cm and diameter 4 cm is:
Answer» The number of solid of solid spheres, each of diameter 6cm that can be made by melting a solid metal cylinder of height 45 cm and diameter 4 cm is:

Discussion

44.	A big triangular field is divided into two parts as shown in the figure below. What is the area of smaller triangular field ? Given- AB = 8 m, AC = 10 m, DE = 3 m, ∠ABC = ∠AED = 90∘
Answer» A big triangular field is divided into two parts as shown in the figure below. What is the area of smaller triangular field ? Given- AB = 8 m, AC = 10 m, DE = 3 m, $∠ A B C$ = $∠ A E D$ = $90^{\circ}$

44.

A big triangular field is divided into two parts as shown in the figure below. What is the area of smaller triangular field ? Given- AB = 8 m, AC = 10 m, DE = 3 m, ∠ABC = ∠AED = 90∘

Answer»

A big triangular field is divided into two parts as shown in the figure below. What is the area of smaller triangular field ?

Given- AB = 8 m, AC = 10 m, DE = 3 m, $∠ A B C$ = $∠ A E D$ = $90^{\circ}$

Discussion

45.	The equation of the circle having (−2,−1) and (2,1) as the endpoints of its diameter is
Answer» The equation of the circle having $(- 2, - 1)$ and $(2, 1)$ as the endpoints of its diameter is

Discussion

46.	If the points (k,2−2k),(1−k,2k) and (−k−4,6−2k) are collinear, possible values of k are
Answer» If the points $(k, 2 - 2 k), (1 - k, 2 k)$ and $(- k - 4, 6 - 2 k)$ are collinear, possible values of $k$ are

Discussion

47.	Cards, each marked with one of the numbers 6, 7, 8, ..., 15, are placed in a box and mixed thoroughly. ONe card is drawn at random from the box. What is the probability of gettinga card with number less than 10 ? (a) 35 (b) 13 (c) 12 (d) 25
Answer» Cards, each marked with one of the numbers 6, 7, 8, ..., 15, are placed in a box and mixed thoroughly. ONe card is drawn at random from the box. What is the probability of gettinga card with number less than 10 ? (a) $\frac{3}{5}$ (b) $\frac{1}{3}$ (c) $\frac{1}{2}$ (d) $\frac{2}{5}$

Discussion

48.	In the given figure, two concentric circles with centre O have radii 21 cm and 42 cm. If ∠AOB = 60 ∘, find the area of the shaded region. [ Use π = \frac{22}{7}.]
Answer» In the given figure, two concentric circles with centre O have radii 21 cm and 42 cm. If $∠$ AOB = 60 $^{\circ}$ , find the area of the shaded region. [ Use $π$ = \frac{22}{7}.]

48.

In the given figure, two concentric circles with centre O have radii 21 cm and 42 cm. If ∠AOB = 60 ∘, find the area of the shaded region. [ Use π = \frac{22}{7}.]

Answer»

In the given figure, two concentric circles with centre O have radii 21 cm and 42 cm. If $∠$ AOB = 60 $^{\circ}$ , find the area of the shaded region. [ Use $π$ = \frac{22}{7}.]

Discussion

49.	A 1.5m tall boy is standing at some distance from a 30m tall building. The angle of elevation from his eyes to the top of the building increases from 30∘ and 60∘ as he walks towards the building. Find the distance he walked towards the building.
Answer» A $1.5 m$ tall boy is standing at some distance from a $30 m$ tall building. The angle of elevation from his eyes to the top of the building increases from $30^{\circ} a n d 60^{\circ}$ as he walks towards the building. Find the distance he walked towards the building.

Discussion

50.	By what number should 1365 be divided to get 31 as quotient and 32 a remainder ?
Answer» By what number should 1365 be divided to get 31 as quotient and 32 a remainder ?

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Question 22 Three cubes of metal whose edges are 6 cm, 8 cm and 10 cm respectively are melted to form a single cube. The edge of the new cube is (a) 12 cm (b) 24 cm (c) 18 cm (d) 20 cm

The points A(-1, -2), B(4,3), C(2,5) and D(-3,0) in that order form which structure?

If the sum of first n terms of an A.P. be equal to the sum of its first m terms, (m≠n), then the sum of its first (m+n) terms will be

Find the compounded ratio of the duplicate ratio of 3 : 5, the reciprocal ratio of 4 : 25, and the sub-duplicate ratio of 16 : 81.

If 12th term of an A.P. is - 13 and the sum of the first four terms is 24, what is the sum of first 10 terms ?

Find ddx[√16−x2]

Find the point that divides A(2, 4) and B(6, 8) in the ratio a : 1.

A tractor wheel covers a distance of 9.42 m on its 1 complete rotation. Then the radius of the wheel is . Take π=3.14

What is the remainder when x2+3x+2 is divided by x-1 ?

Show that exactly one of the numbers n,n+2 or n+4 is divisible by 3

If a1, a2, a3, .... is an A.P. such that a1+ a5 + a10 + a15 + a20 + a24 = 225 then a1 + a2 + a3 + ... + a23 + a24 is equal to

△PQR, right-angled at Q, if PR = 24cm, QR = 12cm, then find the value of ∠QRP.

Ratio of present age of mother and daughter is 8:3 years five yers after ratio of their ages will be 9:3 find their present age

SIMPLY : Sin48 Sec42 + Cos48 Cosec42

If sin theta +cos theta= root 2 Evaluate. Tan theta +cot theta

The condition that one root of ax2 + bx + c = 0 is m times the other is :

Show that only one out of n,n+3,n+6,n+9 is divisible by four

Find the value of the trigonometric functions of cot (−15π4).

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

Sum of the digits of a two digit number is 9 . When we interchange the digits, it is found that the resulting new number is greater than the original number by 27 . What is the two digit number ?

In a ΔABC, line CD is perpendicular to AB. ∠CAD=45∘ and AB =20 cm. The area of triangle ABC is 40cm2. The length of AC will be equal to

The remainder when polynomial x3−ax2+6x−a is divided by (x−1) is

A spherical steel ball is melted to make 8 new identical balls. Then the radius of each new ball is how many times the radius of the original ball?

If x = 2 is a root of equation x2 + 3x - k = 0 then value of k is

In ∆ABC X is middle point of AC.if XYparallel to AB then prove that Y is middle point of AB

A man buys 400, twenty-rupee shares at a discount of 20% and receives a return of 12% and receives a return of 12% on his money. Calculate : (i) the amount invested by him. (ii) the rate of dividend paid by the company.

Point A (3, 1) and B (-1,-3) are two vertices of an isosceles Δ ABC with BC = AC. If C is the third vertex and has a y coordinate of 6, what is the x-coordinate of C?

Find the value of k if 8k + 4 = 6k - 2 = 2 k - 7 are three consecutive terms of an AP.

Vivek invests Rs 4,500 in 8% , Rs 10 shares at Rs 15. He sells the shares when the price rises to Rs 30, and invests the proceeds in 12% Rs 100 shares at Rs 125. Calculate : (i) the sale proceeds (ii) the number of Rs 125 shares he buys. (iii) the change in his annual income from dividend.

The area of the triangle formed by the line x/a+y/b=1 with the coordinate axes is

A solid toy is in the form of a right circular cylinder with a hemispherical shape at one end and a cone at the other end. Their common diameter is 4.2 cm and the heights of the cylindrical and conical portions are 12 cm and 7 cm respectively. The approximate volume of the toy will be

From the following frequency distribution, find the median class: Cost of living index1400−15501550−17001700−18501850−2000Number of weeks815218

Question 2(i) Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial: t2−3,2t4+3t32t2−9t−12

Find whether the following pair of linear equations is consistent or inconsistent: 3x+2y=8 6x−4y=9

If ΔABC and ΔPQR are two similar triangles shown in the figure. AM and PN are the medians on ΔABC and ΔPQR respectively. The ratio of areas of ΔABC and ΔPQR is 9:25. If AM = PO = 5 cm. Find the value of 3(ON) in cm ___

The mode and mean are 26.6 and 28.1 respectively in an asymmetrical distribution. Find out the value of median.

Find the middle term of the AP 6,13,20,......,216

If the numerator of a fraction is increased by 2 and denominator is decreased by 1, it becomes 23. If the numerator is increased by 1 and denominator is increased by 2, it becomes 13. Find the fraction.

In the given figure, PQ is a chord of length 8 cm of a circle with centre O and radius 5 cm. If the tangents to the circle at the points P and Q intersect at 'T', then the length of PT is

Find the mean of the following distribution: Class intervalFrequency0−101010−20620−30830−401240−505 [4 MARKS]

The image of a point A(2, 4) that is reflected in the x-axis (Mx), then in the y-axis (My) and finally in the origin is _____

The number of solid of solid spheres, each of diameter 6cm that can be made by melting a solid metal cylinder of height 45 cm and diameter 4 cm is:

A big triangular field is divided into two parts as shown in the figure below. What is the area of smaller triangular field ? Given- AB = 8 m, AC = 10 m, DE = 3 m, ∠ABC = ∠AED = 90∘

The equation of the circle having (−2,−1) and (2,1) as the endpoints of its diameter is

If the points (k,2−2k),(1−k,2k) and (−k−4,6−2k) are collinear, possible values of k are

Cards, each marked with one of the numbers 6, 7, 8, ..., 15, are placed in a box and mixed thoroughly. ONe card is drawn at random from the box. What is the probability of gettinga card with number less than 10 ? (a) 35 (b) 13 (c) 12 (d) 25

In the given figure, two concentric circles with centre O have radii 21 cm and 42 cm. If ∠AOB = 60 ∘, find the area of the shaded region. [ Use π = \frac{22}{7}.]

A 1.5m tall boy is standing at some distance from a 30m tall building. The angle of elevation from his eyes to the top of the building increases from 30∘ and 60∘ as he walks towards the building. Find the distance he walked towards the building.

By what number should 1365 be divided to get 31 as quotient and 32 a remainder ?