32581 + Interview Questions in Mathematics

1.	There are 2 cubes A and B each of volume X cm3. Cube B is cut into smaller cubes each of volume Y cm3. The surface area and volumes of the resulting cubes are compared S1: The ratio of volumes of A and B = 1:1 S2: The ratio of surface areas of A and B = 1:1
Answer» $T h e r e a r e 2 c u b e s A a n d B e a c h o f v o l u m e X c m^{3}$ . $C u b e B i s c u t i n t o s m a l l e r c u b e s e a c h o f v o l u m e Y c m^{3}$ . $T h e s u r f a c e a r e a a n d v o l u m e s o f t h e r e s u l t i n g c u b e s a r e c o m p a r e d$ S1: The ratio of volumes of A and B = 1:1 S2: The ratio of surface areas of A and B = 1:1

1.

There are 2 cubes A and B each of volume X cm3. Cube B is cut into smaller cubes each of volume Y cm3. The surface area and volumes of the resulting cubes are compared S1: The ratio of volumes of A and B = 1:1 S2: The ratio of surface areas of A and B = 1:1

Answer»

$T h e r e a r e 2 c u b e s A a n d B e a c h o f v o l u m e X c m^{3}$ . $C u b e B i s c u t i n t o s m a l l e r c u b e s e a c h o f v o l u m e Y c m^{3}$ . $T h e s u r f a c e a r e a a n d v o l u m e s o f t h e r e s u l t i n g c u b e s a r e c o m p a r e d$

S1: The ratio of volumes of A and B = 1:1

S2: The ratio of surface areas of A and B = 1:1

2.	Why distance is a scalar quantity but displacement is a vector quantity?
Answer» Why distance is a scalar quantity but displacement is a vector quantity?

3.	If the area of a circle with radius r is equal to the curved surface area of cone with radius r1 and slant height l then the value of r1 in terms of r and l is:
Answer» If the area of a circle with radius $r$ is equal to the curved surface area of cone with radius $r_{1}$ and slant height $l$ then the value of $r_{1}$ in terms of $r$ and $l$ is:

4.	The arithmetic mean and the harmonic mean of two numbers is 10 and 6.4. Then their geometric mean is___
Answer» The arithmetic mean and the harmonic mean of two numbers is 10 and 6.4. Then their geometric mean is___

6.	find the value of k for which the following equation has equal roots (k-12 )x^2+2(k-12)x+2=0
Answer» find the value of k for which the following equation has equal roots (k-12 )x^2+2(k-12)x+2=0

7.	What is the reason behind taking b =3
Answer» What is the reason behind taking b =3

9.	The class interval value of class 30-y is 19. Find the value of 'y'.
Answer» The class interval value of class 30-y is 19. Find the value of 'y'.

10.	The first and last terms of an AP are 1 and 5 respectively and also 5 is the 4th term of the AP. The sum of all terms of this AP is ___.
Answer» The first and last terms of an AP are 1 and 5 respectively and also 5 is the 4th term of the AP. The sum of all terms of this AP is ___.

12.	Q WHEN ANY NATURAL NUMBER IS DIVIDED BY 10 . WHAT IS THE SUM OF ALL POSSIBLE REMINDERS?
Answer» Q WHEN ANY NATURAL NUMBER IS DIVIDED BY 10 . WHAT IS THE SUM OF ALL POSSIBLE REMINDERS?

13.	Find the sum of 28 terms of an A. P. whose nth term is 8n - 5.
Answer» Find the sum of 28 terms of an A. P. whose $n^{t h}$ term is 8n - 5.

14.	The measure of central tendency that is most suitable to find the average male or female height of the region is
Answer» The measure of central tendency that is most suitable to find the average male or female height of the region is

15.	The value of sin120o cos60o + cos120o sin60o is equal to
Answer» The value of sin120^o cos60^o+ cos120^o sin60^ois equal to

18.	Services provided to people are classified and special code numbers are given to them. These codes are called
Answer» Services provided to people are classified and special code numbers are given to them. These codes are called

19.	A conical dome of a palace is supported by a cylindrical pillar, both having the same radius. If the ratio of heights of the cylinder to the cone is 4:3, the ratio of their volumes is ___.
Answer» A conical dome of a palace is supported by a cylindrical pillar, both having the same radius. If the ratio of heights of the cylinder to the cone is 4:3, the ratio of their volumes is ___.

21.	In a fraction, twice the numerator is 2 more than the denominator. If 3 is added to the numerator and denominator , the new fraction is 2\3. Find the original fraction.
Answer» In a fraction, twice the numerator is 2 more than the denominator. If 3 is added to the numerator and denominator , the new fraction is 2\3. Find the original fraction.

17.	The ratio between the base edges of two square pyramids is 1:4. If the heights are also in the same ratio and the volume of the second pyramid is 400 cubic centimetres, what is the volume of the first square pyramid?
Answer» The ratio between the base edges of two square pyramids is 1:4. If the heights are also in the same ratio and the volume of the second pyramid is 400 cubic centimetres, what is the volume of the first square pyramid?

22.	Show that square of an odd integer is of the form 4q+1 for some integer q
Answer» Show that square of an odd integer is of the form 4q+1 for some integer q

23.	The angles of elevation of the top of a tower from two points on the ground at distances a and b metres from the base of the tower and in the same straight line with it are complementary. Prove tht the height of the tower is √ab metre.
Answer» The angles of elevation of the top of a tower from two points on the ground at distances a and b metres from the base of the tower and in the same straight line with it are complementary. Prove tht the height of the tower is $\sqrt{a b}$ metre.

24.	Consider two matrices A and B. (A+B)T = __________
Answer» Consider two matrices A and B. $(A + B)^{T}$ = __________

25.	The length of a diagonal of square is√2(6+2√5)cm. Then find its length of side of square.
Answer» The length of a diagonal of square is√2(6+2√5)cm. Then find its length of side of square.

26.	What can you say about the graph y=x2−12x+40?
Answer» What can you say about the graph $y = x^{2} - 12 x + 40 ?$

27.	ΔABC is an isosceles triangle with AB = AC = 13 cm. The length of altitude from A on BC is 5 cm. Find BC.
Answer» $Δ A B C$ is an isosceles triangle with AB = AC = 13 cm. The length of altitude from A on BC is 5 cm. Find BC.

28.	Which of the following expressions is used to determine the mode?
Answer» Which of the following expressions is used to determine the mode?

29.	Two dice are rolled. Find the probability that the sum of the digits on the upper face is 7.
Answer» Two dice are rolled. Find the probability that the sum of the digits on the upper face is 7.

30.	What is the sub-triplicate ratio of 2197 : 1728?
Answer» What is the sub-triplicate ratio of 2197 : 1728?

Explore topic-wise InterviewSolutions in Current Affairs.

There are 2 cubes A and B each of volume X cm3. Cube B is cut into smaller cubes each of volume Y cm3. The surface area and volumes of the resulting cubes are compared S1: The ratio of volumes of A and B = 1:1 S2: The ratio of surface areas of A and B = 1:1

Why distance is a scalar quantity but displacement is a vector quantity?

If the area of a circle with radius r is equal to the curved surface area of cone with radius r1 and slant height l then the value of r1 in terms of r and l is:

The arithmetic mean and the harmonic mean of two numbers is 10 and 6.4. Then their geometric mean is___

Statements: T V, V # M, M % F Conclusions: a) T # M b) T F

find the value of k for which the following equation has equal roots (k-12 )x^2+2(k-12)x+2=0

What is the reason behind taking b =3

Find the sum of first 10 terms of the A. P. 4 + 6 + 8 + ...............

The class interval value of class 30-y is 19. Find the value of 'y'.

The first and last terms of an AP are 1 and 5 respectively and also 5 is the 4th term of the AP. The sum of all terms of this AP is ___.

Find value of k for infinite Sol for pair of linear equation kx + 3y = 2k + 1 2 ( k + 1)x + 9x = 7k + 1

Q WHEN ANY NATURAL NUMBER IS DIVIDED BY 10 . WHAT IS THE SUM OF ALL POSSIBLE REMINDERS?

Find the sum of 28 terms of an A. P. whose nth term is 8n - 5.

The measure of central tendency that is most suitable to find the average male or female height of the region is

The value of sin120o cos60o + cos120o sin60o is equal to

A (–5, 4), B (–1, –2) C (5, 2) are the vertices of right angled triangle ABC. Find the coordinate of: i) orthocenter ii) circumcentre iii) centroid

The ratio between the base edges of two square pyramids is 1:4. If the heights are also in the same ratio and the volume of the second pyramid is 400 cubic centimetres, what is the volume of the first square pyramid?

Services provided to people are classified and special code numbers are given to them. These codes are called

A conical dome of a palace is supported by a cylindrical pillar, both having the same radius. If the ratio of heights of the cylinder to the cone is 4:3, the ratio of their volumes is ___.

Find the ratio in which origin divides PQ.Ratio being 1 : ____

In a fraction, twice the numerator is 2 more than the denominator. If 3 is added to the numerator and denominator , the new fraction is 2\3. Find the original fraction.

Show that square of an odd integer is of the form 4q+1 for some integer q

The angles of elevation of the top of a tower from two points on the ground at distances a and b metres from the base of the tower and in the same straight line with it are complementary. Prove tht the height of the tower is √ab metre.

Consider two matrices A and B. (A+B)T = __________

The length of a diagonal of square is√2(6+2√5)cm. Then find its length of side of square.

What can you say about the graph y=x2−12x+40?

ΔABC is an isosceles triangle with AB = AC = 13 cm. The length of altitude from A on BC is 5 cm. Find BC.

Which of the following expressions is used to determine the mode?

Two dice are rolled. Find the probability that the sum of the digits on the upper face is 7.

What is the sub-triplicate ratio of 2197 : 1728?

Compute the mode from the following data: Age(in years) 0−55−1010−1515−2020−2525−3030−35Number of patients611182417135

A(-2,-1), B(0,-3), C(1,0) and D(-1,1) are the vertices of quadrilateral ABCD. Then the point of intersection of its diagonals is

In the given figure, ∠AMN=∠MBC=76o. If a, b and c are the lengths of AM, MB and BC respectively then express the length of MN in terms of a, b and c.

Find the roots of the quadratic equations given in Q.1 above by applying the quadratic formula. (iv) 2x2+x+4=0

The equation of a line having a slope of 2 and y-intercept of 6 units is ______.

The first term of an arithmetic sequence is 6 and common difference is 4. Then the algebraic expression for sum of the first 'n' terms its.

If pth,qth and rth term of an AP are a,b,c respectively, then show that (a−b)r+(b−c)p+(c−a)q=0

AD is the median of △ ABC. If area of △ ADB = 22.5 sq cm, then the area of △ADC = ____ sq cm.

Solve the following quadratics x2−x+1=0

‘p’ and ‘q’ are the zeroes of the polynomial ax2+bx+c. The values of a and b are and respectively.

In the given figure, ABCD is a quadrilateral in which AB||DC and P is the midpoint of BC.On producing, AP and DC meet at Q. Prove that (i) AB = CQ, (ii) DQ = DC + AB.

A part of John's salary was cut by the government. What could it have been cut for?

Show that each of the following systems of equations has a unique solution and solve it: 3x+5y=12,5x+3y=4.

Solve each of the following systems of equations by the method of cross-multiplication: x(a−b+aba−b)=y(a+b−aba+b) x+y=2a2

In Fig. 8.62, there are two concetric circles with centre O of radii 5 cm and 3 cm. From an external point P, tangents PA and PB are drawn to these circles. If AP=12 cm, find the length of BP.

The diameter of a coin is 1 cm(Fig). If four such coins be placed on a table so that the rim of each touches that of the other two, find the area of the shaded region. (Take π=3.1416)

In given figure AB is a diameter of a circle. CD is a chord equal to the radius of the circle. AC and BD when extended intersect at a point E. Prove that ∠AEB= 60∘.

If the diameter of a sphere is decreased by 25%, then its curved surface area decreases by:

31.	A person invested 3 times as much money in a scheme giving 5% per annum simple interest than he invested in a scheme giving 2% per annum simple interest. Further, he invested Rs. 6000 more in a scheme giving 3% per annum simple interest than he invested in a scheme giving 2% per annum simple interest. If the total interest from the three investments after a year is Rs. 980, then what is the total amount he invested?
Answer» A person invested 3 times as much money in a scheme giving $5 %$ per annum simple interest than he invested in a scheme giving $2 %$ per annum simple interest. Further, he invested Rs. 6000 more in a scheme giving $3 %$ per annum simple interest than he invested in a scheme giving $2 %$ per annum simple interest. If the total interest from the three investments after a year is Rs. 980, then what is the total amount he invested?

32.	Compute the mode from the following data: Age(in years) 0−55−1010−1515−2020−2525−3030−35Number of patients611182417135
Answer» Compute the mode from the following data: $\begin{matrix} Age(in years) & 0 - 5 & 5 - 10 & 10 - 15 & 15 - 20 & 20 - 25 & 25 - 30 & 30 - 35 Number of patients & 6 & 11 & 18 & 24 & 17 & 13 & 5 \end{matrix}$

33.	A(-2,-1), B(0,-3), C(1,0) and D(-1,1) are the vertices of quadrilateral ABCD. Then the point of intersection of its diagonals is
Answer» A(-2,-1), B(0,-3), C(1,0) and D(-1,1) are the vertices of quadrilateral ABCD. Then the point of intersection of its diagonals is

35.	Find the roots of the quadratic equations given in Q.1 above by applying the quadratic formula. (iv) 2x2+x+4=0
Answer» Find the roots of the quadratic equations given in Q.1 above by applying the quadratic formula. (iv) $2 x^{2} + x + 4 = 0$

36.	The equation of a line having a slope of 2 and y-intercept of 6 units is ______.
Answer» The equation of a line having a slope of 2 and y-intercept of 6 units is ______.

37.	The first term of an arithmetic sequence is 6 and common difference is 4. Then the algebraic expression for sum of the first 'n' terms its.
Answer» The first term of an arithmetic sequence is 6 and common difference is 4. Then the algebraic expression for sum of the first 'n' terms its.

39.	AD is the median of △ ABC. If area of △ ADB = 22.5 sq cm, then the area of △ADC = ____ sq cm.
Answer» AD is the median of △ ABC. If area of △ ADB = 22.5 sq cm, then the area of △ADC = ____ sq cm.

40.	Solve the following quadratics x2−x+1=0
Answer» Solve the following quadratics $x^{2} - x + 1 = 0$

41.	‘p’ and ‘q’ are the zeroes of the polynomial ax2+bx+c. The values of a and b are and respectively.
Answer» ‘p’ and ‘q’ are the zeroes of the polynomial $a x^{2} + b x + c$ . The values of $a$ and $b$ are and respectively.

42.	Alpha Ltd. has 10,000, 8% Debentures of Rs 100 each due for redemption on 31st March 2018. Debenture Redemption Reserve has a balance of Rs 1,90,000 on 31st March,2017. It was decided to invest the required amount towards Debenture Redemption Investment. Investments were realised at 104% less 0.5% brokerage and debentures were redeemed. Record the necessary entries for the redemption of debentures.
Answer» Alpha Ltd. has 10,000, $8 %$ Debentures of Rs 100 each due for redemption on 31st March 2018. Debenture Redemption Reserve has a balance of Rs 1,90,000 on 31st March,2017. It was decided to invest the required amount towards Debenture Redemption Investment. Investments were realised at $104 %$ less $0.5 %$ brokerage and debentures were redeemed. Record the necessary entries for the redemption of debentures.