32581 + Interview Questions in Mathematics

1.	What is the quotient(q) and the remainder(r) when -12 is divided by 5?
Answer» What is the quotient( $q$ ) and the remainder( $r$ ) when -12 is divided by 5?

Discussion

2.	ABCDEF is a regular hexagon with centre O (Fig). If the area of triangle OAB is 9 cm2. Find the area of (i) the hexagon and (ii) the circle in which the hexagon is inscribed.
Answer» ABCDEF is a regular hexagon with centre O (Fig). If the area of triangle OAB is $9 c m^{2}$ . Find the area of (i) the hexagon and (ii) the circle in which the hexagon is inscribed.

2.

ABCDEF is a regular hexagon with centre O (Fig). If the area of triangle OAB is 9 cm2. Find the area of (i) the hexagon and (ii) the circle in which the hexagon is inscribed.

Answer»

ABCDEF is a regular hexagon with centre O (Fig). If the area of triangle OAB is $9 c m^{2}$ . Find the area of (i) the hexagon and (ii) the circle in which the hexagon is inscribed.

Discussion

3.	The set of values of k for which the system of equations x + y + z = 2, 2x + y - z = 3, 3x +2 y + kz = 4 has a unique solution, is _________.
Answer» The set of values of k for which the system of equations x + y + z = 2, 2x + y - z = 3, 3x +2 y + kz = 4 has a unique solution, is _________.

Discussion

4.	When two triangles are similar, their corresponding sides are ___.
Answer» When two triangles are similar, their corresponding sides are ___.

Discussion

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

Discussion

6.	The radii of the circular ends of a frustum of height 6 cm are 14 cm and 6 cm, respectively. Find the slant height of the frustum.
Answer» The radii of the circular ends of a frustum of height 6 cm are 14 cm and 6 cm, respectively. Find the slant height of the frustum.

Discussion

7.	A train travels a distance of 480 km at a uniform speed. If the speed had been 8 km/h less, then it would have taken 3 hours more to cover the same distance. We need to find the speed of the train.
Answer» A train travels a distance of $480 k m$ at a uniform speed. If the speed had been $8 k m / h$ less, then it would have taken $3$ hours more to cover the same distance. We need to find the speed of the train.

Discussion

8.	Find the areas(in cm2) of shaded regions. [Take π=227]
Answer» Find the areas(in $c m^{2}$ ) of shaded regions. [Take $π = \frac{22}{7}$ ]

Discussion

9.	A chord 10 cm long is drawn in a circle whose radius is 52 cm. Find area of both the segments.
Answer» A chord 10 cm long is drawn in a circle whose radius is 5 $\sqrt{2}$ cm. Find area of both the segments.

Discussion

10.	Show that height of the cylinder ofgreatest volume which can be inscribed in a right circular cone ofheight h and semi vertical angle αis one-third that of the cone and the greatest volume of cylinderistan2α.
Answer» Show that height of the cylinder of greatest volume which can be inscribed in a right circular cone of height h and semi vertical angle α is one-third that of the cone and the greatest volume of cylinder istan²α.

Discussion

11.	3x-ky=8 passes through (4,4) , find k
Answer» 3x-ky=8 passes through (4,4) , find k

Discussion

12.	Construct a 3×3 matrix whose elements aij are given by aij=0 if i<j and aij=i+j if i≥j.
Answer» Construct a $3 \times 3$ matrix whose elements $a_{i j}$ are given by $a_{i j} = 0$ if $i < j$ and $a_{i j} = i + j$ if $i \geq j$ .

Discussion

13.	if the four term of G.P. is 4 then find the product of first five term
Answer» if the four term of G.P. is 4 then find the product of first five term

Discussion

14.	Question 8A spherical glass vessel has a cylindrical neck 8 cm long, 2 cm in diameter; the diameter of the spherical part is 8.5 cm. By measuring the amount of water it holds, a child finds its volume to be 345 cm3. Check whether she is correct, taking the above as the inside measurements, and π=3.14.
Answer» Question 8 A spherical glass vessel has a cylindrical neck 8 cm long, 2 cm in diameter; the diameter of the spherical part is 8.5 cm. By measuring the amount of water it holds, a child finds its volume to be 345 $c m^{3}$ . Check whether she is correct, taking the above as the inside measurements, and $π = 3.14$ .

Discussion

15.	Is the product of two irrationals always irrational? Justify your answer.
Answer» Is the product of two irrationals always irrational? Justify your answer.

Discussion

16.	Manish opens a Recurring Deposit Account with the Bank of Rajasthan and deposits ₹600 per month for 20 months. Calculate the maturity value of this account, if the bank pays interest at the rate of 10% per annum.
Answer» Manish opens a Recurring Deposit Account with the Bank of Rajasthan and deposits ₹600 per month for 20 months. Calculate the maturity value of this account, if the bank pays interest at the rate of 10% per annum.

Discussion

17.	A bridge across a valley is 800 metres long. There is a temple in the valley directlybelow the bridge. The angle of depression of the top of the temple from the twoends of the bridge have measure 30 and 60.Find the height of the bridge above the top of the temple.3
Answer» A bridge across a valley is 800 metres long. There is a temple in the valley directlybelow the bridge. The angle of depression of the top of the temple from the twoends of the bridge have measure 30 and 60.Find the height of the bridge above the top of the temple.3

Discussion

18.	Construct an isosceles triangle in which the lengths of each of its equal sides is 6.5 cm and the angle between them is 110∘.
Answer» Construct an isosceles triangle in which the lengths of each of its equal sides is 6.5 cm and the angle between them is $110^{\circ}$ .

Discussion

19.	26. The height of a tower is 15 m. What is the lenght of its shadow on the ground, when angle of elevation of the Sun is 60 degree?
Answer» 26. The height of a tower is 15 m. What is the lenght of its shadow on the ground, when angle of elevation of the Sun is 60 degree?

Discussion

20.	In the figure, O is the center of the circle, PQ is tangent to the circle at A. If ∠PAB=58∘, find ∠ABQ and ∠AQB. [2 MARKS]
Answer» In the figure, O is the center of the circle, PQ is tangent to the circle at A. If $∠ P A B = 58^{\circ}$ , find $∠ A B Q$ and $∠ A Q B$ . [2 MARKS]

20.

In the figure, O is the center of the circle, PQ is tangent to the circle at A. If ∠PAB=58∘, find ∠ABQ and ∠AQB. [2 MARKS]

Answer»

In the figure, O is the center of the circle, PQ is tangent to the circle at A. If $∠ P A B = 58^{\circ}$ , find $∠ A B Q$ and $∠ A Q B$ . [2 MARKS]

Discussion

21.	Question 116 State whether the statements are True or False. Every trapezium is a rectangle.
Answer» Question 116 State whether the statements are True or False. Every trapezium is a rectangle.

Discussion

22.	Find the number of pairs having 16 as their HCF and 136 as their LCM
Answer» Find the number of pairs having 16 as their HCF and 136 as their LCM

Discussion

23.	17.A bag has 3 red and 7 black balls. 2 balls are drawn at random without replacement. If 2nd selection is given to be red, what is the probability that 1st is also red,.
Answer» 17.A bag has 3 red and 7 black balls. 2 balls are drawn at random without replacement. If 2nd selection is given to be red, what is the probability that 1st is also red,.

Discussion

24.	The next term in the series 81, 54, 36, 24, ..... is.
Answer» The next term in the series 81, 54, 36, 24, ..... is.

Discussion

25.	ntIf y=3[x]+5 and y=2[x-1]+9 then [x+y]isn
Answer» ntIf y=3[x]+5 and y=2[x-1]+9 then [x+y]isn

Discussion

26.	One third of a bamboo pole is burried in mud ,one sixth of it is in water and the part above the water is greater than or equal to 3 metre. Find the length of shortest pole.
Answer» One third of a bamboo pole is burried in mud ,one sixth of it is in water and the part above the water is greater than or equal to 3 metre. Find the length of shortest pole.

Discussion

27.	If the angles of elevation of a tower from two points distant a and b (a>b) from its foot and in the same straight line from it are 30° and 60°, then the height of the tower is(a) a+b(b) ab(c) a-b(d) ab
Answer» If the angles of elevation of a tower from two points distant a and b (a>b) from its foot and in the same straight line from it are 30° and 60°, then the height of the tower is (a) $\sqrt{a + b}$ (b) $\sqrt{a b}$ (c) $\sqrt{a - b}$ (d) $\sqrt{\frac{a}{b}}$

Discussion

28.	A company declares 8 percent dividend to the share holders. If a man receives Rs 2,840 as his dividend, find the nominal value of his shares.
Answer» A company declares 8 percent dividend to the share holders. If a man receives Rs 2,840 as his dividend, find the nominal value of his shares.

Discussion

29.	The product of digits of a two-digit number is 12. If the number is 36 more than the number obtained by reversing its digits, then the original number is
Answer» The product of digits of a two-digit number is 12. If the number is 36 more than the number obtained by reversing its digits, then the original number is

Discussion

30.	Solve the following quadratic equations by factorization:x-12x+1+2x+1x-1=52, x≠-12, 1
Answer» Solve the following quadratic equations by factorization: $\frac{x - 1}{2 x + 1} + \frac{2 x + 1}{x - 1} = \frac{5}{2}, x \neq - \frac{1}{2}, 1$

Discussion

31.	If 4x+5y=23 passes through the point (2,a), the value of a is ___
Answer» If $4 x + 5 y = 23$ passes through the point $(2, a)$ , the value of $a$ is ___

Discussion

32.	If for an A.P. a5=a10=5×a, then a15 is....
Answer» If for an A.P. $a_{5} = a_{10} = 5 \times a$ , then $a_{15}$ is....

Discussion

33.	3. if P+3Q+5R+15S= 1/1+3+5,then the value of P is what?
Answer» 3. if P+3Q+5R+15S= 1/1+3+5,then the value of P is what?

Discussion

34.	The value of sin18∘cos72∘ is ______.
Answer» The value of $\frac{s i n 18^{\circ}}{c o s 72^{\circ}}$ is ______.

Discussion

35.	the sum of the numerator the denominator ofa fraction is 4 more than twice the numerator if 3 is added to each of the numerator and denominator their ratio becomes 2:3. find the fraction
Answer» the sum of the numerator the denominator ofa fraction is 4 more than twice the numerator if 3 is added to each of the numerator and denominator their ratio becomes 2:3. find the fraction

Discussion

36.	The sum of a 2 digit number and the number formed by interchanging the digit is 110.If 10 is subtracted from the first ,the new number is 4 more than 5 times the sum of the digits in the first number .Find the first number
Answer» The sum of a 2 digit number and the number formed by interchanging the digit is 110.If 10 is subtracted from the first ,the new number is 4 more than 5 times the sum of the digits in the first number .Find the first number

Discussion

37.	In the given figure, ABC is a triangle in which ∠ABC < 90° and AD ⊥ BC. Prove that AC2 = AB2 + BC2 − 2BC.BD.
Answer» In the given figure, ABC is a triangle in which ∠ABC < 90° and AD ⊥ BC. Prove that AC² = AB² + BC² − 2BC.BD.

37.

In the given figure, ABC is a triangle in which ∠ABC < 90° and AD ⊥ BC. Prove that AC2 = AB2 + BC2 − 2BC.BD.

Answer»

In the given figure, ABC is a triangle in which ∠ABC < 90° and AD ⊥ BC. Prove that AC² = AB² + BC² − 2BC.BD.

Discussion

38.	If we make the graph of y = root(1-x) , then will its domain contain 0 and 1 ??
Answer» If we make the graph of y = root(1-x) , then will its domain contain 0 and 1 ??

Discussion

39.	The midpoints of AB, BC, CA of a AABC are (6, -1). (4, -3), (2, -5) respectively. The centroid of tr. ABC is
Answer» The midpoints of AB, BC, CA of a AABC are (6, -1). (4, -3), (2, -5) respectively. The centroid of tr. ABC is

Discussion

40.	If y=(2x^3)(2x^-3+1)then dy/dx at x=1
Answer» If y=(2x^3)(2x^-3+1)then dy/dx at x=1

Discussion

41.	Question 28(i)The king, queen and jack of clubs are removed from a deck of 52 playing cards and then well shuffled. Now, one card is drawn at random from the remaining cards. Determine the probability that the card is a heart
Answer» Question 28(i) The king, queen and jack of clubs are removed from a deck of 52 playing cards and then well shuffled. Now, one card is drawn at random from the remaining cards. Determine the probability that the card is a heart

Discussion

42.	prove that inA-cosA+1÷sinA+cosA-1=1÷secA-tanA using identity sec2A = 1+tan2A
Answer» prove that inA-cosA+1÷sinA+cosA-1=1÷secA-tanA using identity sec2A = 1+tan2A

Discussion

43.	When the vapor of 22.4 liters of water is condensed, on NTP, how much volume of water is obtained
Answer» When the vapor of 22.4 liters of water is condensed, on NTP, how much volume of water is obtained

Discussion

44.	In the given figure, if ∠BCA=∠RPQ=15∘, then ∠PQR is
Answer» In the given figure, if $∠ B C A = ∠ R P Q = 15^{\circ}$ , then $∠ P Q R$ is

44.

In the given figure, if ∠BCA=∠RPQ=15∘, then ∠PQR is

Answer»

In the given figure, if $∠ B C A = ∠ R P Q = 15^{\circ}$ ,
then $∠ P Q R$ is

Discussion

45.	Two chords AB and CD intersect at point O inside the circle. If OA = 5 cm, OB = 6 cm and OC = 3 cm, then find the value of CD.
Answer» Two chords AB and CD intersect at point O inside the circle. If OA = 5 cm, OB = 6 cm and OC = 3 cm, then find the value of CD.

Discussion

46.	if the equation kx^2+2kx+6=0 has equal roots then find the value of k.
Answer» if the equation kx^2+2kx+6=0 has equal roots then find the value of k.

Discussion

47.	A two digit number is 4 more than 6 times the sum of its digits. If 18 is subtracted from the number the digits are reversed. Find the numbers
Answer» A two digit number is 4 more than 6 times the sum of its digits. If 18 is subtracted from the number the digits are reversed. Find the numbers

Discussion

48.	ABCD is a cyclic quadrilateral whose side AB is a diameter of the circle. If ∠ADC=130∘, find ∠BAC.
Answer» ABCD is a cyclic quadrilateral whose side AB is a diameter of the circle. If $∠ A D C = 130^{\circ}$ , find $∠ B A C$ .

Discussion

49.	In a quadrilateral ABCD, given that ∠A + ∠D = 90°. Prove that AC2 + BD2 = AD2 + BC2.
Answer» In a quadrilateral ABCD, given that ∠A + ∠D = 90°. Prove that AC² + BD² = AD² + BC².

Discussion

50.	The exponent of 7 in 100!
Answer» The exponent of 7 in 100!

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

What is the quotient(q) and the remainder(r) when -12 is divided by 5?

ABCDEF is a regular hexagon with centre O (Fig). If the area of triangle OAB is 9 cm2. Find the area of (i) the hexagon and (ii) the circle in which the hexagon is inscribed.

The set of values of k for which the system of equations x + y + z = 2, 2x + y - z = 3, 3x +2 y + kz = 4 has a unique solution, is _________.

When two triangles are similar, their corresponding sides are ___.

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

The radii of the circular ends of a frustum of height 6 cm are 14 cm and 6 cm, respectively. Find the slant height of the frustum.

A train travels a distance of 480 km at a uniform speed. If the speed had been 8 km/h less, then it would have taken 3 hours more to cover the same distance. We need to find the speed of the train.

Find the areas(in cm2) of shaded regions. [Take π=227]

A chord 10 cm long is drawn in a circle whose radius is 52 cm. Find area of both the segments.

Show that height of the cylinder ofgreatest volume which can be inscribed in a right circular cone ofheight h and semi vertical angle αis one-third that of the cone and the greatest volume of cylinderistan2α.

3x-ky=8 passes through (4,4) , find k

Construct a 3×3 matrix whose elements aij are given by aij=0 if i&lt;j and aij=i+j if i≥j.

if the four term of G.P. is 4 then find the product of first five term

Is the product of two irrationals always irrational? Justify your answer.

Manish opens a Recurring Deposit Account with the Bank of Rajasthan and deposits ₹600 per month for 20 months. Calculate the maturity value of this account, if the bank pays interest at the rate of 10% per annum.

A bridge across a valley is 800 metres long. There is a temple in the valley directlybelow the bridge. The angle of depression of the top of the temple from the twoends of the bridge have measure 30 and 60.Find the height of the bridge above the top of the temple.3

Construct an isosceles triangle in which the lengths of each of its equal sides is 6.5 cm and the angle between them is 110∘.

26. The height of a tower is 15 m. What is the lenght of its shadow on the ground, when angle of elevation of the Sun is 60 degree?

In the figure, O is the center of the circle, PQ is tangent to the circle at A. If ∠PAB=58∘, find ∠ABQ and ∠AQB. [2 MARKS]

Question 116 State whether the statements are True or False. Every trapezium is a rectangle.

Find the number of pairs having 16 as their HCF and 136 as their LCM

17.A bag has 3 red and 7 black balls. 2 balls are drawn at random without replacement. If 2nd selection is given to be red, what is the probability that 1st is also red,.

The next term in the series 81, 54, 36, 24, ..... is.

ntIf y=3[x]+5 and y=2[x-1]+9 then [x+y]isn

One third of a bamboo pole is burried in mud ,one sixth of it is in water and the part above the water is greater than or equal to 3 metre. Find the length of shortest pole.

If the angles of elevation of a tower from two points distant a and b (a>b) from its foot and in the same straight line from it are 30° and 60°, then the height of the tower is(a) a+b(b) ab(c) a-b(d) ab

A company declares 8 percent dividend to the share holders. If a man receives Rs 2,840 as his dividend, find the nominal value of his shares.

The product of digits of a two-digit number is 12. If the number is 36 more than the number obtained by reversing its digits, then the original number is

Solve the following quadratic equations by factorization:x-12x+1+2x+1x-1=52, x≠-12, 1

If 4x+5y=23 passes through the point (2,a), the value of a is ___

If for an A.P. a5=a10=5×a, then a15 is....

3. if P+3Q+5R+15S= 1/1+3+5,then the value of P is what?

The value of sin18∘cos72∘ is ______.

the sum of the numerator the denominator ofa fraction is 4 more than twice the numerator if 3 is added to each of the numerator and denominator their ratio becomes 2:3. find the fraction

The sum of a 2 digit number and the number formed by interchanging the digit is 110.If 10 is subtracted from the first ,the new number is 4 more than 5 times the sum of the digits in the first number .Find the first number

In the given figure, ABC is a triangle in which ∠ABC &lt; 90° and AD ⊥ BC. Prove that AC2 = AB2 + BC2 − 2BC.BD.

If we make the graph of y = root(1-x) , then will its domain contain 0 and 1 ??

The midpoints of AB, BC, CA of a AABC are (6, -1). (4, -3), (2, -5) respectively. The centroid of tr. ABC is

If y=(2x^3)(2x^-3+1)then dy/dx at x=1

Question 28(i)The king, queen and jack of clubs are removed from a deck of 52 playing cards and then well shuffled. Now, one card is drawn at random from the remaining cards. Determine the probability that the card is a heart

prove that inA-cosA+1÷sinA+cosA-1=1÷secA-tanA using identity sec2A = 1+tan2A

When the vapor of 22.4 liters of water is condensed, on NTP, how much volume of water is obtained

In the given figure, if ∠BCA=∠RPQ=15∘, then ∠PQR is

Two chords AB and CD intersect at point O inside the circle. If OA = 5 cm, OB = 6 cm and OC = 3 cm, then find the value of CD.

if the equation kx^2+2kx+6=0 has equal roots then find the value of k.

A two digit number is 4 more than 6 times the sum of its digits. If 18 is subtracted from the number the digits are reversed. Find the numbers

ABCD is a cyclic quadrilateral whose side AB is a diameter of the circle. If ∠ADC=130∘, find ∠BAC.

In a quadrilateral ABCD, given that ∠A + ∠D = 90°. Prove that AC2 + BD2 = AD2 + BC2.

The exponent of 7 in 100!

Construct a 3×3 matrix whose elements aij are given by aij=0 if i<j and aij=i+j if i≥j.

In the given figure, ABC is a triangle in which ∠ABC < 90° and AD ⊥ BC. Prove that AC2 = AB2 + BC2 − 2BC.BD.