32581 + Interview Questions in Mathematics

1.	Match the following (i) MeanA. Typical value(ii) MedianB. Most popular~value(iii) ModeC. Gets highly affected by extreme values
Answer» Match the following $\begin{matrix} (i) Mean & A. Typical value (ii) Median & B. Most popular~value (iii) Mode & C. Gets highly affected by extreme values \end{matrix}$

Discussion

2.	The area of a triangle having vertices (a, b+ c), (b, c + a) and (c, a + b) is ___.
Answer» The area of a triangle having vertices (a, b+ c), (b, c + a) and (c, a + b) is ___.

Discussion

3.	Question 7Find the volume of a sphere whose surface area is 154 cm2.[Assume π=227]
Answer» Question 7 Find the volume of a sphere whose surface area is $154 c m^{2}$ . $[A s s u m e π = \frac{22}{7}]$

Discussion

4.	Find the area of metal sheet required in making a closed hollow cone of base radius 7 cm and height 24 cm.
Answer» Find the area of metal sheet required in making a closed hollow cone of base radius 7 cm and height 24 cm.

Discussion

5.	Represent 0.123¯¯¯¯¯¯¯¯456 in the form of pq, where p and q are integers and q≠0.
Answer» Represent $0.123 ¯ ¯¯¯¯¯¯ ¯ 456$ in the form of $\frac{p}{q}$ , where p and q are integers and $q \neq 0$ .

Discussion

6.	Point A(4, -1) is reflected as A' in the y-axis. Point B on reflection in the x-axis is mapped as B' (-2, 5). Write the co-ordinates of A' and B.
Answer» Point A(4, -1) is reflected as A' in the y-axis. Point B on reflection in the x-axis is mapped as B' (-2, 5). Write the co-ordinates of A' and B.

Discussion

7.	Thw total surface area of a hollow cylinder,which is open from the sides ,is 3575cm2,the area of its basering is 357.5cm2 and its height is 14cm .find the thickness of the cylinder
Answer» Thw total surface area of a hollow cylinder,which is open from the sides ,is 3575cm2,the area of its basering is 357.5cm2 and its height is 14cm .find the thickness of the cylinder

Discussion

8.	Find the slope of the line inclined at an angle of 135∘ with positive direction of x-axis __
Answer» Find the slope of the line inclined at an angle of $135^{\circ}$ with positive direction of x-axis __

Discussion

9.	Which of the following cannot be the probability of an event?(a) 23(b) -1.5(c) 15%(d) 0.7
Answer» Which of the following cannot be the probability of an event? (a) $\frac{2}{3}$ (b) $- 1.5$ (c) $15 %$ (d) $0.7$

Discussion

10.	A circle is inscribed in a square of side 14 m. The ratio of the area of the circle and that ofthe square is(a) π : 3 (b) π : 4 (c) π : 2 (d) π : 1
Answer» A circle is inscribed in a square of side 14 m. The ratio of the area of the circle and that of the square is (a) $π$ : 3 (b) $π$ : 4 (c) $π$ : 2 (d) $π$ : 1

Discussion

11.	Solve by cross multiplication methodax +by = a-b bx - ay = a+b
Answer» Solve by cross multiplication method ax +by = a-b bx - ay = a+b

Discussion

12.	The sum of 4 arithmetic means between 3 and 23 is ___________.
Answer» The sum of 4 arithmetic means between 3 and 23 is ___________.

Discussion

13.	In a circle of radius 4 cm, draw two radii such that the angle between them is 110°. Construct two tangents at the ends of the radii.
Answer» In a circle of radius 4 cm, draw two radii such that the angle between them is 110°. Construct two tangents at the ends of the radii.

Discussion

14.	A man reduced his weight by 2:3. His final weight is 80kg. Find his original weight.
Answer» A man reduced his weight by 2:3. His final weight is 80kg. Find his original weight.

Discussion

15.	Find the sum of the squares of the first n natural numbers.A. n2(n+1)6B. n(n+1)(n−1)6C. n(2n+1)6D. n(n+1)(2n+1)6
Answer» Find the sum of the squares of the first n natural numbers. A. $\frac{n^{2} (n + 1)}{6}$ B. $\frac{n (n + 1) (n - 1)}{6}$ C. $\frac{n (2 n + 1)}{6}$ D. $\frac{n (n + 1) (2 n + 1)}{6}$

15.

Find the sum of the squares of the first n natural numbers.A. n2(n+1)6B. n(n+1)(n−1)6C. n(2n+1)6D. n(n+1)(2n+1)6

Answer»

Find the sum of the squares of the first n natural numbers.

A. $\frac{n^{2} (n + 1)}{6}$

B. $\frac{n (n + 1) (n - 1)}{6}$

C. $\frac{n (2 n + 1)}{6}$

D. $\frac{n (n + 1) (2 n + 1)}{6}$

Discussion

16.	Which of the following number line represents the solution of the inequation: 2y−3<y+2≤3y+5; y∈R?
Answer» Which of the following number line represents the solution of the inequation: $2 y - 3 < y + 2 \leq 3 y + 5; y \in R$ ?

Discussion

17.	If a young man drives his vehicle at 25 km/hr, he has to spend ₹2 per km on petrol. If he drives it at a faster speed of 40 km/hr, the petrol cost increases to ₹5 per km. He has ₹100 to spend on petrol and travel within one hour. Express this as an LPP and solve the same. [CBSE 2007]
Answer» If a young man drives his vehicle at 25 km/hr, he has to spend ₹2 per km on petrol. If he drives it at a faster speed of 40 km/hr, the petrol cost increases to ₹5 per km. He has ₹100 to spend on petrol and travel within one hour. Express this as an LPP and solve the same. [CBSE 2007]

Discussion

18.	A box contains 80 discs, which are numbered from 1 to 80. If one disc is drawn at random from the box, find the probability that it bears a perfect square number.
Answer» A box contains 80 discs, which are numbered from 1 to 80. If one disc is drawn at random from the box, find the probability that it bears a perfect square number.

Discussion

19.	There are 36 members in a student council in a school and the ratio of the number of boys to the number of girls is 3 : 1. How many more girls should be added to the council so that the ratio of number of boys to the number of girls may be 9 :5 ?
Answer» There are 36 members in a student council in a school and the ratio of the number of boys to the number of girls is 3 : 1. How many more girls should be added to the council so that the ratio of number of boys to the number of girls may be 9 :5 ?

Discussion

20.	37. Solve the inequation: x + 1 / x + 2 ≥ 1
Answer» 37. Solve the inequation: x + 1 / x + 2 ≥ 1

Discussion

21.	Find the value of k for which each of the following systems of linear equations has an infinite number of solutions: (k−3)x+3y=k,kx+ky=12.
Answer» Find the value of k for which each of the following systems of linear equations has an infinite number of solutions: $(k - 3) x + 3 y = k, k x + k y = 12.$

21.

Find the value of k for which each of the following systems of linear equations has an infinite number of solutions: (k−3)x+3y=k,kx+ky=12.

Answer»

Find the value of k for which each of the following systems of linear equations has an infinite number of solutions:

$(k - 3) x + 3 y = k, k x + k y = 12.$

Discussion

22.	If a matrix A is of order 3×4 and there exists a matrix B such that both A'B and BA' are defined. Then the order of B is ____
Answer» If a matrix A is of order $3 \times 4$ and there exists a matrix B such that both A'B and BA' are defined. Then the order of B is ____

Discussion

23.	In the given figure, A is the centre of the circle. ∠ABC=45o and AC=7√2cm. Find the area of segment BXC. (Use π=227 )
Answer» In the given figure, A is the centre of the circle. $∠ A B C = 45^{o}$ and $A C = 7 \sqrt{2} c m .$ Find the area of segment BXC. (Use $π = \frac{22}{7}$ )

Discussion

24.	Determine the smallest 3-digit number which is exactly divisible by 6,8,and12.
Answer» Determine the smallest $3$ -digit number which is exactly divisible by $6, 8, and 12$ .

Discussion

25.	Question 14 In figure , PA, QB, RC and SD are all perpendiculars to a line l, AB = 6cm, BC = 9cm, CD = 12cm and SP = 36cm. Find PQ, QR and RS.
Answer» Question 14 In figure , PA, QB, RC and SD are all perpendiculars to a line l, AB = 6cm, BC = 9cm, CD = 12cm and SP = 36cm. Find PQ, QR and RS.

Discussion

26.	Solve for x : 3(81)x+3=9x+1+9x.
Answer» Solve for x : $3 (81)^{x} + 3 = 9^{x + 1} + 9^{x}$ .

Discussion

27.	Find the class marks of classes 10−25 and 35−55. [CBSE 2008]
Answer» Find the class marks of classes 10−25 and 35−55. [CBSE 2008]

Discussion

28.	The height of a conical tent is 28 m and the diameter of the base is 42 m. Find the cost of the canvas used at Rs 20/- per sq. m.
Answer» The height of a conical tent is 28 m and the diameter of the base is 42 m. Find the cost of the canvas used at Rs 20/- per sq. m.

28.

The height of a conical tent is 28 m and the diameter of the base is 42 m. Find the cost of the canvas used at Rs 20/- per sq. m.

Answer»

The height of a conical tent is 28 m and the diameter of the base is 42 m. Find the cost of the canvas used at Rs 20/- per sq. m.

Discussion

29.	If in an equilateral triangle ABC, AD is median and in triangle ABD, AE is median, then AB square: AE square will be_________ .
Answer» If in an equilateral triangle ABC, AD is median and in triangle ABD, AE is median, then AB square: AE square will be_________ .

Discussion

30.	If a sphere is placed inside a right circular cylinder so as to touch the top, base and the lateral surface of the cylinder. If the radius of the sphere is r, the volume of the cylinder and the sphere are in the ratio _________.
Answer» If a sphere is placed inside a right circular cylinder so as to touch the top, base and the lateral surface of the cylinder. If the radius of the sphere is r, the volume of the cylinder and the sphere are in the ratio _________.

Discussion

31.	Very-Short-Answer QuestionsShow that x = −3 is a solution of x2+6x+9=0. [CBSE 2008]
Answer» Very-Short-Answer Questions Show that x = −3 is a solution of $x^{2} + 6 x + 9 = 0$ . [CBSE 2008]

Discussion

32.	In ΔABC, if D is a point on the side AB such that ABAD=3. Find ADDB.
Answer» In $Δ A B C$ , if D is a point on the side AB such that $\frac{A B}{A D} = 3$ . Find $\frac{A D}{D B}$ .

Discussion

33.	A (3, 2) and B (−2, 1) are two vertices of a triangle ABC whose centroid G has the coordinates 53,-13. Find the coordinates of the third vertex C of the triangle.
Answer» A (3, 2) and B (−2, 1) are two vertices of a triangle ABC whose centroid G has the coordinates $(\frac{5}{3}, - \frac{1}{3})$ . Find the coordinates of the third vertex C of the triangle.

Discussion

34.	Question 5 (vi) Prove the following identities, where the angles involved are acute angles for which the expressions is defined. sec A + tan A = √(1+sin A1−sin A)
Answer» Question 5 (vi) Prove the following identities, where the angles involved are acute angles for which the expressions is defined. sec A + tan A = $\sqrt{(\frac{1 + s i n A}{1 - s i n A})}$

Discussion

35.	A man observes the angle of elevation of the top of a building to be 30∘. He walks towards it in horizontal line through its base. On covering 60 m the angle of elevation changes to 60∘. Find the height of the building correct to the nearest metre.
Answer» A man observes the angle of elevation of the top of a building to be $30^{\circ}$ . He walks towards it in horizontal line through its base. On covering 60 m the angle of elevation changes to $60^{\circ}$ . Find the height of the building correct to the nearest metre.

Discussion

36.	If the point representing a complex number lies in the third quadrant, then the point representing its conjugate lies in the ____________.
Answer» If the point representing a complex number lies in the third quadrant, then the point representing its conjugate lies in the ____________.

Discussion

37.	(i) Find the coordinates of the point which divies the join of A(-1, 7) and B(4, -3) in the ratio 2 : 3. (ii) Find the coordinates of the point which divides the join of A (-5, 11) and B(4, -7) in the ratio 7 : 2.
Answer» (i) Find the coordinates of the point which divies the join of A(-1, 7) and B(4, -3) in the ratio 2 : 3. (ii) Find the coordinates of the point which divides the join of A (-5, 11) and B(4, -7) in the ratio 7 : 2.

37.

(i) Find the coordinates of the point which divies the join of A(-1, 7) and B(4, -3) in the ratio 2 : 3. (ii) Find the coordinates of the point which divides the join of A (-5, 11) and B(4, -7) in the ratio 7 : 2.

Answer»

(i) Find the coordinates of the point which divies the join of A(-1, 7) and B(4, -3) in the ratio 2 : 3.

(ii) Find the coordinates of the point which divides the join of A (-5, 11) and B(4, -7) in the ratio 7 : 2.

Discussion

38.	Find the equation of line joining the points (1,−3) and (4,−2).
Answer» Find the equation of line joining the points $(1, - 3)$ and $(4, - 2) .$

Discussion

39.	Find the ratio in which the line segment joining the points A(3, −3) and B(−2, 7) is divided by x-axis.Also, find the point of division. [CBSE 2015]
Answer» Find the ratio in which the line segment joining the points A(3, −3) and B(−2, 7) is divided by x-axis. Also, find the point of division. [CBSE 2015]

Discussion

40.	Which is the largest number that perfectly divides 480 and 270?
Answer» Which is the largest number that perfectly divides 480 and 270?

Discussion

41.	Find the argument of: z= -3 + i
Answer» Find the argument of: z= -3 + i

Discussion

42.	If tan3θ-1tanθ-1=A sec2θ+B tan θ, then A+B=_______.
Answer» If $\frac{\tan^{3} θ - 1}{tanθ - 1} = A \sec^{2} θ + B \tan θ, then A + B =_______.$

Discussion

43.	If cosec θ=2, show that (cotθ+sinθ1+cosθ) = 2.
Answer» If cosec $θ = 2$ , show that $(c o t θ + \frac{s i n θ}{1 + c o s θ})$ = 2.

Discussion

44.	If 5 is one of the root of x2+bx+10=0, then sum of roots of given equation is
Answer» If 5 is one of the root of $x^{2} + b x + 10 = 0$ , then sum of roots of given equation is

Discussion

45.	19.The length of median of through the vertex A of triangle ABC with vertices A(3,-4), B(5,3),C(7,-1) is
Answer» 19.The length of median of through the vertex A of triangle ABC with vertices A(3,-4), B(5,3),C(7,-1) is

Discussion

46.	sin(90−θ)cos(90−θ)cot(90−θ)+sin2θ= __
Answer» $\frac{s i n (90 - θ) c o s (90 - θ)}{c o t (90 - θ)} + s i n^{2} θ =$ __

Discussion

47.	A line through A(-2,6) and B(4,b) is perpendicular to the line 2x - 4y = 5. The value of b is ___.
Answer» A line through A(-2,6) and B(4,b) is perpendicular to the line 2x - 4y = 5. The value of b is ___.

Discussion

48.	Which one could be a solution for the equation 3x+4y = 38 ?
Answer» Which one could be a solution for the equation 3x+4y = 38 ?

Discussion

49.	The number of pairs (x,y) satisfying 2(x^2)y - 3(x^2) + 4y = 2009, where x,y are integers, is:A) 1B) 2C) 4D) None of TheseAlso find the pair(s).
Answer» The number of pairs (x,y) satisfying 2(x^2)y - 3(x^2) + 4y = 2009, where x,y are integers, is: A) 1 B) 2 C) 4 D) None of These Also find the pair(s).

Discussion

50.	In the given figure, AB \|\| QR. Find the length of PB.
Answer» In the given figure, AB \|\| QR. Find the length of PB.

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Match the following (i) MeanA. Typical value(ii) MedianB. Most popular~value(iii) ModeC. Gets highly affected by extreme values

The area of a triangle having vertices (a, b+ c), (b, c + a) and (c, a + b) is ___.

Question 7Find the volume of a sphere whose surface area is 154 cm2.[Assume π=227]

Find the area of metal sheet required in making a closed hollow cone of base radius 7 cm and height 24 cm.

Represent 0.123¯¯¯¯¯¯¯¯456 in the form of pq, where p and q are integers and q≠0.

Point A(4, -1) is reflected as A' in the y-axis. Point B on reflection in the x-axis is mapped as B' (-2, 5). Write the co-ordinates of A' and B.

Thw total surface area of a hollow cylinder,which is open from the sides ,is 3575cm2,the area of its basering is 357.5cm2 and its height is 14cm .find the thickness of the cylinder

Find the slope of the line inclined at an angle of 135∘ with positive direction of x-axis __

Which of the following cannot be the probability of an event?(a) 23(b) -1.5(c) 15%(d) 0.7

A circle is inscribed in a square of side 14 m. The ratio of the area of the circle and that ofthe square is(a) π : 3 (b) π : 4 (c) π : 2 (d) π : 1

Solve by cross multiplication methodax +by = a-b bx - ay = a+b

The sum of 4 arithmetic means between 3 and 23 is ___________.

In a circle of radius 4 cm, draw two radii such that the angle between them is 110°. Construct two tangents at the ends of the radii.

A man reduced his weight by 2:3. His final weight is 80kg. Find his original weight.

Find the sum of the squares of the first n natural numbers.A. n2(n+1)6B. n(n+1)(n−1)6C. n(2n+1)6D. n(n+1)(2n+1)6

Which of the following number line represents the solution of the inequation: 2y−3&lt;y+2≤3y+5; y∈R?

If a young man drives his vehicle at 25 km/hr, he has to spend ₹2 per km on petrol. If he drives it at a faster speed of 40 km/hr, the petrol cost increases to ₹5 per km. He has ₹100 to spend on petrol and travel within one hour. Express this as an LPP and solve the same. [CBSE 2007]

A box contains 80 discs, which are numbered from 1 to 80. If one disc is drawn at random from the box, find the probability that it bears a perfect square number.

There are 36 members in a student council in a school and the ratio of the number of boys to the number of girls is 3 : 1. How many more girls should be added to the council so that the ratio of number of boys to the number of girls may be 9 :5 ?

37. Solve the inequation: x + 1 / x + 2 ≥ 1

Find the value of k for which each of the following systems of linear equations has an infinite number of solutions: (k−3)x+3y=k,kx+ky=12.

If a matrix A is of order 3×4 and there exists a matrix B such that both A'B and BA' are defined. Then the order of B is ____

In the given figure, A is the centre of the circle. ∠ABC=45o and AC=7√2cm. Find the area of segment BXC. (Use π=227 )

Determine the smallest 3-digit number which is exactly divisible by 6,8,and12.

Question 14 In figure , PA, QB, RC and SD are all perpendiculars to a line l, AB = 6cm, BC = 9cm, CD = 12cm and SP = 36cm. Find PQ, QR and RS.

Solve for x : 3(81)x+3=9x+1+9x.

Find the class marks of classes 10−25 and 35−55. [CBSE 2008]

The height of a conical tent is 28 m and the diameter of the base is 42 m. Find the cost of the canvas used at Rs 20/- per sq. m.

If in an equilateral triangle ABC, AD is median and in triangle ABD, AE is median, then AB square: AE square will be_________ .

If a sphere is placed inside a right circular cylinder so as to touch the top, base and the lateral surface of the cylinder. If the radius of the sphere is r, the volume of the cylinder and the sphere are in the ratio _________.

Very-Short-Answer QuestionsShow that x = −3 is a solution of x2+6x+9=0. [CBSE 2008]

In ΔABC, if D is a point on the side AB such that ABAD=3. Find ADDB.

A (3, 2) and B (−2, 1) are two vertices of a triangle ABC whose centroid G has the coordinates 53,-13. Find the coordinates of the third vertex C of the triangle.

Question 5 (vi) Prove the following identities, where the angles involved are acute angles for which the expressions is defined. sec A + tan A = √(1+sin A1−sin A)

A man observes the angle of elevation of the top of a building to be 30∘. He walks towards it in horizontal line through its base. On covering 60 m the angle of elevation changes to 60∘. Find the height of the building correct to the nearest metre.

If the point representing a complex number lies in the third quadrant, then the point representing its conjugate lies in the ____________.

(i) Find the coordinates of the point which divies the join of A(-1, 7) and B(4, -3) in the ratio 2 : 3. (ii) Find the coordinates of the point which divides the join of A (-5, 11) and B(4, -7) in the ratio 7 : 2.

Find the equation of line joining the points (1,−3) and (4,−2).

Find the ratio in which the line segment joining the points A(3, −3) and B(−2, 7) is divided by x-axis.Also, find the point of division. [CBSE 2015]

Which is the largest number that perfectly divides 480 and 270?

Find the argument of: z= -3 + i

If tan3θ-1tanθ-1=A sec2θ+B tan θ, then A+B=_______.

If cosec θ=2, show that (cotθ+sinθ1+cosθ) = 2.

If 5 is one of the root of x2+bx+10=0, then sum of roots of given equation is

19.The length of median of through the vertex A of triangle ABC with vertices A(3,-4), B(5,3),C(7,-1) is

sin(90−θ)cos(90−θ)cot(90−θ)+sin2θ= __

A line through A(-2,6) and B(4,b) is perpendicular to the line 2x - 4y = 5. The value of b is ___.

Which one could be a solution for the equation 3x+4y = 38 ?

The number of pairs (x,y) satisfying 2*(x^2)*y - 3*(x^2) + 4*y = 2009, where x,y are integers, is:A) 1B) 2C) 4D) None of TheseAlso find the pair(s).

In the given figure, AB || QR. Find the length of PB.

Which of the following number line represents the solution of the inequation: 2y−3<y+2≤3y+5; y∈R?

The number of pairs (x,y) satisfying 2(x^2)y - 3(x^2) + 4y = 2009, where x,y are integers, is:A) 1B) 2C) 4D) None of TheseAlso find the pair(s).