24740 + Interview Questions in Mathematics

1.	Question 3 Write whether the following statement is True or False? The graph given below represents the linear equation x + y = 0.
Answer» Question 3 Write whether the following statement is True or False? The graph given below represents the linear equation x + y = 0.

Discussion

2.	If x=√3+√2√3−√2 and y=√3−√2√3+√2, then find the value of x2+y2?
Answer» If $x = \frac{\sqrt{3} + \sqrt{2}}{\sqrt{3} - \sqrt{2}} a n d y = \frac{\sqrt{3} - \sqrt{2}}{\sqrt{3} + \sqrt{2}}$ , then find the value of $x^{2} + y^{2}$ ?

Discussion

3.	ABC is a triangle and M & N are points on AB and AC such that MN \|\| BC. Find the given ratios if AM:MB = 2:3.
Answer» ABC is a triangle and M & N are points on AB and AC such that MN \|\| BC. Find the given ratios if AM:MB = 2:3.

Discussion

4.	Let a and b be two unit vectors. If the vectors c=a+2b and d=5a-4b are perpendicular to each other, then the angle between a and b is
Answer» Let a and b be two unit vectors. If the vectors c=a+2b and d=5a-4b are perpendicular to each other, then the angle between a and b is

Discussion

5.	Angles of a triangle are in the ratio 2 : 4 : 3. The smallest angle of the triangle is
Answer» Angles of a triangle are in the ratio 2 : 4 : 3. The smallest angle of the triangle is

Discussion

6.	Factorize: (3x−2y)2+3(3x−2y)−10
Answer» Factorize: $(3 x - 2 y)^{2} + 3 (3 x - 2 y) - 10$

Discussion

7.	The number x is we more than number y.If the sum of squares of x and y is 34;find the product of x and y.
Answer» The number x is we more than number y.If the sum of squares of x and y is 34;find the product of x and y.

Discussion

8.	An angle is 14∘ more than its complementary angle. What is its measure?
Answer» An angle is 14∘ more than its complementary angle. What is its measure?

Discussion

9.	Question 18 If xy =10, then x and y vary___with each other.
Answer» Question 18 If xy =10, then x and y vary___with each other.

9.

Question 18 If xy =10, then x and y vary___with each other.

Answer»

Question 18

If xy =10, then x and y vary___with each other.

Discussion

10.	Do all polynomials have only one variable? What's the difference between algebraic expression and polynomials?
Answer» Do all polynomials have only one variable? What's the difference between algebraic expression and polynomials?

Discussion

11.	The probability of certain (sure) event is ___ .
Answer» The probability of certain (sure) event is ___ .

Discussion

12.	Question 14 D and E are the mid-points of the sides AB and AC, respectively, of ΔABC.DE is produced to F. To prove that CF is equal and parallel to DA, we need an additional information which is (a) ∠DAE=∠EFC (b) AE=EF (c) DE=EF (d) ∠ADE=∠ECF
Answer» Question 14 D and E are the mid-points of the sides AB and AC, respectively, of $Δ A B C . D E$ is produced to F. To prove that CF is equal and parallel to DA, we need an additional information which is (a) $∠ D A E = ∠ E F C$ (b) $A E = E F$ (c) $D E = E F$ (d) $∠ A D E = ∠ E C F$

Discussion

13.	The measure of each angle (in degrees) in a square and a rectangle is ____.90
Answer» The measure of each angle (in degrees) in a square and a rectangle is ____. 90

Discussion

14.	Simplify (Root5_root2) × (root2_root3)
Answer» Simplify (Root5_root2) × (root2_root3)

Discussion

15.	How many axes and quadrants are there in a Cartesian plane? What are the signs of abscissa and ordinate of a point in the second quadrant? [3 MARKS]
Answer» How many axes and quadrants are there in a Cartesian plane? What are the signs of abscissa and ordinate of a point in the second quadrant? [3 MARKS]

Discussion

16.	If lx^4+mx^3+2x^2+4 is exactly divisible by x^2-x-2,then
Answer» If lx^4+mx^3+2x^2+4 is exactly divisible by x^2-x-2,then

Discussion

17.	Which of the following polynomials has the highest degree?
Answer» Which of the following polynomials has the highest degree?

Discussion

18.	Question 1 (v) Classify 2π as rational or irrational.
Answer» Question 1 (v) Classify $2 π$ as rational or irrational.

Discussion

19.	Curved surface area of a cylinder of radius r and height h is:
Answer» Curved surface area of a cylinder of radius r and height h is:

Discussion

20.	Factorise by splitting the middle term 2x2 – 11x + 12
Answer» Factorise by splitting the middle term 2x² – 11x + 12

Discussion

21.	Solve the following pair of equations. 1x+3y=1 6x−12y=2 (where x≠0,y≠0)
Answer» Solve the following pair of equations. $\frac{1}{x} + \frac{3}{y} = 1$ $\frac{6}{x} - \frac{12}{y} = 2$ (where $x \neq 0, y \neq 0)$

Discussion

22.	If the area of an isosceles right triangle is 8cm, what is the perimeter of the triangle.
Answer» If the area of an isosceles right triangle is 8cm, what is the perimeter of the triangle.

Discussion

23.	A quadrilateral is a ______ if a pair of opposite sides is equal and parallel
Answer» A quadrilateral is a ______ if a pair of opposite sides is equal and parallel

Discussion

24.	Use the following information to answer the next question. The rows in the given table can be correctly matched as
Answer» Use the following information to answer the next question. The rows in the given table can be correctly matched as

24.

Use the following information to answer the next question. The rows in the given table can be correctly matched as

Answer»

Use the following information to answer the next question.

The rows in the given table can be correctly matched as

Discussion

25.	Identify the diagonals of the given quadrilateral.
Answer» Identify the diagonals of the given quadrilateral.

Discussion

26.	The distance between the points A(0,√3 and B (√3+1,1) is ________ units.
Answer» The distance between the points A(0, $\sqrt{3}$ and B $(\sqrt{3} + 1, 1)$ is ________ units.

Discussion

27.	D and F are mid-points of sides AB and AC of ΔABC. A line through F and parallel to AB meets BC at point E. If EF = 3.8 cm, AB =
Answer» D and F are mid-points of sides AB and AC of $Δ A B C$ . A line through F and parallel to AB meets BC at point E. If EF = 3.8 cm, AB =

Discussion

28.	If log4 5 = a and log5 6 = b, then log3 2 is equal to
Answer» If $l o g_{4} 5$ = a and $l o g_{5} 6$ = b, then $l o g_{3} 2$ is equal to

Discussion

29.	Question 4 If a=3+√52, then find the value of a2+1a2.
Answer» Question 4 If $a = \frac{3 + \sqrt{5}}{2}$ , then find the value of $a^{2} + \frac{1}{a^{2}}$ .

Discussion

30.	The window is shown in the shape of a semi-circle with radius 4 ft. The distance from S to T is 2 ft and the measure of arc AB=45∘. Area of the glass in the region ABCD is
Answer» The window is shown in the shape of a semi-circle with radius $4$ ft. The distance from $S$ to $T$ is $2$ ft and the measure of arc $A B = 45^{\circ}$ . Area of the glass in the region $A B C D$ is

Discussion

31.	One of the factors of the determinant ∣∣∣∣∣x53x299x31627∣∣∣∣∣ is
Answer» One of the factors of the determinant $∣ ∣∣∣ ∣ \begin{matrix} x & 5 & 3 x^{2} & 9 & 9 x^{3} & 16 & 27 \end{matrix} ∣ ∣∣∣ ∣$ is

31.

One of the factors of the determinant ∣∣∣∣∣x53x299x31627∣∣∣∣∣ is

Answer»

One of the factors of the determinant

$∣ ∣∣∣ ∣ \begin{matrix} x & 5 & 3 x^{2} & 9 & 9 x^{3} & 16 & 27 \end{matrix} ∣ ∣∣∣ ∣$ is

Discussion

32.	Question 5 Determine, algebraically, the vertices of the triangle formed by the lines 3x – y = 3 2x – 3y = 2 x + 2y = 8
Answer» Question 5 Determine, algebraically, the vertices of the triangle formed by the lines 3x – y = 3 2x – 3y = 2 x + 2y = 8

Discussion

33.	The two intersecting axes or fixed perpendicular lines divide the Cartesian plane into a fixed number of parts. What are the parts called? Also, what's that 'fixed number'?
Answer» The two intersecting axes or fixed perpendicular lines divide the Cartesian plane into a fixed number of parts. What are the parts called? Also, what's that 'fixed number'?

Discussion

34.	A 50.0-kg boy runs at a speed of 10.0 m/s and jumps onto a cart as shown in the figure. The cart is initially at rest. If the speed of the cart with the boy on it is 2.50 m/s, what is the mass of the cart?
Answer» A 50.0-kg boy runs at a speed of 10.0 m/s and jumps onto a cart as shown in the figure. The cart is initially at rest. If the speed of the cart with the boy on it is 2.50 m/s, what is the mass of the cart?

34.

A 50.0-kg boy runs at a speed of 10.0 m/s and jumps onto a cart as shown in the figure. The cart is initially at rest. If the speed of the cart with the boy on it is 2.50 m/s, what is the mass of the cart?

Answer»

A 50.0-kg boy runs at a speed of 10.0 m/s and jumps onto a cart as shown in the figure. The cart is initially at rest. If the speed of the cart with the boy on it is 2.50 m/s, what is the mass of the cart?

Discussion

35.	Expand the following, using suitable identities: (2x−y+z)2 [3 MARKS]
Answer» Expand the following, using suitable identities: ${(2 x - y + z)}^{2}$ [3 MARKS]

Discussion

36.	If two angles of triangle measure 1000 and 400, then the third angle is ______.
Answer» If two angles of triangle measure $100^{0}$ and $40^{0}$ , then the third angle is ______.

Discussion

37.	The volume of parallelopipped formed by following 3 vectors will be___cubic units. →a=3^i−2^j+5^k→b=2^i+2^j−^k→c=−4^i+3^j+2^k
Answer» The volume of parallelopipped formed by following 3 vectors will be___cubic units. $\to a = 3^i - 2^j + 5^k \to b = 2^i + 2^j -^k \to c = - 4^i + 3^j + 2^k$

37.

The volume of parallelopipped formed by following 3 vectors will be___cubic units. →a=3^i−2^j+5^k→b=2^i+2^j−^k→c=−4^i+3^j+2^k

Answer»

The volume of parallelopipped formed by following 3 vectors will be___cubic units.

$\to a = 3^i - 2^j + 5^k \to b = 2^i + 2^j -^k \to c = - 4^i + 3^j + 2^k$

Discussion

38.	2.50505050...in pq form is .
Answer» 2.50505050...in $\frac{p}{q}$ form is .

Discussion

39.	Solve the two equations using method of elimination. a1x+b1y+c1=0 a2x+b2y+c2=0
Answer» Solve the two equations using method of elimination. $a_{1} x + b_{1} y + c_{1} = 0$ $a_{2} x + b_{2} y + c_{2} = 0$

39.

Solve the two equations using method of elimination. a1x+b1y+c1=0 a2x+b2y+c2=0

Answer»

Solve the two equations using method of elimination.

$a_{1} x + b_{1} y + c_{1} = 0$
$a_{2} x + b_{2} y + c_{2} = 0$

Discussion

40.	In each of the figures given below, ABCD is a rectangle. Find the values of x and y in each case.
Answer» In each of the figures given below, $A B C D$ is a rectangle. Find the values of $x$ and $y$ in each case.

40.

In each of the figures given below, ABCD is a rectangle. Find the values of x and y in each case.

Answer»

In each of the figures given below, $A B C D$ is a rectangle. Find the values of $x$ and $y$ in each case.

Discussion

41.	How many irrational numbers lie between √2 and √3? Find any three irrational numbers lying between √2 and √3
Answer» How many irrational numbers lie between $\sqrt{2}$ and $\sqrt{3}$ ? Find any three irrational numbers lying between $\sqrt{2}$ and $\sqrt{3}$

Discussion

42.	In the given figure, △ABC is equilateral. Find (i) ∠BDC, (ii) ∠BEC.
Answer» In the given figure, $△$ ABC is equilateral. Find $(i) ∠ B D C, (i i) ∠ B E C .$

42.

In the given figure, △ABC is equilateral. Find (i) ∠BDC, (ii) ∠BEC.

Answer»

In the given figure, $△$ ABC is equilateral. Find $(i) ∠ B D C, (i i) ∠ B E C .$

Discussion

43.	Prove that the line segments joining the middle points of the sides of a triangle divide it into four congruent triangles.
Answer» Prove that the line segments joining the middle points of the sides of a triangle divide it into four congruent triangles.

Discussion

44.	A hemispherical bowl is made of steel,0.25 cm thick.The inner radius of the bowl is 5 cm.Find the outer curved surface area of the bowl.
Answer» A hemispherical bowl is made of steel,0.25 cm thick.The inner radius of the bowl is 5 cm.Find the outer curved surface area of the bowl.

Discussion

45.	If ABCD is a cyclic quadrilateral with AB as the diameter of the circle and ∠ACD=50∘, then ∠BAD = ___.
Answer» If ABCD is a cyclic quadrilateral with AB as the diameter of the circle and $∠ A C D = 50^{\circ},$ then $∠ B A D$ = ___.

Discussion

46.	The co-ordinates of the point which divides the join of (–1,7) and (4,–3) in the ratio 2:3 is
Answer» The co-ordinates of the point which divides the join of $(- 1, 7)$ and $(4, - 3)$ in the ratio $2 : 3$ is

Discussion

47.	Two equal chords AB and CD intersect at a point P inside the circle. If AP = 10 cm, PC = 5 cm, then the length of chord CD is
Answer» Two equal chords AB and CD intersect at a point P inside the circle. If AP = 10 cm, PC = 5 cm, then the length of chord CD is

47.

Two equal chords AB and CD intersect at a point P inside the circle. If AP = 10 cm, PC = 5 cm, then the length of chord CD is

Answer»

Two equal chords AB and CD intersect at a point P inside the circle. If AP = 10 cm, PC = 5 cm, then the length of chord CD is

Discussion

48.	Factorise: 9a2−4b2−6a+1
Answer» Factorise: $9 a^{2} - 4 b^{2} - 6 a + 1$

48.

Factorise: 9a2−4b2−6a+1

Answer»

Factorise:

$9 a^{2} - 4 b^{2} - 6 a + 1$

Discussion

49.	Arc BAD is known as:
Answer» Arc BAD is known as:

49.

Arc BAD is known as:

Answer»

Arc BAD is known as:

Discussion

50.	What's the geometric proof of a2-b2
Answer» What's the geometric proof of a2-b2

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Question 3 Write whether the following statement is True or False? The graph given below represents the linear equation x + y = 0.

If x=√3+√2√3−√2 and y=√3−√2√3+√2, then find the value of x2+y2?

ABC is a triangle and M &amp; N are points on AB and AC such that MN || BC. Find the given ratios if AM:MB = 2:3.

Let a and b be two unit vectors. If the vectors c=a+2b and d=5a-4b are perpendicular to each other, then the angle between a and b is

Angles of a triangle are in the ratio 2 : 4 : 3. The smallest angle of the triangle is

Factorize: (3x−2y)2+3(3x−2y)−10

The number x is we more than number y.If the sum of squares of x and y is 34;find the product of x and y.

An angle is 14∘ more than its complementary angle. What is its measure?

Question 18 If xy =10, then x and y vary___with each other.

Do all polynomials have only one variable? What's the difference between algebraic expression and polynomials?

The probability of certain (sure) event is ___ .

The measure of each angle (in degrees) in a square and a rectangle is ____.90

Simplify (Root5_root2) × (root2_root3)

How many axes and quadrants are there in a Cartesian plane? What are the signs of abscissa and ordinate of a point in the second quadrant? [3 MARKS]

If lx^4+mx^3+2x^2+4 is exactly divisible by x^2-x-2,then

Which of the following polynomials has the highest degree?

Question 1 (v) Classify 2π as rational or irrational.

Curved surface area of a cylinder of radius r and height h is:

Factorise by splitting the middle term 2x2 – 11x + 12

Solve the following pair of equations. 1x+3y=1 6x−12y=2 (where x≠0,y≠0)

If the area of an isosceles right triangle is 8cm, what is the perimeter of the triangle.

A quadrilateral is a ______ if a pair of opposite sides is equal and parallel

Use the following information to answer the next question. The rows in the given table can be correctly matched as

Identify the diagonals of the given quadrilateral.

The distance between the points A(0,√3 and B (√3+1,1) is ________ units.

D and F are mid-points of sides AB and AC of ΔABC. A line through F and parallel to AB meets BC at point E. If EF = 3.8 cm, AB =

If log4 5 = a and log5 6 = b, then log3 2 is equal to

Question 4 If a=3+√52, then find the value of a2+1a2.

The window is shown in the shape of a semi-circle with radius 4 ft. The distance from S to T is 2 ft and the measure of arc AB=45∘. Area of the glass in the region ABCD is

One of the factors of the determinant ∣∣∣∣∣x53x299x31627∣∣∣∣∣ is

Question 5 Determine, algebraically, the vertices of the triangle formed by the lines 3x – y = 3 2x – 3y = 2 x + 2y = 8

The two intersecting axes or fixed perpendicular lines divide the Cartesian plane into a fixed number of parts. What are the parts called? Also, what's that 'fixed number'?

A 50.0-kg boy runs at a speed of 10.0 m/s and jumps onto a cart as shown in the figure. The cart is initially at rest. If the speed of the cart with the boy on it is 2.50 m/s, what is the mass of the cart?

Expand the following, using suitable identities: (2x−y+z)2 [3 MARKS]

If two angles of triangle measure 1000 and 400, then the third angle is ______.

The volume of parallelopipped formed by following 3 vectors will be___cubic units. →a=3^i−2^j+5^k→b=2^i+2^j−^k→c=−4^i+3^j+2^k

2.50505050...in pq form is .

Solve the two equations using method of elimination. a1x+b1y+c1=0 a2x+b2y+c2=0

In each of the figures given below, ABCD is a rectangle. Find the values of x and y in each case.

How many irrational numbers lie between √2 and √3? Find any three irrational numbers lying between √2 and √3

In the given figure, △ABC is equilateral. Find (i) ∠BDC, (ii) ∠BEC.

Prove that the line segments joining the middle points of the sides of a triangle divide it into four congruent triangles.

A hemispherical bowl is made of steel,0.25 cm thick.The inner radius of the bowl is 5 cm.Find the outer curved surface area of the bowl.

If ABCD is a cyclic quadrilateral with AB as the diameter of the circle and ∠ACD=50∘, then ∠BAD = ___.

The co-ordinates of the point which divides the join of (–1,7) and (4,–3) in the ratio 2:3 is

Two equal chords AB and CD intersect at a point P inside the circle. If AP = 10 cm, PC = 5 cm, then the length of chord CD is

Factorise: 9a2−4b2−6a+1

Arc BAD is known as:

What's the geometric proof of a2-b2

ABC is a triangle and M & N are points on AB and AC such that MN || BC. Find the given ratios if AM:MB = 2:3.