24740 + Interview Questions in Mathematics

1.	Three cubes whose edges are 3 cm, 4 cm and 5 cm respectively are melted to form a single cube. Find the surface area of the new cube.
Answer» Three cubes whose edges are 3 cm, 4 cm and 5 cm respectively are melted to form a single cube. Find the surface area of the new cube.

Discussion

2.	If 8:2 is greater than 5:a, value of a is greater than .
Answer» If 8:2 is greater than 5: $a$ , value of a is greater than .

Discussion

3.	Question 6 (ii)The volume of a right circular cone is 9856cm3. If the diameter of the base is 28 cm, find slant height of the cone.[Assume π=227]
Answer» Question 6 (ii) The volume of a right circular cone is $9856 c m^{3}$ . If the diameter of the base is 28 cm, find slant height of the cone. $[A s s u m e π = \frac{22}{7}]$

Discussion

4.	In an isosceles right triangle ABC, right-angled at B, the longest side is ___?
Answer» In an isosceles right triangle ABC, right-angled at B, the longest side is ___?

Discussion

5.	The solution of the equation 3x+7y=30 if x=y is.
Answer» The solution of the equation $3 x + 7 y = 30$ if $x = y$ is.

Discussion

6.	75. In the adjoining figure quad. ABCD is circumscribed.If the radius of the incircle with centre O is 10cm and AD perpendicular to DC,find the value of x.
Answer» 75. In the adjoining figure quad. ABCD is circumscribed.If the radius of the incircle with centre O is 10cm and AD perpendicular to DC,find the value of x.

Discussion

7.	What is the number of significant figures in (3.20+ 4.80) x 105? (2) 4 (4) 2(3) 3
Answer» What is the number of significant figures in (3.20+ 4.80) x 105? (2) 4 (4) 2(3) 3

Discussion

8.	ABCD is a trapezium in which AB parallel to CD,M and N are midpoint ofAB & CD respectivly . AB=12cm &MN=14cm.Find CD
Answer» ABCD is a trapezium in which AB parallel to CD,M and N are midpoint ofAB & CD respectivly . AB=12cm &MN=14cm.Find CD

Discussion

9.	in a quadriletral ABCD the line segment bisect\angle C and\angle D meet atE prove that \angle A+\angle B =2\angle CE
Answer» in a quadriletral ABCD the line segment bisect\angle C and\angle D meet atE prove that \angle A+\angle B =2\angle CE

Discussion

10.	what is rhombic?
Answer» what is rhombic?

Discussion

11.	Question 1 (v)Without actually performing the long division, state whether 29343 will have a terminating decimal expansion or a non-terminating repeating decimal expansion.
Answer» Question 1 (v) Without actually performing the long division, state whether $\frac{29}{343}$ will have a terminating decimal expansion or a non-terminating repeating decimal expansion.

Discussion

12.	If x−1x=√3, then find the value of x3−1x3.
Answer» If $x - \frac{1}{x} = \sqrt{3}$ , then find the value of $x^{3} - \frac{1}{x^{3}}$ .

Discussion

13.	Question 2The coach of a cricket team buys 3 bats and 6 balls for Rs 3900. Later, she buys another bat and 2 more balls of the same kind for Rs 1300. Represent this situation algebraically and geometrically.
Answer» Question 2 The coach of a cricket team buys 3 bats and 6 balls for Rs 3900. Later, she buys another bat and 2 more balls of the same kind for Rs 1300. Represent this situation algebraically and geometrically.

Discussion

14.	Question 19 In following figure, coordinate of P are A) (-4 , 2) B) (-2, 4) C) (4, -2) D) (2,-4)
Answer» Question 19 In following figure, coordinate of P are A) (-4 , 2) B) (-2, 4) C) (4, -2) D) (2,-4)

Discussion

15.	In the given figure, D and E are mid points of sides AB and AC of △ABC. Which of the following is true?
Answer» In the given figure, D and E are mid points of sides AB and AC of $△$ ABC. Which of the following is true?

15.

In the given figure, D and E are mid points of sides AB and AC of △ABC. Which of the following is true?

Answer»

In the given figure, D and E are mid points of sides AB and AC of $△$ ABC. Which of the following is true?

Discussion

16.	Find the equation of straight line containing the point (3,2) and making positive equal intercepts on axes
Answer» Find the equation of straight line containing the point (3,2) and making positive equal intercepts on axes

Discussion

17.	A group of researchers were given an assignment to collect different types of leaves. The group collected 256 types of leaves. Represent the number of leaves collected in the form of exponential expression with its base being indivisible. [2 MARKS]
Answer» A group of researchers were given an assignment to collect different types of leaves. The group collected 256 types of leaves. Represent the number of leaves collected in the form of exponential expression with its base being indivisible. [2 MARKS]

Discussion

18.	If 8x+1 = 64 , what is the value of 32x+1 ?(a) 1(b) 3(c) 9(d) 27
Answer» If $8^{x + 1}$ = 64 , what is the value of $3^{2 x + 1}$ ? (a) 1 (b) 3 (c) 9 (d) 27

Discussion

19.	ABCD is a parallelogram as shown in figure. If AB=2AD and P is the midpoint of AB, then ∠CPD is equal to
Answer» ABCD is a parallelogram as shown in figure. If $A B = 2 A D$ and P is the midpoint of AB, then $∠ C P D$ is equal to

Discussion

20.	If p:7 is the ratio in which the line segment joining the points (-3, 10) and (6, - 8) is divided by (-1, 6), what is the value of p?2
Answer» If p:7 is the ratio in which the line segment joining the points (-3, 10) and (6, - 8) is divided by (-1, 6), what is the value of p? 2

Discussion

21.	Without actually performing the long division, state whether the following rational number will have a terminating decimal expansion or a non-terminating decimal expansion:7323×52 and 3×7323×3
Answer» Without actually performing the long division, state whether the following rational number will have a terminating decimal expansion or a non-terminating decimal expansion: $\frac{7^{3}}{2^{3} \times 5^{2}}$ and $\frac{3 \times 7^{3}}{2^{3} \times 3}$

Discussion

22.	Simplify(i) 4+54-5+4-54+5(ii) 13+2-25-3-32-5(iii) 2+32-3+2-32+3+3-13+1(iv) 262+3+626+3-836+2
Answer» Simplify (i) $\frac{4 + \sqrt{5}}{4 - \sqrt{5}} + \frac{4 - \sqrt{5}}{4 + \sqrt{5}}$ (ii) $\frac{1}{\sqrt{3} + \sqrt{2}} - \frac{2}{\sqrt{5} - \sqrt{3}} - \frac{3}{\sqrt{2} - \sqrt{5}}$ (iii) $\frac{2 + \sqrt{3}}{2 - \sqrt{3}} + \frac{2 - \sqrt{3}}{2 + \sqrt{3}} + \frac{\sqrt{3} - 1}{\sqrt{3} + 1}$ (iv) $\frac{2 \sqrt{6}}{\sqrt{2} + \sqrt{3}} + \frac{6 \sqrt{2}}{\sqrt{6} + \sqrt{3}} - \frac{8 \sqrt{3}}{\sqrt{6} + \sqrt{2}}$

Discussion

23.	On a number line, points A, B and C are such that d(A,C) = 10, d(C,B) = 8. Find d(A,B) considering all possibilities.
Answer» On a number line, points A, B and C are such that d(A,C) = 10, d(C,B) = 8. Find d(A,B) considering all possibilities.

Discussion

24.	Factorise:23x2-173x-28
Answer» Factorise: $\frac{2}{3} x^{2} - \frac{17}{3} x - 28$

Discussion

25.	If a and b are the degrees of the polynomials x3+3x5+2x+1 and 15, find (a+b)3.
Answer» If $a$ and $b$ are the degrees of the polynomials $x^{3} + 3 x^{5} + 2 x + 1$ and $15$ , find $(a + b)^{3}$ .

Discussion

26.	Prove that 1/2+cot^2(-theta) = 1/2cosec^2(-theta)-cot^2(-theta)
Answer» Prove that 1/2+cot^2(-theta) = 1/2cosec^2(-theta)-cot^2(-theta)

Discussion

27.	Question 7Two parallelograms are on equal bases and between the same parallels the ratio of their areas is:A) 1:2B) 1:1C) 2:1D) 3:1
Answer» Question 7 Two parallelograms are on equal bases and between the same parallels the ratio of their areas is: A) 1:2 B) 1:1 C) 2:1 D) 3:1

Discussion

28.	Define zero or root of a polynomial.
Answer» Define zero or root of a polynomial.

Discussion

29.	For what value of a (x-5) is a factor of x3−3x2 + ax - 10?
Answer» For what value of a (x-5) is a factor of $x^{3} - 3 x^{2}$ + ax - 10?

Discussion

30.	Question 22Which of the points P(0, 3), Q(1, 0),R(0, -1),S(-5, 0) and T(1, 2) do not lie on the x-axis?A) P and R onlyB) Q and S onlyC) P, R and TD) Q, S and T
Answer» Question 22 Which of the points P(0, 3), Q(1, 0),R(0, -1),S(-5, 0) and T(1, 2) do not lie on the x-axis? A) P and R only B) Q and S only C) P, R and T D) Q, S and T

Discussion

31.	Which of the following is irrational?
Answer» Which of the following is irrational?

Discussion

32.	Evaluate:(i) (4x+2y)2(ii) (5x−y)2(iii) (3x+7y)(3x−7y)
Answer» Evaluate: (i) $(4 x + 2 y)^{2}$ (ii) $(5 x - y)^{2}$ (iii) $(3 x + 7 y) (3 x - 7 y)$

Discussion

33.	Choose the correct statements.
Answer» Choose the correct statements.

Discussion

34.	A circle touches all the sides of a triangle formed by 3x+4y=12 with coordinate axes, in the first quadrant. If p and q are sum and product of radii of all such possible circles, then the quadratic equation whose roots are p and q is
Answer» A circle touches all the sides of a triangle formed by $3 x + 4 y = 12$ with coordinate axes, in the first quadrant. If $p$ and $q$ are sum and product of radii of all such possible circles, then the quadratic equation whose roots are $p$ and $q$ is

Discussion

35.	Tuberculosis is spread by _________.
Answer» Tuberculosis is spread by _________.

Discussion

36.	The line 6x + 5y = 9, cuts the x-axis at
Answer» The line 6x + 5y = 9, cuts the x-axis at

Discussion

37.	A right angled triangle ABC is constructed with BC = 3 cm and AB + AC = 9 cm. If B is the right angled, then find the length of AC (in cm).5
Answer» A right angled triangle ABC is constructed with BC = 3 $cm$ and AB + AC = 9 $cm$ . If B is the right angled, then find the length of AC (in cm). 5

Discussion

38.	Verify whether A = {20, 22, 23, 24} and B = {25, 30, 40, 45} are disjoint sets.
Answer» Verify whether A = {20, 22, 23, 24} and B = {25, 30, 40, 45} are disjoint sets.

Discussion

39.	Following information has been given by Rajendra. Prepare a Bank Reconciliation Statement as on 31st Dec. 2016, showing balance as per cash book:(i) Debit balance shown by the pass book ₹ 17,800.(ii) Cheques of ₹ 21,600 were issued in the last week of December, but of these ₹ 14,800 only were presented for payment.(iii) Cheques of ₹ 10,750 were deposited in bank, out of them a cheque of ₹ 4,200 was credited in the first week of January, 2017.(iv) A cheque of ₹ 1,200 was debited in the cash book but was not deposited in bank.(v) Insurance premium paid by bank ₹ 1,450.(vi) A bill of exchange for ₹ 6,200 which was discounted with bank, returned dishonoured but no entry was made in the cash book.(vii) Bank charges and interest charged by bank are ₹ 350.
Answer» Following information has been given by Rajendra. Prepare a Bank Reconciliation Statement as on 31st Dec. 2016, showing balance as per cash book: (i) Debit balance shown by the pass book ₹ 17,800. (ii) Cheques of ₹ 21,600 were issued in the last week of December, but of these ₹ 14,800 only were presented for payment. (iii) Cheques of ₹ 10,750 were deposited in bank, out of them a cheque of ₹ 4,200 was credited in the first week of January, 2017. (iv) A cheque of ₹ 1,200 was debited in the cash book but was not deposited in bank. (v) Insurance premium paid by bank ₹ 1,450. (vi) A bill of exchange for ₹ 6,200 which was discounted with bank, returned dishonoured but no entry was made in the cash book. (vii) Bank charges and interest charged by bank are ₹ 350.

Discussion

40.	Find the capacity in litres of a conical vessel with:(i) radius 7 cm, slant height 25 cm(ii) height 12 cm, slant height 13 cm.
Answer» Find the capacity in litres of a conical vessel with: (i) radius 7 cm, slant height 25 cm (ii) height 12 cm, slant height 13 cm.

Discussion

41.	In the given figure, if ∠B=∠Q, then _____.
Answer» In the given figure, if $∠ B = ∠ Q$ , then _____.

41.

In the given figure, if ∠B=∠Q, then _____.

Answer»

In the given figure, if $∠ B = ∠ Q$ , then _____.

Discussion

42.	Find the value of k, if (1, 3k) lies on the line represented by the equation kx+4y=26.
Answer» Find the value of k, if (1, 3k) lies on the line represented by the equation $k x + 4 y = 26$ .

Discussion

43.	Find the value of x represented by the following set of tiles.
Answer» Find the value of x represented by the following set of tiles.

Discussion

44.	Write the following cubes in expanded form:(3x2+1)3
Answer» Write the following cubes in expanded form: ( $\frac{3 x}{2} + 1)^{3}$

44.

Write the following cubes in expanded form:(3x2+1)3

Answer»

Write the following cubes in expanded form:

( $\frac{3 x}{2} + 1)^{3}$

Discussion

45.	Factorise:8(3a-2b)^2-10(3a-2b)
Answer» Factorise:8(3a-2b)^2-10(3a-2b)

Discussion

46.	A median of a triangle divides it into two ___________.
Answer» A median of a triangle divides it into two ___________.

Discussion

47.	If the areas of three adjacent faces of a cuboid are 8 cm2, 18 cm2 and 25 cm2, Find the volume of the cuboid.
Answer» If the areas of three adjacent faces of a cuboid are 8 $c m^{2}, 18 c m^{2} a n d 25 c m^{2}$ , Find the volume of the cuboid.

Discussion

48.	In the figure, point D and E are on side BC of ∆ABC, such that BD = CE and AD = AE.Show that ∆ ABD≅ ∆ACE.
Answer» In the figure, point D and E are on side BC of $∆$ ABC, such that BD = CE and AD = AE. Show that $∆$ ABD $≅$ $∆$ ACE.

Discussion

49.	8. Prove that area of triangle ACE is equal to 1/4 area ABC.If E is the mid point of median AD of triangle ABC
Answer» 8. Prove that area of triangle ACE is equal to 1/4 area ABC.If E is the mid point of median AD of triangle ABC

Discussion

50.	(i) Find three rational numbers between 5 and -2 (ii) Find three rational numbers between −34 and 12
Answer» (i) Find three rational numbers between 5 and -2 (ii) Find three rational numbers between $- \frac{3}{4}$ and $\frac{1}{2}$

50.

(i) Find three rational numbers between 5 and -2 (ii) Find three rational numbers between −34 and 12

Answer»

(i) Find three rational numbers between 5 and -2

(ii) Find three rational numbers between
$- \frac{3}{4}$ and $\frac{1}{2}$

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Three cubes whose edges are 3 cm, 4 cm and 5 cm respectively are melted to form a single cube. Find the surface area of the new cube.

If 8:2 is greater than 5:a, value of a is greater than .

Question 6 (ii)The volume of a right circular cone is 9856cm3. If the diameter of the base is 28 cm, find slant height of the cone.[Assume π=227]

In an isosceles right triangle ABC, right-angled at B, the longest side is ___?

The solution of the equation 3x+7y=30 if x=y is.

75. In the adjoining figure quad. ABCD is circumscribed.If the radius of the incircle with centre O is 10cm and AD perpendicular to DC,find the value of x.

What is the number of significant figures in (3.20+ 4.80) x 105? (2) 4 (4) 2(3) 3

ABCD is a trapezium in which AB parallel to CD,M and N are midpoint ofAB & CD respectivly . AB=12cm &MN=14cm.Find CD

in a quadriletral ABCD the line segment bisect\angle C and\angle D meet atE prove that \angle A+\angle B =2\angle CE

what is rhombic?

Question 1 (v)Without actually performing the long division, state whether 29343 will have a terminating decimal expansion or a non-terminating repeating decimal expansion.

If x−1x=√3, then find the value of x3−1x3.

Question 2The coach of a cricket team buys 3 bats and 6 balls for Rs 3900. Later, she buys another bat and 2 more balls of the same kind for Rs 1300. Represent this situation algebraically and geometrically.

Question 19 In following figure, coordinate of P are A) (-4 , 2) B) (-2, 4) C) (4, -2) D) (2,-4)

In the given figure, D and E are mid points of sides AB and AC of △ABC. Which of the following is true?

Find the equation of straight line containing the point (3,2) and making positive equal intercepts on axes

A group of researchers were given an assignment to collect different types of leaves. The group collected 256 types of leaves. Represent the number of leaves collected in the form of exponential expression with its base being indivisible. [2 MARKS]

If 8x+1 = 64 , what is the value of 32x+1 ?(a) 1(b) 3(c) 9(d) 27

ABCD is a parallelogram as shown in figure. If AB=2AD and P is the midpoint of AB, then ∠CPD is equal to

If p:7 is the ratio in which the line segment joining the points (-3, 10) and (6, - 8) is divided by (-1, 6), what is the value of p?2

Without actually performing the long division, state whether the following rational number will have a terminating decimal expansion or a non-terminating decimal expansion:7323×52 and 3×7323×3

Simplify(i) 4+54-5+4-54+5(ii) 13+2-25-3-32-5(iii) 2+32-3+2-32+3+3-13+1(iv) 262+3+626+3-836+2

On a number line, points A, B and C are such that d(A,C) = 10, d(C,B) = 8. Find d(A,B) considering all possibilities.

Factorise:23x2-173x-28

If a and b are the degrees of the polynomials x3+3x5+2x+1 and 15, find (a+b)3.

Prove that 1/2+cot^2(-theta) = 1/2cosec^2(-theta)-cot^2(-theta)

Question 7Two parallelograms are on equal bases and between the same parallels the ratio of their areas is:A) 1:2B) 1:1C) 2:1D) 3:1

Define zero or root of a polynomial.

For what value of a (x-5) is a factor of x3−3x2 + ax - 10?

Question 22Which of the points P(0, 3), Q(1, 0),R(0, -1),S(-5, 0) and T(1, 2) do not lie on the x-axis?A) P and R onlyB) Q and S onlyC) P, R and TD) Q, S and T

Which of the following is irrational?

Evaluate:(i) (4x+2y)2(ii) (5x−y)2(iii) (3x+7y)(3x−7y)

Choose the correct statements.

A circle touches all the sides of a triangle formed by 3x+4y=12 with coordinate axes, in the first quadrant. If p and q are sum and product of radii of all such possible circles, then the quadratic equation whose roots are p and q is

Tuberculosis is spread by _________.

The line 6x + 5y = 9, cuts the x-axis at

A right angled triangle ABC is constructed with BC = 3 cm and AB + AC = 9 cm. If B is the right angled, then find the length of AC (in cm).5

Verify whether A = {20, 22, 23, 24} and B = {25, 30, 40, 45} are disjoint sets.

Find the capacity in litres of a conical vessel with:(i) radius 7 cm, slant height 25 cm(ii) height 12 cm, slant height 13 cm.

In the given figure, if ∠B=∠Q, then _____.

Find the value of k, if (1, 3k) lies on the line represented by the equation kx+4y=26.

Find the value of x represented by the following set of tiles.

Write the following cubes in expanded form:(3x2+1)3

Factorise:8(3a-2b)^2-10(3a-2b)

A median of a triangle divides it into two ___________.

If the areas of three adjacent faces of a cuboid are 8 cm2, 18 cm2 and 25 cm2, Find the volume of the cuboid.

In the figure, point D and E are on side BC of ∆ABC, such that BD = CE and AD = AE.Show that ∆ ABD≅ ∆ACE.

8. Prove that area of triangle ACE is equal to 1/4 area ABC.If E is the mid point of median AD of triangle ABC

(i) Find three rational numbers between 5 and -2 (ii) Find three rational numbers between −34 and 12