24740 + Interview Questions in Mathematics

1.	The mean of 25 observations is 36. If the mean of the first 13 observations is 32 and that of the last 13 observations is 39, find the 13th observation.
Answer» The mean of 25 observations is 36. If the mean of the first 13 observations is 32 and that of the last 13 observations is 39, find the 13th observation.

Discussion

2.	The two adjacent sides of a parallelogram are 2i^-4j^-5k^ and 2i^+2j^+3k^. Find the two unit vectors parallel to its diagonals. Using the diagonal vectors, find the area of the parallelogram.
Answer» The two adjacent sides of a parallelogram are $2 \hat{i} - 4 \hat{j} - 5 \hat{k} and 2 \hat{i} + 2 \hat{j} + 3 \hat{k}$ . Find the two unit vectors parallel to its diagonals. Using the diagonal vectors, find the area of the parallelogram.

Discussion

3.	3 out of 9 eggs are broken. What fraction of total eggs are damaged?
Answer» 3 out of 9 eggs are broken. What fraction of total eggs are damaged?

Discussion

4.	Counting numbers are also called as:
Answer» Counting numbers are also called as:

Discussion

5.	if the ratio of complement of x and supplement of y is 1:2, then what will be the ratio of x and y
Answer» if the ratio of complement of x and supplement of y is 1:2, then what will be the ratio of x and y

Discussion

6.	If the (p+q)th term of a G.P. is m and (p−q)th term is n, then pth term will be _____.
Answer» If the $(p + q)^{t h}$ term of a G.P. is m and $(p - q)^{t h}$ term is n, then pth term will be _____.

Discussion

7.	What is polynomial?
Answer» What is polynomial?

Discussion

8.	The probability distribution of x isx0123P(x)0.2kk2kFind the value of k
Answer» The probability distribution of x is $\begin{matrix} x & 0 & 1 & 2 & 3 P (x) & 0.2 & k & k & 2 k \end{matrix}$ Find the value of k

8.

The probability distribution of x isx0123P(x)0.2kk2kFind the value of k

Answer»

The probability distribution of x is

$\begin{matrix} x & 0 & 1 & 2 & 3 P (x) & 0.2 & k & k & 2 k \end{matrix}$

Find the value of k

Discussion

9.	The paint in a certain container is sufficient to paint an area of 9.375 mt sq. how many bricks measuring 22.5 cm * 10 cm *7.5 cm can be painted out of the paint in the container ?
Answer» The paint in a certain container is sufficient to paint an area of 9.375 mt sq. how many bricks measuring 22.5 cm * 10 cm *7.5 cm can be painted out of the paint in the container ?

Discussion

10.	Question 18 (i) A box contains 90 discs which are numbered from 1 to 90. If one disc is drawn at random from the box, find the probability that it bears a two-digit number.
Answer» Question 18 (i) A box contains 90 discs which are numbered from 1 to 90. If one disc is drawn at random from the box, find the probability that it bears a two-digit number.

Discussion

11.	In the given figure, JKLM is a square with sides of length 6 units. Points A and B are the mid points of sides KL and LM respectively. If a point is selected at random from the interior of the square. What is the probability that the point will be chosen from the interior of ΔJAB?
Answer» In the given figure, JKLM is a square with sides of length 6 units. Points A and B are the mid points of sides KL and LM respectively. If a point is selected at random from the interior of the square. What is the probability that the point will be chosen from the interior of ΔJAB?

Discussion

12.	What could be an example of finding algebraic factor of a number ?
Answer» What could be an example of finding algebraic factor of a number ?

Discussion

13.	What property of a rectangle do we use if we need to construct a rectangle whose adjacent sides are given?
Answer» What property of a rectangle do we use if we need to construct a rectangle whose adjacent sides are given?

Discussion

14.	The histogram below represents marks of students in a Mathematics exam with passing marks as 30. How many students failed in the exam?
Answer» The histogram below represents marks of students in a Mathematics exam with passing marks as 30. How many students failed in the exam?

14.

The histogram below represents marks of students in a Mathematics exam with passing marks as 30. How many students failed in the exam?

Answer»

The histogram below represents marks of students in a Mathematics exam with passing marks as 30. How many students failed in the exam?

Discussion

15.	If two parallel lines are intersected by a transversal, then the bisectors of any two corresponding angles are
Answer» If two parallel lines are intersected by a transversal, then the bisectors of any two corresponding angles are

Discussion

16.	Question 166 Both the pairs of opposite angles of a quadrilateral are equal and supplementary. Find the measure of each angle.
Answer» Question 166 Both the pairs of opposite angles of a quadrilateral are equal and supplementary. Find the measure of each angle.

Discussion

17.	Which of the following given sequences can be represented as a polynomial in one variable?
Answer» Which of the following given sequences can be represented as a polynomial in one variable?

Discussion

18.	Question 1If three angles of a quadrilateral are each equal to 75∘, the fourth angle isa) 150∘b) 135∘c) 45∘d) 75∘
Answer» Question 1 If three angles of a quadrilateral are each equal to $75^{\circ}$ , the fourth angle is a) $150^{\circ}$ b) $135^{\circ}$ c) $45^{\circ}$ d) $75^{\circ}$

Discussion

19.	Question 5If x=√3+√2√3−√2 and y=√3−√2√3+√2, then find the value of x2+y2?
Answer» Question 5 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

20.	Question 2Prove that 3+2√5 is irrational.
Answer» Question 2 Prove that $3 + 2 \sqrt{5}$ is irrational.

Discussion

21.	Show that:(i) 11+xa-b+11+xb-a=1(ii) xaa-bxaa+b÷xbb-axbb+aa+b=1(iii) x1a-b1a-cx1b-c1b-ax1c-a1c-b=1(iv) xa2+b2xaba+bxb2+c2xbcb+cxc2+a2xaca+c=x2a3+b3+c3(v) xa-ba+bxb-cb+cxc-ac+a=1(vi) xa-a-11a-1aa+1=x(vii) ax+1ay+1x+yay+2az+2y+zaz+3ax+3z+x=1(viii) 3a3ba+b3b3cb+c3c3ac+a=1
Answer» Show that: (i) $\frac{1}{1 + x^{a - b}} + \frac{1}{1 + x^{b - a}} = 1$ (ii) ${[\{\frac{x^{a (a - b)}}{x^{a (a + b)}}\} \div \{\frac{x^{b (b - a)}}{x^{b (b + a)}}\}]}^{a + b} = 1$ (iii) ${(x^{\frac{1}{a - b}})}^{\frac{1}{a - c}} {(x^{\frac{1}{b - c}})}^{\frac{1}{b - a}} {(x^{\frac{1}{c - a}})}^{\frac{1}{c - b}} = 1$ (iv) ${(\frac{x^{a^{2} + b^{2}}}{x^{a b}})}^{a + b} {(\frac{x^{b^{2} + c^{2}}}{x^{b c}})}^{b + c} {(\frac{x^{c^{2} + a^{2}}}{x^{a c}})}^{a + c} = x^{2 (a^{3} + b^{3} + c^{3})}$ (v) ${(x^{a - b})}^{a + b} {(x^{b - c})}^{b + c} {(x^{c - a})}^{c + a} = 1$ (vi) ${\{{(x^{a - a^{- 1}})}^{\frac{1}{a - 1}}\}}^{\frac{a}{a + 1}} = x$ (vii) ${(\frac{a^{x + 1}}{a^{y + 1}})}^{x + y} {(\frac{a^{y + 2}}{a^{z + 2}})}^{y + z} {(\frac{a^{z + 3}}{a^{x + 3}})}^{z + x} = 1$ (viii) ${(\frac{3^{a}}{3^{b}})}^{a + b} {(\frac{3^{b}}{3^{c}})}^{b + c} {(\frac{3^{c}}{3^{a}})}^{c + a} = 1$

Discussion

22.	From a point O in the interior of triangle ABC, perpendiculars OD, OE and OF are drawn to the sides BC,CA and AB respectively. Prove that-(i) AF^2 + BD^2 + CE^2 = OA^2 +OB^2 + OC^2 - OD^2 - OE^2 - OF^2.(ii) AF^2 + BD^2 + CE^2 = AE^2 + CD^2 + BF^2
Answer» From a point O in the interior of triangle ABC, perpendiculars OD, OE and OF are drawn to the sides BC,CA and AB respectively. Prove that- (i) AF^2 + BD^2 + CE^2 = OA^2 +OB^2 + OC^2 - OD^2 - OE^2 - OF^2. (ii) AF^2 + BD^2 + CE^2 = AE^2 + CD^2 + BF^2

Discussion

23.	19. A cone of height 24 cm has a curved surface area of 550 cm2 . Find its volume.
Answer» 19. A cone of height 24 cm has a curved surface area of 550 cm2 . Find its volume.

Discussion

24.	Derivation of formula of volume of cuboid
Answer» Derivation of formula of volume of cuboid

Discussion

25.	Simplify (2+√52−√5)+(2−√52+√5).
Answer» Simplify $(\frac{2 + \sqrt{5}}{2 - \sqrt{5}}) + (\frac{2 - \sqrt{5}}{2 + \sqrt{5}})$ .

Discussion

26.	62.Find the zeros of the following polynomial by factorization method and verify the relation between the zeros and the coefficients of the polynomial first 4 x square + 5 root 2 X -3,
Answer» 62.Find the zeros of the following polynomial by factorization method and verify the relation between the zeros and the coefficients of the polynomial first 4 x square + 5 root 2 X -3,

Discussion

27.	Line AB \|\| CD and transversal XY meets AB at M and CD at N. If ∠AMX=x and ∠CNX=2x−60, then x= .
Answer» Line AB \|\| CD and transversal XY meets AB at M and CD at N. If $∠ A M X = x and ∠ C N X = 2 x - 60$ , then $x =$ .

Discussion

28.	Find the equation of the hyperbola whose eccentricity is (4/3) ,focus is (0,4) and the directrix is the line 4y-9=0
Answer» Find the equation of the hyperbola whose eccentricity is (4/3) ,focus is (0,4) and the directrix is the line 4y-9=0

Discussion

29.	What is the length (in terms of π) of the arc that subtends an angle of 36° at the centre of a circle of radius 5 cm?
Answer» What is the length (in terms of π) of the arc that subtends an angle of 36° at the centre of a circle of radius 5 cm?

Discussion

30.	Find the maximum possible exterior angle in a regular polygon.
Answer» Find the maximum possible exterior angle in a regular polygon.

Discussion

31.	An irrational number between 2 and 2.5 is(a) 11(b) 5(c) 22.5(d) 12.5
Answer» An irrational number between 2 and 2.5 is (a) $\sqrt{11}$ (b) $\sqrt{5}$ (c) $\sqrt{22.5}$ (d) $\sqrt{12.5}$

Discussion

32.	Using the remainder theorem, find the remainder, when p(x) is divided by g(x), where p(x)=2x3−9x2+x+15,g(x)=2x−3
Answer» Using the remainder theorem, find the remainder, when p(x) is divided by g(x), where $p (x) = 2 x^{3} - 9 x^{2} + x + 15, g (x) = 2 x - 3$

Discussion

33.	Set up an equation in the following case:The teacher tells the class that the highest marks obtained by a student in her class is twice the lowest marks plus 7. The highest score is 87. (Take the lowest score to be l. )
Answer» Set up an equation in the following case: The teacher tells the class that the highest marks obtained by a student in her class is twice the lowest marks plus 7. The highest score is 87. (Take the lowest score to be l. )

Discussion

34.	Please give me theorems with proper explanation of CH quadrilaterals.
Answer» Please give me theorems with proper explanation of CH quadrilaterals.

Discussion

35.	In a parallelogram PQRS, T and U are the points on the diagonal QS such that ST = QU, then quadrilateral PTRU is aOptions:ParallelogramRhombusSquareRectangleIt is a parallelogram but it can also be rhombus??
Answer» In a parallelogram PQRS, T and U are the points on the diagonal QS such that ST = QU, then quadrilateral PTRU is a Options: Parallelogram Rhombus Square Rectangle It is a parallelogram but it can also be rhombus??

Discussion

36.	On 31st March, 2018, Cash Book of Mahesh showed debit bank balance of ₹ 75,000. When compared with the Bank Statement, following facts were discovered. On 30th March, two cheques of ₹ 5,000 and ₹ 7,000 were deposited in the bank but were not realised till date. On 28th March, three cheques of ₹ 6,000, ₹ 8,000 and ₹ 12,000 were issued but none of these were presented to the bank for payment. On 31st March, bank credited ₹ 1,250 as interest but this was not recorded in the Cash Book. Similarly, the bank had charged ₹ 150 as bank charges but this was not recorded in the Cash Book.Bank paid insurance premium of ₹ 5,000 but it was recorded as ₹ 500 in Cash Book. Prepare Bank Reconcilation Statement on 31st March, 2018.
Answer» On 31st March, 2018, Cash Book of Mahesh showed debit bank balance of ₹ 75,000. When compared with the Bank Statement, following facts were discovered. On 30th March, two cheques of ₹ 5,000 and ₹ 7,000 were deposited in the bank but were not realised till date. On 28th March, three cheques of ₹ 6,000, ₹ 8,000 and ₹ 12,000 were issued but none of these were presented to the bank for payment. On 31st March, bank credited ₹ 1,250 as interest but this was not recorded in the Cash Book. Similarly, the bank had charged ₹ 150 as bank charges but this was not recorded in the Cash Book. Bank paid insurance premium of ₹ 5,000 but it was recorded as ₹ 500 in Cash Book. Prepare Bank Reconcilation Statement on 31st March, 2018.

Discussion

37.	Question 83 (xiii)Multiply the following:b3,3b2,7ab5
Answer» Question 83 (xiii) Multiply the following: $b^{3}, 3 b^{2}, 7 a b^{5}$

Discussion

38.	In the given square ABCD, a line segment DE cuts the side BC at E and the diagonal AC at O such that ∠ COD=120∘. Find the measure of ∠ OEC.
Answer» In the given square ABCD, a line segment DE cuts the side BC at E and the diagonal AC at O such that $∠ C O D = 120^{\circ} .$ Find the measure of $∠ O E C .$

Discussion

39.

Krishan started his business on 1st April, 2017 with a Capital of ₹ 1,00,000. On 31st March, 2018, his assets were : ₹ Cash 3,200 Stock 34,800 Debtors 31,000 Plant 85,000 He owed ₹ 12,000 to sundry creditors and ₹ 10,000 to his brother on that date. He withdrew ₹ 2,000 per month for the private expenses. Ascertain his profit.

Answer» Krishan started his business on 1st April, 2017 with a Capital of ₹ 1,00,000. On 31st March, 2018, his assets were :

	₹
Cash	3,200
Stock	34,800
Debtors	31,000
Plant	85,000

He owed ₹ 12,000 to sundry creditors and ₹ 10,000 to his brother on that date. He withdrew ₹ 2,000 per month for the private expenses. Ascertain his profit.

Discussion

40.	If the 9th term in the expansion of ⎛⎜⎝3log3√25x−1+7+3−18log3(5x−1+1)⎞⎟⎠10 is 180, then the value(s) of x is/are
Answer» If the $9^{th}$ term in the expansion of ${⎛ ⎜ ⎝ 3^{{log}_{3} \sqrt{25^{x - 1} + 7}} + 3^{- \frac{1}{8} {log}_{3} (5^{x - 1} + 1)} ⎞ ⎟ ⎠}^{10}$ is $180$ , then the value(s) of $x$ is/are

Discussion

41.	On a square handkerchief, nine circular designs each of radius 7 cm are made (see Fig. 12.29). Find the area of the remaining portion of the handkerchief.
Answer» On a square handkerchief, nine circular designs each of radius 7 cm are made (see Fig. 12.29). Find the area of the remaining portion of the handkerchief.

41.

On a square handkerchief, nine circular designs each of radius 7 cm are made (see Fig. 12.29). Find the area of the remaining portion of the handkerchief.

Answer»

On a square handkerchief, nine circular designs each of radius 7 cm are made (see Fig. 12.29). Find the area of the remaining portion of the handkerchief.

Discussion

42.	What is the meaning of b and c in the equation for parabolic curve? I think c will be y-intercept but what about b?
Answer» What is the meaning of b and c in the equation for parabolic curve? I think c will be y-intercept but what about b?

Discussion

43.	A sphere of radius 13 cm is cut by a plane whose distance from the centre of the sphere is 5cm. What is the circumference of the section so obtained?
Answer» A sphere of radius 13 cm is cut by a plane whose distance from the centre of the sphere is 5cm. What is the circumference of the section so obtained?

Discussion

44.	xlog9 x>9 implies
Answer» $x^{l o g_{9} x} > 9$ implies

Discussion

45.	If random error in an experiment for 30 observations is a then random error in the experiment for 120 observations will be
Answer» If random error in an experiment for 30 observations is a then random error in the experiment for 120 observations will be

Discussion

46.	At age four, Mozart's father began taking him on tours of the capitals of Europe, in order to demonstrate his musical talents.
Answer» At age four, Mozart's father began taking him on tours of the capitals of Europe, in order to demonstrate his musical talents.

Discussion

47.	In given figure, EB⊥AC, BG⊥AE and CF⊥AE Prove that: (i) ΔABG∼ΔDCB (ii) BCBD=BEBA
Answer» In given figure, $E B ⊥ A C, B G ⊥ A E$ and $C F ⊥ A E$ Prove that: (i) $Δ A B G \sim Δ D C B$ (ii) $\frac{B C}{B D} = \frac{B E}{B A}$

Discussion

48.	Question 88 (xii)Factorise the following expression.lx+my+mx+ly
Answer» Question 88 (xii) Factorise the following expression. $l x + m y + m x + l y$

Discussion

49.	Show that the quadrilateral whose vertices are (2, −1), (3, 4) (−2, 3) and (−3,−2) is a rhombus.
Answer» Show that the quadrilateral whose vertices are (2, −1), (3, 4) (−2, 3) and (−3,−2) is a rhombus.

Discussion

50.	In ΔABC,AB=9 cm,AC=15 cm and DE\|\|BC. If ABAD=3, sort in ascending order of length.
Answer» In $Δ A B C, A B = 9 c m, A C = 15 c m$ and $D E \| \| B C .$ If $\frac{A B}{A D} = 3$ , sort in ascending order of length.

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

The mean of 25 observations is 36. If the mean of the first 13 observations is 32 and that of the last 13 observations is 39, find the 13th observation.

The two adjacent sides of a parallelogram are 2i^-4j^-5k^ and 2i^+2j^+3k^. Find the two unit vectors parallel to its diagonals. Using the diagonal vectors, find the area of the parallelogram.

3 out of 9 eggs are broken. What fraction of total eggs are damaged?

Counting numbers are also called as:

if the ratio of complement of x and supplement of y is 1:2, then what will be the ratio of x and y

If the (p+q)th term of a G.P. is m and (p−q)th term is n, then pth term will be _____.

What is polynomial?

The probability distribution of x isx0123P(x)0.2kk2kFind the value of k

The paint in a certain container is sufficient to paint an area of 9.375 mt sq. how many bricks measuring 22.5 cm * 10 cm *7.5 cm can be painted out of the paint in the container ?

Question 18 (i) A box contains 90 discs which are numbered from 1 to 90. If one disc is drawn at random from the box, find the probability that it bears a two-digit number.

In the given figure, JKLM is a square with sides of length 6 units. Points A and B are the mid points of sides KL and LM respectively. If a point is selected at random from the interior of the square. What is the probability that the point will be chosen from the interior of ΔJAB?

What could be an example of finding algebraic factor of a number ?

What property of a rectangle do we use if we need to construct a rectangle whose adjacent sides are given?

The histogram below represents marks of students in a Mathematics exam with passing marks as 30. How many students failed in the exam?

If two parallel lines are intersected by a transversal, then the bisectors of any two corresponding angles are

Question 166 Both the pairs of opposite angles of a quadrilateral are equal and supplementary. Find the measure of each angle.

Which of the following given sequences can be represented as a polynomial in one variable?

Question 1If three angles of a quadrilateral are each equal to 75∘, the fourth angle isa) 150∘b) 135∘c) 45∘d) 75∘

Question 5If x=√3+√2√3−√2 and y=√3−√2√3+√2, then find the value of x2+y2?

Question 2Prove that 3+2√5 is irrational.

Show that:(i) 11+xa-b+11+xb-a=1(ii) xaa-bxaa+b÷xbb-axbb+aa+b=1(iii) x1a-b1a-cx1b-c1b-ax1c-a1c-b=1(iv) xa2+b2xaba+bxb2+c2xbcb+cxc2+a2xaca+c=x2a3+b3+c3(v) xa-ba+bxb-cb+cxc-ac+a=1(vi) xa-a-11a-1aa+1=x(vii) ax+1ay+1x+yay+2az+2y+zaz+3ax+3z+x=1(viii) 3a3ba+b3b3cb+c3c3ac+a=1

From a point O in the interior of triangle ABC, perpendiculars OD, OE and OF are drawn to the sides BC,CA and AB respectively. Prove that-(i) AF^2 + BD^2 + CE^2 = OA^2 +OB^2 + OC^2 - OD^2 - OE^2 - OF^2.(ii) AF^2 + BD^2 + CE^2 = AE^2 + CD^2 + BF^2

19. A cone of height 24 cm has a curved surface area of 550 cm2 . Find its volume.

Derivation of formula of volume of cuboid

Simplify (2+√52−√5)+(2−√52+√5).

62.Find the zeros of the following polynomial by factorization method and verify the relation between the zeros and the coefficients of the polynomial first 4 x square + 5 root 2 X -3,

Line AB || CD and transversal XY meets AB at M and CD at N. If ∠AMX=x and ∠CNX=2x−60, then x= .

Find the equation of the hyperbola whose eccentricity is (4/3) ,focus is (0,4) and the directrix is the line 4y-9=0

What is the length (in terms of π) of the arc that subtends an angle of 36° at the centre of a circle of radius 5 cm?

Find the maximum possible exterior angle in a regular polygon.

An irrational number between 2 and 2.5 is(a) 11(b) 5(c) 22.5(d) 12.5

Using the remainder theorem, find the remainder, when p(x) is divided by g(x), where p(x)=2x3−9x2+x+15,g(x)=2x−3

Set up an equation in the following case:The teacher tells the class that the highest marks obtained by a student in her class is twice the lowest marks plus 7. The highest score is 87. (Take the lowest score to be l. )

Please give me theorems with proper explanation of CH quadrilaterals.

In a parallelogram PQRS, T and U are the points on the diagonal QS such that ST = QU, then quadrilateral PTRU is aOptions:ParallelogramRhombusSquareRectangleIt is a parallelogram but it can also be rhombus??

Question 83 (xiii)Multiply the following:b3,3b2,7ab5

In the given square ABCD, a line segment DE cuts the side BC at E and the diagonal AC at O such that ∠ COD=120∘. Find the measure of ∠ OEC.

If the 9th term in the expansion of ⎛⎜⎝3log3√25x−1+7+3−18log3(5x−1+1)⎞⎟⎠10 is 180, then the value(s) of x is/are

On a square handkerchief, nine circular designs each of radius 7 cm are made (see Fig. 12.29). Find the area of the remaining portion of the handkerchief.

What is the meaning of b and c in the equation for parabolic curve? I think c will be y-intercept but what about b?

A sphere of radius 13 cm is cut by a plane whose distance from the centre of the sphere is 5cm. What is the circumference of the section so obtained?

xlog9 x&gt;9 implies

If random error in an experiment for 30 observations is a then random error in the experiment for 120 observations will be

At age four, Mozart's father began taking him on tours of the capitals of Europe, in order to demonstrate his musical talents.

In given figure, EB⊥AC, BG⊥AE and CF⊥AE Prove that: (i) ΔABG∼ΔDCB (ii) BCBD=BEBA

Question 88 (xii)Factorise the following expression.lx+my+mx+ly

Show that the quadrilateral whose vertices are (2, −1), (3, 4) (−2, 3) and (−3,−2) is a rhombus.

In ΔABC,AB=9 cm,AC=15 cm and DE||BC. If ABAD=3, sort in ascending order of length.

xlog9 x>9 implies