24740 + Interview Questions in Mathematics

1.	Find the correct option when x is the subject of the formula of given expression. a(x–b)=a2+bx
Answer» Find the correct option when x is the subject of the formula of given expression. $a (x - b) = a^{2} + b x$

1.

Find the correct option when x is the subject of the formula of given expression. a(x–b)=a2+bx

Answer»

Find the correct option when x is the subject of the formula of given expression.

$a (x - b) = a^{2} + b x$

2.	Draw graph of the following x+y=4
Answer» Draw graph of the following x+y=4

Discussion

3.	For √3x2 to be irrational, x should be
Answer» For $\sqrt{3} x^{2}$ to be irrational, x should be

Discussion

4.	Simplify √128.
Answer» Simplify $\sqrt{128}$ .

Discussion

5.	133, 73, 89, 108, 94, 104, 94, 85, 100, 120
Answer» 133, 73, 89, 108, 94, 104, 94, 85, 100, 120

Discussion

6.	Find the mode of the following items. 0,6,5,1,6,4,3,0,2,6,5,6
Answer» Find the mode of the following items. 0,6,5,1,6,4,3,0,2,6,5,6

Discussion

7.	The inverse of the function is f(x)=10x−10−x10x+10−x+1 is
Answer» The inverse of the function is $f (x) = \frac{10^{x} - 10^{- x}}{10^{x} + 10^{- x}} + 1$ is

Discussion

8.	If O is the center of the circle, then the value of θ in the adjoining figure is
Answer» If O is the center of the circle, then the value of $θ$ in the adjoining figure is

Discussion

9.	Factorise:9x2 – 16y2
Answer» Factorise: 9x² – 16y²

Discussion

10.	The area of a regular hexagon of side 6 cm is __________.
Answer» The area of a regular hexagon of side 6 cm is __________.

Discussion

11.	Find the least fraction, which must be multiplied to (124 −12 +3616 −116 +28)to make it an integer.
Answer» Find the least fraction, which must be multiplied to $(1 \frac{2}{4} - \frac{1}{2} + 3 \frac{6}{16} - \frac{1}{16} + \frac{2}{8})$ to make it an integer.

Discussion

12.	Question 18 Show that p – 1 is a factor of p10–1 and also of p11–1.
Answer» Question 18 Show that p – 1 is a factor of $p^{10} - 1$ and also of $p^{11} - 1$ .

Discussion

13.	If x - 2 and x - 12 both are the factors of the polynomial nx2 − 5x + m, then show that m = n= 2
Answer» If $x - 2$ and $x - \frac{1}{2}$ both are the factors of the polynomial nx² − 5x + m, then show that $m = n = 2$

Discussion

14.	Find the zero of the polynomial x2-bxy + cy2 where -b =p-q and c =-pq
Answer» Find the zero of the polynomial x²-bxy + cy²where -b =p-q and c =-pq

Discussion

15.	The image of the point (–5, 7) in y-axis has the coordinates(a) (5, 7)(b) (–5, –7)(c) (5, –7)(d) (7, –5)
Answer» The image of the point (–5, 7) in y-axis has the coordinates (a) (5, 7) (b) (–5, –7) (c) (5, –7) (d) (7, –5)

Discussion

16.	The area of a regular hexagon of side ‘a’ is the sum of the areas of the ___ equilateral triangles with side a.
Answer» The area of a regular hexagon of side ‘a’ is the sum of the areas of the ___ equilateral triangles with side a.

Discussion

17.	In the given figure, if MN and PQ are parallel, find the value of X + Y in degrees.105
Answer» In the given figure, if MN and PQ are parallel, find the value of $X + Y$ in degrees. 105

Discussion

18.	If (a, 4) lies on the graph of 3x + y = 10, then the value of a is(a) 3(b) 1(c) 3(d) 4
Answer» If (a, 4) lies on the graph of 3x + y = 10, then the value of a is (a) 3 (b) 1 (c) 3 (d) 4

Discussion

19.	If a+b+c=0 proove that a²+ab+b²=b²+bc+c²=c²+ac+a²
Answer» If a+b+c=0 proove that a²+ab+b²=b²+bc+c²=c²+ac+a²

Discussion

20.	1. A polynomial leaves remainder 5 when divided by x-3. It also leave remainder 7 when divided by x-4. Find remainder when it divided by (x-3)(x-4
Answer» 1. A polynomial leaves remainder 5 when divided by x-3. It also leave remainder 7 when divided by x-4. Find remainder when it divided by (x-3)(x-4

Discussion

21.	The parallel sides of an isosceles trapezium are in the ratio 2:3. If its height is 8cm and area is 240cm2, then its perimeter is _______________ cm
Answer» The parallel sides of an isosceles trapezium are in the ratio $2 : 3$ . If its height is $8 c m$ and area is $240 c m^{2}$ , then its perimeter is _______________ cm

Discussion

22.	A polynomial leaves remainder 5 when divided by (x-3) it also leaves remainder 7 when divided by (x-4). Find remainder when it divided by (x-3)(x-4)
Answer» A polynomial leaves remainder 5 when divided by (x-3) it also leaves remainder 7 when divided by (x-4). Find remainder when it divided by (x-3)(x-4)

Discussion

23.	Match the following if in ΔABC, ∠B=900, ∠C=θ and AB = 9 cm and BC = 12 cm.
Answer» Match the following if in $Δ$ ABC, $∠ B = 90^{0},$ $∠ C = θ$ and AB = 9 cm and BC = 12 cm.

Discussion

24.	Radius of circle is 10 cm. There are two chords of length 16 cm each. What will be the distance of these chords from the centre of the circle ?
Answer» Radius of circle is 10 cm. There are two chords of length 16 cm each. What will be the distance of these chords from the centre of the circle ?

Discussion

25.	Question 6(iv)Using identities, evaluate:9982
Answer» Question 6(iv) Using identities, evaluate: $998^{2}$

Discussion

26.	The mean of a data set with 12 observations is calculated as 19.25. If one more value is included in the data, then for the new data with 13 observations, mean becomes 20. Value of this 13th observation is
Answer» The mean of a data set with 12 observations is calculated as 19.25. If one more value is included in the data, then for the new data with 13 observations, mean becomes 20. Value of this 13th observation is

Discussion

27.	Rationalize the denominator of 1(√5+√2) .
Answer» Rationalize the denominator of $\frac{1}{(\sqrt{5} + \sqrt{2})}$ .

Discussion

28.	In ∆ABC, prove that: a cos B+cos C-1+b cos C+cos A-1+ccos A+cos B-1=0
Answer» In ∆ABC, prove that: $a (\cos B + \cos C - 1) + b (\cos C + \cos A - 1) + c (\cos A + \cos B - 1) = 0$

Discussion

29.	Question 65The walls and ceiling of a room are to be plastered. The length, breadth and height of the room are 4.5 m, 3 m and 350 cm respectively. Find the cost of plastering at the rate of Rs. 8 per m2.
Answer» Question 65 The walls and ceiling of a room are to be plastered. The length, breadth and height of the room are 4.5 m, 3 m and 350 cm respectively. Find the cost of plastering at the rate of Rs. 8 per $m^{2}$ .

29.

Question 65The walls and ceiling of a room are to be plastered. The length, breadth and height of the room are 4.5 m, 3 m and 350 cm respectively. Find the cost of plastering at the rate of Rs. 8 per m2.

Answer»

Question 65

The walls and ceiling of a room are to be plastered. The length, breadth and height of the room are 4.5 m, 3 m and 350 cm respectively. Find the cost of plastering at the rate of Rs. 8 per $m^{2}$ .

Discussion

30.	Question 133An inch is approximately equal to 0.02543 metres. Write this distance in standard form.
Answer» Question 133 An inch is approximately equal to 0.02543 metres. Write this distance in standard form.

30.

Question 133An inch is approximately equal to 0.02543 metres. Write this distance in standard form.

Answer»

Question 133

An inch is approximately equal to 0.02543 metres. Write this distance in standard form.

Discussion

31.	If a polynomial of the form y = f(x) cuts the X-axis at 3 points and Y-axis at 2 points, then the number of zeroes of the polynomial would be ___
Answer» If a polynomial of the form y = f(x) cuts the X-axis at $3$ points and Y-axis at $2$ points, then the number of zeroes of the polynomial would be ___

Discussion

32.	Find the remainder when x3+3x2+3x+1 is divided by(i) x + 1(ii) x−12
Answer» Find the remainder when $x^{3} + 3 x^{2} + 3 x + 1$ is divided by (i) x + 1 (ii) $x - \frac{1}{2}$

Discussion

33.	Mark each pair of numbers given below on the number line and check whether the distance between them is equal to the number got by subtracting the smaller from the larger:(i) 1, −5(ii) −3, −4(iii) −1, 1(iv) 0, 4(v) 0, −4(vi)
Answer» Mark each pair of numbers given below on the number line and check whether the distance between them is equal to the number got by subtracting the smaller from the larger: (i) 1, −5 (ii) −3, −4 (iii) −1, 1 (iv) 0, 4 (v) 0, −4 (vi)

33.

Mark each pair of numbers given below on the number line and check whether the distance between them is equal to the number got by subtracting the smaller from the larger:(i) 1, −5(ii) −3, −4(iii) −1, 1(iv) 0, 4(v) 0, −4(vi)

Answer»

Mark each pair of numbers given below on the number line and check whether the distance between them is equal to the number got by subtracting the smaller from the larger:

(i) 1, −5

(ii) −3, −4

(iii) −1, 1

(iv) 0, 4

(v) 0, −4

(vi)

Discussion

34.	State True of False.(x+5)(x−5) = x2+25.
Answer» State True of False. $(x + 5) (x - 5)$ = $x^{2} + 25$ .

Discussion

35.	The sum of two angles of a triangle is equal to its third angle . Determine he measure of the third angle .
Answer» The sum of two angles of a triangle is equal to its third angle . Determine he measure of the third angle .

Discussion

36.	Find the distance of the point (2, 3) from the origin.
Answer» Find the distance of the point (2, 3) from the origin.

Discussion

37.	If A={1,2,3}, B={2,4,5} and C={4,1,9}, then A∩(B∪C)= ___.
Answer» If $A = {1, 2, 3}, B = {2, 4, 5}$ and $C = {4, 1, 9},$ then $A \cap (B \cup C)$ = ___.

Discussion

38.	l and m are two parallel lines intersected by another pair of parallel lines p and q (see the given figure). Show that △ABC≅△CDA.
Answer» $l$ and $m$ are two parallel lines intersected by another pair of parallel lines $p$ and $q$ (see the given figure). Show that $△ A B C ≅ △ C D A$ .

38.

l and m are two parallel lines intersected by another pair of parallel lines p and q (see the given figure). Show that △ABC≅△CDA.

Answer»

$l$ and $m$ are two parallel lines intersected by another pair of parallel lines $p$ and $q$ (see the given figure). Show that $△ A B C ≅ △ C D A$ .

Discussion

39.	In ΔPQR, right angled at Q and P = R, then sin P cos R + cos P sin R is
Answer» In ΔPQR, right angled at Q and P = R, then sin P cos R + cos P sin R is

Discussion

40.	If the arithmetic mean of 7, 5, 13, x and 9 is 10, then the value x is(a) 10(b) 12(c) 14(d) 16
Answer» If the arithmetic mean of 7, 5, 13, x and 9 is 10, then the value x is (a) 10 (b) 12 (c) 14 (d) 16

Discussion

41.	Ifx=√5+2√65−2√6,then x2(x−10)2=
Answer» $I f x = \sqrt{\frac{5 + 2 \sqrt{6}}{5 - 2 \sqrt{6}}}, t h e n x^{2} (x - 10)^{2} =$

Discussion

42.	Line l is the bisector of an angle ∠A and B is any point on l. BP and BQ are perpendiculars from B to the arms of ∠A (see the given figure). Show that:(i) ΔAPB ≅ ΔAQB(ii) BP = BQ or B is equidistant from the arms of ∠A.
Answer» Line l is the bisector of an angle ∠A and B is any point on l. BP and BQ are perpendiculars from B to the arms of ∠A (see the given figure). Show that: (i) ΔAPB ≅ ΔAQB (ii) BP = BQ or B is equidistant from the arms of ∠A.

42.

Line l is the bisector of an angle ∠A and B is any point on l. BP and BQ are perpendiculars from B to the arms of ∠A (see the given figure). Show that:(i) ΔAPB ≅ ΔAQB(ii) BP = BQ or B is equidistant from the arms of ∠A.

Answer»

Line l is the bisector of an angle ∠A and B is any point on l. BP and BQ are perpendiculars from B to the arms of ∠A (see the given figure). Show that:

(i) ΔAPB ≅ ΔAQB

(ii) BP = BQ or B is equidistant from the arms of ∠A.

Discussion

43.	From three non- collinear points we can draw
Answer» From three non- collinear points we can draw

Discussion

44.	In Δ ABC; AB =AC and ∠ A : \angle B \) = 8: 5; find angle A.
Answer» In $Δ$ ABC; AB =AC and $∠$ A : \angle B \) = 8: 5; find angle A.

Discussion

45.	What is the median class for the data? Class intervalfrequency0−10710−201320−301430−40540−5011 [2 MARKS]
Answer» What is the median class for the data? $\begin{matrix} C l a s s i n t e r v a l & f r e q u e n c y 0 - 10 & 7 10 - 20 & 13 20 - 30 & 14 30 - 40 & 5 40 - 50 & 11 \end{matrix}$ [2 MARKS]

Discussion

46.	△ ABC is a right triangle right angled at A. If AB = 24 cm and AC = 7 cm, then BC =(a) 31 cm(b) 17 cm(c) 25 cm(d) 28 cm
Answer» △ ABC is a right triangle right angled at A. If AB = 24 cm and AC = 7 cm, then BC = (a) 31 cm (b) 17 cm (c) 25 cm (d) 28 cm

Discussion

47.	If 10 pens cost ₹60 , what is the cost of 13 such pens?
Answer» If 10 pens cost ₹60 , what is the cost of 13 such pens?

Discussion

48.	Locate √5.6 on the number line
Answer» Locate $\sqrt{5.6}$ on the number line

Discussion

49.	In a deck of playing cards, 2 new suits are introduced which are red and black in color respectively. If the number and types of cards in the new suits are same as the standard suits. Find the probability that I will get a face card on a random draw of 1 card. Also find the probability if the new suits were not introduced
Answer» In a deck of playing cards, 2 new suits are introduced which are red and black in color respectively. If the number and types of cards in the new suits are same as the standard suits. Find the probability that I will get a face card on a random draw of 1 card. Also find the probability if the new suits were not introduced

Discussion

50.	Prove that:(i) 3×5-3 ÷ 3-13 5×3×566=35(ii) 93/2-3×50-181-1/2 = 15(iii) 14-2-3×82/3×40+916-1/2 = 163(iv) 21/2×31/3×41/410-1/5×53/5 ÷ 34/3×5-7/54-3/5×6=10(v) 14 +(0.01)-1/2-(27)2/3 =32(vi) 2n + 2n -12n+1-2n=32(vii) 64125-2/3 + 12566251/4 + 25643 = 6516(viii) 3-3×62×9852×1/253×(15)-4/3×31/3=282(ix) (0.6)0-(0.1)-138-1323+-13-1=-32
Answer» Prove that: (i) $\sqrt{3 \times 5^{- 3}} \div \sqrt[3]{3^{- 1}} \sqrt{5} \times \sqrt[6]{3 \times 5^{6}} = \frac{3}{5}$ (ii) $9^{3 / 2} - 3 \times 5^{0} - {(\frac{1}{81})}^{-}^{1 / 2} = 15$ (iii) ${(\frac{1}{4})}^{- 2} - 3 \times 8^{2 / 3} \times 4^{0} + {(\frac{9}{16})}^{- 1 / 2} = \frac{16}{3}$ (iv) $\frac{2^{1 / 2} \times 3^{1 / 3} \times 4^{1 / 4}}{10^{- 1 / 5} \times 5^{3 / 5}} \div \frac{3^{4 / 3} \times 5^{- 7 / 5}}{4^{- 3 / 5} \times 6} = 10$ (v) $\sqrt{\frac{1}{4} + (0.01)^{- 1 / 2}} - (27)^{2 / 3} = \frac{3}{2}$ (vi) $\frac{2^{n} + 2^{n - 1}}{2^{n + 1} - 2^{n}} = \frac{3}{2}$ (vii) ${(\frac{64}{125})}^{- 2 / 3} + \frac{1}{{(\frac{256}{625})}^{1 / 4}} + (\frac{\sqrt{25}}{\sqrt[3]{64}}) = \frac{65}{16}$ (viii) $\frac{3^{- 3} \times 6^{2} \times \sqrt{98}}{5^{2} \times \sqrt[3]{1 / 25} \times (15) -^{4 / 3} \times 3^{1 / 3}} = 28 \sqrt{2}$ (ix) $\frac{(0.6)^{0} - (0.1) - 1}{{(\frac{3}{8})}^{- 1} {(\frac{3}{2})}^{3} + {(- \frac{1}{3})}^{- 1}} = - \frac{3}{2}$

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Find the correct option when x is the subject of the formula of given expression. a(x–b)=a2+bx

Draw graph of the following x+y=4

For √3x2 to be irrational, x should be

Simplify √128.

133, 73, 89, 108, 94, 104, 94, 85, 100, 120

Find the mode of the following items. 0,6,5,1,6,4,3,0,2,6,5,6

The inverse of the function is f(x)=10x−10−x10x+10−x+1 is

If O is the center of the circle, then the value of θ in the adjoining figure is

Factorise:9x2 – 16y2

The area of a regular hexagon of side 6 cm is __________.

Find the least fraction, which must be multiplied to (124 −12 +3616 −116 +28)to make it an integer.

Question 18 Show that p – 1 is a factor of p10–1 and also of p11–1.

If x - 2 and x - 12 both are the factors of the polynomial nx2 − 5x + m, then show that m = n= 2

Find the zero of the polynomial x2-bxy + cy2 where -b =p-q and c =-pq

The image of the point (–5, 7) in y-axis has the coordinates(a) (5, 7)(b) (–5, –7)(c) (5, –7)(d) (7, –5)

The area of a regular hexagon of side ‘a’ is the sum of the areas of the ___ equilateral triangles with side a.

In the given figure, if MN and PQ are parallel, find the value of X + Y in degrees.105

If (a, 4) lies on the graph of 3x + y = 10, then the value of a is(a) 3(b) 1(c) 3(d) 4

If a+b+c=0 proove that a²+ab+b²=b²+bc+c²=c²+ac+a²

1. A polynomial leaves remainder 5 when divided by x-3. It also leave remainder 7 when divided by x-4. Find remainder when it divided by (x-3)(x-4

The parallel sides of an isosceles trapezium are in the ratio 2:3. If its height is 8cm and area is 240cm2, then its perimeter is _______________ cm

A polynomial leaves remainder 5 when divided by (x-3) it also leaves remainder 7 when divided by (x-4). Find remainder when it divided by (x-3)(x-4)

Match the following if in ΔABC, ∠B=900, ∠C=θ and AB = 9 cm and BC = 12 cm.

Radius of circle is 10 cm. There are two chords of length 16 cm each. What will be the distance of these chords from the centre of the circle ?

Question 6(iv)Using identities, evaluate:9982

The mean of a data set with 12 observations is calculated as 19.25. If one more value is included in the data, then for the new data with 13 observations, mean becomes 20. Value of this 13th observation is

Rationalize the denominator of 1(√5+√2) .

In ∆ABC, prove that: a cos B+cos C-1+b cos C+cos A-1+ccos A+cos B-1=0

Question 65The walls and ceiling of a room are to be plastered. The length, breadth and height of the room are 4.5 m, 3 m and 350 cm respectively. Find the cost of plastering at the rate of Rs. 8 per m2.

Question 133An inch is approximately equal to 0.02543 metres. Write this distance in standard form.

If a polynomial of the form y = f(x) cuts the X-axis at 3 points and Y-axis at 2 points, then the number of zeroes of the polynomial would be ___

Find the remainder when x3+3x2+3x+1 is divided by(i) x + 1(ii) x−12

Mark each pair of numbers given below on the number line and check whether the distance between them is equal to the number got by subtracting the smaller from the larger:(i) 1, −5(ii) −3, −4(iii) −1, 1(iv) 0, 4(v) 0, −4(vi)

State True of False.(x+5)(x−5) = x2+25.

The sum of two angles of a triangle is equal to its third angle . Determine he measure of the third angle .

Find the distance of the point (2, 3) from the origin.

If A={1,2,3}, B={2,4,5} and C={4,1,9}, then A∩(B∪C)= ___.

l and m are two parallel lines intersected by another pair of parallel lines p and q (see the given figure). Show that △ABC≅△CDA.

In ΔPQR, right angled at Q and P = R, then sin P cos R + cos P sin R is

If the arithmetic mean of 7, 5, 13, x and 9 is 10, then the value x is(a) 10(b) 12(c) 14(d) 16

Ifx=√5+2√65−2√6,then x2(x−10)2=

Line l is the bisector of an angle ∠A and B is any point on l. BP and BQ are perpendiculars from B to the arms of ∠A (see the given figure). Show that:(i) ΔAPB ≅ ΔAQB(ii) BP = BQ or B is equidistant from the arms of ∠A.

From three non- collinear points we can draw

In Δ ABC; AB =AC and ∠ A : \angle B \) = 8: 5; find angle A.

What is the median class for the data? Class intervalfrequency0−10710−201320−301430−40540−5011 [2 MARKS]

△ ABC is a right triangle right angled at A. If AB = 24 cm and AC = 7 cm, then BC =(a) 31 cm(b) 17 cm(c) 25 cm(d) 28 cm

If 10 pens cost ₹60 , what is the cost of 13 such pens?

Locate √5.6 on the number line