24740 + Interview Questions in Mathematics

1.	Find the length of diagonal BD of the given rhombus.
Answer» Find the length of diagonal BD of the given rhombus.

1.

Find the length of diagonal BD of the given rhombus.

Answer»

Find the length of diagonal BD of the given rhombus.

Discussion

2.	Question 86 (ii)Using suitable identities, evaluate the following:(49)2
Answer» Question 86 (ii) Using suitable identities, evaluate the following: $(49)^{2}$

2.

Question 86 (ii)Using suitable identities, evaluate the following:(49)2

Answer»

Question 86 (ii)

Using suitable identities, evaluate the following:

$(49)^{2}$

Discussion

3.	Find:3215
Answer» Find: $32^{\frac{1}{5}}$

Discussion

4.	Question 2Write ‘True’ or ‘False’ and justify your answer in the following :A solid cylinder of radius r and height h is placed over other cylinder of same height and radius. The total surface area of the shape so formed is 4πrh+4πr2.
Answer» Question 2 Write ‘True’ or ‘False’ and justify your answer in the following : A solid cylinder of radius r and height h is placed over other cylinder of same height and radius. The total surface area of the shape so formed is $4 π r h + 4 π r^{2}$ .

Discussion

5.	Factorize:a2 + b2 + 2bc − c2
Answer» Factorize: a² + b² + 2bc − c²

Discussion

6.	Show that the bisectors of angles of a parallelogram forma rectangle
Answer» Show that the bisectors of angles of a parallelogram forma rectangle

Discussion

7.	Half the perimeter of a rectangular garden whose length is 4 m more than its width is 36 m. Find the dimensions of the garden.
Answer» Half the perimeter of a rectangular garden whose length is 4 m more than its width is 36 m. Find the dimensions of the garden.

Discussion

8.	Question 1Is zero a rational number? Can you write it in the form pq, where p and q are integers and q≠0?
Answer» Question 1 Is zero a rational number? Can you write it in the form $\frac{p}{q}$ , where p and q are integers and $q \neq 0$ ?

Discussion

9.	Question 9Write True or False and justify your answer :If A, B, C and D are four points such that ∠BAC=45∘ and ∠BDC=45∘ , then A, B, C, D are concyclic.
Answer» Question 9 Write True or False and justify your answer : If A, B, C and D are four points such that $∠ B A C = 45^{\circ}$ and $∠ B D C = 45^{\circ}$ , then A, B, C, D are concyclic.

Discussion

10.	Pair the number with the corresponding arrow card.
Answer» Pair the number with the corresponding arrow card.

Discussion

11.	In figure, ABC is a quadrant of a circle of radius 14 cm and a semicircle is drawn with BC as diameter. Find the area of the shaded region (in cm2).___
Answer» In figure, ABC is a quadrant of a circle of radius 14 cm and a semicircle is drawn with BC as diameter. Find the area of the shaded region (in $c m^{2}$ ). ___

11.

In figure, ABC is a quadrant of a circle of radius 14 cm and a semicircle is drawn with BC as diameter. Find the area of the shaded region (in cm2).___

Answer»

In figure, ABC is a quadrant of a circle of radius 14 cm and a semicircle is drawn with BC as diameter. Find the area of the shaded region (in $c m^{2}$ ).

___

Discussion

12.	find (x-y)3 +(y-z)3 + (z-x)3 find x+1/x if x2 +1/x2=34 factorise x2-y2x-y find the value of x3+y3+12xy - 64 when x+y=4 if x and y are two positive real numbers such that x2 - 4y2=40 xy=6 find x+2y if abc are all nonzero and a+b+c=0 prove that a2/bc+b2/ac+c2/ab=3 (m+2n)2+101(m+2n)+100
Answer» find (x-y)³ +(y-z)³ + (z-x)³ find x+1/x if x² +1/x²=34 factorise x²-y²x-y find the value of x³+y³+12xy - 64 when x+y=4 if x and y are two positive real numbers such that x² - 4y²=40 xy=6 find x+2y if abc are all nonzero and a+b+c=0 prove that a²/bc+b²/ac+c²/ab=3 (m+2n)²+101(m+2n)+100

12.

find (x-y)3 +(y-z)3 + (z-x)3 find x+1/x if x2 +1/x2=34 factorise x2-y2x-y find the value of x3+y3+12xy - 64 when x+y=4 if x and y are two positive real numbers such that x2 - 4y2=40 xy=6 find x+2y if abc are all nonzero and a+b+c=0 prove that a2/bc+b2/ac+c2/ab=3 (m+2n)2+101(m+2n)+100

Answer»

find (x-y)³ +(y-z)³ + (z-x)³

find x+1/x if x² +1/x²=34

factorise x²-y²x-y

find the value of x³+y³+12xy - 64 when x+y=4

if x and y are two positive real numbers such that x² - 4y²=40 xy=6 find x+2y

if abc are all nonzero and a+b+c=0 prove that a²/bc+b²/ac+c²/ab=3

(m+2n)²+101(m+2n)+100

Discussion

13.	f(x) = (ax² + 6x - 8)/(a + 6x - 8x²) find interval of a for which f is onto, f: R to R
Answer» f(x) = (ax² + 6x - 8)/(a + 6x - 8x²) find interval of a for which f is onto, f: R to R

Discussion

14.	A solid has ___ dimensions.
Answer» A solid has ___ dimensions.

Discussion

15.	What is the distance of the point (6,18) from the X-axis?
Answer» What is the distance of the point (6,18) from the X-axis?

Discussion

16.	Prove that the line segment joining the mid-point of the hypotenuse of a right triangle to its opposite vertex is half the hypotenuse.
Answer» Prove that the line segment joining the mid-point of the hypotenuse of a right triangle to its opposite vertex is half the hypotenuse.

Discussion

17.	if cot^{-1}x=a(pi)+b\lbrack†an^{-1}(1/x)\rbrack,x
Answer» if cot^{-1}x=a(pi)+b\lbrack†an^{-1}(1/x)\rbrack,x<0 then the value of a i

Discussion

18.	Plot the graph of y=5x-5
Answer» Plot the graph of y=5x-5

Discussion

19.	Let X be a set having 3 elements and Y be a set having 4 elements. If α is the number of one-one functions from X to Y and β is the number of onto functions from Y to X, then the value of (β−α) is
Answer» Let $X$ be a set having $3$ elements and $Y$ be a set having $4$ elements. If $α$ is the number of one-one functions from $X$ to $Y$ and $β$ is the number of onto functions from $Y$ to $X,$ then the value of $(β - α)$ is

Discussion

20.	Find the coordinates of the centre of a circle which passes through the points A(1,2), B(3,-4) and C(5,-6).
Answer» Find the coordinates of the centre of a circle which passes through the points A(1,2), B(3,-4) and C(5,-6).

Discussion

21.	If x = 2 then what is the value of y in 3x - 4y = 10 ?
Answer» If x = 2 then what is the value of y in 3x - 4y = 10 ?

Discussion

22.	Tap on the shape that can be divided into two symmetrical parts using a diagonal.
Answer» Tap on the shape that can be divided into two symmetrical parts using a diagonal.

Discussion

23.	If X={8n−7n−1\| n ϵ N} and Y={49n−49\| n ϵ N}, then
Answer» If $X = {8^{n} - 7 n - 1 \| n ϵ N}$ and $Y = {49 n - 49 \| n ϵ N}$ , then

Discussion

24.	The distance of a point (2, 3) from the y- axis is
Answer» The distance of a point (2, 3) from the y- axis is

Discussion

25.	Two points having same abscissae but different ordinate lie on(a) x-axis(b) y-axis(c) a line parallel to y-axis(d) a line parallel to x-axis
Answer» Two points having same abscissae but different ordinate lie on (a) x-axis (b) y-axis (c) a line parallel to y-axis (d) a line parallel to x-axis

Discussion

26.	Question 16If AD and PM are medians of triangles ABC and PQR, respectively where ΔABC∼ΔPQR. Prove that ABPQ=ADPM.
Answer» Question 16 If AD and PM are medians of triangles ABC and PQR, respectively where $Δ A B C \sim Δ P Q R$ . Prove that $\frac{A B}{P Q} = \frac{A D}{P M}$ .

Discussion

27.	The ages of 30 workers in a factory are as follows Age2425262728Frequency57846 (i) Find the probability that a worker selected at random is older than 25 (ii) Find the probability that the age of a worker is an odd number. (iii) Find the probability that the age of a worker is an even number. (iv) What is the sum of answers two and three? Why?
Answer» The ages of 30 workers in a factory are as follows $\begin{matrix} A g e & 24 & 25 & 26 & 27 & 28 F r e q u e n c y & 5 & 7 & 8 & 4 & 6 \end{matrix}$ (i) Find the probability that a worker selected at random is older than 25 (ii) Find the probability that the age of a worker is an odd number. (iii) Find the probability that the age of a worker is an even number. (iv) What is the sum of answers two and three? Why?

27.

The ages of 30 workers in a factory are as follows Age2425262728Frequency57846 (i) Find the probability that a worker selected at random is older than 25 (ii) Find the probability that the age of a worker is an odd number. (iii) Find the probability that the age of a worker is an even number. (iv) What is the sum of answers two and three? Why?

Answer»

The ages of 30 workers in a factory are as follows

$\begin{matrix} A g e & 24 & 25 & 26 & 27 & 28 F r e q u e n c y & 5 & 7 & 8 & 4 & 6 \end{matrix}$

(i) Find the probability that a worker selected at random is older than 25
(ii) Find the probability that the age of a worker is an odd number.
(iii) Find the probability that the age of a worker is an even number.
(iv) What is the sum of answers two and three? Why?

Discussion

28.	The length of the perpendicular drawn from the point P (3, 4, 5) on y-axis is(a) 10(b) 34(c) 113(d) 512
Answer» The length of the perpendicular drawn from the point P (3, 4, 5) on y-axis is (a) 10 (b) $\sqrt{34}$ (c) $\sqrt{113}$ (d) 512

Discussion

29.	Prove that two lines perpendicular to same line are parallel to each other
Answer» Prove that two lines perpendicular to same line are parallel to each other

Discussion

30.	How many numbers are there divisible by 3 between 9 and 150.
Answer» How many numbers are there divisible by 3 between 9 and 150.

Discussion

31.	The mean of 1, 7, 5, 3, 4, and 4 is m. The observations 3, 2, 4, 2, 3, 3 and p have mean (m - 1) and median q. Find p q.
Answer» The mean of 1, 7, 5, 3, 4, and 4 is m. The observations 3, 2, 4, 2, 3, 3 and p have mean (m - 1) and median q. Find p q.

Discussion

32.	4. A chord PQ of a circle is parallel to the tangents drawn at a point R of the circle. Prove that R bisects the arc PRQ
Answer» 4. A chord PQ of a circle is parallel to the tangents drawn at a point R of the circle. Prove that R bisects the arc PRQ

Discussion

33.	In the given figure AB is the side of a regular hexagon and BC is the side of a regular pentagon. Find ∠ AOC.
Answer» In the given figure AB is the side of a regular hexagon and BC is the side of a regular pentagon. Find $∠$ AOC.

33.

In the given figure AB is the side of a regular hexagon and BC is the side of a regular pentagon. Find ∠ AOC.

Answer»

In the given figure AB is the side of a regular hexagon and BC is the side of a regular pentagon. Find $∠$ AOC.

Discussion

34.	(1 + tan θ + sec θ) (1 + cot θ − cosec θ) =(a) 0(b) 1(c) 1(d) −1
Answer» (1 + tan θ + sec θ) (1 + cot θ − cosec θ) = (a) 0 (b) 1 (c) 1 (d) −1

Discussion

35.	If (x+1) is a factor of the polynomial (2x2+kx) then the value of k is (a) -2 (b) -3 (c) 2 (d)3
Answer» If $(x + 1)$ is a factor of the polynomial $(2 x^{2} + k x)$ then the value of k is (a) -2 (b) -3 (c) 2 (d)3

Discussion

36.	Factorise: a(a-2b-c)+2bc
Answer» Factorise: a(a-2b-c)+2bc

Discussion

37.	The base diameter and height of a metallic solid cylinder are 18 cm and 24 cm respectively. If the cylinder is melted to form cylinders of base diameter 12 cm and height 6 cm, how many such small cylinders will be formed?9
Answer» The base diameter and height of a metallic solid cylinder are 18 cm and 24 cm respectively. If the cylinder is melted to form cylinders of base diameter 12 cm and height 6 cm, how many such small cylinders will be formed? 9

Discussion

38.	The slant height of a cone is increased by 10%. If the radius remains the same, the curved surface area is increased by(a) 10%(b) 12.1%(c) 20%(d) 21%
Answer» The slant height of a cone is increased by 10%. If the radius remains the same, the curved surface area is increased by (a) 10% (b) 12.1% (c) 20% (d) 21%

Discussion

39.	Question 90 Area of a ΔPQR right angled at Q is 60 cm2 in the figure. If the smallest side is 8 cm long, find the length of the order two sides.
Answer» Question 90 Area of a $Δ P Q R$ right angled at Q is $60 c m^{2}$ in the figure. If the smallest side is 8 cm long, find the length of the order two sides.

39.

Question 90 Area of a ΔPQR right angled at Q is 60 cm2 in the figure. If the smallest side is 8 cm long, find the length of the order two sides.

Answer»

Question 90

Area of a $Δ P Q R$ right angled at Q is $60 c m^{2}$ in the figure. If the smallest side is 8 cm long, find the length of the order two sides.

Discussion

40.	In figure, line segments AB and CD bisect each other at O. Which of the following statements is true?(i) ΔAOC ≅ ΔDOB(ii) ΔAOC ≅ ΔBOD(iii) ΔAOC ≅ ΔODBState the three pairs of matching parts you have used to arrive at the answer.
Answer» In figure, line segments AB and CD bisect each other at O. Which of the following statements is true? (i) ΔAOC ≅ ΔDOB (ii) ΔAOC ≅ ΔBOD (iii) ΔAOC ≅ ΔODB State the three pairs of matching parts you have used to arrive at the answer.

40.

In figure, line segments AB and CD bisect each other at O. Which of the following statements is true?(i) ΔAOC ≅ ΔDOB(ii) ΔAOC ≅ ΔBOD(iii) ΔAOC ≅ ΔODBState the three pairs of matching parts you have used to arrive at the answer.

Answer» In figure, line segments AB and CD bisect each other at O. Which of the following statements is true?

(i) ΔAOC ≅ ΔDOB

(ii) ΔAOC ≅ ΔBOD

(iii) ΔAOC ≅ ΔODB

State the three pairs of matching parts you have used to arrive at the answer.

Discussion

41.	Factorize:x2+1235x+135
Answer» Factorize: $x^{2} + \frac{12}{35} x + \frac{1}{35}$

Discussion

42.	In the expression xy+3x+4y, 3x is a___.
Answer» In the expression $x y + 3 x + 4 y$ , $3 x$ is a___.

Discussion

43.	Draw a line parallel to y-axis at a distance of 4 units from the origin in the positive direction of x-axis
Answer» Draw a line parallel to y-axis at a distance of 4 units from the origin in the positive direction of x-axis

Discussion

44.	Verify that (i) 1 and 2 are the zeros of the polynomial, p(x)=x2−3x+2. (ii) 2 and -3 are the zeros of the polynomial, q(x)=x2+x−6. (iii) 0 and 3 are the zeros of the polynomial, r(x)=x2−3x.
Answer» Verify that (i) 1 and 2 are the zeros of the polynomial, $p (x) = x^{2} - 3 x + 2$ . (ii) 2 and -3 are the zeros of the polynomial, $q (x) = x^{2} + x - 6.$ (iii) 0 and 3 are the zeros of the polynomial, $r (x) = x^{2} - 3 x$ .

Discussion

45.	What fraction of the rectangle ABCD is shaded?
Answer» What fraction of the rectangle ABCD is shaded?

Discussion

46.	If the improper fraction 86211 can be written as the mixed fraction 78pq, find p + q.
Answer» $If the improper fraction 86211 can be written as the mixed fraction 78pq, find p + q.$

Discussion

47.	In the given figure, AB = 8 cm, BC = 6 cm, AC = 10 cm, then the area of ΔABC is equal to
Answer» In the given figure, AB = 8 cm, BC = 6 cm, AC = 10 cm, then the area of $Δ A B C$ is equal to

Discussion

48.	If f(x)=(25−x4)1/4,0<x<√5, then f(f(13))=
Answer» If $f (x) = {(25 - x^{4})}^{1 / 4}, 0 < x < \sqrt{5}$ , then $f (f (\frac{1}{3})) =$

Discussion

49.	Factorizei) 27m3−216n3 ii) 343a3−512b3
Answer» Factorize i) $27 m^{3} - 216 n^{3}$ ii) $343 a^{3} - 512 b^{3}$

Discussion

50.	If I draw two circles of radius 3 cm and 5cm with common centre and draw a line AB such that it is a chord to both the circles and length of CD is 2√5 cm, then find the distance of the chords from the centre and the length AC.
Answer» If I draw two circles of radius 3 cm and 5cm with common centre and draw a line AB such that it is a chord to both the circles and length of CD is $2 \sqrt{5}$ cm, then find the distance of the chords from the centre and the length AC.

50.

If I draw two circles of radius 3 cm and 5cm with common centre and draw a line AB such that it is a chord to both the circles and length of CD is 2√5 cm, then find the distance of the chords from the centre and the length AC.

Answer»

If I draw two circles of radius 3 cm and 5cm with common centre and draw a line AB such that it is a chord to both the circles and length of CD is $2 \sqrt{5}$ cm, then find the distance of the chords from the centre and the length AC.

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Find the length of diagonal BD of the given rhombus.

Question 86 (ii)Using suitable identities, evaluate the following:(49)2

Find:3215

Question 2Write ‘True’ or ‘False’ and justify your answer in the following :A solid cylinder of radius r and height h is placed over other cylinder of same height and radius. The total surface area of the shape so formed is 4πrh+4πr2.

Factorize:a2 + b2 + 2bc − c2

Show that the bisectors of angles of a parallelogram forma rectangle

Half the perimeter of a rectangular garden whose length is 4 m more than its width is 36 m. Find the dimensions of the garden.

Question 1Is zero a rational number? Can you write it in the form pq, where p and q are integers and q≠0?

Question 9Write True or False and justify your answer :If A, B, C and D are four points such that ∠BAC=45∘ and ∠BDC=45∘ , then A, B, C, D are concyclic.

Pair the number with the corresponding arrow card.

In figure, ABC is a quadrant of a circle of radius 14 cm and a semicircle is drawn with BC as diameter. Find the area of the shaded region (in cm2).___

find (x-y)3 +(y-z)3 + (z-x)3 find x+1/x if x2 +1/x2=34 factorise x2-y2x-y find the value of x3+y3+12xy - 64 when x+y=4 if x and y are two positive real numbers such that x2 - 4y2=40 xy=6 find x+2y if abc are all nonzero and a+b+c=0 prove that a2/bc+b2/ac+c2/ab=3 (m+2n)2+101(m+2n)+100

f(x) = (ax² + 6x - 8)/(a + 6x - 8x²) find interval of a for which f is onto, f: R to R

A solid has ___ dimensions.

What is the distance of the point (6,18) from the X-axis?

Prove that the line segment joining the mid-point of the hypotenuse of a right triangle to its opposite vertex is half the hypotenuse.

if cot^{-1}x=a(pi)+b\lbrack†an^{-1}(1/x)\rbrack,x

Plot the graph of y=5x-5

Let X be a set having 3 elements and Y be a set having 4 elements. If α is the number of one-one functions from X to Y and β is the number of onto functions from Y to X, then the value of (β−α) is

Find the coordinates of the centre of a circle which passes through the points A(1,2), B(3,-4) and C(5,-6).

If x = 2 then what is the value of y in 3x - 4y = 10 ?

Tap on the shape that can be divided into two symmetrical parts using a diagonal.

If X={8n−7n−1| n ϵ N} and Y={49n−49| n ϵ N}, then

The distance of a point (2, 3) from the y- axis is

Two points having same abscissae but different ordinate lie on(a) x-axis(b) y-axis(c) a line parallel to y-axis(d) a line parallel to x-axis

Question 16If AD and PM are medians of triangles ABC and PQR, respectively where ΔABC∼ΔPQR. Prove that ABPQ=ADPM.

The length of the perpendicular drawn from the point P (3, 4, 5) on y-axis is(a) 10(b) 34(c) 113(d) 512

Prove that two lines perpendicular to same line are parallel to each other

How many numbers are there divisible by 3 between 9 and 150.

The mean of 1, 7, 5, 3, 4, and 4 is m. The observations 3, 2, 4, 2, 3, 3 and p have mean (m - 1) and median q. Find p q.

4. A chord PQ of a circle is parallel to the tangents drawn at a point R of the circle. Prove that R bisects the arc PRQ

In the given figure AB is the side of a regular hexagon and BC is the side of a regular pentagon. Find ∠ AOC.

(1 + tan θ + sec θ) (1 + cot θ − cosec θ) =(a) 0(b) 1(c) 1(d) −1

If (x+1) is a factor of the polynomial (2x2+kx) then the value of k is (a) -2 (b) -3 (c) 2 (d)3

Factorise: a(a-2b-c)+2bc

The base diameter and height of a metallic solid cylinder are 18 cm and 24 cm respectively. If the cylinder is melted to form cylinders of base diameter 12 cm and height 6 cm, how many such small cylinders will be formed?9

The slant height of a cone is increased by 10%. If the radius remains the same, the curved surface area is increased by(a) 10%(b) 12.1%(c) 20%(d) 21%

Question 90 Area of a ΔPQR right angled at Q is 60 cm2 in the figure. If the smallest side is 8 cm long, find the length of the order two sides.

In figure, line segments AB and CD bisect each other at O. Which of the following statements is true?(i) ΔAOC ≅ ΔDOB(ii) ΔAOC ≅ ΔBOD(iii) ΔAOC ≅ ΔODBState the three pairs of matching parts you have used to arrive at the answer.

Factorize:x2+1235x+135

In the expression xy+3x+4y, 3x is a___.

Draw a line parallel to y-axis at a distance of 4 units from the origin in the positive direction of x-axis

Verify that (i) 1 and 2 are the zeros of the polynomial, p(x)=x2−3x+2. (ii) 2 and -3 are the zeros of the polynomial, q(x)=x2+x−6. (iii) 0 and 3 are the zeros of the polynomial, r(x)=x2−3x.

What fraction of the rectangle ABCD is shaded?

If the improper fraction 86211 can be written as the mixed fraction 78pq, find p + q.

In the given figure, AB = 8 cm, BC = 6 cm, AC = 10 cm, then the area of ΔABC is equal to

If f(x)=(25−x4)1/4,0&lt;x&lt;√5, then f(f(13))=

Factorizei) 27m3−216n3 ii) 343a3−512b3

If I draw two circles of radius 3 cm and 5cm with common centre and draw a line AB such that it is a chord to both the circles and length of CD is 2√5 cm, then find the distance of the chords from the centre and the length AC.

If f(x)=(25−x4)1/4,0<x<√5, then f(f(13))=