32581 + Interview Questions in Mathematics

1.	The wheels of a car are of diameter 80 cm each. How many complete revolutions does each wheel make in 10 minutes when the car is travelling at a speed of 66 km per hour?
Answer» The wheels of a car are of diameter $80$ cm each. How many complete revolutions does each wheel make in $10$ minutes when the car is travelling at a speed of $66$ km per hour?

Discussion

2.	If the mth and the nth term of an A.P are 1n and 1m respectively, then find its mnth term.
Answer» If the $m^{t h}$ and the $n^{t h}$ term of an A.P are $\frac{1}{n}$ and $\frac{1}{m}$ respectively, then find its $m n^{t h}$ term.

Discussion

3.	The areas of two similar triangles are 49 cm2 and 64 cm2 respectively. The ratio of their corresponding sides is
Answer» The areas of two similar triangles are $49 c m^{2}$ and $64 c m^{2}$ respectively. The ratio of their corresponding sides is

Discussion

4.	Find a point with an X-coordinate of 5 on the line 3x - 8y + 17 = 0. [2 MARKS]
Answer» Find a point with an X-coordinate of 5 on the line 3x - 8y + 17 = 0. [2 MARKS]

Discussion

5.	Question 4 To construct a triangle similar to a given ΔABC with its sides of 37 the corresponding sides of Δ ABC , first draw a ray BX such that ∠CBX is an acute angle and X lies on the opposite side of A with respect to BC. Then locate point B1,B2,B3.... on BX at equal distances and next step is to join (A) B10 to C (B) B3 to C (C) B7 to C (D) B4 to C
Answer» Question 4 To construct a triangle similar to a given $Δ$ ABC with its sides of $\frac{3}{7}$ the corresponding sides of $Δ$ ABC , first draw a ray BX such that $∠$ CBX is an acute angle and X lies on the opposite side of A with respect to BC. Then locate point $B_{1}, B_{2}, B_{3} . . . .$ on BX at equal distances and next step is to join (A) $B_{10}$ to C (B) $B_{3}$ to C (C) $B_{7}$ to C (D) $B_{4}$ to C

Discussion

6.	Question 22 Which term of the AP –2, –7, –12,.. will be –77? Find the sum of this AP upto the term –77.
Answer» Question 22 Which term of the AP –2, –7, –12,.. will be –77? Find the sum of this AP upto the term –77.

Discussion

7.	Question 6 The 21st term of an AP whose first two terms are – 3 and 4, is A) 17 B) 137 C) 143 D) -143
Answer» Question 6 The $21^{s t}$ term of an AP whose first two terms are – 3 and 4, is A) 17 B) 137 C) 143 D) -143

Discussion

8.	The largest angle of a triangle, whose sides are 12, 18 and 20 inches, is bisected. Find the lengths of the segments created when the angle bisector intersects the opposite side of the triangle.
Answer» The largest angle of a triangle, whose sides are 12, 18 and 20 inches, is bisected. Find the lengths of the segments created when the angle bisector intersects the opposite side of the triangle.

Discussion

9.	The line segment AB was divided in the ratio 4:7 by taking two parallel rays from the points A and B. The number of arcs to be made on the ray AX is: ___
Answer» The line segment AB was divided in the ratio 4:7 by taking two parallel rays from the points A and B. The number of arcs to be made on the ray AX is: ___

Discussion

10.	Let S1, S2,....... be squares such that for each n≥1, the length of a side of Sn equals the length of a diagonal of Sn+1. If the length of a side of S1 is 10 cm, then for which of the following values of n is the area of Sn greater then 1sq cm
Answer» Let $S_{1}$ , $S_{2}$ ,....... be squares such that for each n≥1, the length of a side of $S_{n}$ equals the length of a diagonal of $S_{n + 1}$ . If the length of a side of $S_{1}$ is 10 cm, then for which of the following values of n is the area of $S_{n}$ greater then 1sq cm

10.

Let S1, S2,....... be squares such that for each n≥1, the length of a side of Sn equals the length of a diagonal of Sn+1. If the length of a side of S1 is 10 cm, then for which of the following values of n is the area of Sn greater then 1sq cm

Answer»

Let $S_{1}$ , $S_{2}$ ,....... be squares such that for each n≥1, the length

of a side of $S_{n}$ equals the length of a diagonal of $S_{n + 1}$ . If the

length of a side of $S_{1}$ is 10 cm, then for which of the following

values of n is the area of $S_{n}$ greater then 1sq cm

Discussion

11.	In figure shown below, PSSQ= PTTR and∠PST= ∠PRQ. Then ΔPQR is a/an __ triangle.
Answer» In figure shown below, $\frac{P S}{S Q}$ = $\frac{P T}{T R}$ and $∠$ PST= $∠$ PRQ. Then $Δ$ PQR is a/an __ triangle.

11.

In figure shown below, PSSQ= PTTR and∠PST= ∠PRQ. Then ΔPQR is a/an __ triangle.

Answer»

In figure shown below, $\frac{P S}{S Q}$ = $\frac{P T}{T R}$ and $∠$ PST= $∠$ PRQ. Then $Δ$ PQR is a/an __ triangle.

Discussion

12.	If A and B are two events such that P(A) = 12 and P(B) = 23, then
Answer» If A and B are two events such that P(A) = $\frac{1}{2}$ and P(B) = $\frac{2}{3}$ , then

Discussion

13.	Find the number of terms in an AP formed by all 3 digit numbers which when divided by 5 leaves a remainder of 3
Answer» Find the number of terms in an AP formed by all 3 digit numbers which when divided by 5 leaves a remainder of 3

Discussion

14.	Prove that (sinθ+cosecθ)2+(cosθ+secθ)2=7+tan2θ+cot2θ.
Answer» Prove that $(s i n θ + c o s e c θ)^{2} + (c o s θ + s e c θ)^{2} = 7 + t a n^{2} θ + c o t^{2} θ$ .

Discussion

15.	Question 6 In the given figure, the side QR of ΔPQR is produced to a point S. If the bisector of ∠PQR and ∠PRS meet at point T, then prove that ∠QTR=12∠QPR.
Answer» Question 6 In the given figure, the side QR of $Δ P Q R$ is produced to a point S. If the bisector of $∠ P Q R a n d ∠ P R S$ meet at point T, then prove that $∠ Q T R = \frac{1}{2} ∠ Q P R .$

Discussion

16.	Obtain all the zeroes of p(x) = x4-3x3-x2+4x-6 if two of its zeroes are -root 2 and +root 2.
Answer» Obtain all the zeroes of p(x) = x⁴-3x³-x²+4x-6 if two of its zeroes are -root 2 and +root 2.

Discussion

17.	A bag contains 4 black, 6 white and 8 red balls. One ball is drawn at random from the bag. Find the probability that the ball drawn is: i) white ii) not red iii) red or white iv) red and white v) neither black nor white vi) either red or black [6 MARKS]
Answer» A bag contains 4 black, 6 white and 8 red balls. One ball is drawn at random from the bag. Find the probability that the ball drawn is: i) white ii) not red iii) red or white iv) red and white v) neither black nor white vi) either red or black [6 MARKS]

Discussion

18.	A hemispherical bowl made of brass has inner radius of 3.5 cm. Find the cost of tin-plating the inner part of the bowl as well as tin plating a plate that exactly fits as a lid on bowl. Tin plating is done at the rate of ₹10 per 100 sq.cm.
Answer» A hemispherical bowl made of brass has inner radius of 3.5 cm. Find the cost of tin-plating the inner part of the bowl as well as tin plating a plate that exactly fits as a lid on bowl. Tin plating is done at the rate of ₹10 per 100 sq.cm.

Discussion

19.	The centre of a circle is (2x-1,3x+1). Find x if the circle passes through (-3,-1) and the length of its diameter is 20 unit
Answer» The centre of a circle is (2x-1,3x+1). Find x if the circle passes through (-3,-1) and the length of its diameter is 20 unit

Discussion

20.	Find the midpoint of the line segment joining the points A(-2,8) and B(-6,-4). [1 MARK]
Answer» Find the midpoint of the line segment joining the points A(-2,8) and B(-6,-4). [1 MARK]

Discussion

21.	Q. Prove that the product of two consecutive positive integer is divisible by 2.
Answer» Q. Prove that the product of two consecutive positive integer is divisible by 2.

Discussion

22.	Question 80(ii) In Delhi University, in the year 2009-10, 49000 seats were available for' admission to various courses at graduation level. Out of these 28200 seats were for the students of General Category while 7400 seats were reserved for SC and 3700 seats for ST. Find the percentage of seats' available for students of SC Category and ST Category taken together.
Answer» Question 80(ii) In Delhi University, in the year 2009-10, 49000 seats were available for' admission to various courses at graduation level. Out of these 28200 seats were for the students of General Category while 7400 seats were reserved for SC and 3700 seats for ST. Find the percentage of seats' available for students of SC Category and ST Category taken together.

22.

Question 80(ii) In Delhi University, in the year 2009-10, 49000 seats were available for' admission to various courses at graduation level. Out of these 28200 seats were for the students of General Category while 7400 seats were reserved for SC and 3700 seats for ST. Find the percentage of seats' available for students of SC Category and ST Category taken together.

Answer»

Question 80(ii)

In Delhi University, in the year 2009-10, 49000 seats were available for' admission to various courses at graduation level. Out of these 28200 seats were for the students of General Category while 7400 seats were reserved for SC and 3700 seats for ST. Find the percentage of seats' available for students of SC Category and ST Category taken together.

Discussion

23.	In the 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. [2 MARKS]
Answer» In the 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. [2 MARKS]

23.

In the 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. [2 MARKS]

Answer»

In the 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. [2 MARKS]

Discussion

24.	Determine the ratio in which the graph of the equation 3x + y = 9 divides line segment joining the points A (2,7) and B (1,3).
Answer» Determine the ratio in which the graph of the equation 3x + y = 9 divides line segment joining the points A (2,7) and B (1,3).

Discussion

25.	The scores of 11 cricket players in a match is given below: 121 ,14 ,11 ,9 ,1 ,14 ,101 ,81 ,51 ,7 ,14 Find the median and mode of the given data .
Answer» The scores of 11 cricket players in a match is given below: 121 ,14 ,11 ,9 ,1 ,14 ,101 ,81 ,51 ,7 ,14 Find the median and mode of the given data .

25.

The scores of 11 cricket players in a match is given below: 121 ,14 ,11 ,9 ,1 ,14 ,101 ,81 ,51 ,7 ,14 Find the median and mode of the given data .

Answer»

The scores of 11 cricket players in a match is given below:

121 ,14 ,11 ,9 ,1 ,14 ,101 ,81 ,51 ,7 ,14

Find the median and mode of the given data .

Discussion

26.	A tower is 100√3 m high. Find the angle of elevation of its top from a point 100 m away from its foot.
Answer» A tower is 100 $\sqrt{3}$ m high. Find the angle of elevation of its top from a point 100 m away from its foot.

Discussion

27.	Question 12 Prove that 1+sec θ−tan θ1+sec θ+tan θ=1−sin θcos θ
Answer» Question 12 Prove that $\frac{1 + s e c θ - t a n θ}{1 + s e c θ + t a n θ} = \frac{1 - s i n θ}{c o s θ}$

Discussion

28.	find the ratio in which line segment joining the points joining the points (-3,5) and (2,6) is divided by y axis
Answer» find the ratio in which line segment joining the points joining the points (-3,5) and (2,6) is divided by y axis

Discussion

29.	Question 2 (ii) Verify that each of the following is an AP and then write its next three terms. 5,143,133,4,⋯
Answer» Question 2 (ii) Verify that each of the following is an AP and then write its next three terms. $5, \frac{14}{3}, \frac{13}{3}, 4, \dots$

Discussion

30.	In the given fig. AD is the median and E is the mid point of AD. If extended BE meets AC at F, prove that FA = one third CA
Answer» In the given fig. AD is the median and E is the mid point of AD. If extended BE meets AC at F, prove that FA = one third CA

Discussion

31.	2 : 3 :: 6 : x are in proportion. Find x.
Answer» 2 : 3 :: 6 : x are in proportion. Find x.

Discussion

32.	Progressive taxation in direct taxes enables to bring equality in the
Answer» Progressive taxation in direct taxes enables to bring equality in the

Discussion

33.	If the length of a shadow cast by a pole is √3 times the length of the pole, then the angle of elevation of the sun is
Answer» If the length of a shadow cast by a pole is √3 times the length of the pole, then the angle of elevation of the sun is

Discussion

34.	Question 3 (iv) The points A(x1,y1),B(x2,y2) and C(x3,y3) are the vertices of Δ ABC. What are the coordinates of the centroid of the triangle ABC?
Answer» Question 3 (iv) The points $A (x_{1}, y_{1}), B (x_{2}, y_{2}) a n d C (x_{3}, y_{3})$ are the vertices of $Δ$ ABC. What are the coordinates of the centroid of the triangle ABC?

Discussion

35.	Draw graph of following pair of linear equations: y = 2(x - 1) 4x + y = 4 Also write the coordinate of the points where these lines meets x-axis and y - axis.
Answer» Draw graph of following pair of linear equations: y = 2(x - 1) 4x + y = 4 Also write the coordinate of the points where these lines meets x-axis and y - axis.

Discussion

36.	A man lying on a 6 m tall building finds that the angle of elevation of a 24 m high pillar and the angle of depression of its base are complementary angles. Find the distance of the man from the pillar.
Answer» A man lying on a 6 m tall building finds that the angle of elevation of a 24 m high pillar and the angle of depression of its base are complementary angles. Find the distance of the man from the pillar.

Discussion

37.	Find the 7th term from the end of AP: 7,10,13,....184
Answer» Find the 7th term from the end of AP: 7,10,13,....184

Discussion

38.	Question 4 If the HCF of 65 and 117 is expressible in the form 65m - 117, then the value of m is A) 4 B) 2 C) 1 D) 3
Answer» Question 4 If the HCF of 65 and 117 is expressible in the form 65m - 117, then the value of m is A) 4 B) 2 C) 1 D) 3

Discussion

39.	Question 2(ii) Represent the following situations in the form of quadratic equations. (ii) The product of two consecutive positive integers is 306. We need to find the integers.
Answer» Question 2(ii) Represent the following situations in the form of quadratic equations. (ii) The product of two consecutive positive integers is $306$ . We need to find the integers.

Discussion

40.	In what ratio the line segment joining the points (-1, 3) and (4, -7) divided by the point (2, -3)?
Answer» In what ratio the line segment joining the points (-1, 3) and (4, -7) divided by the point (2, -3)?

Discussion

41.	While finding the roots of the quadratic equation 3x2- 2√6 x + 2 = 0 using factorization method, the given equation is reduced to the form (ax+b)(cx+d). The values of a and d are
Answer» While finding the roots of the quadratic equation 3 $x^{2}$ - 2 $\sqrt{6}$ x + 2 = 0 using factorization method, the given equation is reduced to the form (ax+b)(cx+d). The values of a and d are

Discussion

42.	Degree of a constant polynomial is _____.
Answer» Degree of a constant polynomial is _____.

Discussion

43.	Question 1(i) Find the roots of the following quadratic equations by factorisation: (i) x2−3x−10=0
Answer» Question 1(i) Find the roots of the following quadratic equations by factorisation: (i) $x^{2} - 3 x - 10 = 0$

Discussion

44.	The equation of the circle having (6,7) and (4,3) as the endpoints of its diameter is
Answer» The equation of the circle having $(6, 7)$ and $(4, 3)$ as the endpoints of its diameter is

Discussion

45.	D and E are the points on the sides AB and AC respectively of a ΔABC such that: AD = 8 cm, DB =12 cm, AE = 6cm and CE = 9 cm. Prove that BC=52DE.
Answer» D and E are the points on the sides AB and AC respectively of a $Δ A B C$ such that: AD = 8 cm, DB =12 cm, AE = 6cm and CE = 9 cm. Prove that $B C = \frac{5}{2} D E$ .

Discussion

46.	Factorise : 1) 12x2−7x+1 2) 2x2+7x+3 [4 MARKS]
Answer» Factorise : $1) 12 x^{2} - 7 x + 1$ $2) 2 x^{2} + 7 x + 3$ [4 MARKS]

Discussion

47.	Question 16 Show that: (i) x + 3 is a factor of 69+11x–x2+x3. (ii) 2x – 3 is a factor of x+2x3–9x2+12.
Answer» Question 16 Show that: (i) x + 3 is a factor of $69 + 11 x - x^{2} + x^{3}$ . (ii) 2x – 3 is a factor of $x + 2 x^{3} - 9 x^{2} + 12$ .

Discussion

48.	Adjacent angles of a parallelogram are ___.
Answer» Adjacent angles of a parallelogram are ___.

Discussion

49.	AD is an altitude of an equilateral triangle ABC. On AD as base, another equilateral triangle ADE is constructed. Prove that Area (ΔADE): Area (ΔABC)=3:4.
Answer» AD is an altitude of an equilateral triangle ABC. On AD as base, another equilateral triangle ADE is constructed. Prove that Area $(Δ A D E)$ : Area $(Δ A B C) = 3 : 4$ .

Discussion

50.	While dividing a segment in a given ratio, we can not draw the ray at angles ______ and _____.
Answer» While dividing a segment in a given ratio, we can not draw the ray at angles ______ and _____.

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

The wheels of a car are of diameter 80 cm each. How many complete revolutions does each wheel make in 10 minutes when the car is travelling at a speed of 66 km per hour?

If the mth and the nth term of an A.P are 1n and 1m respectively, then find its mnth term.

The areas of two similar triangles are 49 cm2 and 64 cm2 respectively. The ratio of their corresponding sides is

Find a point with an X-coordinate of 5 on the line 3x - 8y + 17 = 0. [2 MARKS]

Question 22 Which term of the AP –2, –7, –12,.. will be –77? Find the sum of this AP upto the term –77.

Question 6 The 21st term of an AP whose first two terms are – 3 and 4, is A) 17 B) 137 C) 143 D) -143

The largest angle of a triangle, whose sides are 12, 18 and 20 inches, is bisected. Find the lengths of the segments created when the angle bisector intersects the opposite side of the triangle.

The line segment AB was divided in the ratio 4:7 by taking two parallel rays from the points A and B. The number of arcs to be made on the ray AX is: ___

Let S1, S2,....... be squares such that for each n≥1, the length of a side of Sn equals the length of a diagonal of Sn+1. If the length of a side of S1 is 10 cm, then for which of the following values of n is the area of Sn greater then 1sq cm

In figure shown below, PSSQ= PTTR and∠PST= ∠PRQ. Then ΔPQR is a/an __ triangle.

If A and B are two events such that P(A) = 12 and P(B) = 23, then

Find the number of terms in an AP formed by all 3 digit numbers which when divided by 5 leaves a remainder of 3

Prove that (sinθ+cosecθ)2+(cosθ+secθ)2=7+tan2θ+cot2θ.

Question 6 In the given figure, the side QR of ΔPQR is produced to a point S. If the bisector of ∠PQR and ∠PRS meet at point T, then prove that ∠QTR=12∠QPR.

Obtain all the zeroes of p(x) = x4-3x3-x2+4x-6 if two of its zeroes are -root 2 and +root 2.

A bag contains 4 black, 6 white and 8 red balls. One ball is drawn at random from the bag. Find the probability that the ball drawn is: i) white ii) not red iii) red or white iv) red and white v) neither black nor white vi) either red or black [6 MARKS]

A hemispherical bowl made of brass has inner radius of 3.5 cm. Find the cost of tin-plating the inner part of the bowl as well as tin plating a plate that exactly fits as a lid on bowl. Tin plating is done at the rate of ₹10 per 100 sq.cm.

The centre of a circle is (2x-1,3x+1). Find x if the circle passes through (-3,-1) and the length of its diameter is 20 unit

Find the midpoint of the line segment joining the points A(-2,8) and B(-6,-4). [1 MARK]

Q. Prove that the product of two consecutive positive integer is divisible by 2.

In the 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. [2 MARKS]

Determine the ratio in which the graph of the equation 3x + y = 9 divides line segment joining the points A (2,7) and B (1,3).

The scores of 11 cricket players in a match is given below: 121 ,14 ,11 ,9 ,1 ,14 ,101 ,81 ,51 ,7 ,14 Find the median and mode of the given data .

A tower is 100√3 m high. Find the angle of elevation of its top from a point 100 m away from its foot.

Question 12 Prove that 1+sec θ−tan θ1+sec θ+tan θ=1−sin θcos θ

find the ratio in which line segment joining the points joining the points (-3,5) and (2,6) is divided by y axis

Question 2 (ii) Verify that each of the following is an AP and then write its next three terms. 5,143,133,4,⋯

In the given fig. AD is the median and E is the mid point of AD. If extended BE meets AC at F, prove that FA = one third CA

2 : 3 :: 6 : x are in proportion. Find x.

Progressive taxation in direct taxes enables to bring equality in the

If the length of a shadow cast by a pole is √3 times the length of the pole, then the angle of elevation of the sun is

Question 3 (iv) The points A(x1,y1),B(x2,y2) and C(x3,y3) are the vertices of Δ ABC. What are the coordinates of the centroid of the triangle ABC?

Draw graph of following pair of linear equations: y = 2(x - 1) 4x + y = 4 Also write the coordinate of the points where these lines meets x-axis and y - axis.

A man lying on a 6 m tall building finds that the angle of elevation of a 24 m high pillar and the angle of depression of its base are complementary angles. Find the distance of the man from the pillar.

Find the 7th term from the end of AP: 7,10,13,....184

Question 4 If the HCF of 65 and 117 is expressible in the form 65m - 117, then the value of m is A) 4 B) 2 C) 1 D) 3

Question 2(ii) Represent the following situations in the form of quadratic equations. (ii) The product of two consecutive positive integers is 306. We need to find the integers.

In what ratio the line segment joining the points (-1, 3) and (4, -7) divided by the point (2, -3)?

While finding the roots of the quadratic equation 3x2- 2√6 x + 2 = 0 using factorization method, the given equation is reduced to the form (ax+b)(cx+d). The values of a and d are

Degree of a constant polynomial is _____.

Question 1(i) Find the roots of the following quadratic equations by factorisation: (i) x2−3x−10=0

The equation of the circle having (6,7) and (4,3) as the endpoints of its diameter is

D and E are the points on the sides AB and AC respectively of a ΔABC such that: AD = 8 cm, DB =12 cm, AE = 6cm and CE = 9 cm. Prove that BC=52DE.

Factorise : 1) 12x2−7x+1 2) 2x2+7x+3 [4 MARKS]

Question 16 Show that: (i) x + 3 is a factor of 69+11x–x2+x3. (ii) 2x – 3 is a factor of x+2x3–9x2+12.

Adjacent angles of a parallelogram are ___.

AD is an altitude of an equilateral triangle ABC. On AD as base, another equilateral triangle ADE is constructed. Prove that Area (ΔADE): Area (ΔABC)=3:4.

While dividing a segment in a given ratio, we can not draw the ray at angles ______ and _____.

While dividing a segment in a given ratio, we can not draw the ray at angles __ and _.