32581 + Interview Questions in Mathematics

1.	A box contains 20 cards numbered from 1 to 20. A card is drawn at random from the box. Find the probability that the number on the drawn card is(i) divisible by 2 or 3 (ii) a prime number
Answer» A box contains 20 cards numbered from 1 to 20. A card is drawn at random from the box. Find the probability that the number on the drawn card is (i) divisible by 2 or 3 (ii) a prime number

1.

A box contains 20 cards numbered from 1 to 20. A card is drawn at random from the box. Find the probability that the number on the drawn card is(i) divisible by 2 or 3 (ii) a prime number

Answer»

A box contains 20 cards numbered from 1 to 20. A card is drawn at random from the box. Find the probability that the number on the drawn card is

(i) divisible by 2 or 3 (ii) a prime number

Discussion

2.	Q.67 Area of the triangle formed between the lines y = \vert x\vert and y = 7 is
Answer» Q.67 Area of the triangle formed between the lines y = \vert x\vert and y = 7 is

Discussion

3.	What is the locus of the centre of a cycle wheel?
Answer» What is the locus of the centre of a cycle wheel?

Discussion

4.	The value of tan 55°cot 35°+ cot 1° cot 2° cot 3° .... cot 90°, is(a) −2(b) 2(c) 1(d) 0
Answer» The value of $\frac{\tan 55 °}{\cot 35 °}$ + cot 1° cot 2° cot 3° .... cot 90°, is (a) −2 (b) 2 (c) 1 (d) 0

Discussion

5.	If B = {1, 3, 5, 7, 9}, the set-builder representation of B is _________.
Answer» If B = {1, 3, 5, 7, 9}, the set-builder representation of B is _________.

Discussion

6.	In compound interest, when the interest is compounded half-yearly, the principal changes every __________.
Answer» In compound interest, when the interest is compounded half-yearly, the principal changes every __________.

Discussion

7.	Let P be the point of intersection of the diagonal of a parallelogram ABCD and O is any point. If OA→+OB→+OC→+OD→=λOP→, Then λ=__________________.
Answer» Let P be the point of intersection of the diagonal of a parallelogram ABCD and O is any point. If $\vec{O A} + \vec{O B} + \vec{O C} + \vec{O D} = λ \vec{O P}, Then λ =__________________.$

Discussion

8.	Mr.Amol purchased 50 shares of Face Value Rs100 when the Market value of the share was Rs 80. Company had given 20% dividend. Find the rate of return on investment.
Answer» Mr.Amol purchased 50 shares of Face Value Rs100 when the Market value of the share was Rs 80. Company had given 20% dividend. Find the rate of return on investment.

Discussion

9.	150 spherical marbles, each of diameter 14 cm, are dropped in a cylindrical vessel of diameter 7 cm containing some water, which are completely immersed in water. Find the rise in the level of water in the vessel.
Answer» 150 spherical marbles, each of diameter 14 cm, are dropped in a cylindrical vessel of diameter 7 cm containing some water, which are completely immersed in water. Find the rise in the level of water in the vessel.

Discussion

10.	The coefficient of variation of a distribution is:
Answer» The coefficient of variation of a distribution is:

Discussion

11.	Question 3Draw two concentric circles of radii 3 cm and 5 cm. Taking a point on outer circle construct the pair of tangents to the other. Measure the length of a tangent and verify it by actual calculation.
Answer» Question 3 Draw two concentric circles of radii 3 cm and 5 cm. Taking a point on outer circle construct the pair of tangents to the other. Measure the length of a tangent and verify it by actual calculation.

Discussion

12.	In the figure, the ∠ABC=30°. If CB=18 m , then AB = and AC = .
Answer» In the figure, the $∠ A B C = 30 °$ . If $C B = 18 m$ , then AB = and AC = .

Discussion

13.	If cos3θ=√32, 0°<3θ<90°, the value of θ (in degrees) is10
Answer» If $cos 3 θ = \frac{\sqrt{3}}{2}$ , $0 ° < 3 θ < 90 °$ , the value of $θ$ (in degrees) is 10

Discussion

14.	The sum of n terms of an AP is 5n2−3n. Find the AP and hence find its 10th term
Answer» The sum of n terms of an AP is $5 n^{2} - 3 n$ . Find the AP and hence find its 10th term

Discussion

15.	If f(x)=√x g(x) where g(4)=2 andg'(4)=3, find f'(4)
Answer» If f(x)=√x g(x) where g(4)=2 andg'(4)=3, find f'(4)

Discussion

16.	Prove that for all points on the line joining the origin and the point (4, 2) the x-coordinates is double the y-coordinates. What is the equation of this line?
Answer» Prove that for all points on the line joining the origin and the point (4, 2) the x-coordinates is double the y-coordinates. What is the equation of this line?

Discussion

17.	Convert 411 into decimal form.
Answer» Convert $\frac{4}{11}$ into decimal form.

Discussion

18.	Question 1 Is the area of the circle inscribed in a square of side a cm, πa2 cm2=? Given reasons for your answer.
Answer» Question 1 Is the area of the circle inscribed in a square of side a cm, $π a^{2} c m^{2} = ?$ Given reasons for your answer.

Discussion

19.	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

20.	A the if runs with a uniform speed of 200m per minute.After one minute a policeman runs after the theif to catch him. He goes with a speed of 100 m per minute in the first minute and increses his speed by 10m per minute. After how many minutes the policeman will catch the their?
Answer» A the if runs with a uniform speed of 200m per minute.After one minute a policeman runs after the theif to catch him. He goes with a speed of 100 m per minute in the first minute and increses his speed by 10m per minute. After how many minutes the policeman will catch the their?

Discussion

21.	The numbers a,b are chosen from the set {1,2,3,4,---,10} such that a ≤ b with replacement. The probability that a divides b is
Answer» The numbers a,b are chosen from the set {1,2,3,4,---,10} such that $a \leq b$ with replacement. The probability that a divides b is

Discussion

22.	In a ΔPQR, let →a=−−→QR,→b=−−→RP and→c=−−→PQ. If \|→a\|=12,\|→b\|=4√3 and →b.→c=24, then which of the following is/are true:
Answer» In a $Δ P Q R,$ let $\to a = - - \to Q R, \to b = - - \to R P$ and $\to c = - - \to P Q$ . If $\| \to a \| = 12, \| \to b \| = 4 \sqrt{3}$ and $\to b . \to c = 24,$ then which of the following is/are true:

Discussion

23.	A hollow sphere of external and internal diameters 8 cm and 4 cm, respectively is melted into a solid cone of base diameter 8 cm. Find the height of the cone. [CBSE 2013C]
Answer» A hollow sphere of external and internal diameters 8 cm and 4 cm, respectively is melted into a solid cone of base diameter 8 cm. Find the height of the cone. [CBSE 2013C]

Discussion

24.	Draw any circle. Take any point A on it and construct tangent at A without using the centre of the circle.
Answer» Draw any circle. Take any point A on it and construct tangent at A without using the centre of the circle.

Discussion

25.	The least count of a vernier caliper is 0.01 cm and 10 divisions of the vernier scale is equal to n divisions of main scale. The value of n will be (1 division of main scale is 1 mm)
Answer» The least count of a vernier caliper is $0.01 cm$ and $10$ divisions of the vernier scale is equal to $n$ divisions of main scale. The value of $n$ will be ( $1$ division of main scale is $1 mm$ )

Discussion

26.	Find the centroids of the triangles whose vertices are given below.(1) (–7,6),(2,–2),(8,5)(2) (3,–5),(4,3),(11,–4)(3) (4,7),(8,4),(7,11)
Answer» Find the centroids of the triangles whose vertices are given below. (1) $(- 7, 6), (2, - 2), (8, 5)$ (2) $(3, - 5), (4, 3), (11, - 4)$ (3) $(4, 7), (8, 4), (7, 11)$

26.

Find the centroids of the triangles whose vertices are given below.(1) (–7,6),(2,–2),(8,5)(2) (3,–5),(4,3),(11,–4)(3) (4,7),(8,4),(7,11)

Answer»

Find the centroids of the triangles whose vertices are given below.
(1) $(- 7, 6), (2, - 2), (8, 5)$

(2) $(3, - 5), (4, 3), (11, - 4)$

(3) $(4, 7), (8, 4), (7, 11)$

Discussion

27.	A dealer sells an article for Rs.75 and gains as much per cent as the cost price of the article. Find the cost price of the article.
Answer» A dealer sells an article for Rs.75 and gains as much per cent as the cost price of the article. Find the cost price of the article.

Discussion

28.	Mark the correct alternative in each of the following:If x+2≤9, then(a) x∈(-7, 11)(b) x∈[-11, 7](c) x∈(-∞, -7) ∪ (11, ∞)(d) x∈(-∞, -7) ∪ [11, ∞)
Answer» Mark the correct alternative in each of the following: If $\|x + 2\|$ $\leq$ 9, then (a) x $\in$ ( $-$ 7, 11) (b) x $\in$ [ $-$ 11, 7] (c) x $\in$ ( $-$ $\infty$ , $-$ 7) $\cup$ (11, $\infty$ ) (d) x $\in$ ( $-$ $\infty$ , $-$ 7) $\cup$ [11, $\infty$ )

Discussion

29.	What will be the angle in each sector of the triangle if all the circles have equal radius?
Answer» What will be the angle in each sector of the triangle if all the circles have equal radius?

Discussion

30.	The rates for the entrance tickets at a water theme park are listed below CategoryWeekdayWeekendpricepriceAdults400500Senior200250CitizensChildren300400 What is the dimension of the matrix formed by listing the weekday and weekend rates along the column of the matrix?
Answer» The rates for the entrance tickets at a water theme park are listed below $\begin{matrix} Category & Weekday & Weekend price & price Adults & 400 & 500 Senior & 200 & 250 Citizens Children & 300 & 400 \end{matrix}$ What is the dimension of the matrix formed by listing the weekday and weekend rates along the column of the matrix?

Discussion

31.	Solve the following quadratic equations by factorization:x-4x-5+x-6x-7=103; x≠5, 7
Answer» Solve the following quadratic equations by factorization: $\frac{x - 4}{x - 5} + \frac{x - 6}{x - 7} = \frac{10}{3}; x \neq 5, 7$

Discussion

32.	Find the circumference of the inner and the outer circles, shown in the adjoining figure? (Take π = 3.14)
Answer» Find the circumference of the inner and the outer circles, shown in the adjoining figure? (Take π = 3.14)

Discussion

33.	Find out the wrong number in the series given below :1,3,7,15,30,63
Answer» Find out the wrong number in the series given below : $1, 3, 7, 15, 30, 63$

Discussion

34.	points A ( -1,7) and B ( 5 ,y ) lie on circle with center o ( 2,-3y) . find the value of y . hence find the radius of the circle if y is positive
Answer» points A ( -1,7) and B ( 5 ,y ) lie on circle with center o ( 2,-3y) . find the value of y . hence find the radius of the circle if y is positive

Discussion

35.	In the finger-raising game, which number has the maximum probability of occurrence as the sum? What is this probability?
Answer» In the finger-raising game, which number has the maximum probability of occurrence as the sum? What is this probability?

Discussion

36.	Show that the points (−3, 2), (−5,−5), (2, −3) and (4, 4) are the vertices of a rhombus. Find the area of this rhombus.
Answer» Show that the points (−3, 2), (−5,−5), (2, −3) and (4, 4) are the vertices of a rhombus. Find the area of this rhombus.

Discussion

37.	Fill in the Blank.If Mode − Mean =36, then Median − Mean = ___________.
Answer» Fill in the Blank. If Mode $-$ Mean $= 36$ , then Median $-$ Mean $=$ ___________.

Discussion

38.	A box has 100 pens of which 10 are defective. The probability that out of a sample of 5 pens drawn one by one with replacement and atmost one is defective is
Answer» A box has $100$ pens of which $10$ are defective. The probability that out of a sample of $5$ pens drawn one by one with replacement and atmost one is defective is

Discussion

39.	In the figure, ABCD is a square of side 14 cm with centres A, B, C, and D four circles are drawn such that each circle touch externally two of the remaining three circles. Find the area of the shaded region. [3 MARKS]
Answer» In the figure, ABCD is a square of side 14 cm with centres A, B, C, and D four circles are drawn such that each circle touch externally two of the remaining three circles. Find the area of the shaded region. [3 MARKS]

39.

In the figure, ABCD is a square of side 14 cm with centres A, B, C, and D four circles are drawn such that each circle touch externally two of the remaining three circles. Find the area of the shaded region. [3 MARKS]

Answer»

In the figure, ABCD is a square of side 14 cm with centres A, B, C, and D four circles are drawn such that each circle touch externally two of the remaining three circles. Find the area of the shaded region. [3 MARKS]

Discussion

40.	In the given figure, chord EF \|\| chord GH. Prove that, chord EG ≅ chord FH. Fill in the blanks and write the proof.
Answer» In the given figure, chord EF \|\| chord GH. Prove that, chord EG ≅ chord FH. Fill in the blanks and write the proof.

Discussion

41.	If median AD of a triangle ABC makes angle π6 with side BC, then the value of (cotB−cotC)2 is equal to:
Answer» If median $A D$ of a triangle $A B C$ makes angle $\frac{π}{6}$ with side $B C$ , then the value of $(cot B - cot C)^{2}$ is equal to:

Discussion

42.	Question 82At a particular time, the length of the shadow of Qutub Minar whose height is 72 m is 80 m. What will be the height of an electric pole, the length of whose shadow at the same time is 1000 cm?
Answer» Question 82 At a particular time, the length of the shadow of Qutub Minar whose height is 72 m is 80 m. What will be the height of an electric pole, the length of whose shadow at the same time is 1000 cm?

42.

Question 82At a particular time, the length of the shadow of Qutub Minar whose height is 72 m is 80 m. What will be the height of an electric pole, the length of whose shadow at the same time is 1000 cm?

Answer»

Question 82

At a particular time, the length of the shadow of Qutub Minar whose height is 72 m is 80 m. What will be the height of an electric pole, the length of whose shadow at the same time is 1000 cm?

Discussion

43.	The value of sin θ cos(90° – θ) + cos θ sin (90° – θ) is ___________.
Answer» The value of sin θ cos(90° – θ) + cos θ sin (90° – θ) is ___________.

Discussion

44.	Question 1 (iii)Find the sum of the following APs(iii) 0.6, 1.7, 2.8 ,…….., to 100 terms
Answer» Question 1 (iii) Find the sum of the following APs (iii) 0.6, 1.7, 2.8 ,…….., to 100 terms

Discussion

45.	44. If an AP consists of n terms with first term a and nth term L show that the sum of the mth term from beginning and the mth term from end is ( a + L ).
Answer» 44. If an AP consists of n terms with first term a and nth term L show that the sum of the mth term from beginning and the mth term from end is ( a + L ).

Discussion

46.	The internal and external diameters of a hollow hemispherical vessel are 21 cm and 25.2 cm respectively. The cost of painting 1 cm2 of the surface is 10 paise. Find the total cost to paint the vessel all over.
Answer» The internal and external diameters of a hollow hemispherical vessel are 21 cm and 25.2 cm respectively. The cost of painting 1 cm² of the surface is 10 paise. Find the total cost to paint the vessel all over.

Discussion

47.	Sony Media Ltd.issued 50,000 shares of ₹ 10 each payable ₹ 3 on application , ₹ 4 on allotment and balance on first and final call . Applications were received for 1,00,000 shares and allotment was made as follows :(i) Applicants for 60,000 shares were allotted 30,000 shares,(ii) Applicants for 40,000 shares were allotted 20,000 shares,Anupam to whom 1,000 shares were allotted from category(i) failed to pay the allotment money.Pass journal entries up to allotment .
Answer» Sony Media Ltd.issued 50,000 shares of ₹ 10 each payable ₹ 3 on application , ₹ 4 on allotment and balance on first and final call . Applications were received for 1,00,000 shares and allotment was made as follows : (i) Applicants for 60,000 shares were allotted 30,000 shares, (ii) Applicants for 40,000 shares were allotted 20,000 shares, Anupam to whom 1,000 shares were allotted from category (i) failed to pay the allotment money. Pass journal entries up to allotment .

Discussion

48.	a and b are the zeroes of a quadratic polynomial p(x), and k is any constant. Then general form of polynomial is.
Answer» $a a n d b$ are the zeroes of a quadratic polynomial $p (x)$ , and $k$ is any constant. Then general form of polynomial is.

Discussion

49.	10. If (5a-3b) ÷ a=(4a+b-2c)÷(a+4b-2c)=(a+2b-3c)÷(4a-4c),then prove that, 6a=4b=3c
Answer» 10. If (5a-3b) ÷ a=(4a+b-2c)÷(a+4b-2c)=(a+2b-3c)÷(4a-4c),then prove that, 6a=4b=3c

Discussion

50.	significant figures addition and subtraction
Answer» significant figures addition and subtraction

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

A box contains 20 cards numbered from 1 to 20. A card is drawn at random from the box. Find the probability that the number on the drawn card is(i) divisible by 2 or 3 (ii) a prime number

Q.67 Area of the triangle formed between the lines y = \vert x\vert and y = 7 is

What is the locus of the centre of a cycle wheel?

The value of tan 55°cot 35°+ cot 1° cot 2° cot 3° .... cot 90°, is(a) −2(b) 2(c) 1(d) 0

If B = {1, 3, 5, 7, 9}, the set-builder representation of B is _________.

In compound interest, when the interest is compounded half-yearly, the principal changes every __________.

Let P be the point of intersection of the diagonal of a parallelogram ABCD and O is any point. If OA→+OB→+OC→+OD→=λOP→, Then λ=__________________.

Mr.Amol purchased 50 shares of Face Value Rs100 when the Market value of the share was Rs 80. Company had given 20% dividend. Find the rate of return on investment.

150 spherical marbles, each of diameter 14 cm, are dropped in a cylindrical vessel of diameter 7 cm containing some water, which are completely immersed in water. Find the rise in the level of water in the vessel.

The coefficient of variation of a distribution is:

Question 3Draw two concentric circles of radii 3 cm and 5 cm. Taking a point on outer circle construct the pair of tangents to the other. Measure the length of a tangent and verify it by actual calculation.

In the figure, the ∠ABC=30°. If CB=18 m , then AB = and AC = .

If cos3θ=√32, 0°&lt;3θ&lt;90°, the value of θ (in degrees) is10

The sum of n terms of an AP is 5n2−3n. Find the AP and hence find its 10th term

If f(x)=√x g(x) where g(4)=2 andg'(4)=3, find f'(4)

Prove that for all points on the line joining the origin and the point (4, 2) the x-coordinates is double the y-coordinates. What is the equation of this line?

Convert 411 into decimal form.

Question 1 Is the area of the circle inscribed in a square of side a cm, πa2 cm2=? Given reasons for your answer.

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

A the if runs with a uniform speed of 200m per minute.After one minute a policeman runs after the theif to catch him. He goes with a speed of 100 m per minute in the first minute and increses his speed by 10m per minute. After how many minutes the policeman will catch the their?

The numbers a,b are chosen from the set {1,2,3,4,---,10} such that a ≤ b with replacement. The probability that a divides b is

In a ΔPQR, let →a=−−→QR,→b=−−→RP and→c=−−→PQ. If |→a|=12,|→b|=4√3 and →b.→c=24, then which of the following is/are true:

A hollow sphere of external and internal diameters 8 cm and 4 cm, respectively is melted into a solid cone of base diameter 8 cm. Find the height of the cone. [CBSE 2013C]

Draw any circle. Take any point A on it and construct tangent at A without using the centre of the circle.

The least count of a vernier caliper is 0.01 cm and 10 divisions of the vernier scale is equal to n divisions of main scale. The value of n will be (1 division of main scale is 1 mm)

Find the centroids of the triangles whose vertices are given below.(1) (–7,6),(2,–2),(8,5)(2) (3,–5),(4,3),(11,–4)(3) (4,7),(8,4),(7,11)

A dealer sells an article for Rs.75 and gains as much per cent as the cost price of the article. Find the cost price of the article.

Mark the correct alternative in each of the following:If x+2≤9, then(a) x∈(-7, 11)(b) x∈[-11, 7](c) x∈(-∞, -7) ∪ (11, ∞)(d) x∈(-∞, -7) ∪ [11, ∞)

What will be the angle in each sector of the triangle if all the circles have equal radius?

The rates for the entrance tickets at a water theme park are listed below CategoryWeekdayWeekendpricepriceAdults400500Senior200250CitizensChildren300400 What is the dimension of the matrix formed by listing the weekday and weekend rates along the column of the matrix?

Solve the following quadratic equations by factorization:x-4x-5+x-6x-7=103; x≠5, 7

Find the circumference of the inner and the outer circles, shown in the adjoining figure? (Take π = 3.14)

Find out the wrong number in the series given below :1,3,7,15,30,63

points A ( -1,7) and B ( 5 ,y ) lie on circle with center o ( 2,-3y) . find the value of y . hence find the radius of the circle if y is positive

In the finger-raising game, which number has the maximum probability of occurrence as the sum? What is this probability?

Show that the points (−3, 2), (−5,−5), (2, −3) and (4, 4) are the vertices of a rhombus. Find the area of this rhombus.

Fill in the Blank.If Mode − Mean =36, then Median − Mean = ___________.

A box has 100 pens of which 10 are defective. The probability that out of a sample of 5 pens drawn one by one with replacement and atmost one is defective is

In the figure, ABCD is a square of side 14 cm with centres A, B, C, and D four circles are drawn such that each circle touch externally two of the remaining three circles. Find the area of the shaded region. [3 MARKS]

In the given figure, chord EF || chord GH. Prove that, chord EG ≅ chord FH. Fill in the blanks and write the proof.

If median AD of a triangle ABC makes angle π6 with side BC, then the value of (cotB−cotC)2 is equal to:

Question 82At a particular time, the length of the shadow of Qutub Minar whose height is 72 m is 80 m. What will be the height of an electric pole, the length of whose shadow at the same time is 1000 cm?

The value of sin θ cos(90° – θ) + cos θ sin (90° – θ) is ___________.

Question 1 (iii)Find the sum of the following APs(iii) 0.6, 1.7, 2.8 ,…….., to 100 terms

44. If an AP consists of n terms with first term a and nth term L show that the sum of the mth term from beginning and the mth term from end is ( a + L ).

The internal and external diameters of a hollow hemispherical vessel are 21 cm and 25.2 cm respectively. The cost of painting 1 cm2 of the surface is 10 paise. Find the total cost to paint the vessel all over.

a and b are the zeroes of a quadratic polynomial p(x), and k is any constant. Then general form of polynomial is.

10. If (5a-3b) ÷ a=(4a+b-2c)÷(a+4b-2c)=(a+2b-3c)÷(4a-4c),then prove that, 6a=4b=3c

significant figures addition and subtraction

If cos3θ=√32, 0°<3θ<90°, the value of θ (in degrees) is10