32581 + Interview Questions in Mathematics

1.	ABC is an equilateral triangle of side 16 cm. Taking A,B and C as centres, three sectors are drawn from each vertex of radii 4 cm,6 cm and 8 cm as shown in the given figure. The area of the shaded region is
Answer» $A B C$ is an equilateral triangle of side $16 cm$ . Taking $A, B$ and $C$ as centres, three sectors are drawn from each vertex of radii $4 cm, 6 cm$ and $8 cm$ as shown in the given figure. The area of the shaded region is

Discussion

2.	Question 195 Construct a parallelogram HOME with HO = 6 cm, HE = 4 cm and OE = 3 cm.
Answer» Question 195 Construct a parallelogram HOME with HO = 6 cm, HE = 4 cm and OE = 3 cm.

Discussion

3.	The circumference of two circles are in the ratio 2 : 3. Find the ratio of their areas.
Answer» The circumference of two circles are in the ratio 2 : 3. Find the ratio of their areas.

Discussion

4.	On the admission of Rao, goodwill of Murty and Shah is valued at ₹ 30,000. Rao is to get 1/4th share of profits. Previously Murty and Shah shared profits in the ratio of 3 : 2. Rao is unable to bring amount of goodwill. Give Journal entries in the books of Murty and Shah when:(a) there is no Goodwill Account and(b) Goodwill appears in the books at ₹ 10,000.
Answer» On the admission of Rao, goodwill of Murty and Shah is valued at ₹ 30,000. Rao is to get 1/4th share of profits. Previously Murty and Shah shared profits in the ratio of 3 : 2. Rao is unable to bring amount of goodwill. Give Journal entries in the books of Murty and Shah when: (a) there is no Goodwill Account and (b) Goodwill appears in the books at ₹ 10,000.

Discussion

5.	An aeroplane when 900 m high, passes vertically above another aeroplane at an instant when their angles of elevation from the same observation point are 60∘ and 45∘ respectively. Approximately, by how many meters is the aeroplane higher than the other?
Answer» An aeroplane when $900 m$ high, passes vertically above another aeroplane at an instant when their angles of elevation from the same observation point are $60^{\circ}$ and $45^{\circ}$ respectively. Approximately, by how many meters is the aeroplane higher than the other?

Discussion

6.	If two rectangles ABCD and PQRS whose sides are parallel to the coordinate axes are drawn as shown in below figure then the coordinates of 'Q' is ___
Answer» If two rectangles ABCD and PQRS whose sides are parallel to the coordinate axes are drawn as shown in below figure then the coordinates of 'Q' is ___

6.

If two rectangles ABCD and PQRS whose sides are parallel to the coordinate axes are drawn as shown in below figure then the coordinates of 'Q' is ___

Answer»

If two rectangles ABCD and PQRS whose sides are parallel to the coordinate axes are drawn as shown in below figure then the coordinates of 'Q' is ___

Discussion

7.

If the mean of the following frequency distribution is 24, find the value of p. [CBSE 2013] Class 0−10 10−20 20−30 30−40 40−50 Frequency 3 4 p 3 2

Answer» If the mean of the following frequency distribution is 24, find the value of p. [CBSE 2013]

Class	0−10	10−20	20−30	30−40	40−50
Frequency	3	4	p	3	2

Discussion

8.	If (−4,0) and (1,−1) are two vertices of a triangle whose area is 4 sq.units, then locus of centroid of the triangle is
Answer» If $(- 4, 0)$ and $(1, - 1)$ are two vertices of a triangle whose area is $4 sq.units$ , then locus of centroid of the triangle is

Discussion

9.	If n = 23 ✕ 34 ✕ 54 ✕ 7, then the number of consecutive zeros in n, where n is a natural number, is(a) 2(b) 3(c) 4(d) 7
Answer» If n = 2³ ✕ 3⁴ ✕ 5⁴ ✕ 7, then the number of consecutive zeros in n, where n is a natural number, is (a) 2 (b) 3 (c) 4 (d) 7

Discussion

10.	Question 1(v)Find the roots of the following quadratic equations by factorization:(v)100x2−20x+1=0
Answer» Question 1(v) Find the roots of the following quadratic equations by factorization: $(v) 100 x^{2} - 20 x + 1 = 0$

Discussion

11.	The quadratic polynomial in x whose zeros are -a and 2a is
Answer» The quadratic polynomial in x whose zeros are -a and 2a is

Discussion

12.	Find the angle subtended at the centre of a circle of radius 5 cm by an arc of length (5π/3) cm.
Answer» Find the angle subtended at the centre of a circle of radius 5 cm by an arc of length (5π/3) cm.

Discussion

13.	If the mean of the data is 60, find the value of p Class markfrequency25−351235−451645−55p55−651565−75875−851985−9513
Answer» If the mean of the data is 60, find the value of p $\begin{matrix} C l a s s m a r k & f r e q u e n c y 25 - 35 & 12 35 - 45 & 16 45 - 55 & p 55 - 65 & 15 65 - 75 & 8 75 - 85 & 19 85 - 95 & 13 \end{matrix}$

Discussion

14.	11. Let R(x) be the remainder upon dividing x⁴⁴+ x³³+ x²²+ x¹¹+ 1 by the polynomial x⁴+ x³+ x² + x + 1. Find R(1) + 2R(2) + 3R(3).
Answer» 11. Let R(x) be the remainder upon dividing x⁴⁴+ x³³+ x²²+ x¹¹+ 1 by the polynomial x⁴+ x³+ x² + x + 1. Find R(1) + 2R(2) + 3R(3).

Discussion

15.	If the number of police officers (a) is 4 less than 3 times the number of traffic control stations (d), then how many police officers will be there for 50 control stations?146
Answer» If the number of police officers (a) is 4 less than 3 times the number of traffic control stations (d), then how many police officers will be there for 50 control stations? 146

Discussion

16.	Tick the correct answer in the following and justify your choice: If the perimeter and the area of a circle are numerically equal, then the radius of the circle is(A) 2 units (B) π units (C) 4 units (D)7 units
Answer» Tick the correct answer in the following and justify your choice: If the perimeter and the area of a circle are numerically equal, then the radius of the circle is (A) 2 units (B) π units (C) 4 units (D)7 units

16.

Tick the correct answer in the following and justify your choice: If the perimeter and the area of a circle are numerically equal, then the radius of the circle is(A) 2 units (B) π units (C) 4 units (D)7 units

Answer»

Tick the correct answer in the following and justify your choice: If the perimeter and the area of a circle are numerically equal, then the radius of the circle is

(A) 2 units (B) π units (C) 4 units (D)7 units

Discussion

17.	Given: sin(B+C)=√32 sin(A+C)=sin B and sin A=12 Find sin(A+B−C)
Answer» Given: $s i n (B + C) = \frac{\sqrt{3}}{2}$ $s i n (A + C) = s i n B$ and $s i n A = \frac{1}{2}$ Find $s i n (A + B - C)$

Discussion

18.	67. What is zero moment dipole
Answer» 67. What is zero moment dipole

Discussion

19.	If the line y = 3x + k touches the circle x2 + y2 = 16, then find the value of k. [NCERT EXEMPLAR]
Answer» If the line y = $\sqrt{3}$ x + k touches the circle x² + y² = 16, then find the value of k. [NCERT EXEMPLAR]

Discussion

20.	If 0 < arg (z) < π, then arg (z) – arg (–z) = ____________.
Answer» If 0 < arg (z) < π, then arg (z) – arg (–z) = ____________.

Discussion

21.	If a=√mnsec3θ and b=√mntan3θ, then the value of a43−b43√mn
Answer» If $a = \sqrt{m n {sec}^{3} θ} a n d b = \sqrt{m n {tan}^{3} θ},$ then the value of $\frac{a^{\frac{4}{3}} - b^{\frac{4}{3}}}{\sqrt{m n}}$

Discussion

22.	The adjacent figure shows two arcs P and Q. Arc P is part of the circle with centre O and radius OA. Arc Q is a part of the circle with centre M and radius AM, where M is the mid-point of AB. Area enclosed by the arc P is
Answer» The adjacent figure shows two arcs P and Q. Arc P is part of the circle with centre O and radius OA. Arc Q is a part of the circle with centre M and radius AM, where M is the mid-point of AB. Area enclosed by the arc P is

Discussion

23.	Find the volume of the figure given below.
Answer» Find the volume of the figure given below.

23.

Find the volume of the figure given below.

Answer»

Find the volume of the figure given below.

Discussion

24.	A. Find the sum of the following arithmetic series.(1) 2 + 5 + 8 + ……. upto 12 terms(2) 1 + 4 + 7 + ……..upto 22 terms(3) 3 + 7 + 11 + …….upto 35 terms(4) Find the sum of arithmetic series which contains 25 terms and whose middle term is 20.B. In an A.P. if(1) Tn = 4n + 3 find S15(2) Tn = 5 − 2n find S20C. (1) Find the sum of all the first ‘n’ odd Natural numbers.(2) Find the sum of all Natural numbers between 101 and 201 which are divisible by 4.
Answer» A. Find the sum of the following arithmetic series. (1) 2 + 5 + 8 + ……. upto 12 terms (2) 1 + 4 + 7 + ……..upto 22 terms (3) 3 + 7 + 11 + …….upto 35 terms (4) Find the sum of arithmetic series which contains 25 terms and whose middle term is 20. B. In an A.P. if (1) T_n = 4n + 3 find S₁₅ (2) T_n = 5 − 2n find S₂₀ C. (1) Find the sum of all the first ‘n’ odd Natural numbers. (2) Find the sum of all Natural numbers between 101 and 201 which are divisible by 4.

24.

A. Find the sum of the following arithmetic series.(1) 2 + 5 + 8 + ……. upto 12 terms(2) 1 + 4 + 7 + ……..upto 22 terms(3) 3 + 7 + 11 + …….upto 35 terms(4) Find the sum of arithmetic series which contains 25 terms and whose middle term is 20.B. In an A.P. if(1) Tn = 4n + 3 find S15(2) Tn = 5 − 2n find S20C. (1) Find the sum of all the first ‘n’ odd Natural numbers.(2) Find the sum of all Natural numbers between 101 and 201 which are divisible by 4.

Answer»

A. Find the sum of the following arithmetic series.

(1) 2 + 5 + 8 + ……. upto 12 terms

(2) 1 + 4 + 7 + ……..upto 22 terms

(3) 3 + 7 + 11 + …….upto 35 terms

(4) Find the sum of arithmetic series which contains 25 terms and whose middle term is 20.

B. In an A.P. if

(1) T_n = 4n + 3 find S₁₅

(2) T_n = 5 − 2n find S₂₀

C. (1) Find the sum of all the first ‘n’ odd Natural numbers.

(2) Find the sum of all Natural numbers between 101 and 201 which are divisible by 4.

Discussion

25.	Two circles touch each other externally. The sum of their areas is 130pcm2 and the distance between their centres is 14cm. Find the radius of each circle.
Answer» Two circles touch each other externally. The sum of their areas is 130pcm² and the distance between their centres is 14cm. Find the radius of each circle.

Discussion

26.	Mark the correct alternative in each of the following:The ratio of the length of a rod and its shadow is 1 : 3. The angle of elevation of the sum is(a) 30°(b) 45°(c) 60°(d) 90°
Answer» Mark the correct alternative in each of the following: The ratio of the length of a rod and its shadow is 1 : $\sqrt{3}$ . The angle of elevation of the sum is (a) 30° (b) 45° (c) 60° (d) 90°

Discussion

27.	Write the number of real roots of the equation x2 + 3 \|x\| + 2 = 0.
Answer» Write the number of real roots of the equation x² + 3 \|x\| + 2 = 0.

Discussion

28.	In the given figure, a square is inscribed in a circle with centre O. Find:(i) ∠ BOC(ii) ∠ OCB(iii) ∠ COD(iv) ∠ BODIs BD a diameter of the circle?
Answer» In the given figure, a square is inscribed in a circle with centre O. Find: (i) ∠ BOC (ii) ∠ OCB (iii) ∠ COD (iv) ∠ BOD Is BD a diameter of the circle?

Discussion

29.	If a coin is tossed 3 times, what is the probability of getting atleast one tail?
Answer» If a coin is tossed 3 times, what is the probability of getting atleast one tail?

Discussion

30.	If the equations 3x^2+4x+2=0 and px^2+qx+r=0 have a common root where p, q, r belong to set of real numbers and p is not equal to 0 then the value of (q+r) /p is :
Answer» If the equations 3x^2+4x+2=0 and px^2+qx+r=0 have a common root where p, q, r belong to set of real numbers and p is not equal to 0 then the value of (q+r) /p is :

Discussion

31.	If α and β are the zeros of the quadratic polynomial f(x)=x2+6x+2, then evaluate: α2β+β2α [3 MARKS]
Answer» If $α$ and $β$ are the zeros of the quadratic polynomial $f (x) = x^{2} + 6 x + 2$ , then evaluate: $\frac{α^{2}}{β} + \frac{β^{2}}{α}$ [3 MARKS]

Discussion

32.	The points (6, 6), (0, 6) and (6, 0) are the vertices of a right triangle as shown in the figure. Find the distance between its centroid and D (point of median of AB).
Answer» The points (6, 6), (0, 6) and (6, 0) are the vertices of a right triangle as shown in the figure. Find the distance between its centroid and D (point of median of AB).

Discussion

33.	13. If xyz+xy+yz+xz+x+y+z=384 where x,y,z are positive integer's then find value of x+y+z
Answer» 13. If xyz+xy+yz+xz+x+y+z=384 where x,y,z are positive integer's then find value of x+y+z

Discussion

34.	Ten years ago , P was half of Q's age. If the ratio of their present ages is 3:4. What will be the total of their present ages
Answer» Ten years ago , P was half of Q's age. If the ratio of their present ages is 3:4. What will be the total of their present ages

Discussion

35.	Evaluate the following limits:limx→-1x3-3x+1x-1
Answer» Evaluate the following limits: $\lim_{x \to - 1} \frac{x^{3} - 3 x + 1}{x - 1}$

Discussion

36.	Solve the following quadratic equations by factorization:x2 − x − a(a + 1) = 0
Answer» Solve the following quadratic equations by factorization: x² − x − a(a + 1) = 0

Discussion

37.	Find the probability that a leep year has 53 Sunday.
Answer» Find the probability that a leep year has 53 Sunday.

Discussion

38.	∑gx = 8y + 18, ∑g = 10. If the mean of the distribution is 5 , what is the value of y?
Answer» $\sum g_{x}$ = 8y + 18, $\sum g$ = 10. If the mean of the distribution is $5$ , what is the value of $y$ ?

Discussion

39.	The value of tan 0° is
Answer» The value of tan 0° is

Discussion

40.	The runs scored by three batsmen A, B and C in a cricket test match are given below. The values at the top are the runs scored in their 1st and 2nd innings respectively. The value at the bottom of the 'Y-shaped' structure is given by a relation considering the scores of both the innings. For batsmen A and B, the resultant term is already given, can you find the missing term for the batsman C using the same relation?
Answer» The runs scored by three batsmen A, B and C in a cricket test match are given below. The values at the top are the runs scored in their 1st and 2nd innings respectively. The value at the bottom of the 'Y-shaped' structure is given by a relation considering the scores of both the innings. For batsmen A and B, the resultant term is already given, can you find the missing term for the batsman C using the same relation?

Discussion

41.	The natural number is three times greater than its square root by 4. What is the number?
Answer» The natural number is three times greater than its square root by 4. What is the number?

Discussion

42.	A train covers a distance of 480 km at a uniform speed. If the speed had been 8 km/h less then it would have taken 3 hours more to cover the same distance. Find the usual speed of the train. [CBSE 2013C]
Answer» A train covers a distance of 480 km at a uniform speed. If the speed had been 8 km/h less then it would have taken 3 hours more to cover the same distance. Find the usual speed of the train. [CBSE 2013C]

Discussion

43.	Write the maximum and minimum values of sin θ.
Answer» Write the maximum and minimum values of sin θ.

Discussion

44.	If (a, -a) is the solution of the equation 2x + 3y + 5 = 0, find the value of a.5
Answer» If (a, -a) is the solution of the equation 2x + 3y + 5 = 0, find the value of a. 5

Discussion

45.	The number (1+√3)2 is a/an ____________.
Answer» The number ${(1 + \sqrt{3})}^{2}$ is a/an ____________.

Discussion

46.	The length of the shadow of a tower standing on level ground is found to be 2x metres longer when the sun's elevation is 30∘ than when it was 45∘. The height of the tower is (a) (2√3x) m (b) (3√2x) m (c) (√3−1)x m (d) (√3+1)x m
Answer» The length of the shadow of a tower standing on level ground is found to be 2x metres longer when the sun's elevation is $30^{\circ}$ than when it was $45^{\circ}$ . The height of the tower is (a) $(2 \sqrt{3} x) m$ (b) $(3 \sqrt{2} x) m$ (c) $(\sqrt{3} - 1) x m$ (d) $(\sqrt{3} + 1) x m$

46.

The length of the shadow of a tower standing on level ground is found to be 2x metres longer when the sun's elevation is 30∘ than when it was 45∘. The height of the tower is (a) (2√3x) m (b) (3√2x) m (c) (√3−1)x m (d) (√3+1)x m

Answer»

The length of the shadow of a tower standing on level ground is found to be 2x metres longer when the sun's elevation is $30^{\circ}$ than when it was $45^{\circ}$ . The height of the tower is

(a) $(2 \sqrt{3} x) m$

(b) $(3 \sqrt{2} x) m$

(c) $(\sqrt{3} - 1) x m$

(d) $(\sqrt{3} + 1) x m$

Discussion

47.	The first term of an AP is p and its common difference is q. find its 10th term.
Answer» The first term of an AP is p and its common difference is q. find its 10th term.

Discussion

48.	The sum of the reciprocals of Rehman's ages (in years) 3 years ago and 5 years from now is 13. Find his present age.
Answer» The sum of the reciprocals of Rehman's ages (in years) $3$ years ago and $5$ years from now is $\frac{1}{3}$ . Find his present age.

Discussion

49.

From the following Balance Sheet, prepare Comparative Balance Sheet of Sun Ltd.: Particulars Note No. 31st March, 2019 (₹) 31st March, 2018 (₹) I. EQUITY AND LIABILITIES 1. Shareholder's Funds (a) Share Capital 3,50,000 3,00,000 2. Non-Current Liabilities Long-term Borrowings 1,00,000 2,00,000 3. Current Liabilities : Trade Payables 1,50,000 1,00,000 Total 6,00,000 6,00,000 II. ASSETS 1. Non-Current Assets Fixed Assets (Tangible) 4,00,000 3,00,000 2. Current Assets Trade Receivables 2,00,000 3,00,000 Total 6,00,000 6,00,000

Answer» From the following Balance Sheet, prepare Comparative Balance Sheet of Sun Ltd.:


Particulars	Note No.	31st March, 2019 (₹)	31st March, 2018 (₹)
I. EQUITY AND LIABILITIES 1. Shareholder's Funds
(a) Share Capital		3,50,000	3,00,000
2. Non-Current Liabilities
Long-term Borrowings		1,00,000	2,00,000
3. Current Liabilities :
Trade Payables		1,50,000	1,00,000
Total		6,00,000	6,00,000
II. ASSETS
1. Non-Current Assets
Fixed Assets (Tangible)		4,00,000	3,00,000
2. Current Assets
Trade Receivables		2,00,000	3,00,000
Total		6,00,000	6,00,000

Discussion

50.	If the HCF of 60 and 168 is 12, find the LCM.840
Answer» If the HCF of 60 and 168 is 12, find the LCM. 840

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

ABC is an equilateral triangle of side 16 cm. Taking A,B and C as centres, three sectors are drawn from each vertex of radii 4 cm,6 cm and 8 cm as shown in the given figure. The area of the shaded region is

Question 195 Construct a parallelogram HOME with HO = 6 cm, HE = 4 cm and OE = 3 cm.

The circumference of two circles are in the ratio 2 : 3. Find the ratio of their areas.

An aeroplane when 900 m high, passes vertically above another aeroplane at an instant when their angles of elevation from the same observation point are 60∘ and 45∘ respectively. Approximately, by how many meters is the aeroplane higher than the other?

If two rectangles ABCD and PQRS whose sides are parallel to the coordinate axes are drawn as shown in below figure then the coordinates of 'Q' is ___

If the mean of the following frequency distribution is 24, find the value of p. [CBSE 2013] Class 0−10 10−20 20−30 30−40 40−50 Frequency 3 4 p 3 2

If (−4,0) and (1,−1) are two vertices of a triangle whose area is 4 sq.units, then locus of centroid of the triangle is

If n = 23 ✕ 34 ✕ 54 ✕ 7, then the number of consecutive zeros in n, where n is a natural number, is(a) 2(b) 3(c) 4(d) 7

Question 1(v)Find the roots of the following quadratic equations by factorization:(v)100x2−20x+1=0

The quadratic polynomial in x whose zeros are -a and 2a is

Find the angle subtended at the centre of a circle of radius 5 cm by an arc of length (5π/3) cm.

If the mean of the data is 60, find the value of p Class markfrequency25−351235−451645−55p55−651565−75875−851985−9513

11. Let R(x) be the remainder upon dividing x⁴⁴+ x³³+ x²²+ x¹¹+ 1 by the polynomial x⁴+ x³+ x² + x + 1. Find R(1) + 2R(2) + 3R(3).

If the number of police officers (a) is 4 less than 3 times the number of traffic control stations (d), then how many police officers will be there for 50 control stations?146

Tick the correct answer in the following and justify your choice: If the perimeter and the area of a circle are numerically equal, then the radius of the circle is(A) 2 units (B) π units (C) 4 units (D)7 units

Given: sin(B+C)=√32 sin(A+C)=sin B and sin A=12 Find sin(A+B−C)

67. What is zero moment dipole

If the line y = 3x + k touches the circle x2 + y2 = 16, then find the value of k. [NCERT EXEMPLAR]

If 0 < arg (z) < π, then arg (z) – arg (–z) = ____________.

If a=√mnsec3θ and b=√mntan3θ, then the value of a43−b43√mn

The adjacent figure shows two arcs P and Q. Arc P is part of the circle with centre O and radius OA. Arc Q is a part of the circle with centre M and radius AM, where M is the mid-point of AB. Area enclosed by the arc P is

Find the volume of the figure given below.

Two circles touch each other externally. The sum of their areas is 130pcm2 and the distance between their centres is 14cm. Find the radius of each circle.

Mark the correct alternative in each of the following:The ratio of the length of a rod and its shadow is 1 : 3. The angle of elevation of the sum is(a) 30°(b) 45°(c) 60°(d) 90°

Write the number of real roots of the equation x2 + 3 |x| + 2 = 0.

In the given figure, a square is inscribed in a circle with centre O. Find:(i) ∠ BOC(ii) ∠ OCB(iii) ∠ COD(iv) ∠ BODIs BD a diameter of the circle?

If a coin is tossed 3 times, what is the probability of getting atleast one tail?

If the equations 3x^2+4x+2=0 and px^2+qx+r=0 have a common root where p, q, r belong to set of real numbers and p is not equal to 0 then the value of (q+r) /p is :

If α and β are the zeros of the quadratic polynomial f(x)=x2+6x+2, then evaluate: α2β+β2α [3 MARKS]

The points (6, 6), (0, 6) and (6, 0) are the vertices of a right triangle as shown in the figure. Find the distance between its centroid and D (point of median of AB).

13. If xyz+xy+yz+xz+x+y+z=384 where x,y,z are positive integer's then find value of x+y+z

Ten years ago , P was half of Q's age. If the ratio of their present ages is 3:4. What will be the total of their present ages

Evaluate the following limits:limx→-1x3-3x+1x-1

Solve the following quadratic equations by factorization:x2 − x − a(a + 1) = 0

Find the probability that a leep year has 53 Sunday.

∑gx = 8y + 18, ∑g = 10. If the mean of the distribution is 5 , what is the value of y?

The value of tan 0° is

The natural number is three times greater than its square root by 4. What is the number?

A train covers a distance of 480 km at a uniform speed. If the speed had been 8 km/h less then it would have taken 3 hours more to cover the same distance. Find the usual speed of the train. [CBSE 2013C]

Write the maximum and minimum values of sin θ.

If (a, -a) is the solution of the equation 2x + 3y + 5 = 0, find the value of a.5

The number (1+√3)2 is a/an ____________.

The length of the shadow of a tower standing on level ground is found to be 2x metres longer when the sun's elevation is 30∘ than when it was 45∘. The height of the tower is (a) (2√3x) m (b) (3√2x) m (c) (√3−1)x m (d) (√3+1)x m

The first term of an AP is p and its common difference is q. find its 10th term.

The sum of the reciprocals of Rehman's ages (in years) 3 years ago and 5 years from now is 13. Find his present age.

If the HCF of 60 and 168 is 12, find the LCM.840