32581 + Interview Questions in Mathematics

1.	Write the condition of collinearity of points (x1, y1), (x2, y2) and (x3, y3).
Answer» Write the condition of collinearity of points (x1, y1), (x2, y2) and (x3, y3).

Discussion

2.	Show that the system 2x+3y−1=0,4x+6y−4=0 has no solution.
Answer» Show that the system $2 x + 3 y - 1 = 0, 4 x + 6 y - 4 = 0$ has no solution.

Discussion

3.	How many terms of the series 1, 4, 16,..... must be taken to have their sum equal to 341 ?
Answer» How many terms of the series 1, 4, 16,..... must be taken to have their sum equal to 341 ?

Discussion

4.	In the adjoining figure, if BC=a,AC=b,AB=c and ∠CAB=120∘, then which of the following is the correct relation?
Answer» In the adjoining figure, if $B C = a, A C = b, A B = c$ and $∠ C A B = 120^{\circ}$ , then which of the following is the correct relation?

4.

In the adjoining figure, if BC=a,AC=b,AB=c and ∠CAB=120∘, then which of the following is the correct relation?

Answer»

In the adjoining figure, if $B C = a, A C = b, A B = c$ and $∠ C A B = 120^{\circ}$ ,
then which of the following is the correct relation?

Discussion

5.	Prove the following trigonometric identities.cos2 θsin θ-cosec θ+sin θ=0
Answer» Prove the following trigonometric identities. $\frac{\cos^{2} θ}{\sin θ} - cosec θ + \sin θ = 0$

Discussion

6.	Write the sum of the exponents of prime factors in the prime factorization of 98.
Answer» Write the sum of the exponents of prime factors in the prime factorization of 98.

Discussion

7.	The vertices of a triangle are the points (1, 2), (2, 3), (3, 1). Find the centre and radius of its circumcircle.
Answer» The vertices of a triangle are the points (1, 2), (2, 3), (3, 1). Find the centre and radius of its circumcircle.

Discussion

8.	Question 1 (i)Fill in the blanks in the following table, given that a is the first term, d the common difference and an the nth term of the A.P.adnan738……
Answer» Question 1 (i) Fill in the blanks in the following table, given that a is the first term, d the common difference and $a_{n}$ the $n^{t h}$ term of the A.P. $\begin{matrix} a & d & n & a_{n} 7 & 3 & 8 & \dots \dots \end{matrix}$

Discussion

9.	If cosθ=35, show that sinθ-cotθ2tanθ=3160.
Answer» If $\cos θ = \frac{3}{5}$ , show that $\frac{(\sin θ - \cot θ)}{2 \tan θ} = \frac{3}{160}$ .

Discussion

10.	Four equal circles, each of radius 5 cm, touch each other, as shown in the figure. Find the area included between them. [ Take π=3.14.]
Answer» Four equal circles, each of radius 5 cm, touch each other, as shown in the figure. Find the area included between them. [ Take $π = 3.14.$ ]

10.

Four equal circles, each of radius 5 cm, touch each other, as shown in the figure. Find the area included between them. [ Take π=3.14.]

Answer»

Four equal circles, each of radius 5 cm, touch each other, as shown in the figure. Find the area included between them.

[ Take $π = 3.14.$ ]

Discussion

11.	60 can be prime factorised as 60=
Answer» $60$ can be prime factorised as $60$ =

Discussion

12.	Four equal circles, each of radius a, touch each other. Show that the area between them is 67a2 (Take π = 22/7).
Answer» Four equal circles, each of radius a, touch each other. Show that the area between them is $\frac{6}{7} a^{2}$ (Take π = 22/7).

Discussion

13.	If the roots of the equation a2+b2x2-2ac+bdx+c2+d2=0 are equal, prove that ab=cd.
Answer» If the roots of the equation $(a^{2} + b^{2}) x^{2} - 2 (a c + b d) x + (c^{2} + d^{2}) = 0$ are equal, prove that $\frac{a}{b} = \frac{c}{d}$ .

Discussion

14.	Which of the lines represented by the following equations would pass through only the x-axis?
Answer» Which of the lines represented by the following equations would pass through only the x-axis?

Discussion

15.	The height of a conical vessel is 3.5 cm. If its capacity is 3.3 litres of milk, find the diameter of its base.
Answer» The height of a conical vessel is 3.5 cm. If its capacity is 3.3 litres of milk, find the diameter of its base.

Discussion

16.	Find the value of k for which each of the following system of equations have infinitely many solutions :8x+5y=9kx+10y=18
Answer» Find the value of k for which each of the following system of equations have infinitely many solutions : $8 x + 5 y = 9 k x + 10 y = 18$

Discussion

17.	Which term of the A.P. 21, 42, 63, 84, ... is 210?(a) 9th(b) 10th(c) 11th(d) 12th
Answer» Which term of the A.P. 21, 42, 63, 84, ... is 210? (a) 9^th (b) 10^th (c) 11^th (d) 12^th

Discussion

18.	36. Given the system of equations [3x]+{y}+x-y=1 and [-y]-{x}-x+y=1 then
Answer» 36. Given the system of equations [3x]+{y}+x-y=1 and [-y]-{x}-x+y=1 then

Discussion

19.	17. Let 1/(a1-2i) , 1/(a2-2i) ,1/(a3-2i) ,1/(a4-2i), 1/(a5-2i), 1/(a6-2i), 1/(a7-2i), 1/(a8-2i) are vertices of regular octagon. If the area of octagan is A. Then the value of 82A is ( where aj belongs to R for j=1,2,3,4,5,6,7,8 and i=-1 )
Answer» 17. Let 1/(a1-2i) , 1/(a2-2i) ,1/(a3-2i) ,1/(a4-2i), 1/(a5-2i), 1/(a6-2i), 1/(a7-2i), 1/(a8-2i) are vertices of regular octagon. If the area of octagan is A. Then the value of 82A is ( where aj belongs to R for j=1,2,3,4,5,6,7,8 and i=-1 )

Discussion

20.	Solve: _/3x = 2_/3 +x Please note that _/ = under root
Answer» Solve: _/3x = 2_/3 +x Please note that _/ = under root

20.

Solve: _/3x = 2_/3 +x Please note that _/ = under root

Answer»

Solve:

_/3x = 2_/3 +x

Please note that _/ = under root

Discussion

21.	sin 750 = [MNR 1979]
Answer» sin $75^{0}$ = [MNR 1979]

21.

sin 750 = [MNR 1979]

Answer»

sin $75^{0}$ =

[MNR 1979]

Discussion

22.	Sin2A = 2SinA is true when A =(A) 0°(B) 30°(C) 45°(D) 60°
Answer» Sin2A = 2SinA is true when A = (A) 0° (B) 30° (C) 45° (D) 60°

Discussion

23.	If a coin is tossed twice, Is the probability of getting two heads equal to the probability of getting no heads at all? Also find the probability of i) Getting two heads ii) Getting no heads
Answer» If a coin is tossed twice, Is the probability of getting two heads equal to the probability of getting no heads at all? Also find the probability of i) Getting two heads ii) Getting no heads

23.

If a coin is tossed twice, Is the probability of getting two heads equal to the probability of getting no heads at all? Also find the probability of i) Getting two heads ii) Getting no heads

Answer»

If a coin is tossed twice,

Is the probability of getting two heads equal to the probability of getting no heads at all? Also find the probability of

i) Getting two heads

ii) Getting no heads

Discussion

24.

How are the following dealt with in the accounts of a Not-for-Profit Organisation ? Case I Dr. (₹) Cr. (₹) Case II Dr. (₹) Cr. (₹) Prize Fund Prizes Paid Match Expenses 12,000 15,000 50,000 Match Fund Match Expenses Investments of Match Fund Interest on Match Fund Investments Prizes Paid 35,000 60,000 19,000 1,00,000 3,000

Answer» How are the following dealt with in the accounts of a Not-for-Profit Organisation ?

Case I	Dr. (₹)	Cr. (₹)	Case II	Dr. (₹)	Cr. (₹)
Prize Fund Prizes Paid Match Expenses	12,000 15,000	50,000	Match Fund Match Expenses Investments of Match Fund Interest on Match Fund Investments Prizes Paid	35,000 60,000 19,000	1,00,000 3,000

Discussion

25.	In a triangle ABC, the perpendicular AD from point A, on the side BC meets the side BC at point D. If BD = 8 cm, DC = 2 cm and AD = 4 cm. Then, angle BAC is ________
Answer» In a triangle ABC, the perpendicular AD from point A, on the side BC meets the side BC at point D. If BD = 8 cm, DC = 2 cm and AD = 4 cm. Then, angle BAC is ________

Discussion

26.	You are given a dart board of radius R cm. What is the probability that you hit the bull's eye of radius r cm?
Answer» You are given a dart board of radius R cm. What is the probability that you hit the bull's eye of radius r cm?

Discussion

27.	Find the sum of the series452−432+442−422+432−412+422−402+⋯upto 15 terms.
Answer» Find the sum of the series $45^{2} - 43^{2} + 44^{2} - 42^{2} + 43^{2} - 41^{2} + 42^{2} - 40^{2} + \dots u p t o 15 t e r m s$ .

Discussion

28.	If the vertices of a triangle have integral coordinates, then the triangle cannot be ___________.
Answer» If the vertices of a triangle have integral coordinates, then the triangle cannot be ___________.

Discussion

29.	To divide AB in the ratio 5:1, after some stages, we draw an arc with centre at A6, repeat the same with equal radius at A5. Then mark the first arc (A6 and A5) at C1 and mark the same for second arc (A5 and A4) at C2. This is done in order to:
Answer» To divide AB in the ratio 5:1, after some stages, we draw an arc with centre at $A_{6}$ , repeat the same with equal radius at $A_{5}$ . Then mark the first arc ( $A_{6}$ and $A_{5}$ ) at $C_{1}$ and mark the same for second arc ( $A_{5}$ and $A_{4}$ ) at $C_{2}$ . This is done in order to:

29.

To divide AB in the ratio 5:1, after some stages, we draw an arc with centre at A6, repeat the same with equal radius at A5. Then mark the first arc (A6 and A5) at C1 and mark the same for second arc (A5 and A4) at C2. This is done in order to:

Answer»

To divide AB in the ratio 5:1, after some stages, we draw an arc with centre at $A_{6}$ , repeat the same with equal radius at $A_{5}$ . Then mark the first arc ( $A_{6}$ and $A_{5}$ ) at $C_{1}$ and mark the same for second arc ( $A_{5}$ and $A_{4}$ ) at $C_{2}$ . This is done in order to:

Discussion

30.	A man of height 60 cm is walking away from the base of a building at a speed of 2.2 m/s. If the building is 7.2 m of height, then the length of the shadow of man after 5s will be
Answer» A man of height 60 cm is walking away from the base of a building at a speed of 2.2 m/s. If the building is 7.2 m of height, then the length of the shadow of man after 5s will be

Discussion

31.	If a matrix has 8 elements, how many possible orders can it have?
Answer» If a matrix has 8 elements, how many possible orders can it have?

Discussion

32.	In a school, there are two bells, one in the primary school and the other in the secondary school. Both the bells ring after every class. The primary school has classes 45 minutes each whereas the secondary school has classes every 1 hour. Find when both the bells ring at the same time again if both classes start at the same time?
Answer» In a school, there are two bells, one in the primary school and the other in the secondary school. Both the bells ring after every class. The primary school has classes 45 minutes each whereas the secondary school has classes every 1 hour. Find when both the bells ring at the same time again if both classes start at the same time?

Discussion

33.	The radii of the ends of a frustum of a cone of slant height l are r1 and r2. The curved surface area of the frustum of the cone is
Answer» The radii of the ends of a frustum of a cone of slant height $l$ are $r_{1}$ and $r_{2}$ . The curved surface area of the frustum of the cone is

Discussion

34.	If ⎡⎢⎣x+3z+42y−7−6a−10b−3−210⎤⎥⎦=⎡⎢⎣063y−2−6−32c+22b+4−210⎤⎥⎦, then the value of a is:
Answer» If $⎡ ⎢ ⎣ \begin{matrix} x + 3 & z + 4 & 2 y - 7 - 6 & a - 1 & 0 b - 3 & - 21 & 0 \end{matrix} ⎤ ⎥ ⎦ = ⎡ ⎢ ⎣ \begin{matrix} 0 & 6 & 3 y - 2 - 6 & - 3 & 2 c + 2 2 b + 4 & - 21 & 0 \end{matrix} ⎤ ⎥ ⎦$ , then the value of $a$ is:

Discussion

35.	Very-Short and Short-Answer QuestionsFind an AP whose 4th term is 9 and the sum of its 6th and 13th terms is 40. [CBSE 2011]
Answer» Very-Short and Short-Answer Questions Find an AP whose 4th term is 9 and the sum of its 6th and 13th terms is 40. [CBSE 2011]

Discussion

36.	Question 1 (ii)Find the sum of the following APs(ii) − 37, − 33, − 29 ,…, to 12 terms
Answer» Question 1 (ii) Find the sum of the following APs (ii) − 37, − 33, − 29 ,…, to 12 terms

Discussion

37.	A number is selected from first 50 natural numbers. What is the probability that it is a multiple of 3 or 5?(a) 1325(b) 2150(c) 1225(d) 2350
Answer» A number is selected from first 50 natural numbers. What is the probability that it is a multiple of 3 or 5? (a) $\frac{13}{25}$ (b) $\frac{21}{50}$ (c) $\frac{12}{25}$ (d) $\frac{23}{50}$

Discussion

38.	A function is described as:For the function, its range will be
Answer» A function is described as: For the function, its range will be

Discussion

39.	What is Abhay's score in C++?
Answer» What is Abhay's score in C++?

Discussion

40.	If the swimmer takes 15 second in downstream and 30 second in upstream to cover same distance .Then what will be the time taken by the swimmer to covers same distance.
Answer» If the swimmer takes 15 second in downstream and 30 second in upstream to cover same distance .Then what will be the time taken by the swimmer to covers same distance.

Discussion

41.	The sum of two irrational number is an irrational number (True/False).
Answer» The sum of two irrational number is an irrational number (True/False).

Discussion

42.	Sahil standing at bottom of the building observes angle of Elevation of top of tower to be 60°. From top of the building angle of Elevation of top of the tower is 45°. Find height of the tower if height of the building is 10m.
Answer» Sahil standing at bottom of the building observes angle of Elevation of top of tower to be 60°. From top of the building angle of Elevation of top of the tower is 45°. Find height of the tower if height of the building is 10m.

Discussion

43.	During a practice match, a softball pitcher throws a ball whose height can be modeled by the equation h = −16t2 + 24t + 1, where h = height in feet and t = time in seconds. How long does it take for the ball to reach a height of 6 feet?
Answer» During a practice match, a softball pitcher throws a ball whose height can be modeled by the equation h = $- 16 t^{2}$ + 24t + 1, where h = height in feet and t = time in seconds. How long does it take for the ball to reach a height of 6 feet?

Discussion

44.	A frequency polygon is constructed by plotting the coordinates of ___ and their respective frequency.
Answer» A frequency polygon is constructed by plotting the coordinates of ___ and their respective frequency.

Discussion

45.	In a circular dartboard of radius 20 cm, there are 5 concentric circles. The radius of each successive inner concentric circle is 4 cm less than the preceding the outer concentric circle. What is the probability that the dart hits the smallest circle?
Answer» In a circular dartboard of radius 20 cm, there are 5 concentric circles. The radius of each successive inner concentric circle is 4 cm less than the preceding the outer concentric circle. What is the probability that the dart hits the smallest circle?

Discussion

46.	In the figure AB is the diameter and CD is parallel to the diameter. AB = 8cm, BD = 2cm, find CD.
Answer» In the figure AB is the diameter and CD is parallel to the diameter. AB = 8cm, BD = 2cm, find CD.

46.

In the figure AB is the diameter and CD is parallel to the diameter. AB = 8cm, BD = 2cm, find CD.

Answer»

In the figure AB is the diameter and CD is parallel to the diameter. AB = 8cm, BD = 2cm, find CD.

Discussion

47.	Question 5 (ii)It costs Rs. 2200 to paint the inner curved surface of a cylindrical vessel 10 m deep. If the cost of painting is at the rate of Rs 20per m2, find:(ii) The radius of the base.
Answer» Question 5 (ii) It costs Rs. 2200 to paint the inner curved surface of a cylindrical vessel 10 m deep. If the cost of painting is at the rate of $R s 20 p e r m^{2}$ , find: (ii) The radius of the base.

47.

Question 5 (ii)It costs Rs. 2200 to paint the inner curved surface of a cylindrical vessel 10 m deep. If the cost of painting is at the rate of Rs 20per m2, find:(ii) The radius of the base.

Answer»

Question 5 (ii)

It costs Rs. 2200 to paint the inner curved surface of a cylindrical vessel 10 m deep. If the cost of painting is at the rate of $R s 20 p e r m^{2}$ , find:

(ii) The radius of the base.

Discussion

48.	Question 1 (iv) Express each number as the product of its prime factors: iv) 5005
Answer» Question 1 (iv) Express each number as the product of its prime factors: iv) 5005

Discussion

49.	A spherical ball of iron has been melted and made into smaller balls. If the radius of each smaller ball is one-fourth of the radius of the original one, how many such balls can be made?
Answer» A spherical ball of iron has been melted and made into smaller balls. If the radius of each smaller ball is one-fourth of the radius of the original one, how many such balls can be made?

Discussion

50.	The radii of the escribed circles of triangle ABC are r_a, r_{b } and r_c respectively. If r_a+r_c = 3R and r_b +r_c =2Rthen the smallest angle of the triangle is (where R is the circuradius of triangle ABC)
Answer» The radii of the escribed circles of triangle ABC are r_a, r_{b } and r_c respectively. If r_a+r_c = 3R and r_b +r_c =2Rthen the smallest angle of the triangle is (where R is the circuradius of triangle ABC)

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Write the condition of collinearity of points (x1, y1), (x2, y2) and (x3, y3).

Show that the system 2x+3y−1=0,4x+6y−4=0 has no solution.

How many terms of the series 1, 4, 16,..... must be taken to have their sum equal to 341 ?

In the adjoining figure, if BC=a,AC=b,AB=c and ∠CAB=120∘, then which of the following is the correct relation?

Prove the following trigonometric identities.cos2 θsin θ-cosec θ+sin θ=0

Write the sum of the exponents of prime factors in the prime factorization of 98.

The vertices of a triangle are the points (1, 2), (2, 3), (3, 1). Find the centre and radius of its circumcircle.

Question 1 (i)Fill in the blanks in the following table, given that a is the first term, d the common difference and an the nth term of the A.P.adnan738……

If cosθ=35, show that sinθ-cotθ2tanθ=3160.

Four equal circles, each of radius 5 cm, touch each other, as shown in the figure. Find the area included between them. [ Take π=3.14.]

60 can be prime factorised as 60=

Four equal circles, each of radius a, touch each other. Show that the area between them is 67a2 (Take π = 22/7).

If the roots of the equation a2+b2x2-2ac+bdx+c2+d2=0 are equal, prove that ab=cd.

Which of the lines represented by the following equations would pass through only the x-axis?

The height of a conical vessel is 3.5 cm. If its capacity is 3.3 litres of milk, find the diameter of its base.

Find the value of k for which each of the following system of equations have infinitely many solutions :8x+5y=9kx+10y=18

Which term of the A.P. 21, 42, 63, 84, ... is 210?(a) 9th(b) 10th(c) 11th(d) 12th

36. Given the system of equations [3x]+{y}+x-y=1 and [-y]-{x}-x+y=1 then

17. Let 1/(a1-2i) , 1/(a2-2i) ,1/(a3-2i) ,1/(a4-2i), 1/(a5-2i), 1/(a6-2i), 1/(a7-2i), 1/(a8-2i) are vertices of regular octagon. If the area of octagan is A. Then the value of 82A is ( where aj belongs to R for j=1,2,3,4,5,6,7,8 and i=-1 )

Solve: _/3x = 2_/3 +x Please note that _/ = under root

sin 750 = [MNR 1979]

Sin2A = 2SinA is true when A =(A) 0°(B) 30°(C) 45°(D) 60°

If a coin is tossed twice, Is the probability of getting two heads equal to the probability of getting no heads at all? Also find the probability of i) Getting two heads ii) Getting no heads

In a triangle ABC, the perpendicular AD from point A, on the side BC meets the side BC at point D. If BD = 8 cm, DC = 2 cm and AD = 4 cm. Then, angle BAC is ________

You are given a dart board of radius R cm. What is the probability that you hit the bull's eye of radius r cm?

Find the sum of the series452−432+442−422+432−412+422−402+⋯upto 15 terms.

If the vertices of a triangle have integral coordinates, then the triangle cannot be ___________.

To divide AB in the ratio 5:1, after some stages, we draw an arc with centre at A6, repeat the same with equal radius at A5. Then mark the first arc (A6 and A5) at C1 and mark the same for second arc (A5 and A4) at C2. This is done in order to:

A man of height 60 cm is walking away from the base of a building at a speed of 2.2 m/s. If the building is 7.2 m of height, then the length of the shadow of man after 5s will be

If a matrix has 8 elements, how many possible orders can it have?

The radii of the ends of a frustum of a cone of slant height l are r1 and r2. The curved surface area of the frustum of the cone is

If ⎡⎢⎣x+3z+42y−7−6a−10b−3−210⎤⎥⎦=⎡⎢⎣063y−2−6−32c+22b+4−210⎤⎥⎦, then the value of a is:

Very-Short and Short-Answer QuestionsFind an AP whose 4th term is 9 and the sum of its 6th and 13th terms is 40. [CBSE 2011]

Question 1 (ii)Find the sum of the following APs(ii) − 37, − 33, − 29 ,…, to 12 terms

A number is selected from first 50 natural numbers. What is the probability that it is a multiple of 3 or 5?(a) 1325(b) 2150(c) 1225(d) 2350

A function is described as:For the function, its range will be

What is Abhay's score in C++?

If the swimmer takes 15 second in downstream and 30 second in upstream to cover same distance .Then what will be the time taken by the swimmer to covers same distance.

The sum of two irrational number is an irrational number (True/False).

Sahil standing at bottom of the building observes angle of Elevation of top of tower to be 60°. From top of the building angle of Elevation of top of the tower is 45°. Find height of the tower if height of the building is 10m.

During a practice match, a softball pitcher throws a ball whose height can be modeled by the equation h = −16t2 + 24t + 1, where h = height in feet and t = time in seconds. How long does it take for the ball to reach a height of 6 feet?

A frequency polygon is constructed by plotting the coordinates of ___ and their respective frequency.

In a circular dartboard of radius 20 cm, there are 5 concentric circles. The radius of each successive inner concentric circle is 4 cm less than the preceding the outer concentric circle. What is the probability that the dart hits the smallest circle?

In the figure AB is the diameter and CD is parallel to the diameter. AB = 8cm, BD = 2cm, find CD.

Question 5 (ii)It costs Rs. 2200 to paint the inner curved surface of a cylindrical vessel 10 m deep. If the cost of painting is at the rate of Rs 20per m2, find:(ii) The radius of the base.

Question 1 (iv) Express each number as the product of its prime factors: iv) 5005

A spherical ball of iron has been melted and made into smaller balls. If the radius of each smaller ball is one-fourth of the radius of the original one, how many such balls can be made?

The radii of the escribed circles of triangle ABC are r_a, r_{b } and r_c respectively. If r_a+r_c = 3R and r_b +r_c =2Rthen the smallest angle of the triangle is (where R is the circuradius of triangle ABC)