32581 + Interview Questions in Mathematics Page 241 InterviewSolution

12001.	Consider an arithmetic series and a geometric series having four initial terms from the set {11,8,21,16,26,32,4}. If the last terms of these seris are the maximum possible four digit numbers, then the number of common terms in these two series is equal to
Answer» Consider an arithmetic series and a geometric series having four initial terms from the set ${11, 8, 21, 16, 26, 32, 4}$ . If the last terms of these seris are the maximum possible four digit numbers, then the number of common terms in these two series is equal to

Discussion

12002.	Use Euclid's division lemma to show that the square of any positive integer is either of the form 3m or 3m+1 for some integer m.
Answer» Use Euclid's division lemma to show that the square of any positive integer is either of the form 3m or 3m+1 for some integer m.

Discussion

12003.	The line y=x-2 cuts the parabola y2=8x in the points A and B. The normals at A and B intersect at G. A line passing through G intersects the parabola at right angles at the point C, and the tangents at A and B intersect at the point T. n nt(a) The sum of the abcissa and the ordinate of point C is n nt(B) Minimum radius of circle passing through A and B is
Answer» The line y=x-2 cuts the parabola y2=8x in the points A and B. The normals at A and B intersect at G. A line passing through G intersects the parabola at right angles at the point C, and the tangents at A and B intersect at the point T. n nt(a) The sum of the abcissa and the ordinate of point C is n nt(B) Minimum radius of circle passing through A and B is

Discussion

12004.	The area of the base of a cone is 2464 cm^2 and the curved surface is 3080 cm^2 . Its volume is
Answer» The area of the base of a cone is 2464 cm^2 and the curved surface is 3080 cm^2 . Its volume is

Discussion

12005.	The zero of the polynomial p(x) = ax+b is
Answer» The zero of the polynomial p(x) = ax+b is

Discussion

12006.	The length (in units ) of a line segment intercepted between the coordinate axes by the line joining the points (1,2) and (3,4) is
Answer» The length (in units ) of a line segment intercepted between the coordinate axes by the line joining the points (1,2) and (3,4) is

Discussion

12007.	Question 2 (ii)Find the sum of those integers from 1 to 500 which are multiples of 2 as well as of 5.
Answer» Question 2 (ii) Find the sum of those integers from 1 to 500 which are multiples of 2 as well as of 5.

Discussion

12008.	A physical quantity p is being calculated by the equation p=qr.q is measured with an error of +20% whereas r is measured with an error of-20%. the error in p is
Answer» A physical quantity p is being calculated by the equation p=qr.q is measured with an error of +20% whereas r is measured with an error of-20%. the error in p is

Discussion

12009.	Find the volume of the square pyramid, if one the triangular faces is given below.
Answer» Find the volume of the square pyramid, if one the triangular faces is given below.

Discussion

12010.	81.A cone is 8.4cm high and radius of its base is 2.1cm . It melted and recast into a sphere . Find the radius of sphere
Answer» 81.A cone is 8.4cm high and radius of its base is 2.1cm . It melted and recast into a sphere . Find the radius of sphere

Discussion

12011.	Draw a line segment of length 8.6 cm and divide it in the ratio 3:5 .Measure the two parts .
Answer» Draw a line segment of length 8.6 cm and divide it in the ratio 3:5 .Measure the two parts .

Discussion

12012.	Find the value of tan 48∘.tan 23∘.tan 42∘.tan 67∘ .
Answer» Find the value of $t a n 48^{\circ} . t a n 23^{\circ} . t a n 42^{\circ} . t a n 67^{\circ}$ .

Discussion

12013.	A pipe of internal diameter 20cm from a canal is connected to a cylindrical tank of radius 5m and height 2m. If water flows through the pipe at 6km/hr, how much time will it take for the tank to be filled?
Answer» A pipe of internal diameter 20cm from a canal is connected to a cylindrical tank of radius 5m and height 2m. If water flows through the pipe at 6km/hr, how much time will it take for the tank to be filled?

Discussion

12014.	A capsule of medicine is in the shape of a sphere of diameter 3.5 mm.How much medicine in mm3 is needed to fill this capsule?[Assume π=227]
Answer» A capsule of medicine is in the shape of a sphere of diameter 3.5 mm. How much medicine $i n m m^{3}$ is needed to fill this capsule? $[A s s u m e π = \frac{22}{7}]$

Discussion

12015.	In the figure, AB is the common tangent to the 2 circles intersecting at C & D. Write down the numerical value of ∠ACB + ∠ADB. Give reasons for your answer.
Answer» In the figure, AB is the common tangent to the 2 circles intersecting at C & D. Write down the numerical value of ∠ACB + ∠ADB. Give reasons for your answer.

12015.

In the figure, AB is the common tangent to the 2 circles intersecting at C & D. Write down the numerical value of ∠ACB + ∠ADB. Give reasons for your answer.

Answer»

In the figure, AB is the common tangent to the 2 circles intersecting at C & D. Write down the numerical value of ∠ACB + ∠ADB. Give reasons for your answer.

Discussion

12016.	Zeroes of the quadratic polynomial ax2 + bx + c and roots of the quadratic equation ax2 + bx + c = 0 are__________
Answer» Zeroes of the quadratic polynomial ax² + bx + c and roots of the quadratic equation ax² + bx + c = 0 are__________

Discussion

12017.	5x2-2/4x2-x+3 is less than 1
Answer» 5x2-2/4x2-x+3 is less than 1

Discussion

12018.	Shubendhu owns 560 shares of a company. The face value of each share is Rs. 25. The company declares a dividend of 9%. Calculate: (i) The dividend that Shubendhu will get. (ii) The rate of interest on his investment if Shubendhu had paid Rs. 30 for each share.
Answer» Shubendhu owns 560 shares of a company. The face value of each share is Rs. 25. The company declares a dividend of $9 %$ . Calculate: (i) The dividend that Shubendhu will get. (ii) The rate of interest on his investment if Shubendhu had paid Rs. 30 for each share.

12018.

Shubendhu owns 560 shares of a company. The face value of each share is Rs. 25. The company declares a dividend of 9%. Calculate: (i) The dividend that Shubendhu will get. (ii) The rate of interest on his investment if Shubendhu had paid Rs. 30 for each share.

Answer»

Shubendhu owns 560 shares of a company. The face value of each share is Rs. 25. The company declares a dividend of $9 %$ . Calculate:

(i) The dividend that Shubendhu will get.

(ii) The rate of interest on his investment if Shubendhu had paid Rs. 30 for each share.

Discussion

12019.	If B × A = {(x, a), (x, b), (x, c), (y, a), (y, b), (y, c), (z, a), (z, b), (z, c)}. Find set A and set B.
Answer» If B $\times$ A = {(x, a), (x, b), (x, c), (y, a), (y, b), (y, c), (z, a), (z, b), (z, c)}. Find set A and set B.

Discussion

12020.	If one cm on the ground shows 228 I'm on the ground, then find out 1 cm = 228 km A)12 cm = B)312cm= C)2cm= D)14 cm =
Answer» If one cm on the ground shows 228 I'm on the ground, then find out 1 cm = 228 km A) $\frac{1}{2}$ cm = B) $3 \frac{1}{2}$ cm= C)2cm= D) $\frac{1}{4}$ cm =

Discussion

12021.	If x+3y=6 and 2x−3y=12 intersect, what is the value of x? 6
Answer» If $x + 3 y = 6$ and $2 x - 3 y = 12$ intersect, what is the value of x? 6

Discussion

12022.	In the given figure P is the object and P' is the image. The line AB is which is the perpendicular bisector of PP' is called as ______.
Answer» In the given figure P is the object and P' is the image. The line AB is which is the perpendicular bisector of PP' is called as ______.

Discussion

12023.	Question 6The length of a tangent from a point A at distance 5 cm from the centre of the circle is 4 cm. Find the radius of the circle.
Answer» Question 6 The length of a tangent from a point A at distance 5 cm from the centre of the circle is 4 cm. Find the radius of the circle.

Discussion

12024.	Find the value of: sec 29∘cosec 61∘ + 2cot8∘cot17∘cot45∘cot73∘cot82∘. ___
Answer» Find the value of: $\frac{s e c 29^{\circ}}{c o s e c 61^{\circ}}$ + $2 c o t 8^{\circ} c o t 17^{\circ} c o t 45^{\circ} c o t 73^{\circ} c o t 82^{\circ}$ . ___

Discussion

12025.	The distance between the points (-1, 5) and (2, 1) is ___ units.
Answer» The distance between the points (-1, 5) and (2, 1) is ___ units.

Discussion

12026.	A tower 8 m high throws a shadow 8 m long on the ground. Find the angle of elevation of the sun.
Answer» A tower 8 m high throws a shadow 8 m long on the ground. Find the angle of elevation of the sun.

Discussion

12027.	The value of the limit limx→π24√2(sin3x+sinx)(2sin2xsin3x2+cos5x2)−(√2+√2cos2x+cos3x2) is
Answer» The value of the limit $lim x \to \frac{π}{2} \frac{4 \sqrt{2} (sin 3 x + sin x)}{(2 sin 2 x sin \frac{3 x}{2} + cos \frac{5 x}{2}) - (\sqrt{2} + \sqrt{2} cos 2 x + cos \frac{3 x}{2})}$ is

Discussion

12028.	Nature of root(s) of x−1x−1=x+42x+2:
Answer» Nature of root(s) of $\frac{x - 1}{x - 1} = \frac{x + 4}{2 x + 2}$ :

Discussion

12029.	Question 1Draw a line segment of length 7 cm. Find a point P on it which divides it in the ratio 3:5.
Answer» Question 1 Draw a line segment of length 7 cm. Find a point P on it which divides it in the ratio 3:5.

Discussion

12030.	Find the value of k for which each of the following system of equations have no solution :kx-5y=26x+2y=7
Answer» Find the value of k for which each of the following system of equations have no solution : $k x - 5 y = 2 6 x + 2 y = 7$

Discussion

12031.	Draw a pair of tangents to a circle of radius 5 cm which are inclined to each other at an angle of 60°. Give the justification of the construction.
Answer» Draw a pair of tangents to a circle of radius 5 cm which are inclined to each other at an angle of 60°. Give the justification of the construction.

Discussion

12032.	The value of k for which the equation 3x2+4kx+2=0 and 2x2+3x-2-0 have a common root, is
Answer» The value of k for which the equation 3x2+4kx+2=0 and 2x2+3x-2-0 have a common root, is

Discussion

12033.	A sector is made into a hollow cone by bringing the radii together. If the radius of the cone is equal to its vertical height then the central angle of the sector isa) 45 root 2b) 90 root 2c) 180 root 2d) 120 root 2
Answer» A sector is made into a hollow cone by bringing the radii together. If the radius of the cone is equal to its vertical height then the central angle of the sector is a) 45 root 2 b) 90 root 2 c) 180 root 2 d) 120 root 2

Discussion

12034.	In the figure, ABC is a triangle in which ∠BAC=30∘. Then the triangle BOC is:
Answer» In the figure, ABC is a triangle in which $∠ B A C = 30^{\circ}$ . Then the triangle BOC is:

12034.

In the figure, ABC is a triangle in which ∠BAC=30∘. Then the triangle BOC is:

Answer»

In the figure, ABC is a triangle in which $∠ B A C = 30^{\circ}$ . Then the triangle BOC is:

Discussion

12035.	Evaluate each of the following tan 45ocosec 30o+sec 60ocot 45o−5 sin 90o2 cos 0o
Answer» Evaluate each of the following $\frac{t a n 45^{o}}{c o s e c 30^{o}} + \frac{s e c 60^{o}}{c o t 45^{o}} - \frac{5 s i n 90^{o}}{2 c o s 0^{o}}$

12035.

Evaluate each of the following tan 45ocosec 30o+sec 60ocot 45o−5 sin 90o2 cos 0o

Answer»

Evaluate each of the following

$\frac{t a n 45^{o}}{c o s e c 30^{o}} + \frac{s e c 60^{o}}{c o t 45^{o}} - \frac{5 s i n 90^{o}}{2 c o s 0^{o}}$

Discussion

12036.	The product of four consecutive natural numbers which are multiples of five is 15,000. Find those natural numbers .
Answer» The product of four consecutive natural numbers which are multiples of five is 15,000. Find those natural numbers .

Discussion

12037.	mod of x minus 3 plus mod of 4 minus x is equal to 1 . find the value of x
Answer» mod of x minus 3 plus mod of 4 minus x is equal to 1 . find the value of x

Discussion

12038.	A man standing on the deck of a ship, which is 10 m above the water level, observes the angle of elevation of the top of a hill as 60∘, and the angle of depression of the base of the hill as 30∘. Find the distance of the hill from the ship and the height of the hill. [3 MARKS]
Answer» A man standing on the deck of a ship, which is 10 m above the water level, observes the angle of elevation of the top of a hill as $60^{\circ}$ , and the angle of depression of the base of the hill as $30^{\circ}$ . Find the distance of the hill from the ship and the height of the hill. [3 MARKS]

Discussion

12039.	Mean of the goals scored by Ronaldo and Messi for each year for the past 5 years is 48 and 50 respectively. Standard deviation for each of them is 6 and 4 respectively. Who is more consistent?
Answer» Mean of the goals scored by Ronaldo and Messi for each year for the past 5 years is 48 and 50 respectively. Standard deviation for each of them is 6 and 4 respectively. Who is more consistent?

Discussion

12040.	Solve the following quadratic equations by factorization:x-122=4
Answer» Solve the following quadratic equations by factorization: ${(x - \frac{1}{2})}^{2} = 4$

Discussion

12041.	{ 14. The sum of the series }1+(1+2+4)+(4+6+9)+}{(9+12+16)+...+(361+380+400) is }20^n. Then n
Answer» { 14. The sum of the series }1+(1+2+4)+(4+6+9)+}{(9+12+16)+...+(361+380+400) is }20^n. Then n

Discussion

12042.	In the given figure, O is the centre of the circumcircle ABC. Tangents at A and C intersect at P. Given angle AOB = 140o and angle APC = 80o; find the angle BAC.
Answer» In the given figure, O is the centre of the circumcircle ABC. Tangents at A and C intersect at P. Given angle AOB = $140^{o}$ and angle APC = $80^{o}$ ; find the angle BAC.

12042.

In the given figure, O is the centre of the circumcircle ABC. Tangents at A and C intersect at P. Given angle AOB = 140o and angle APC = 80o; find the angle BAC.

Answer»

In the given figure, O is the centre of the circumcircle ABC. Tangents at A and C intersect at P. Given angle AOB = $140^{o}$ and angle APC = $80^{o}$ ; find the angle BAC.

Discussion

12043.	A factory is designed as shown in the figure. There are 150 people working in the factory and each occupy a space of 0.5 m3. Find the maximum volume available to place machinery in the factory. (Take π=227)
Answer» A factory is designed as shown in the figure. There are 150 people working in the factory and each occupy a space of 0.5 $m^{3}$ . Find the maximum volume available to place machinery in the factory. (Take $π = \frac{22}{7}$ )

12043.

A factory is designed as shown in the figure. There are 150 people working in the factory and each occupy a space of 0.5 m3. Find the maximum volume available to place machinery in the factory. (Take π=227)

Answer»

A factory is designed as shown in the figure. There are 150 people working in the factory and each occupy a space of 0.5 $m^{3}$ . Find the maximum volume available to place machinery in the factory. (Take $π = \frac{22}{7}$ )

Discussion

12044.	What are the numbers of significant figures in (3.20 + 4.80) × 10^5
Answer» What are the numbers of significant figures in (3.20 + 4.80) × 10^5

Discussion

12045.	A wire 40cm long is bent into a rectangular frame 15 cm × 5 cm and placed perpendicular to a field of induction 0.8 T in 0.5 sec, the frame is changed into a square frame and the field is increased to 1.4T The e.m.f induced in the frame
Answer» A wire 40cm long is bent into a rectangular frame 15 cm $\times$ 5 cm and placed perpendicular to a field of induction 0.8 T in 0.5 sec, the frame is changed into a square frame and the field is increased to 1.4T The e.m.f induced in the frame

Discussion

12046.	A sector of central and 216° is cut out from a circle of radius 25 centimetres and it is rolled up into a cone. What is the base-radius and height of this cone? What is its volume?
Answer» A sector of central and 216° is cut out from a circle of radius 25 centimetres and it is rolled up into a cone. What is the base-radius and height of this cone? What is its volume?

Discussion

12047.	Find the largest number that divides 59 and 54 leaving remainders 3 and 5 respectively
Answer» Find the largest number that divides 59 and 54 leaving remainders 3 and 5 respectively

Discussion

12048.	Lateral surface area of the cube is _________.
Answer» Lateral surface area of the cube is _________.

Discussion

12049.	The speed of a boat in still water is 8 km/hr. It can go 15 km upstream and 22 km downstream in 5 hours. Find the speed of the stream.
Answer» The speed of a boat in still water is 8 km/hr. It can go 15 km upstream and 22 km downstream in 5 hours. Find the speed of the stream.

Discussion

12050.	Question 3 From an external point P, two tangents , PA and PB are drawn to a circle with centre O. At one point E on the circle tangent is drawn which intersects PA and PB at C and D, respectively. If PA = 10 cm, find the perimeter of the triangle PCD.
Answer» Question 3 From an external point P, two tangents , PA and PB are drawn to a circle with centre O. At one point E on the circle tangent is drawn which intersects PA and PB at C and D, respectively. If PA = 10 cm, find the perimeter of the triangle PCD.

Discussion

Explore topic-wise InterviewSolutions in .

Consider an arithmetic series and a geometric series having four initial terms from the set {11,8,21,16,26,32,4}. If the last terms of these seris are the maximum possible four digit numbers, then the number of common terms in these two series is equal to

Use Euclid's division lemma to show that the square of any positive integer is either of the form 3m or 3m+1 for some integer m.

The area of the base of a cone is 2464 cm^2 and the curved surface is 3080 cm^2 . Its volume is

The zero of the polynomial p(x) = ax+b is

The length (in units ) of a line segment intercepted between the coordinate axes by the line joining the points (1,2) and (3,4) is

Question 2 (ii)Find the sum of those integers from 1 to 500 which are multiples of 2 as well as of 5.

A physical quantity p is being calculated by the equation p=qr.q is measured with an error of +20% whereas r is measured with an error of-20%. the error in p is

Find the volume of the square pyramid, if one the triangular faces is given below.

81.A cone is 8.4cm high and radius of its base is 2.1cm . It melted and recast into a sphere . Find the radius of sphere

Draw a line segment of length 8.6 cm and divide it in the ratio 3:5 .Measure the two parts .

Find the value of tan 48∘.tan 23∘.tan 42∘.tan 67∘ .

A pipe of internal diameter 20cm from a canal is connected to a cylindrical tank of radius 5m and height 2m. If water flows through the pipe at 6km/hr, how much time will it take for the tank to be filled?

A capsule of medicine is in the shape of a sphere of diameter 3.5 mm.How much medicine in mm3 is needed to fill this capsule?[Assume π=227]

In the figure, AB is the common tangent to the 2 circles intersecting at C &amp; D. Write down the numerical value of ∠ACB + ∠ADB. Give reasons for your answer.

Zeroes of the quadratic polynomial ax2 + bx + c and roots of the quadratic equation ax2 + bx + c = 0 are__________

5x*2-2/4x*2-x+3 is less than 1

Shubendhu owns 560 shares of a company. The face value of each share is Rs. 25. The company declares a dividend of 9%. Calculate: (i) The dividend that Shubendhu will get. (ii) The rate of interest on his investment if Shubendhu had paid Rs. 30 for each share.

If B × A = {(x, a), (x, b), (x, c), (y, a), (y, b), (y, c), (z, a), (z, b), (z, c)}. Find set A and set B.

If one cm on the ground shows 228 I'm on the ground, then find out 1 cm = 228 km A)12 cm = B)312cm= C)2cm= D)14 cm =

If x+3y=6 and 2x−3y=12 intersect, what is the value of x? 6

In the given figure P is the object and P' is the image. The line AB is which is the perpendicular bisector of PP' is called as ______.

Question 6The length of a tangent from a point A at distance 5 cm from the centre of the circle is 4 cm. Find the radius of the circle.

Find the value of: sec 29∘cosec 61∘ + 2cot8∘cot17∘cot45∘cot73∘cot82∘. ___

The distance between the points (-1, 5) and (2, 1) is ___ units.

A tower 8 m high throws a shadow 8 m long on the ground. Find the angle of elevation of the sun.

The value of the limit limx→π24√2(sin3x+sinx)(2sin2xsin3x2+cos5x2)−(√2+√2cos2x+cos3x2) is

Nature of root(s) of x−1x−1=x+42x+2:

Question 1Draw a line segment of length 7 cm. Find a point P on it which divides it in the ratio 3:5.

Find the value of k for which each of the following system of equations have no solution :kx-5y=26x+2y=7

Draw a pair of tangents to a circle of radius 5 cm which are inclined to each other at an angle of 60°. Give the justification of the construction.

The value of k for which the equation 3x2+4kx+2=0 and 2x2+3x-2-0 have a common root, is

A sector is made into a hollow cone by bringing the radii together. If the radius of the cone is equal to its vertical height then the central angle of the sector isa) 45 root 2b) 90 root 2c) 180 root 2d) 120 root 2

In the figure, ABC is a triangle in which ∠BAC=30∘. Then the triangle BOC is:

Evaluate each of the following tan 45ocosec 30o+sec 60ocot 45o−5 sin 90o2 cos 0o

The product of four consecutive natural numbers which are multiples of five is 15,000. Find those natural numbers .

mod of x minus 3 plus mod of 4 minus x is equal to 1 . find the value of x

A man standing on the deck of a ship, which is 10 m above the water level, observes the angle of elevation of the top of a hill as 60∘, and the angle of depression of the base of the hill as 30∘. Find the distance of the hill from the ship and the height of the hill. [3 MARKS]

Mean of the goals scored by Ronaldo and Messi for each year for the past 5 years is 48 and 50 respectively. Standard deviation for each of them is 6 and 4 respectively. Who is more consistent?

Solve the following quadratic equations by factorization:x-122=4

{ 14. The sum of the series }1+(1+2+4)+(4+6+9)+}{(9+12+16)+...+(361+380+400) is }20^n. Then n

In the given figure, O is the centre of the circumcircle ABC. Tangents at A and C intersect at P. Given angle AOB = 140o and angle APC = 80o; find the angle BAC.

A factory is designed as shown in the figure. There are 150 people working in the factory and each occupy a space of 0.5 m3. Find the maximum volume available to place machinery in the factory. (Take π=227)

What are the numbers of significant figures in (3.20 + 4.80) × 10^5

A wire 40cm long is bent into a rectangular frame 15 cm × 5 cm and placed perpendicular to a field of induction 0.8 T in 0.5 sec, the frame is changed into a square frame and the field is increased to 1.4T The e.m.f induced in the frame

A sector of central and 216° is cut out from a circle of radius 25 centimetres and it is rolled up into a cone. What is the base-radius and height of this cone? What is its volume?

Find the largest number that divides 59 and 54 leaving remainders 3 and 5 respectively

Lateral surface area of the cube is _________.

The speed of a boat in still water is 8 km/hr. It can go 15 km upstream and 22 km downstream in 5 hours. Find the speed of the stream.

Question 3 From an external point P, two tangents , PA and PB are drawn to a circle with centre O. At one point E on the circle tangent is drawn which intersects PA and PB at C and D, respectively. If PA = 10 cm, find the perimeter of the triangle PCD.

In the figure, AB is the common tangent to the 2 circles intersecting at C & D. Write down the numerical value of ∠ACB + ∠ADB. Give reasons for your answer.

5x2-2/4x2-x+3 is less than 1