32581 + Interview Questions in Mathematics Page 154 InterviewSolution

7651.	The length of shadow of a tower on the plane ground is 3 times the height of the tower. The angle of elevation of sun is(a) 45° (b) 30° (c) 60° (d) 90° [CBSE 2012]
Answer» The length of shadow of a tower on the plane ground is $\sqrt{3}$ times the height of the tower. The angle of elevation of sun is (a) 45° (b) 30° (c) 60° (d) 90° [CBSE 2012]

Discussion

7652.	What is tangent of a circle?
Answer» What is tangent of a circle?

Discussion

7653.	Which of the following is a arthemetic progression?(1) n^2+n+1(2)n^2+2n+3(3)n^3+1(4)2n+3
Answer» Which of the following is a arthemetic progression? (1) n^2+n+1 (2)n^2+2n+3 (3)n^3+1 (4)2n+3

Discussion

7654.	√a.√b= √ab not true only when
Answer» √a.√b= √ab not true only when

Discussion

7655.	The angles of elevations of the top of a tower from two points at a distance of 4M and 9M from the base of the tower and in the same straight line with it are 60 degree and 30 degree. find the height of the tower.
Answer» The angles of elevations of the top of a tower from two points at a distance of 4M and 9M from the base of the tower and in the same straight line with it are 60 degree and 30 degree. find the height of the tower.

Discussion

7656.	A spherical glass vessel has a cylindrical neck 7 cm long and 4 cm in diameter. The diameter of the spherical part is 21 cm. Find the quantity of water it can hold. [Use π=22/7.]
Answer» A spherical glass vessel has a cylindrical neck 7 cm long and 4 cm in diameter. The diameter of the spherical part is 21 cm. Find the quantity of water it can hold. $[U s e π = 22 / 7.]$

Discussion

7657.	If tan2 θ=1−a2, prove that sec θ+(tan3 θ×cosec θ)=(2−a2)32.
Answer» If $t a n^{2} θ = 1 - a^{2}$ , prove that $s e c θ + (t a n^{3} θ \times c o s e c θ) = (2 - a^{2})^{\frac{3}{2}}$ .

Discussion

7658.	The zero of p(x) = 5x - 75 is ___
Answer» The zero of p(x) = 5x - 75 is ___

Discussion

7659.	If sum of the zeroes of mx2+3m+2x is equal to their product. Then value of m is:
Answer» If sum of the zeroes of $m x^{2} + 3 m + 2 x$ is equal to their product. Then value of m is:

Discussion

7660.	If the radius of a circle is 5 cm & length of a tangent PA from an external point P is 12 cm.Find the distance of point P from the centre of circle.
Answer» If the radius of a circle is 5 cm & length of a tangent PA from an external point P is 12 cm.Find the distance of point P from the centre of circle.

Discussion

7661.	if f[x] = x^2/a+b/ac*-x/b-1/c find zeroes of this polynomial
Answer» if f[x] = x^2/a+b/ac*-x/b-1/c find zeroes of this polynomial

Discussion

7662.	If 3 is the least prime factor of number a and 7 is the least prime factor of number b, then the least prime factor of a + b, is(a) 2(b) 3(c) 5(d) 10
Answer» If 3 is the least prime factor of number a and 7 is the least prime factor of number b, then the least prime factor of a + b, is (a) 2 (b) 3 (c) 5 (d) 10

Discussion

7663.	Question 13As observed from the top of a 75 m high lighthouse from the sea-level, the angles of depression of two ships are 30∘ and 45∘. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships.
Answer» Question 13 As observed from the top of a 75 m high lighthouse from the sea-level, the angles of depression of two ships are $30^{\circ}$ and $45^{\circ}$ . If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships.

Discussion

7664.	The conditions for ax+by+c=0 to be a linear equation in two variables (x,y) are
Answer» The conditions for $a x + b y + c = 0$ to be a linear equation in two variables $(x, y)$ are

7664.

The conditions for ax+by+c=0 to be a linear equation in two variables (x,y) are

Answer»

The conditions for $a x + b y + c = 0$ to be a linear equation in two variables $(x, y)$ are

Discussion

7665.	Draw a circle with centre P and radius 3.4 cm. Take point Q at a distance 5.5 cm from the centre. Construct tangents to the circle from point Q.
Answer» Draw a circle with centre P and radius 3.4 cm. Take point Q at a distance 5.5 cm from the centre. Construct tangents to the circle from point Q.

Discussion

7666.	Two circular pieces of equal radii and maximum area, touching each other are cut out from a rectangular cardboard of dimensions 14 cm ⨯ 7 cm. Find the area of the remaining cardboard. [CBSE 2013]
Answer» Two circular pieces of equal radii and maximum area, touching each other are cut out from a rectangular cardboard of dimensions 14 cm ⨯ 7 cm. Find the area of the remaining cardboard. [CBSE 2013]

Discussion

7667.	In the given right angled isosceles triangle ABC, if AC = 10cm then the area of triangle (in cm2) is ___.
Answer» In the given right angled isosceles triangle ABC, if AC = 10cm then the area of triangle (in $c m^{2}$ ) is ___.

7667.

In the given right angled isosceles triangle ABC, if AC = 10cm then the area of triangle (in cm2) is ___.

Answer»

In the given right angled isosceles triangle ABC, if AC = 10cm then the area of triangle (in $c m^{2}$ ) is

___.

Discussion

7668.	If three point (h, 0), (a, b) and (0, k) lie ona line, show that.
Answer» If three point (h, 0), (a, b) and (0, k) lie on a line, show that.

Discussion

7669.	√10×√15 is equal to A) 6√5 B) 5√6 C) √25 D) 10√5
Answer» $\sqrt{10} \times \sqrt{15}$ is equal to A) $6 \sqrt{5}$ B) $5 \sqrt{6}$ C) $\sqrt{25}$ D) $10 \sqrt{5}$

Discussion

7670.	Find the value of k for which the following system of linear equations has no solutions:kx+3y=k-312x+ky=k
Answer» Find the value of k for which the following system of linear equations has no solutions: $k x + 3 y = k - 3 12 x + k y = k$

Discussion

7671.

The runs scored by two batsmen A and B in six innings are given as follows: Batsman A 48 50 54 46 48 54 Batsman B 46 44 43 46 45 46 Determine (i) Who is a better run getter? (ii) Who is a consistent player?

Answer»

The runs scored by two batsmen A and B in six innings are given as follows:

Batsman A	48	50	54	46	48	54
Batsman B	46	44	43	46	45	46

Determine (i) Who is a better run getter? (ii) Who is a consistent player?

Discussion

7672.	The number of solutions of the equations of the equation x2+[x]−4x+3=0 is Where [ ] denotes G.I.F.
Answer» The number of solutions of the equations of the equation $x^{2} + [x] - 4 x + 3 = 0$ is Where [ ] denotes G.I.F.

Discussion

7673.	Prove that root 7 divided by 2 is irrational
Answer» Prove that root 7 divided by 2 is irrational

Discussion

7674.	Draw a circle of radius 3.5 cm. Draw the tangents to the circle which are perpendicular to each other.
Answer» Draw a circle of radius 3.5 cm. Draw the tangents to the circle which are perpendicular to each other.

Discussion

7675.	What number should be added to 2, 4, 7 so that resulting numbers are in continued proportion.
Answer» What number should be added to 2, 4, 7 so that resulting numbers are in continued proportion.

Discussion

7676.	The area of a circle which encloses a square of side 10 cm is :
Answer» The area of a circle which encloses a square of side 10 cm is :

Discussion

7677.	If sin(B+C)=√32 and sin A=12, find B+C and A.
Answer» If $s i n (B + C) = \frac{\sqrt{3}}{2} a n d s i n A = \frac{1}{2}$ , find $B + C a n d A$ .

Discussion

7678.	The 2nd term of an AP is 13 and its 5th term is 25. What is its 17th term.(a) 69(b) 73(c) 77(d) 81
Answer» The 2nd term of an AP is 13 and its 5th term is 25. What is its 17th term. (a) 69 (b) 73 (c) 77 (d) 81

Discussion

7679.

The following distribution gives the number of accidents met by 160 workers in a factory during a month. No. of accidents (x): 0 1 2 3 4 No. of workers (f): 70 52 34 3 1 Find the average number of accidents per worker.

Answer» The following distribution gives the number of accidents met by 160 workers in a factory during a month.

No. of accidents (x):	0	1	2	3	4
No. of workers (f):	70	52	34	3	1

Find the average number of accidents per worker.

Discussion

7680.	Draw an equilateral triangle. Find its circumcentre (C), incentre (I), centroid (G) and orthocentre (O). Write your observation.
Answer» Draw an equilateral triangle. Find its circumcentre (C), incentre (I), centroid (G) and orthocentre (O). Write your observation.

Discussion

7681.	Find the value of k for which the following pair of linear equations have infinitely many solutions:2x+3y=7, k-1x+k+2y=3k
Answer» Find the value of k for which the following pair of linear equations have infinitely many solutions: $2 x + 3 y = 7, (k - 1) x + (k + 2) y = 3 k$

Discussion

7682.	In the given figure, BC is a tangent to the circle with centre O. OE bisects AP. Prove that ΔAEO ~Δ ABC.
Answer» In the given figure, BC is a tangent to the circle with centre O. OE bisects AP. Prove that ΔAEO $~$ Δ ABC.

Discussion

7683.	The distance between the points (0, 5) and (5, 0) is __________.
Answer» The distance between the points (0, 5) and (5, 0) is __________.

Discussion

7684.	A card is drawn at random from a pack of playing cards. The probability that it is a non-face card of black colour is
Answer» A card is drawn at random from a pack of playing cards. The probability that it is a non-face card of black colour is

Discussion

7685.	You ask someone to say a (natural) number less than 10. What is the probability that the number is a prime? What is the number asked is to be less than 100?
Answer» You ask someone to say a (natural) number less than 10. What is the probability that the number is a prime? What is the number asked is to be less than 100?

Discussion

7686.	S/r1+s/r2+s/r3-s/r is equal to
Answer» S/r1+s/r2+s/r3-s/r is equal to

Discussion

7687.	Metallic spheres of radii 6 cm, 8 cm and 10 cm respectively are melted to form a single solid sphere. Find the radius of the resulting sphere(in cm).
Answer» Metallic spheres of radii 6 cm, 8 cm and 10 cm respectively are melted to form a single solid sphere. Find the radius of the resulting sphere(in cm).

Discussion

7688.	66. A boy is standing on a horizontal plane finds a bird flying at a distance of 100 metre from him at an elevation of 30 degree. a girl standing on the roof of 20 metre high building find the angle of elevation of the same bird to be 45 degree . Both the boy and the girl opposite sides of the bird find the distance of Bird from the girl Click here to view details:
Answer» 66. A boy is standing on a horizontal plane finds a bird flying at a distance of 100 metre from him at an elevation of 30 degree. a girl standing on the roof of 20 metre high building find the angle of elevation of the same bird to be 45 degree . Both the boy and the girl opposite sides of the bird find the distance of Bird from the girl Click here to view details:

Discussion

7689.	Question 15 Area of sector of central angle 200∘ of a circle is 770 cm2. Find the length of the corresponding arc of this sector.
Answer» Question 15 Area of sector of central angle $200^{\circ}$ of a circle is $770 c m^{2}$ . Find the length of the corresponding arc of this sector.

Discussion

7690.	Prove that the points (4, 5), (7, 6), (6, 3), (3, 2) are the vertices of a parallelogram. Is it a rectangle.
Answer» Prove that the points (4, 5), (7, 6), (6, 3), (3, 2) are the vertices of a parallelogram. Is it a rectangle.

Discussion

7691.	Prove that 6+√2 is irrational.
Answer» Prove that $6 + \sqrt{2}$ is irrational.

Discussion

7692.	896 mL of a mixture of CO and CO2 weigh 1.28 gat NTP. Calculate the volume of CO2 in the mixture6.at NTP.(2) 672 ml(1) 448 ml(4) 500 ml(3) 224 ml
Answer» 896 mL of a mixture of CO and CO2 weigh 1.28 gat NTP. Calculate the volume of CO2 in the mixture6.at NTP.(2) 672 ml(1) 448 ml(4) 500 ml(3) 224 ml

Discussion

7693.	Prove that out of any two consecutive positive integers one and only one is even
Answer» Prove that out of any two consecutive positive integers one and only one is even

Discussion

7694.	David deposited ₹300 per month in a recurring deposit account. If he gets ₹7725 at the end of two years on maturity, find the rate of interest (in %) on recurring deposit.7
Answer» David deposited ₹300 per month in a recurring deposit account. If he gets ₹7725 at the end of two years on maturity, find the rate of interest (in %) on recurring deposit. 7

Discussion

7695.	Question 2 (iii)Find the surface area of a sphere of diameter:(iii) 3.5 m[Assume π=227]
Answer» Question 2 (iii) Find the surface area of a sphere of diameter: (iii) 3.5 m $[A s s u m e π = \frac{22}{7}]$

7695.

Question 2 (iii)Find the surface area of a sphere of diameter:(iii) 3.5 m[Assume π=227]

Answer»

Question 2 (iii)

Find the surface area of a sphere of diameter:

(iii) 3.5 m

$[A s s u m e π = \frac{22}{7}]$

Discussion

7696.	(2x+1)3 with ldenities
Answer» (2x+1)3 with ldenities

Discussion

7697.	A hollow sphere of internal & external radii 6 cm & 8 cm respectively is melted & recast into small cones of base radius 2 cm & height 8 cm. Find number of cones.
Answer» A hollow sphere of internal & external radii 6 cm & 8 cm respectively is melted & recast into small cones of base radius 2 cm & height 8 cm. Find number of cones.

Discussion

7698.	Find the equation of a line parallel to 2x + 3y = 5 and passing through the mid-point of the segment joining P (-3, 4) and Q (1, -2)
Answer» Find the equation of a line parallel to 2x + 3y = 5 and passing through the mid-point of the segment joining P (-3, 4) and Q (1, -2)

Discussion

7699.	49.Sin theta = sin 9theta
Answer» 49.Sin theta = sin 9theta

Discussion

7700.	A school wants to award its students for the values of Honesty, Regularity and Hard work with a total cash award of Rs 6,000. Three times the award money for Hard work added to that given for honesty amounts to Rs 11,000. The award money given for Honesty and Hard work together is double the one given for Regularity. Represent the above situation algebraically and find the award money for each value, using matrix method. Apart from these values, namely, Honesty, Regularity and Hard work, suggest one more value which the school must include for awards.
Answer» A school wants to award its students for the values of Honesty, Regularity and Hard work with a total cash award of Rs 6,000. Three times the award money for Hard work added to that given for honesty amounts to Rs 11,000. The award money given for Honesty and Hard work together is double the one given for Regularity. Represent the above situation algebraically and find the award money for each value, using matrix method. Apart from these values, namely, Honesty, Regularity and Hard work, suggest one more value which the school must include for awards.

Discussion

Explore topic-wise InterviewSolutions in .

The length of shadow of a tower on the plane ground is 3 times the height of the tower. The angle of elevation of sun is(a) 45° (b) 30° (c) 60° (d) 90° [CBSE 2012]

What is tangent of a circle?

Which of the following is a arthemetic progression?(1) n^2+n+1(2)n^2+2n+3(3)n^3+1(4)2n+3

√a.√b= √ab not true only when

The angles of elevations of the top of a tower from two points at a distance of 4M and 9M from the base of the tower and in the same straight line with it are 60 degree and 30 degree. find the height of the tower.

A spherical glass vessel has a cylindrical neck 7 cm long and 4 cm in diameter. The diameter of the spherical part is 21 cm. Find the quantity of water it can hold. [Use π=22/7.]

If tan2 θ=1−a2, prove that sec θ+(tan3 θ×cosec θ)=(2−a2)32.

The zero of p(x) = 5x - 75 is ___

If sum of the zeroes of mx2+3m+2x is equal to their product. Then value of m is:

If the radius of a circle is 5 cm & length of a tangent PA from an external point P is 12 cm.Find the distance of point P from the centre of circle.

if f[x] = x^2/a+b/ac*-x/b-1/c find zeroes of this polynomial

If 3 is the least prime factor of number a and 7 is the least prime factor of number b, then the least prime factor of a + b, is(a) 2(b) 3(c) 5(d) 10

Question 13As observed from the top of a 75 m high lighthouse from the sea-level, the angles of depression of two ships are 30∘ and 45∘. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships.

The conditions for ax+by+c=0 to be a linear equation in two variables (x,y) are

Draw a circle with centre P and radius 3.4 cm. Take point Q at a distance 5.5 cm from the centre. Construct tangents to the circle from point Q.

Two circular pieces of equal radii and maximum area, touching each other are cut out from a rectangular cardboard of dimensions 14 cm ⨯ 7 cm. Find the area of the remaining cardboard. [CBSE 2013]

In the given right angled isosceles triangle ABC, if AC = 10cm then the area of triangle (in cm2) is ___.

If three point (h, 0), (a, b) and (0, k) lie ona line, show that.

√10×√15 is equal to A) 6√5 B) 5√6 C) √25 D) 10√5

Find the value of k for which the following system of linear equations has no solutions:kx+3y=k-312x+ky=k

The runs scored by two batsmen A and B in six innings are given as follows: Batsman A 48 50 54 46 48 54 Batsman B 46 44 43 46 45 46 Determine (i) Who is a better run getter? (ii) Who is a consistent player?

The number of solutions of the equations of the equation x2+[x]−4x+3=0 is Where [ ] denotes G.I.F.

Prove that root 7 divided by 2 is irrational

Draw a circle of radius 3.5 cm. Draw the tangents to the circle which are perpendicular to each other.

What number should be added to 2, 4, 7 so that resulting numbers are in continued proportion.

The area of a circle which encloses a square of side 10 cm is :

If sin(B+C)=√32 and sin A=12, find B+C and A.

The 2nd term of an AP is 13 and its 5th term is 25. What is its 17th term.(a) 69(b) 73(c) 77(d) 81

The following distribution gives the number of accidents met by 160 workers in a factory during a month. No. of accidents (x): 0 1 2 3 4 No. of workers (f): 70 52 34 3 1 Find the average number of accidents per worker.

Draw an equilateral triangle. Find its circumcentre (C), incentre (I), centroid (G) and orthocentre (O). Write your observation.

Find the value of k for which the following pair of linear equations have infinitely many solutions:2x+3y=7, k-1x+k+2y=3k

In the given figure, BC is a tangent to the circle with centre O. OE bisects AP. Prove that ΔAEO ~Δ ABC.

The distance between the points (0, 5) and (5, 0) is __________.

A card is drawn at random from a pack of playing cards. The probability that it is a non-face card of black colour is

You ask someone to say a (natural) number less than 10. What is the probability that the number is a prime? What is the number asked is to be less than 100?

S/r1+s/r2+s/r3-s/r is equal to

Metallic spheres of radii 6 cm, 8 cm and 10 cm respectively are melted to form a single solid sphere. Find the radius of the resulting sphere(in cm).

Question 15 Area of sector of central angle 200∘ of a circle is 770 cm2. Find the length of the corresponding arc of this sector.

Prove that the points (4, 5), (7, 6), (6, 3), (3, 2) are the vertices of a parallelogram. Is it a rectangle.

Prove that 6+√2 is irrational.

896 mL of a mixture of CO and CO2 weigh 1.28 gat NTP. Calculate the volume of CO2 in the mixture6.at NTP.(2) 672 ml(1) 448 ml(4) 500 ml(3) 224 ml

Prove that out of any two consecutive positive integers one and only one is even

David deposited ₹300 per month in a recurring deposit account. If he gets ₹7725 at the end of two years on maturity, find the rate of interest (in %) on recurring deposit.7

Question 2 (iii)Find the surface area of a sphere of diameter:(iii) 3.5 m[Assume π=227]

(2x+1)3 with ldenities

A hollow sphere of internal &amp; external radii 6 cm &amp; 8 cm respectively is melted &amp; recast into small cones of base radius 2 cm &amp; height 8 cm. Find number of cones.

Find the equation of a line parallel to 2x + 3y = 5 and passing through the mid-point of the segment joining P (-3, 4) and Q (1, -2)

49.Sin theta = sin 9theta

A hollow sphere of internal & external radii 6 cm & 8 cm respectively is melted & recast into small cones of base radius 2 cm & height 8 cm. Find number of cones.