32581 + Interview Questions in Mathematics Page 100 InterviewSolution

4951.	Two identical cubes of side 4 cm are placed one above the other, forming a cuboid. Find the total surface area of the cuboid thus formed.
Answer» Two identical cubes of side 4 cm are placed one above the other, forming a cuboid. Find the total surface area of the cuboid thus formed.

Discussion

4952.	In a circular dartboard of radius 20 cm, there are 5 concentric circles. the radius of each inner concentric circle is 4 cm less than the outer concentric circle. Find the probability that a dart hits anywhere in the smallest circle assuming that the dart doesn't hit on the boundary of any circle.
Answer» In a circular dartboard of radius 20 cm, there are 5 concentric circles. the radius of each inner concentric circle is 4 cm less than the outer concentric circle. Find the probability that a dart hits anywhere in the smallest circle assuming that the dart doesn't hit on the boundary of any circle.

Discussion

4953.	Tangents are drawn from the point(3,4)totheellipse4x^2+9y^2-36=0 touching ellipse at point A and B find the ortho centre of△ PAB
Answer» Tangents are drawn from the point(3,4)totheellipse4x^2+9y^2-36=0 touching ellipse at point A and B find the ortho centre of△ PAB

Discussion

4954.	A girl fills a cylindrical bucket whose height is 32 cm and radius is 18 cm with sand. She empties the bucket on the ground and makes a conical heap of the sand. If the height of the conical heap is 24 cm, then find the slant height of the cone formed.
Answer» A girl fills a cylindrical bucket whose height is 32 cm and radius is 18 cm with sand. She empties the bucket on the ground and makes a conical heap of the sand. If the height of the conical heap is 24 cm, then find the slant height of the cone formed.

Discussion

4955.	What is the difference between the interfascicular cambium and intra fascicular cambium ?
Answer» What is the difference between the interfascicular cambium and intra fascicular cambium ?

Discussion

4956.	A toy is in the form of a cone of radius 3. 5 cm mounted on a hemisphere of same radius on its circular face. The total height of the toy is 15.5 cm. Find the total surface area of the toy.
Answer» A toy is in the form of a cone of radius 3. 5 cm mounted on a hemisphere of same radius on its circular face. The total height of the toy is 15.5 cm. Find the total surface area of the toy.

Discussion

4957.	A storage tank consists of a circular cylinder with a hemisphere adjoined on either end. If the external diameter of the cylinder by 1.4 m and its length be 8 m, find the cost of painting it on the outside at the rate of Rs. 10 per m2.
Answer» A storage tank consists of a circular cylinder with a hemisphere adjoined on either end. If the external diameter of the cylinder by 1.4 m and its length be 8 m, find the cost of painting it on the outside at the rate of Rs. 10 per m².

Discussion

4958.	If a 1.5 m tall girl stands at a distance of 3 m from a lamp-post and casts a shadow of length 4.5 m on the ground, then the height of the lamp-post is(a) 1.5 m(b) 2 m(c) 2.5 m(d) 2.8 m
Answer» If a 1.5 m tall girl stands at a distance of 3 m from a lamp-post and casts a shadow of length 4.5 m on the ground, then the height of the lamp-post is (a) 1.5 m (b) 2 m (c) 2.5 m (d) 2.8 m

Discussion

4959.	A boy bought a book for ₹x and sold it for ₹26. If his loss was x percent, find the second degree equation from which we can find cost price of the book.
Answer» A boy bought a book for ₹x and sold it for ₹26. If his loss was x percent, find the second degree equation from which we can find cost price of the book.

Discussion

4960.	A spherical ball of radius 3 cm is melted and recast into three spherical balls. The radii of the two balls are 1.5 cm and 2.0 cm. Find the radius of third ball.
Answer» A spherical ball of radius 3 cm is melted and recast into three spherical balls. The radii of the two balls are 1.5 cm and 2.0 cm. Find the radius of third ball.

Discussion

4961.	ntProve that (a+b){(b+c)(c+a)}=2a(b+c)n ntn nt(a, b, c are with vector sign)n
Answer» ntProve that (a+b){(b+c)(c+a)}=2a(b+c)n ntn nt(a, b, c are with vector sign)n

Discussion

4962.

Construct a frequency table from the following data: Marks No. of students less than 10 6 less than 20 15 less than 30 30 less than 40 39 less than 50 53 less than 60 70

Answer» Construct a frequency table from the following data:

Marks	No. of students
less than 10	6
less than 20	15
less than 30	30
less than 40	39
less than 50	53
less than 60	70

Discussion

4963.	How many silver coins, 1.75 cm in diameter and of thickness 2 mm, must be melted to form a cuboid of dimensions?
Answer» How many silver coins, 1.75 cm in diameter and of thickness 2 mm, must be melted to form a cuboid of dimensions?

Discussion

4964.	Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.
Answer» Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.

4964.

Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.

Answer»

Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.

Discussion

4965.	Using prime factorization, find the HCF and LCM of(i) 36, 84(ii) 23, 31(iii) 96, 404(iv) 144, 198(v) 396, 1080(vi) 1152, 1664
Answer» Using prime factorization, find the HCF and LCM of (i) 36, 84 (ii) 23, 31 (iii) 96, 404 (iv) 144, 198 (v) 396, 1080 (vi) 1152, 1664

Discussion

4966.	If k, 2k − 1 and 2k + 1 are three consecutive terms of an A.P., the value of k is(a) −2(b) 3(c) −3(d) 6
Answer» If k, 2k − 1 and 2k + 1 are three consecutive terms of an A.P., the value of k is (a) −2 (b) 3 (c) −3 (d) 6

Discussion

4967.	Sec70°Sin20°-Cos20°Cosec70° Evaluate
Answer» Sec70°Sin20°-Cos20°Cosec70° Evaluate

Discussion

4968.	In the given figure, ABCD is a parallelogram with x : y = 1 : 1 and OE \|\| AD. Then, (area of ΔADC + area of ΔBOC) : area of ΔODC is
Answer» In the given figure, ABCD is a parallelogram with x : y = 1 : 1 and OE \|\| AD. Then, (area of $Δ A D C$ + area of $Δ B O C$ ) : area of $Δ O D C$ is

Discussion

4969.	Question 11Show that 12n cannot end with the digit 0 or 5 for any natural number n.
Answer» Question 11 Show that $12^{n}$ cannot end with the digit 0 or 5 for any natural number n.

Discussion

4970.

Electricity used by some families is shown in the following table. Find the mode for use of electricity. Use of electricity (Unit) 0 - 20 20 - 40 40 - 60 60 - 80 80 - 100 100 - 120 No. of families 13 50 70 100 80 17

Answer» Electricity used by some families is shown in the following table. Find the mode for use of electricity.

Use of electricity (Unit)	0 - 20	20 - 40	40 - 60	60 - 80	80 - 100	100 - 120
No. of families	13	50	70	100	80	17

Discussion

4971.	If the point P(2,1) lies on the line segment joining points A(4,2) and B(8,4) then
Answer» If the point P(2,1) lies on the line segment joining points A(4,2) and B(8,4) then

Discussion

4972.	47. For the same amount of work adult has done 6 hours less than a child. If they together come and work it would take 13hours12minute. Find the time taken by the child to complete this work
Answer» 47. For the same amount of work adult has done 6 hours less than a child. If they together come and work it would take 13hours12minute. Find the time taken by the child to complete this work

Discussion

4973.	Question 2 (iv)Fill in the blanks:(iv) The common point of a tangent to a circle and the circle is called___.
Answer» Question 2 (iv) Fill in the blanks: (iv) The common point of a tangent to a circle and the circle is called___.

Discussion

4974.	The distance between the points (-3,0) and (4,0) is ___ units.
Answer» The distance between the points (-3,0) and (4,0) is ___ units.

Discussion

4975.	A man sees a train passing a bridge 1 km long. The length of the train is half that of the bridge. If the train clears the bridge in 2 minutes, find the speed of the train in km/hr. [4 MARKS]
Answer» A man sees a train passing a bridge 1 km long. The length of the train is half that of the bridge. If the train clears the bridge in 2 minutes, find the speed of the train in km/hr. [4 MARKS]

Discussion

4976.	The diameter of a sphere is 6 cm. It is melted and drawn in to a wire of diameter 2 mm. The length of the wire is(a) 12 m(b) 18 m(c) 36 m(d) 66 m
Answer» The diameter of a sphere is 6 cm. It is melted and drawn in to a wire of diameter 2 mm. The length of the wire is (a) 12 m (b) 18 m (c) 36 m (d) 66 m

Discussion

4977.	Question 2 (iii)Find the roots of the quadratic equations given in Q.1 above by applying the quadratic formula.(iii) 4x2+4√3x+3=0
Answer» Question 2 (iii) Find the roots of the quadratic equations given in Q.1 above by applying the quadratic formula. (iii) $4 x^{2} + 4 \sqrt{3} x + 3 = 0$

Discussion

4978.	An arc of length 20π cm subtends an angle of 144∘ at the centre of a circle. Find the radius of the circle.
Answer» An arc of length $20 π c m$ subtends an angle of $144^{\circ}$ at the centre of a circle. Find the radius of the circle.

Discussion

4979.	When 0o <θ< 90o and 3tan2 θ - 1 = 0. Then θ is equal to
Answer» When 0^o <θ< 90^o and 3tan² θ - 1 = 0. Then θ is equal to

Discussion

4980.	Two lines are drawn through the point (1, 3) one of slope and the other of slope −2. Write the coordinates of one more point on each of these lines. Prove that these lines are perpendicular to each other.
Answer» Two lines are drawn through the point (1, 3) one of slope and the other of slope −2. Write the coordinates of one more point on each of these lines. Prove that these lines are perpendicular to each other.

Discussion

4981.	Points A and b are 70km. a part on a highway. A car starts from A and another car starts from B simultaneously. If they travel in the same direction, they meet in 7 hours, but if they travel towards each other, they meet in one hour. Find the speed of the two cars.
Answer» Points A and b are 70km. a part on a highway. A car starts from A and another car starts from B simultaneously. If they travel in the same direction, they meet in 7 hours, but if they travel towards each other, they meet in one hour. Find the speed of the two cars.

Discussion

4982.	Question 4 Is it true to say that area of segment of a circle is less than the areas of its corresponding sector? Why?
Answer» Question 4 Is it true to say that area of segment of a circle is less than the areas of its corresponding sector? Why?

Discussion

4983.	In the given figure, CD and AB are intersecting chords and EF is a tangent to the circle. If OD = 4 cm, OB = 12 cm, OA = 4 cm and DE = 4 cm, then the length of EF is equal to
Answer» In the given figure, CD and AB are intersecting chords and EF is a tangent to the circle. If OD = 4 cm, OB = 12 cm, OA = 4 cm and DE = 4 cm, then the length of EF is equal to

Discussion

4984.	In the given figure, ABCD is a quadrilateral in which diagonal BD = 24 cm, AL ⊥ BD and CM ⊥ BD such that AL = 9 cm and CM = 12 cm. Calculate the area of the quadrilateral.
Answer» In the given figure, ABCD is a quadrilateral in which diagonal BD = 24 cm, AL $⊥$ BD and CM $⊥$ BD such that AL = 9 cm and CM = 12 cm. Calculate the area of the quadrilateral.

Discussion

4985.	Question 1 (i)Which of the following form an AP? Justify your answer.–1, –1, –1, –1, ……
Answer» Question 1 (i) Which of the following form an AP? Justify your answer. –1, –1, –1, –1, ……

Discussion

4986.	Question 4A well of diameter 3 m is dug 14 m deep. The earth taken out of it has been spread evenly all around it in the shape of a circular ring of width 4 m to form an embankment. Find the height of the embankment.
Answer» Question 4 A well of diameter 3 m is dug 14 m deep. The earth taken out of it has been spread evenly all around it in the shape of a circular ring of width 4 m to form an embankment. Find the height of the embankment.

Discussion

4987.	If cos3θ=√32; 0<θ<200, then the value of θ is:
Answer» If $cos 3 θ = \frac{\sqrt{3}}{2}; 0 < θ < 200$ , then the value of $θ$ is:

Discussion

4988.	The angle of elevation of the top of a tower from a distance 100 m from its foot is 30∘. The height of the tower is
Answer» The angle of elevation of the top of a tower from a distance 100 m from its foot is $30^{\circ}$ . The height of the tower is

Discussion

4989.	Question 5Write ‘True’ or ‘False’ and justify your answer in each of the following:If cosA+cos2A=1, then sin2A+sin4A=1
Answer» Question 5 Write ‘True’ or ‘False’ and justify your answer in each of the following: If $c o s A + c o s^{2} A = 1$ , then $s i n^{2} A + s i n^{4} A = 1$

Discussion

4990.	Rani, Molu and Rahul are three friends. They have ropes of length 2m, 3m and 5m respectively. If they tie a stone to one end of their ropes and swing them around, whose stone will travel along the biggest circle?
Answer» Rani, Molu and Rahul are three friends. They have ropes of length 2m, 3m and 5m respectively. If they tie a stone to one end of their ropes and swing them around, whose stone will travel along the biggest circle?

Discussion

4991.	The largest sphere is carved out of a cube of a side 7 cm. Find the volume of the sphere. (Approximate value)
Answer» The largest sphere is carved out of a cube of a side 7 cm. Find the volume of the sphere. (Approximate value)

Discussion

4992.	Question 19 The probability that a non-leap your selected at random will contains 53 Sunday is (a) 17 (b) 27 (c) 37 (d) 57
Answer» Question 19 The probability that a non-leap your selected at random will contains 53 Sunday is (a) $\frac{1}{7}$ (b) $\frac{2}{7}$ (c) $\frac{3}{7}$ (d) $\frac{5}{7}$

Discussion

4993.	Question 76 Solve the following: 4(3p+2)-5(6p-1)=2(p-8)-6(7p-4)
Answer» Question 76 Solve the following: 4(3p+2)-5(6p-1)=2(p-8)-6(7p-4)

4993.

Question 76 Solve the following: 4(3p+2)-5(6p-1)=2(p-8)-6(7p-4)

Answer»

Question 76

Solve the following:

4(3p+2)-5(6p-1)=2(p-8)-6(7p-4)

Discussion

4994.	A copper wire of diameter 6 mm is evenly wrapped on a cylinder of length 18 cm and diameter 49 cm to cover its whole surface. Find the length and the volume of the wire. If the density of the copper be 8.8 g per cm3, then find the weight of the wire.
Answer» A copper wire of diameter 6 mm is evenly wrapped on a cylinder of length 18 cm and diameter 49 cm to cover its whole surface. Find the length and the volume of the wire. If the density of the copper be 8.8 g per cm³, then find the weight of the wire.

Discussion

4995.	If A and B are two events, then the probability of occurrence of exactly one of A and B is _____________.
Answer» If A and B are two events, then the probability of occurrence of exactly one of A and B is _____________.

Discussion

4996.	A right triangle is formed by connecting the 3 coordinates A, B and C. Find the area of the ΔABC, if AB and BC are parallel to the coordinate axes as shown in figure.
Answer» A right triangle is formed by connecting the 3 coordinates A, B and C. Find the area of the $Δ A B C$ , if AB and BC are parallel to the coordinate axes as shown in figure.

Discussion

4997.	The minute hand of a clock is √21 cm long. Find the area described by the minute hand on the face of the clock between 7.00 AM and 7.05 AM.
Answer» The minute hand of a clock is $\sqrt{21}$ cm long. Find the area described by the minute hand on the face of the clock between 7.00 AM and 7.05 AM.

Discussion

4998.	Find the value of x.
Answer» Find the value of $x$ .

Discussion

4999.	If the points (−2, −1), (1, 0), (x, 3) and (1, y) form a parallelogram, find the values of x and y.
Answer» If the points (−2, −1), (1, 0), (x, 3) and (1, y) form a parallelogram, find the values of x and y.

Discussion

5000.	Find the common difference of an A.P. whose first term is 5 and the sum of its first four terms is half the sum of the next four terms.
Answer» Find the common difference of an A.P. whose first term is 5 and the sum of its first four terms is half the sum of the next four terms.

Discussion

Explore topic-wise InterviewSolutions in .

Two identical cubes of side 4 cm are placed one above the other, forming a cuboid. Find the total surface area of the cuboid thus formed.

In a circular dartboard of radius 20 cm, there are 5 concentric circles. the radius of each inner concentric circle is 4 cm less than the outer concentric circle. Find the probability that a dart hits anywhere in the smallest circle assuming that the dart doesn't hit on the boundary of any circle.

Tangents are drawn from the point(3,4)totheellipse4x^2+9y^2-36=0 touching ellipse at point A and B find the ortho centre of△ PAB

A girl fills a cylindrical bucket whose height is 32 cm and radius is 18 cm with sand. She empties the bucket on the ground and makes a conical heap of the sand. If the height of the conical heap is 24 cm, then find the slant height of the cone formed.

What is the difference between the interfascicular cambium and intra fascicular cambium ?

A toy is in the form of a cone of radius 3. 5 cm mounted on a hemisphere of same radius on its circular face. The total height of the toy is 15.5 cm. Find the total surface area of the toy.

A storage tank consists of a circular cylinder with a hemisphere adjoined on either end. If the external diameter of the cylinder by 1.4 m and its length be 8 m, find the cost of painting it on the outside at the rate of Rs. 10 per m2.

If a 1.5 m tall girl stands at a distance of 3 m from a lamp-post and casts a shadow of length 4.5 m on the ground, then the height of the lamp-post is(a) 1.5 m(b) 2 m(c) 2.5 m(d) 2.8 m

A boy bought a book for ₹x and sold it for ₹26. If his loss was x percent, find the second degree equation from which we can find cost price of the book.

A spherical ball of radius 3 cm is melted and recast into three spherical balls. The radii of the two balls are 1.5 cm and 2.0 cm. Find the radius of third ball.

ntProve that (a+b){(b+c)(c+a)}=2a(b+c)n ntn nt(a, b, c are with vector sign)n

Construct a frequency table from the following data: Marks No. of students less than 10 6 less than 20 15 less than 30 30 less than 40 39 less than 50 53 less than 60 70

How many silver coins, 1.75 cm in diameter and of thickness 2 mm, must be melted to form a cuboid of dimensions?

Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.

Using prime factorization, find the HCF and LCM of(i) 36, 84(ii) 23, 31(iii) 96, 404(iv) 144, 198(v) 396, 1080(vi) 1152, 1664

If k, 2k − 1 and 2k + 1 are three consecutive terms of an A.P., the value of k is(a) −2(b) 3(c) −3(d) 6

Sec70°Sin20°-Cos20°Cosec70° Evaluate

In the given figure, ABCD is a parallelogram with x : y = 1 : 1 and OE || AD. Then, (area of ΔADC + area of ΔBOC) : area of ΔODC is

Question 11Show that 12n cannot end with the digit 0 or 5 for any natural number n.

Electricity used by some families is shown in the following table. Find the mode for use of electricity. Use of electricity (Unit) 0 - 20 20 - 40 40 - 60 60 - 80 80 - 100 100 - 120 No. of families 13 50 70 100 80 17

If the point P(2,1) lies on the line segment joining points A(4,2) and B(8,4) then

47. For the same amount of work adult has done 6 hours less than a child. If they together come and work it would take 13hours12minute. Find the time taken by the child to complete this work

Question 2 (iv)Fill in the blanks:(iv) The common point of a tangent to a circle and the circle is called___.

The distance between the points (-3,0) and (4,0) is ___ units.

A man sees a train passing a bridge 1 km long. The length of the train is half that of the bridge. If the train clears the bridge in 2 minutes, find the speed of the train in km/hr. [4 MARKS]

The diameter of a sphere is 6 cm. It is melted and drawn in to a wire of diameter 2 mm. The length of the wire is(a) 12 m(b) 18 m(c) 36 m(d) 66 m

Question 2 (iii)Find the roots of the quadratic equations given in Q.1 above by applying the quadratic formula.(iii) 4x2+4√3x+3=0

An arc of length 20π cm subtends an angle of 144∘ at the centre of a circle. Find the radius of the circle.

When 0o &lt;θ&lt; 90o and 3tan2 θ - 1 = 0. Then θ is equal to

Two lines are drawn through the point (1, 3) one of slope and the other of slope −2. Write the coordinates of one more point on each of these lines. Prove that these lines are perpendicular to each other.

Points A and b are 70km. a part on a highway. A car starts from A and another car starts from B simultaneously. If they travel in the same direction, they meet in 7 hours, but if they travel towards each other, they meet in one hour. Find the speed of the two cars.

Question 4 Is it true to say that area of segment of a circle is less than the areas of its corresponding sector? Why?

In the given figure, CD and AB are intersecting chords and EF is a tangent to the circle. If OD = 4 cm, OB = 12 cm, OA = 4 cm and DE = 4 cm, then the length of EF is equal to

In the given figure, ABCD is a quadrilateral in which diagonal BD = 24 cm, AL ⊥ BD and CM ⊥ BD such that AL = 9 cm and CM = 12 cm. Calculate the area of the quadrilateral.

Question 1 (i)Which of the following form an AP? Justify your answer.–1, –1, –1, –1, ……

Question 4A well of diameter 3 m is dug 14 m deep. The earth taken out of it has been spread evenly all around it in the shape of a circular ring of width 4 m to form an embankment. Find the height of the embankment.

If cos3θ=√32; 0&lt;θ&lt;200, then the value of θ is:

The angle of elevation of the top of a tower from a distance 100 m from its foot is 30∘. The height of the tower is

Question 5Write ‘True’ or ‘False’ and justify your answer in each of the following:If cosA+cos2A=1, then sin2A+sin4A=1

Rani, Molu and Rahul are three friends. They have ropes of length 2m, 3m and 5m respectively. If they tie a stone to one end of their ropes and swing them around, whose stone will travel along the biggest circle?

The largest sphere is carved out of a cube of a side 7 cm. Find the volume of the sphere. (Approximate value)

Question 19 The probability that a non-leap your selected at random will contains 53 Sunday is (a) 17 (b) 27 (c) 37 (d) 57

Question 76 Solve the following: 4(3p+2)-5(6p-1)=2(p-8)-6(7p-4)

A copper wire of diameter 6 mm is evenly wrapped on a cylinder of length 18 cm and diameter 49 cm to cover its whole surface. Find the length and the volume of the wire. If the density of the copper be 8.8 g per cm3, then find the weight of the wire.

If A and B are two events, then the probability of occurrence of exactly one of A and B is _____________.

A right triangle is formed by connecting the 3 coordinates A, B and C. Find the area of the ΔABC, if AB and BC are parallel to the coordinate axes as shown in figure.

The minute hand of a clock is √21 cm long. Find the area described by the minute hand on the face of the clock between 7.00 AM and 7.05 AM.

Find the value of x.

If the points (−2, −1), (1, 0), (x, 3) and (1, y) form a parallelogram, find the values of x and y.

Find the common difference of an A.P. whose first term is 5 and the sum of its first four terms is half the sum of the next four terms.

When 0o <θ< 90o and 3tan2 θ - 1 = 0. Then θ is equal to

If cos3θ=√32; 0<θ<200, then the value of θ is: