32581 + Interview Questions in Mathematics Page 20 InterviewSolution

951.	An integer is chosen at random between 1 to 100 .find the probability that it is:(i) divisible by 8 (i)not divisible by 8.
Answer» An integer is chosen at random between 1 to 100 .find the probability that it is:(i) divisible by 8 (i)not divisible by 8.

Discussion

952.	Evaluate: cos225∘–sin265∘–tan245∘
Answer» Evaluate: ${cos}^{2} 25^{\circ} - {sin}^{2} 65^{\circ} - {tan}^{2} 45^{\circ}$

952.

Evaluate: cos225∘–sin265∘–tan245∘

Answer»

Evaluate:

${cos}^{2} 25^{\circ} - {sin}^{2} 65^{\circ} - {tan}^{2} 45^{\circ}$

Discussion

953.	Find x and y, if 2[130x]+[y012]=[5618]
Answer» Find $x$ and $y,$ if $2 [\begin{matrix} 1 & 3 0 & x \end{matrix}] + [\begin{matrix} y & 0 1 & 2 \end{matrix}] = [\begin{matrix} 5 & 6 1 & 8 \end{matrix}]$

Discussion

954.	A wooden toy is in the shape of a cone mounted on a cylinder, as shown in the figure. The total height of the toy is 26 cm, while the height of the conical part is 6 cm. The diameter of the base of the conical part is 5 cm and that of the cylindrical part is 4 cm. The conical part and the cylindrical part are respectively painted red and white. Find the area to be painted by each of these colours. [Take π=22/7.]
Answer» A wooden toy is in the shape of a cone mounted on a cylinder, as shown in the figure. The total height of the toy is 26 cm, while the height of the conical part is 6 cm. The diameter of the base of the conical part is 5 cm and that of the cylindrical part is 4 cm. The conical part and the cylindrical part are respectively painted red and white. Find the area to be painted by each of these colours. $[T a k e π = 22 / 7.]$

954.

A wooden toy is in the shape of a cone mounted on a cylinder, as shown in the figure. The total height of the toy is 26 cm, while the height of the conical part is 6 cm. The diameter of the base of the conical part is 5 cm and that of the cylindrical part is 4 cm. The conical part and the cylindrical part are respectively painted red and white. Find the area to be painted by each of these colours. [Take π=22/7.]

Answer»

A wooden toy is in the shape of a cone mounted on a cylinder, as shown in the figure. The total height of the toy is 26 cm, while the height of the conical part is 6 cm. The diameter of the base of the conical part is 5 cm and that of the cylindrical part is 4 cm. The conical part and the cylindrical part are respectively painted red and white. Find the area to be painted by each of these colours. $[T a k e π = 22 / 7.]$

Discussion

955.	The sum of four consecutive numbers in an AP is 32. The ratio of the product of the first and the last term to the product of the two middle terms is 7:15 . Find the numbers
Answer» The sum of four consecutive numbers in an AP is 32. The ratio of the product of the first and the last term to the product of the two middle terms is 7:15 . Find the numbers

Discussion

956.	The size of the minimum address bus which can be used to access a memory of size 1024×8 bit is ______10
Answer» $The size of the minimum address bus which can be used to access a memory of size 1024 \times 8 bit is ______$ 10

Discussion

957.	In triangle ABC, AB = AC = 8 cm, BC = 4 cm and P is a point in side AC such that AP = 6 cm. Prove that Δ BPC is similar to Δ ABC. Also, find the length of BP.
Answer» In triangle ABC, AB = AC = 8 cm, BC = 4 cm and P is a point in side AC such that AP = 6 cm. Prove that $Δ$ BPC is similar to $Δ$ ABC. Also, find the length of BP.

Discussion

958.	The pair of equation y=0 and y= -5 has _____ solution
Answer» The pair of equation y=0 and y= -5 has _____ solution

Discussion

959.	17×9 can be estimated to .
Answer» $17 \times 9$ can be estimated to .

Discussion

960.	From a solid cylinder of height 7n cm and base diameter 12 cm, a conical cavity of same height and same base diameter is hollowed out. Find the total surface area of the remaining solid. [Use =227] OR A cylindrical bucket, 32 cm high and with radius of base 18 cm, is filled with sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is 24 cm, then find the radius and slant height of the heap.
Answer» From a solid cylinder of height 7n cm and base diameter 12 cm, a conical cavity of same height and same base diameter is hollowed out. Find the total surface area of the remaining solid. [Use $= \frac{22}{7}$ ] OR A cylindrical bucket, 32 cm high and with radius of base 18 cm, is filled with sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is 24 cm, then find the radius and slant height of the heap.

Discussion

961.	4x3+x2+5x+8 = (x+1) × .
Answer» $4 x^{3} + x^{2} + 5 x + 8$ = $(x + 1)$ $\times$ .

Discussion

962.	Find the 2 consecutive odd positive integer sum of whose square is 290
Answer» Find the 2 consecutive odd positive integer sum of whose square is 290

Discussion

963.	The radii of ends of a frustum are 14 cm and 6 cm respectively and its height is 6 cm. Find its i) curved surface area ii) total surface areaiii ) volume (π= 3.14)
Answer» The radii of ends of a frustum are 14 cm and 6 cm respectively and its height is 6 cm. Find its i) curved surface area ii) total surface area iii ) volume ( $π$ = 3.14)

Discussion

964.	The coordinates of a point on x-axis which lies on the perpendicular bisector of the line segment joining the points (7, 6) and (−3, 4) are(a) (0, 2)(b) (3, 0)(c) (0, 3)(d) (2, 0)
Answer» The coordinates of a point on x-axis which lies on the perpendicular bisector of the line segment joining the points (7, 6) and (−3, 4) are (a) (0, 2) (b) (3, 0) (c) (0, 3) (d) (2, 0)

Discussion

965.	The value of n – 1Pr + r n – 1Pr – 1 is __________.
Answer» The value of ^{n – 1}P_r + r ^{n – 1}P_r_{– 1} is __________.

Discussion

966.	In the given figure, ABCD is a trapezium. The curved surface area of the solid obtained when given trapezium is revolved about AD is
Answer» In the given figure, ABCD is a trapezium. The curved surface area of the solid obtained when given trapezium is revolved about AD is

Discussion

967.	Distance between points A(-1,2)and B(3,4)?
Answer» Distance between points A(-1,2)and B(3,4)?

Discussion

968.	In the given figure, if AOC is a diameter of the circle and AXB = 12 are BYC, then ∠BOC = __________.
Answer» In the given figure, if AOC is a diameter of the circle and AXB = $\frac{1}{2}$ are BYC, then ∠BOC = __________.

Discussion

969.	In the figure below, ΔABC is equilateral and O is its circumcentre.Prove that the length of AD is equal to the radius of the circle.
Answer» In the figure below, ΔABC is equilateral and O is its circumcentre. Prove that the length of AD is equal to the radius of the circle.

969.

In the figure below, ΔABC is equilateral and O is its circumcentre.Prove that the length of AD is equal to the radius of the circle.

Answer»

In the figure below, ΔABC is equilateral and O is its circumcentre.

Prove that the length of AD is equal to the radius of the circle.

Discussion

970.	Three consecutive integers add up to 51. What are these integers?
Answer» Three consecutive integers add up to 51. What are these integers?

Discussion

971.	If a, b and c are in A.P, then which of the following seies does not form an A.P.?
Answer» If a, b and c are in A.P, then which of the following seies does not form an A.P.?

Discussion

972.	The first and the last terms of an AP are 5 and 45 respectively. If the sum of all its terms is 400, find the common difference and the number of terms. [CBSE 2012, 14]
Answer» The first and the last terms of an AP are 5 and 45 respectively. If the sum of all its terms is 400, find the common difference and the number of terms. [CBSE 2012, 14]

Discussion

973.	Find the frequency of 40 in the given set of data.10, 40, 80, 100, 60, 40, 30, 40, 20, 40.4
Answer» Find the frequency of 40 in the given set of data. 10, 40, 80, 100, 60, 40, 30, 40, 20, 40. 4

Discussion

974.	In what ratio does the point P(p,-1) divides the line segment joining the points A(1,-3) B(6,2) hence find value of p?
Answer» In what ratio does the point P(p,-1) divides the line segment joining the points A(1,-3) B(6,2) hence find value of p?

Discussion

975.	Question 7In Fig. 12.25, ABCD is a square of side 14 cm. With centres A, B, C and D, four circles are drawn such that each circle touches externally two of the remaining three circles. Find the area of the shaded region.
Answer» Question 7 In Fig. 12.25, ABCD is a square of side 14 cm. With centres A, B, C and D, four circles are drawn such that each circle touches externally two of the remaining three circles. Find the area of the shaded region.

Discussion

976.	36. Find the equation of a circle with centre (1/2 , 1/4) and radius 1/12 .
Answer» 36. Find the equation of a circle with centre (1/2 , 1/4) and radius 1/12 .

Discussion

977.	Write a pair of irrational numbers whose difference is irrational.
Answer» Write a pair of irrational numbers whose difference is irrational.

Discussion

978.	A quadrilateral ABCD is drawn to circumscribe a circle (see given figure) Prove that AB + CD = AD + BC
Answer» A quadrilateral ABCD is drawn to circumscribe a circle (see given figure) Prove that AB + CD = AD + BC

978.

A quadrilateral ABCD is drawn to circumscribe a circle (see given figure) Prove that AB + CD = AD + BC

Answer»

A quadrilateral ABCD is drawn to circumscribe a circle (see given figure) Prove that AB + CD = AD + BC

Discussion

979.	For a triangle ABC, which of the following statements is true?
Answer» For a triangle ABC, which of the following statements is true?

Discussion

980.	If a person is looking down at an object, then the angle the man’s line of sight makes with his eye level is the angle of ___.
Answer» If a person is looking down at an object, then the angle the man’s line of sight makes with his eye level is the angle of ___.

Discussion

981.	From the given data, find the average speed of Jack (in km/hr).
Answer» From the given data, find the average speed of Jack (in km/hr).

981.

From the given data, find the average speed of Jack (in km/hr).

Answer»

From the given data, find the average speed of Jack (in km/hr).

Discussion

982.	The slant height of a conical mountain is 2.5 km and the area of its base is 1.54 km2. Find the height of the mountain.
Answer» The slant height of a conical mountain is 2.5 km and the area of its base is 1.54 $k m^{2}$ . Find the height of the mountain.

Discussion

983.	Question 20 A pen stand made of wood is in the shape of a cuboid with four conical depressions and a cubical depression to hold the pens and pins, respectively. The dimension of the cuboid are 10 cm, 5 cm and 4 cm. The radius of each of the conical depressions is 0.5 cm and the depth is 2.1 cm. The edge of the cubical depression is 3 cm. Find the volume of the wood in the entire stand.
Answer» Question 20 A pen stand made of wood is in the shape of a cuboid with four conical depressions and a cubical depression to hold the pens and pins, respectively. The dimension of the cuboid are 10 cm, 5 cm and 4 cm. The radius of each of the conical depressions is 0.5 cm and the depth is 2.1 cm. The edge of the cubical depression is 3 cm. Find the volume of the wood in the entire stand.

Discussion

984.	Write down the decimal expansions of those rational numbers in Question 1 above which have terminating decimal expansions.
Answer» Write down the decimal expansions of those rational numbers in Question 1 above which have terminating decimal expansions.

Discussion

985.	It is required to colour paint a glass cylindrical chimney of height 20 m and base diameter 14 m. Find the area to be painted.(π=227)
Answer» It is required to colour paint a glass cylindrical chimney of height 20 m and base diameter 14 m. Find the area to be painted.( $π = \frac{22}{7}$ )

Discussion

986.	In the given figure, tangents PQ and PR are drawn from an external point to a circle with centre O, such that ∠RPQ=30°. A chord RS is drawn parallel to the tangent PQ. Find ∠RQS. [CBSE 2015]
Answer» In the given figure, tangents PQ and PR are drawn from an external point to a circle with centre O, such that $∠ RPQ = 30 °$ . A chord RS is drawn parallel to the tangent PQ. Find $∠ RQS$ . [CBSE 2015]

Discussion

987.	x=-t^3+(t*-3)solve for dx/dtand integrate of this
Answer» x=-t^3+(t*-3) solve for dx/dt and integrate of this

Discussion

988.	A two digit number is to be formed from the digits 0, 1, 2, 3, 4. Repetition of the digits is allowed. Find the probability that the number so formed is a -(1) prime number(2) multiple of 4(3) multiple of 11.
Answer» A two digit number is to be formed from the digits 0, 1, 2, 3, 4. Repetition of the digits is allowed. Find the probability that the number so formed is a - (1) prime number (2) multiple of 4 (3) multiple of 11.

Discussion

989.	Find the coordinates of a point P, which lies on the line segment joining the points A (− 2, − 2) and B (2, − 4) such that AP=37AB
Answer» Find the coordinates of a point P, which lies on the line segment joining the points A (− 2, − 2) and B (2, − 4) such that $AP = \frac{3}{7} AB$

Discussion

990.	If the third and the eighth terms of an AP are 9 and -6 respectively, which term of this AP is zero?
Answer» If the third and the eighth terms of an AP are 9 and -6 respectively, which term of this AP is zero?

Discussion

991.	ABC is a right angled triangle with ∠ABC=90∘, the centre of the circle passing through A,B,C lies on _______.
Answer» ABC is a right angled triangle with $∠$ ABC= $90^{\circ}$ , the centre of the circle passing through A,B,C lies on _______.

Discussion

992.	What will be the cost of making a closed cone of tin sheet having radius of base 6 m and slant height 8 m if the rate of making isRs.10 per sq.m ?
Answer» What will be the cost of making a closed cone of tin sheet having radius of base 6 m and slant height 8 m if the rate of making is Rs.10 per sq.m ?

Discussion

993.	If x^2-1 is a factor of ax^4+bx^3+cx^3 +dx+e, then show that a+c+e=b+d=0.
Answer» If x^2-1 is a factor of ax^4+bx^3+cx^3 +dx+e, then show that a+c+e=b+d=0.

Discussion

994.	Rajiv purchases a table for Rs. 756 including sales tax. If the sales tax is 8% find the sale price.
Answer» Rajiv purchases a table for Rs. 756 including sales tax. If the sales tax is 8% find the sale price.

Discussion

995.	Question 21 (ii) Find the sum: (4−1n)+(4−2n)+(4−3n)+⋯upto n terms
Answer» Question 21 (ii) Find the sum: $(4 - \frac{1}{n}) + (4 - \frac{2}{n}) + (4 - \frac{3}{n}) + \dots u p t o n t e r m s$

Discussion

996.	If x=acos3θ and y=bsin3θ, prove that (xa)23+(yb)23=1
Answer» If $x = a c o s^{3} θ$ and $y = b s i n^{3} θ$ , prove that ${(\frac{x}{a})}^{\frac{2}{3}} + {(\frac{y}{b})}^{\frac{2}{3}} = 1$

Discussion

997.	If a wire is bent into the shape of a square, then the area of the square is 81 cm2 . When wire is bent into a semi-circular shape, then the area of the semi-circle will be(a) 22 cm2(b) 44 cm2(c) 77 cm2(d) 154 cm2
Answer» If a wire is bent into the shape of a square, then the area of the square is 81 cm² . When wire is bent into a semi-circular shape, then the area of the semi-circle will be (a) 22 cm² (b) 44 cm² (c) 77 cm² (d) 154 cm²

Discussion

998.	A toy is in the form of a cone surmounted on a hemisphere. The diameter of the base and the height of the cone are 6 cm and 4 cm, respectively. Determine the surface area of the toy. (Use π = 3.14)
Answer» A toy is in the form of a cone surmounted on a hemisphere. The diameter of the base and the height of the cone are 6 cm and 4 cm, respectively. Determine the surface area of the toy. (Use π = 3.14)

Discussion

999.	compute the modal value of the following frequency x : 95 105 115 125 135 145 155 165 175 y : 4 2 18 22 21 19 10 3 2by groping table & analysis table
Answer» compute the modal value of the following frequency x : 95 105 115 125 135 145 155 165 175 y : 4 2 18 22 21 19 10 3 2 by groping table & analysis table

Discussion

1000.	A 1.5-m-tall boy is standing at some distance from a 30-m-tall building. The angle of elevation from his eyes to the top of the building increases from 30∘ to 60∘ as he walks towards the building. Find the distance he walked towards the building. [4 MARKS]
Answer» A 1.5-m-tall boy is standing at some distance from a 30-m-tall building. The angle of elevation from his eyes to the top of the building increases from $30^{\circ}$ to $60^{\circ}$ as he walks towards the building. Find the distance he walked towards the building. [4 MARKS]

Discussion

Explore topic-wise InterviewSolutions in .

An integer is chosen at random between 1 to 100 .find the probability that it is:(i) divisible by 8 (i)not divisible by 8.

Evaluate: cos225∘–sin265∘–tan245∘

Find x and y, if 2[130x]+[y012]=[5618]

The sum of four consecutive numbers in an AP is 32. The ratio of the product of the first and the last term to the product of the two middle terms is 7:15 . Find the numbers

The size of the minimum address bus which can be used to access a memory of size 1024×8 bit is ______10

In triangle ABC, AB = AC = 8 cm, BC = 4 cm and P is a point in side AC such that AP = 6 cm. Prove that Δ BPC is similar to Δ ABC. Also, find the length of BP.

The pair of equation y=0 and y= -5 has _____ solution

17×9 can be estimated to .

4x3+x2+5x+8 = (x+1) × .

Find the 2 consecutive odd positive integer sum of whose square is 290

The radii of ends of a frustum are 14 cm and 6 cm respectively and its height is 6 cm. Find its i) curved surface area ii) total surface areaiii ) volume (π= 3.14)

The coordinates of a point on x-axis which lies on the perpendicular bisector of the line segment joining the points (7, 6) and (−3, 4) are(a) (0, 2)(b) (3, 0)(c) (0, 3)(d) (2, 0)

The value of n – 1Pr + r n – 1Pr – 1 is __________.

In the given figure, ABCD is a trapezium. The curved surface area of the solid obtained when given trapezium is revolved about AD is

Distance between points A(-1,2)and B(3,4)?

In the given figure, if AOC is a diameter of the circle and AXB = 12 are BYC, then ∠BOC = __________.

In the figure below, ΔABC is equilateral and O is its circumcentre.Prove that the length of AD is equal to the radius of the circle.

Three consecutive integers add up to 51. What are these integers?

If a, b and c are in A.P, then which of the following seies does not form an A.P.?

The first and the last terms of an AP are 5 and 45 respectively. If the sum of all its terms is 400, find the common difference and the number of terms. [CBSE 2012, 14]

Find the frequency of 40 in the given set of data.10, 40, 80, 100, 60, 40, 30, 40, 20, 40.4

In what ratio does the point P(p,-1) divides the line segment joining the points A(1,-3) B(6,2) hence find value of p?

Question 7In Fig. 12.25, ABCD is a square of side 14 cm. With centres A, B, C and D, four circles are drawn such that each circle touches externally two of the remaining three circles. Find the area of the shaded region.

36. Find the equation of a circle with centre (1/2 , 1/4) and radius 1/12 .

Write a pair of irrational numbers whose difference is irrational.

A quadrilateral ABCD is drawn to circumscribe a circle (see given figure) Prove that AB + CD = AD + BC

For a triangle ABC, which of the following statements is true?

If a person is looking down at an object, then the angle the man’s line of sight makes with his eye level is the angle of ___.

From the given data, find the average speed of Jack (in km/hr).

The slant height of a conical mountain is 2.5 km and the area of its base is 1.54 km2. Find the height of the mountain.

Write down the decimal expansions of those rational numbers in Question 1 above which have terminating decimal expansions.

It is required to colour paint a glass cylindrical chimney of height 20 m and base diameter 14 m. Find the area to be painted.(π=227)

In the given figure, tangents PQ and PR are drawn from an external point to a circle with centre O, such that ∠RPQ=30°. A chord RS is drawn parallel to the tangent PQ. Find ∠RQS. [CBSE 2015]

x=-t^3+(t*-3)solve for dx/dtand integrate of this

A two digit number is to be formed from the digits 0, 1, 2, 3, 4. Repetition of the digits is allowed. Find the probability that the number so formed is a -(1) prime number(2) multiple of 4(3) multiple of 11.

Find the coordinates of a point P, which lies on the line segment joining the points A (− 2, − 2) and B (2, − 4) such that AP=37AB

If the third and the eighth terms of an AP are 9 and -6 respectively, which term of this AP is zero?

ABC is a right angled triangle with ∠ABC=90∘, the centre of the circle passing through A,B,C lies on _______.

What will be the cost of making a closed cone of tin sheet having radius of base 6 m and slant height 8 m if the rate of making isRs.10 per sq.m ?

If x^2-1 is a factor of ax^4+bx^3+cx^3 +dx+e, then show that a+c+e=b+d=0.

Rajiv purchases a table for Rs. 756 including sales tax. If the sales tax is 8% find the sale price.

Question 21 (ii) Find the sum: (4−1n)+(4−2n)+(4−3n)+⋯upto n terms

If x=acos3θ and y=bsin3θ, prove that (xa)23+(yb)23=1

If a wire is bent into the shape of a square, then the area of the square is 81 cm2 . When wire is bent into a semi-circular shape, then the area of the semi-circle will be(a) 22 cm2(b) 44 cm2(c) 77 cm2(d) 154 cm2

A toy is in the form of a cone surmounted on a hemisphere. The diameter of the base and the height of the cone are 6 cm and 4 cm, respectively. Determine the surface area of the toy. (Use π = 3.14)

compute the modal value of the following frequency x : 95 105 115 125 135 145 155 165 175 y : 4 2 18 22 21 19 10 3 2by groping table & analysis table

A 1.5-m-tall boy is standing at some distance from a 30-m-tall building. The angle of elevation from his eyes to the top of the building increases from 30∘ to 60∘ as he walks towards the building. Find the distance he walked towards the building. [4 MARKS]