32581 + Interview Questions in Mathematics Page 80 InterviewSolution

3951.	Select the correct graph for the equation y=−x2+(m+n)x+mn, if m > 0 and n > 0.
Answer» Select the correct graph for the equation $y = - x^{2} + (m + n) x + m n$ , if m > 0 and n > 0.

Discussion

3952.	If x=A[e^(-kt/2)]cos(pt+€) and A,k,p,€ are constant then prove that d²x/dt²+kdx/dt+n²x=0 where n²=p²+¼k²
Answer» If x=A[e^(-kt/2)]cos(pt+€) and A,k,p,€ are constant then prove that d²x/dt²+kdx/dt+n²x=0 where n²=p²+¼k²

Discussion

3953.	Consider a square ABCD of diagonal length 4√3. The square is folded along the diagonal AC so that the plane of ΔABC is perpendicular to the plane of ΔADC. The shortest distance between AB and CD is
Answer» Consider a square ABCD of diagonal length 4√3. The square is folded along the diagonal AC so that the plane of ΔABC is perpendicular to the plane of ΔADC. The shortest distance between AB and CD is

Discussion

3954.	(a) It is required to make a hollow cone 24 cm high whose base radius is 7 cm. Find the area of the sheet metal required including the base. Also, find the capacity of this cone. (b) The radius and the slant height of a cone are in the ratio 4 : 7. If its curved surface area is 792 cm2, find its radius (Use π=227) [6 MARKS]
Answer» (a) It is required to make a hollow cone 24 cm high whose base radius is 7 cm. Find the area of the sheet metal required including the base. Also, find the capacity of this cone. (b) The radius and the slant height of a cone are in the ratio 4 : 7. If its curved surface area is 792 $c m^{2}$ , find its radius $(U s e π = \frac{22}{7})$ [6 MARKS]

Discussion

3955.	Identify the incorrect statement.
Answer» Identify the incorrect statement.

Discussion

3956.	In a particular section of Class IX, 40 students were asked about the months of their birth and the following graph was prepared for the data so obtained: Find the probability that a student of the class was born in August.
Answer» In a particular section of Class IX, 40 students were asked about the months of their birth and the following graph was prepared for the data so obtained: Find the probability that a student of the class was born in August.

Discussion

3957.	Water is dripping out from a conical funnel a uniform rate of 4 cm cube per second through a tiny hole at the vortex in the bottom when the slant height of the water is 3 cm find the rate of decrease of slant height of the water given that the Vertical angle of the funnel is 120 degree
Answer» Water is dripping out from a conical funnel a uniform rate of 4 cm cube per second through a tiny hole at the vortex in the bottom when the slant height of the water is 3 cm find the rate of decrease of slant height of the water given that the Vertical angle of the funnel is 120 degree

Discussion

3958.	If the point C (–1,2) divides the lines segment AB in the ratio 3 : 4, where the co-ordinates of A is (2, 5), then coordinates of B is
Answer» If the point C (–1,2) divides the lines segment AB in the ratio 3 : 4, where the co-ordinates of A is (2, 5), then coordinates of B is

Discussion

3959.	Taylor purchased a rectangular plot of area 634 m2. The length of the plot is 2 m more than thrice its breadth. Then find the approximate values of length and breadth of the plot.
Answer» Taylor purchased a rectangular plot of area $634 m^{2}$ . The length of the plot is 2 m more than thrice its breadth. Then find the approximate values of length and breadth of the plot.

Discussion

3960.	Which of the following represents a pair of dependent equations?
Answer» Which of the following represents a pair of dependent equations?

Discussion

3961.	In a right triangle ABC, right-angled at B, if tan A = 1, then what equals 2 sin A cos A?1
Answer» In a right triangle ABC, right-angled at B, if tan A = 1, then what equals 2 sin A cos A? 1

Discussion

3962.	If sec theta =13/5 then find sin theta +cos theta
Answer» If sec theta =13/5 then find sin theta +cos theta

Discussion

3963.	Which of the following are not quadratic polynomials? (i) 3+4x–7x2 (ii) 8x2–15 (iii) 6x – 15 (iv) 4x3–3x
Answer» Which of the following are not quadratic polynomials? (i) $3 + 4 x - 7 x^{2}$ (ii) $8 x^{2} - 15$ (iii) 6x – 15 (iv) $4 x^{3} - 3 x$

3963.

Which of the following are not quadratic polynomials? (i) 3+4x–7x2 (ii) 8x2–15 (iii) 6x – 15 (iv) 4x3–3x

Answer»

Which of the following are not quadratic polynomials?
(i) $3 + 4 x - 7 x^{2}$

(ii) $8 x^{2} - 15$

(iii) 6x – 15

(iv) $4 x^{3} - 3 x$

Discussion

3964.	In △ABC, AB = 3 cm, AC = 4 cm and AD is the bisector of ∠A. Then, BD : DC is —
Answer» In $△$ ABC, AB = 3 cm, AC = 4 cm and AD is the bisector of $∠$ A. Then, BD : DC is —

Discussion

3965.	In △ABC, DE is parallel to base BC, with D on AB and E on AC. If ADDB=23, find BCDE
Answer» In $△ A B C$ , DE is parallel to base BC, with D on AB and E on AC. If $\frac{A D}{D B} = \frac{2}{3}$ , find $\frac{B C}{D E}$

Discussion

3966.	Question 11Simplify: (1+tan2 θ)(1−sin θ)(1+sin θ)
Answer» Question 11 Simplify: $(1 + t a n^{2} θ) (1 - s i n θ) (1 + s i n θ)$

Discussion

3967.	The volume of ship and the volume of its model is given. In which of the following cases is K= 120
Answer» The volume of ship and the volume of its model is given. In which of the following cases is K= $\frac{1}{20}$

Discussion

3968.	The diameter of the base of a right circular cone is 42 cm and its height is 20 cm. Find the curved surface area of the cone.
Answer» The diameter of the base of a right circular cone is 42 cm and its height is 20 cm. Find the curved surface area of the cone.

Discussion

3969.	Question 7 The curved surface area of a frustum of a cone is π(r1+r2)l, where l=√h2+(r1+r2)2 r1 and r2 are the radii of the two ends of the frustum and h is the vertical height.
Answer» Question 7 The curved surface area of a frustum of a cone is $π (r_{1} + r_{2}) l$ , where $l = \sqrt{h^{2} + (r_{1} + r_{2})^{2}}$ $r_{1} a n d r_{2}$ are the radii of the two ends of the frustum and h is the vertical height.

Discussion

3970.	Find the lengths of the medians of a triangle whose vertices are A (−1,3), B(1,−1) and C(5, 1).
Answer» Find the lengths of the medians of a triangle whose vertices are A (−1,3), B(1,−1) and C(5, 1).

Discussion

3971.	The value of sec−1(2√3)+cot−1(−1√3)+tan−1√3 is
Answer» The value of ${sec}^{- 1} (\frac{2}{\sqrt{3}}) + {cot}^{- 1} (- \frac{1}{\sqrt{3}}) + {tan}^{- 1} \sqrt{3}$ is

Discussion

3972.	Find the sum of all even integers between 101 and 999.
Answer» Find the sum of all even integers between 101 and 999.

Discussion

3973.	One of the zero of cubic polynomial ax^3+bx^2+cx+d is 0(zero).Find the other two zeroes.
Answer» One of the zero of cubic polynomial ax^3+bx^2+cx+d is 0(zero). Find the other two zeroes.

Discussion

3974.	Identify the matrix whose order is 4×3
Answer» Identify the matrix whose order is $4 \times 3$

Discussion

3975.	The zeros of the polynomial f(x) = 2x³ - 9x² + x + 12 are:
Answer» The zeros of the polynomial f(x) = 2x³ - 9x² + x + 12 are:

Discussion

3976.	In the given figure below, OACB is a quadrant of a circle. The radius OA = 3.5 cm, OD = 2 cm. Calculate the area of the shaded region.
Answer» In the given figure below, OACB is a quadrant of a circle. The radius OA = 3.5 cm, OD = 2 cm. Calculate the area of the shaded region.

3976.

In the given figure below, OACB is a quadrant of a circle. The radius OA = 3.5 cm, OD = 2 cm. Calculate the area of the shaded region.

Answer»

In the given figure below, OACB is a quadrant of a circle. The radius OA = 3.5 cm, OD = 2 cm. Calculate the area of the shaded region.

Discussion

3977.	Question 80Solve the following:Rs. 13500 are to be distributed among Salma, Kiran and Jenifer in such a way that Salma gets Rs. 1000 more than Kiran and Jenifer gets Rs. 500 more than Kiran. Find the money received by Jenifer.
Answer» Question 80 Solve the following: Rs. 13500 are to be distributed among Salma, Kiran and Jenifer in such a way that Salma gets Rs. 1000 more than Kiran and Jenifer gets Rs. 500 more than Kiran. Find the money received by Jenifer.

3977.

Question 80Solve the following:Rs. 13500 are to be distributed among Salma, Kiran and Jenifer in such a way that Salma gets Rs. 1000 more than Kiran and Jenifer gets Rs. 500 more than Kiran. Find the money received by Jenifer.

Answer»

Question 80

Solve the following:

Rs. 13500 are to be distributed among Salma, Kiran and Jenifer in such a way that Salma gets Rs. 1000 more than Kiran and Jenifer gets Rs. 500 more than Kiran. Find the money received by Jenifer.

Discussion

3978.	The area of a rectangular plot is 528 m2. The length of the plot (in metres) is one metre more then twice its breadth. Find the length and the breadth of the plot.
Answer» The area of a rectangular plot is 528 m². The length of the plot (in metres) is one metre more then twice its breadth. Find the length and the breadth of the plot.

Discussion

3979.	5. A solid cylinder has diameter 28cm and height 24cm. A conical cavity of the same diameter and same height is drilled out from this solid. Find the whole surface area of the coni cal solid
Answer» 5. A solid cylinder has diameter 28cm and height 24cm. A conical cavity of the same diameter and same height is drilled out from this solid. Find the whole surface area of the coni cal solid

Discussion

3980.	The probability of India winning an India-Pakistan match could be
Answer» The probability of India winning an India-Pakistan match could be

Discussion

3981.	The shaded region OAB is known as:
Answer» The shaded region OAB is known as:

3981.

The shaded region OAB is known as:

Answer»

The shaded region OAB is known as:

Discussion

3982.	On dividing a positive integer n by 9 we get 7 as remainder. What will be the remainder if (3n−1) is divided by 9?
Answer» On dividing a positive integer $n$ by $9$ we get $7$ as remainder. What will be the remainder if $(3 n - 1)$ is divided by $9$ ?

Discussion

3983.	If cos(A+B) = 0 then sin(A-B) can be equal to
Answer» If cos(A+B) = 0 then sin(A-B) can be equal to

Discussion

3984.	Two years ago, a father was five times as old as his son. Two years later, his age will be 8 more than three times the age of the son. Find the present ages of father and son.
Answer» Two years ago, a father was five times as old as his son. Two years later, his age will be 8 more than three times the age of the son. Find the present ages of father and son.

Discussion

3985.	A chord of a circle of radius 20 cm sub tends an angle of 900 at the centre . Find the area of the corresponding major segment of the circle( Use π = 3.14)
Answer» A chord of a circle of radius 20 cm sub tends an angle of 90⁰ at the centre . Find the area of the corresponding major segment of the circle ( Use $π = 3.14$ )

Discussion

3986.	A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to 1 cm and the height of the cone is equal to its radius. Find the volume of the solid in terms of π. [2 MARKS]
Answer» A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to 1 cm and the height of the cone is equal to its radius. Find the volume of the solid in terms of $π$ . [2 MARKS]

Discussion

3987.	Under Exclusive method, (a) the upper class limit of a class is excluded in the class interval (b) the upper class limit of a class is included in the class interval (c) the lower class limit of a class is excluded in the class interval (d) the lower class limit of a class is included in the class interval
Answer» Under Exclusive method, (a) the upper class limit of a class is excluded in the class interval (b) the upper class limit of a class is included in the class interval (c) the lower class limit of a class is excluded in the class interval (d) the lower class limit of a class is included in the class interval

3987.

Under Exclusive method, (a) the upper class limit of a class is excluded in the class interval (b) the upper class limit of a class is included in the class interval (c) the lower class limit of a class is excluded in the class interval (d) the lower class limit of a class is included in the class interval

Answer»

Under Exclusive method,

(a) the upper class limit of a class is excluded in the class interval

(b) the upper class limit of a class is included in the class interval

(c) the lower class limit of a class is excluded in the class interval

(d) the lower class limit of a class is included in the class interval

Discussion

3988.	A container shaped like a right circular cylinder having diameter 12 cm and height 15 cm is full of ice cream. The ice cream is to be filled into cones of height 12 cm and diameter 6 cm, having a hemispherical shape on the top. Find the number of such cones which can be filled with ice cream.
Answer» A container shaped like a right circular cylinder having diameter 12 cm and height 15 cm is full of ice cream. The ice cream is to be filled into cones of height 12 cm and diameter 6 cm, having a hemispherical shape on the top. Find the number of such cones which can be filled with ice cream.

Discussion

3989.	If BC \|\| EF and FG \|\| CD then, AEAB= ?
Answer» If BC \|\| EF and FG \|\| CD then, $\frac{A E}{A B} =$ ?

Discussion

3990.	The term for reduction in marked price is___
Answer» The term for reduction in marked price is___

Discussion

3991.	If AB is a tangent to a circle at B and ACD any other chord then ABsquare=ACAD.
Answer» If AB is a tangent to a circle at B and ACD any other chord then ABsquare=ACAD.

Discussion

3992.	Draw a circle of radius 3.4 cm and centre E. Take a point F on the circle. Take another point A such that E-F-A and FA = 4.1 cm. Draw tangents to the circle from point A.
Answer» Draw a circle of radius 3.4 cm and centre E. Take a point F on the circle. Take another point A such that E-F-A and FA = 4.1 cm. Draw tangents to the circle from point A.

Discussion

3993.	In the given figure, PQ is a chord of length 8cm of a circle of radius 5cm. The tangents at P and Q intersect at a point T. Find the length TP. [4 MARKS]
Answer» In the given figure, PQ is a chord of length 8cm of a circle of radius 5cm. The tangents at P and Q intersect at a point T. Find the length TP. [4 MARKS]

3993.

In the given figure, PQ is a chord of length 8cm of a circle of radius 5cm. The tangents at P and Q intersect at a point T. Find the length TP. [4 MARKS]

Answer»

In the given figure, PQ is a chord of length 8cm of a circle of radius 5cm. The tangents at P and Q intersect at a point T. Find the length TP. [4 MARKS]

Discussion

3994.	If cosec A + cot A=11/2 then find tan A
Answer» If cosec A + cot A=11/2 then find tan A

Discussion

3995.	Question 2 (iii) Find the LCM and HCF of 336, 54 and verify that LCM × HCF = product of the two numbers.
Answer» Question 2 (iii) Find the LCM and HCF of 336, 54 and verify that LCM $\times$ HCF = product of the two numbers.

Discussion

3996.	In figure, ABCD is a trapezium in which AB \|\| DC and AB = 2DC. Determine the ratio of the areas of △AOB and △COD.
Answer» In figure, ABCD is a trapezium in which AB \|\| DC and AB = 2DC. Determine the ratio of the areas of $△$ AOB and $△$ COD.

3996.

In figure, ABCD is a trapezium in which AB || DC and AB = 2DC. Determine the ratio of the areas of △AOB and △COD.

Answer»

In figure, ABCD is a trapezium in which AB || DC and AB = 2DC. Determine the ratio of the areas of $△$ AOB and $△$ COD.

Discussion

3997.	1 + tan2A = sec2A is valid for which of the following ranges
Answer» 1 + $t a n^{2} A$ = $s e c^{2} A$ is valid for which of the following ranges

Discussion

3998.	Write a rational number between √3 and 2.
Answer» Write a rational number between $\sqrt{3}$ and 2.

Discussion

3999.	To construct a triangle similar to ΔABC in which BC = 4.5 cm, ∠B=45∘ and ∠C=60∘, using a scale factor of 37, BC will be divided in the ratio (i) 3 : 4 (ii) 4 : 7 (c) 3 : 10 (d) 3 : 7
Answer» To construct a triangle similar to $Δ A B C$ in which BC = 4.5 cm, $∠ B = 45^{\circ} a n d ∠ C = 60^{\circ},$ using a scale factor of $\frac{3}{7},$ BC will be divided in the ratio (i) 3 : 4 (ii) 4 : 7 (c) 3 : 10 (d) 3 : 7

3999.

To construct a triangle similar to ΔABC in which BC = 4.5 cm, ∠B=45∘ and ∠C=60∘, using a scale factor of 37, BC will be divided in the ratio (i) 3 : 4 (ii) 4 : 7 (c) 3 : 10 (d) 3 : 7

Answer»

To construct a triangle similar to $Δ A B C$ in which BC = 4.5 cm, $∠ B = 45^{\circ} a n d ∠ C = 60^{\circ},$ using a scale factor of $\frac{3}{7},$ BC will be divided in the ratio

(i) 3 : 4 (ii) 4 : 7 (c) 3 : 10 (d) 3 : 7

Discussion

4000.	An aeroplane departed 30 minutes later than its scheduled time and in order to reach its destination which is 1500 km away on time, it had to increase its speed by 250 km/hr. Its original speed is ___ km/hr.
Answer» An aeroplane departed 30 minutes later than its scheduled time and in order to reach its destination which is 1500 km away on time, it had to increase its speed by 250 km/hr. Its original speed is ___ km/hr.

Discussion

Explore topic-wise InterviewSolutions in .

Select the correct graph for the equation y=−x2+(m+n)x+mn, if m &gt; 0 and n &gt; 0.

If x=A[e^(-kt/2)]cos(pt+€) and A,k,p,€ are constant then prove that d²x/dt²+kdx/dt+n²x=0 where n²=p²+¼k²

Consider a square ABCD of diagonal length 4√3. The square is folded along the diagonal AC so that the plane of ΔABC is perpendicular to the plane of ΔADC. The shortest distance between AB and CD is

Identify the incorrect statement.

In a particular section of Class IX, 40 students were asked about the months of their birth and the following graph was prepared for the data so obtained: Find the probability that a student of the class was born in August.

Water is dripping out from a conical funnel a uniform rate of 4 cm cube per second through a tiny hole at the vortex in the bottom when the slant height of the water is 3 cm find the rate of decrease of slant height of the water given that the Vertical angle of the funnel is 120 degree

If the point C (–1,2) divides the lines segment AB in the ratio 3 : 4, where the co-ordinates of A is (2, 5), then coordinates of B is

Taylor purchased a rectangular plot of area 634 m2. The length of the plot is 2 m more than thrice its breadth. Then find the approximate values of length and breadth of the plot.

Which of the following represents a pair of dependent equations?

In a right triangle ABC, right-angled at B, if tan A = 1, then what equals 2 sin A cos A?1

If sec theta =13/5 then find sin theta +cos theta

Which of the following are not quadratic polynomials? (i) 3+4x–7x2 (ii) 8x2–15 (iii) 6x – 15 (iv) 4x3–3x

In △ABC, AB = 3 cm, AC = 4 cm and AD is the bisector of ∠A. Then, BD : DC is —

In △ABC, DE is parallel to base BC, with D on AB and E on AC. If ADDB=23, find BCDE

Question 11Simplify: (1+tan2 θ)(1−sin θ)(1+sin θ)

The volume of ship and the volume of its model is given. In which of the following cases is K= 120

The diameter of the base of a right circular cone is 42 cm and its height is 20 cm. Find the curved surface area of the cone.

Question 7 The curved surface area of a frustum of a cone is π(r1+r2)l, where l=√h2+(r1+r2)2 r1 and r2 are the radii of the two ends of the frustum and h is the vertical height.

Find the lengths of the medians of a triangle whose vertices are A (−1,3), B(1,−1) and C(5, 1).

The value of sec−1(2√3)+cot−1(−1√3)+tan−1√3 is

Find the sum of all even integers between 101 and 999.

One of the zero of cubic polynomial ax^3+bx^2+cx+d is 0(zero).Find the other two zeroes.

Identify the matrix whose order is 4×3

The zeros of the polynomial f(x) = 2x³ - 9x² + x + 12 are:

In the given figure below, OACB is a quadrant of a circle. The radius OA = 3.5 cm, OD = 2 cm. Calculate the area of the shaded region.

Question 80Solve the following:Rs. 13500 are to be distributed among Salma, Kiran and Jenifer in such a way that Salma gets Rs. 1000 more than Kiran and Jenifer gets Rs. 500 more than Kiran. Find the money received by Jenifer.

The area of a rectangular plot is 528 m2. The length of the plot (in metres) is one metre more then twice its breadth. Find the length and the breadth of the plot.

5. A solid cylinder has diameter 28cm and height 24cm. A conical cavity of the same diameter and same height is drilled out from this solid. Find the whole surface area of the coni cal solid

The probability of India winning an India-Pakistan match could be

The shaded region OAB is known as:

On dividing a positive integer n by 9 we get 7 as remainder. What will be the remainder if (3n−1) is divided by 9?

If cos(A+B) = 0 then sin(A-B) can be equal to

Two years ago, a father was five times as old as his son. Two years later, his age will be 8 more than three times the age of the son. Find the present ages of father and son.

A chord of a circle of radius 20 cm sub tends an angle of 900 at the centre . Find the area of the corresponding major segment of the circle( Use π = 3.14)

A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to 1 cm and the height of the cone is equal to its radius. Find the volume of the solid in terms of π. [2 MARKS]

A container shaped like a right circular cylinder having diameter 12 cm and height 15 cm is full of ice cream. The ice cream is to be filled into cones of height 12 cm and diameter 6 cm, having a hemispherical shape on the top. Find the number of such cones which can be filled with ice cream.

If BC || EF and FG || CD then, AEAB= ?

The term for reduction in marked price is___

If AB is a tangent to a circle at B and ACD any other chord then ABsquare=ACAD.

Draw a circle of radius 3.4 cm and centre E. Take a point F on the circle. Take another point A such that E-F-A and FA = 4.1 cm. Draw tangents to the circle from point A.

In the given figure, PQ is a chord of length 8cm of a circle of radius 5cm. The tangents at P and Q intersect at a point T. Find the length TP. [4 MARKS]

If cosec A + cot A=11/2 then find tan A

Question 2 (iii) Find the LCM and HCF of 336, 54 and verify that LCM × HCF = product of the two numbers.

In figure, ABCD is a trapezium in which AB || DC and AB = 2DC. Determine the ratio of the areas of △AOB and △COD.

1 + tan2A = sec2A is valid for which of the following ranges

Write a rational number between √3 and 2.

To construct a triangle similar to ΔABC in which BC = 4.5 cm, ∠B=45∘ and ∠C=60∘, using a scale factor of 37, BC will be divided in the ratio (i) 3 : 4 (ii) 4 : 7 (c) 3 : 10 (d) 3 : 7

An aeroplane departed 30 minutes later than its scheduled time and in order to reach its destination which is 1500 km away on time, it had to increase its speed by 250 km/hr. Its original speed is ___ km/hr.

Select the correct graph for the equation y=−x2+(m+n)x+mn, if m > 0 and n > 0.