32581 + Interview Questions in Mathematics Page 107 InterviewSolution

5301.	Two pipes running together can fill a cistern in 3113 minutes. If one pipe takes 3 minutes more than the other to fill it, find the time in which faster pipe would fill the cistern.
Answer» Two pipes running together can fill a cistern in $3 \frac{1}{13}$ minutes. If one pipe takes 3 minutes more than the other to fill it, find the time in which faster pipe would fill the cistern.

Discussion

5302.	Which of the following equations have a unique solution?
Answer» Which of the following equations have a unique solution?

Discussion

5303.	AB is a chord of a circle with centre O. If ∠AOB=50∘ and AB = 18 cm, then find the diameter of the circle. sin 25∘=0.42
Answer» AB is a chord of a circle with centre O. If $∠ A O B = 50^{\circ}$ and AB = 18 cm, then find the diameter of the circle. $s i n 25^{\circ} = 0.42$

5303.

AB is a chord of a circle with centre O. If ∠AOB=50∘ and AB = 18 cm, then find the diameter of the circle. sin 25∘=0.42

Answer»

AB is a chord of a circle with centre O. If $∠ A O B = 50^{\circ}$ and AB = 18 cm, then find the diameter of the circle. $s i n 25^{\circ} = 0.42$

Discussion

5304.	If a + b + c = 0 and a2 + b2 + c2 = 16, find the value of ab + bc + ca.
Answer» If a + b + c = 0 and a² + b² + c² = 16, find the value of ab + bc + ca.

Discussion

5305.	Solve each of the following equations by using the method of completing the square: √3x2+10x+7√3=0
Answer» Solve each of the following equations by using the method of completing the square: $\sqrt{3} x^{2} + 10 x + 7 \sqrt{3} = 0$

Discussion

5306.	Draw a circle of radius 6 cm. From a point 10 cm away from its centre, construct the pair of tangents to the circle and measure their lengths.
Answer» Draw a circle of radius 6 cm. From a point 10 cm away from its centre, construct the pair of tangents to the circle and measure their lengths.

Discussion

5307.	The range of f(x)=√x−4+√14−2x is
Answer» The range of $f (x) = \sqrt{x - 4} + \sqrt{14 - 2 x}$ is

Discussion

5308.	The sides of a right triangle are a, a+d, a+2d. a and d are both positive. The ratio of a to d is: a. 1:3 b.1:4 c. 2:1 d.3:1 e. 3:4
Answer» The sides of a right triangle are a, a+d, a+2d. a and d are both positive. The ratio of a to d is: a. 1:3 b.1:4 c. 2:1 d.3:1 e. 3:4

Discussion

5309.	Mark the correct alternative in each of the following:By what number 435 be multiplied to get 237?(a) 39135 (b) 8591 (c) 9185 (d) None of these
Answer» Mark the correct alternative in each of the following: By what number $4 \frac{3}{5}$ be multiplied to get $2 \frac{3}{7}$ ? (a) $\frac{391}{35}$ (b) $\frac{85}{91}$ (c) $\frac{91}{85}$ (d) None of these

Discussion

5310.	Write down the equation of the line whose gradient is 32 and which passes through P, where P divides the line segment joining A(-2, 6) and B(3, -4) in the ratio 2 : 3.
Answer» Write down the equation of the line whose gradient is $\frac{3}{2}$ and which passes through P, where P divides the line segment joining A(-2, 6) and B(3, -4) in the ratio 2 : 3.

Discussion

5311.	36. A person wanted to distribute 96 apples and 112 orange among poor children in an orphange.He packed all the fruits in boxes in such a way that each box contains fruits of the same variety, and also every box contains an equal no. of fruits. i) Find the minimum no. of boxes in which all fruits can be packed.
Answer» 36. A person wanted to distribute 96 apples and 112 orange among poor children in an orphange.He packed all the fruits in boxes in such a way that each box contains fruits of the same variety, and also every box contains an equal no. of fruits. i) Find the minimum no. of boxes in which all fruits can be packed.

Discussion

5312.	Find the smallest number which leaves remainders 8 and 12 when divided by 28 and 32 respectively.
Answer» Find the smallest number which leaves remainders 8 and 12 when divided by 28 and 32 respectively.

Discussion

5313.	15. The difference between the semi-perimeter and the sides of a triangle ABC are 8cm , 7cm , 5cm respectively . The area of the triangle is
Answer» 15. The difference between the semi-perimeter and the sides of a triangle ABC are 8cm , 7cm , 5cm respectively . The area of the triangle is

Discussion

5314.	In the given figure O is the centre of the circle and AB is a tangent at B. If AB = 15 cm and AC =7.5 cm, find the radius of the circle.
Answer» In the given figure O is the centre of the circle and AB is a tangent at B. If AB = 15 cm and AC =7.5 cm, find the radius of the circle.

Discussion

5315.	A sphere of maximum volume is cut-out from a solid hemisphere of radius r, what is the ratio of the volume of the hemisphere to that of the cut-out sphere?
Answer» A sphere of maximum volume is cut-out from a solid hemisphere of radius r, what is the ratio of the volume of the hemisphere to that of the cut-out sphere?

Discussion

5316.	Each observation in a raw data is first multiplied by 3, then 6 is added. It is then divided by 3 and subsequently reduced by 6. Which of the following statements is true?
Answer» Each observation in a raw data is first multiplied by 3, then 6 is added. It is then divided by 3 and subsequently reduced by 6. Which of the following statements is true?

Discussion

5317.	For what values of k, the kth terms of two APS given below are equal? ¡)1,7,113,19,....¡¡)64,63,62,61
Answer» For what values of k, the kth terms of two APS given below are equal? ¡)1,7,113,19,....¡¡)64,63,62,61

Discussion

5318.	Two lights flash at 3 minutes and 8 minutes respectively. If they flash together at 7:00 then at what time next they flash together?
Answer» Two lights flash at 3 minutes and 8 minutes respectively. If they flash together at 7:00 then at what time next they flash together?

Discussion

5319.	In the given frequency distribution, which is the median term?Age in yearsNumber of people15316817101810195204
Answer» In the given frequency distribution, which is the median term? $\begin{matrix} Age in years & Number of people 15 & 3 16 & 8 17 & 10 18 & 10 19 & 5 20 & 4 \end{matrix}$

Discussion

5320.	The value of x∈R for which vectors →a=(1,−2,3), →b=(−2,3,−4), →c=(1,−1,x) form a linearly dependent system is
Answer» The value of $x \in R$ for which vectors $\to a = (1, - 2, 3),$ $\to b = (- 2, 3, - 4),$ $\to c = (1, - 1, x)$ form a linearly dependent system is

Discussion

5321.	Question 7Two sides and the perimeter of a triangle are respectively three times the corresponding sides and the perimeter of the other triangle. Are the two triangles similar? Why?
Answer» Question 7 Two sides and the perimeter of a triangle are respectively three times the corresponding sides and the perimeter of the other triangle. Are the two triangles similar? Why?

Discussion

5322.	A square ABCD is inscribed in a circle of 10 units. The area of the circle not included in the square is
Answer» A square ABCD is inscribed in a circle of 10 units. The area of the circle not included in the square is

5322.

A square ABCD is inscribed in a circle of 10 units. The area of the circle not included in the square is

Answer»

A square ABCD is inscribed in a circle of 10 units. The area of the circle not included in the square is

Discussion

5323.	If diameter of a road roller is 0.9 m and its length is 1.4 m, how much area of a field will be pressed in its 500 rotations ?
Answer» If diameter of a road roller is 0.9 m and its length is 1.4 m, how much area of a field will be pressed in its 500 rotations ?

Discussion

5324.	A juice seller sells juice from a big cylindrical container of height 35.2 cm and radius 10 cm. He charges ₹ 10 for each cylindrical glass of juice whose height is 10 cm and radius is 4 cm. Find the total amount of money he earns by selling the juice.(Take π=227)
Answer» A juice seller sells juice from a big cylindrical container of height 35.2 cm and radius 10 cm. He charges ₹ 10 for each cylindrical glass of juice whose height is 10 cm and radius is 4 cm. Find the total amount of money he earns by selling the juice.(Take $π = \frac{22}{7}$ )

Discussion

5325.	Solve the following quadratic equations by factorization:5x2 − 3x − 2 = 0
Answer» Solve the following quadratic equations by factorization: 5x² − 3x − 2 = 0

Discussion

5326.	105.How to determine whether a curve is continuous or discontinuous?
Answer» 105.How to determine whether a curve is continuous or discontinuous?

Discussion

5327.	If f(x)=x2+1, then find fof.
Answer» $If f (x) = x^{2} + 1, then find f o f$ .

Discussion

5328.	If x = 6 is a zero of quadratic polynomial 3x2–mx−24, then the value of m is __
Answer» If x = 6 is a zero of quadratic polynomial $3 x^{2} - m x - 24$ , then the value of m is __

Discussion

5329.	Draw and describe the locus of a point in rhombus ABCD which is equidistant from AB and AD.
Answer» Draw and describe the locus of a point in rhombus ABCD which is equidistant from AB and AD.

Discussion

5330.	Prove the following trigonometric identities.11+sinA+11-sinA=2 sec2A
Answer» Prove the following trigonometric identities. $\frac{1}{1 + \sin A} + \frac{1}{1 - \sin A} = 2 \sec^{2} A$

Discussion

5331.	Construct a ∠ABC = 60∘ . Mark a point D on BC such that BD = 6 cm. Find the radius of the circle to touch AB at B and also pass through D.
Answer» Construct a $∠$ ABC = 60 $^{\circ}$ . Mark a point D on BC such that BD = 6 cm. Find the radius of the circle to touch AB at B and also pass through D.

Discussion

5332.	ABC and DEF are similar triangles, identify the corresponding sides.
Answer» ABC and DEF are similar triangles, identify the corresponding sides.

Discussion

5333.	Find the distances between the following points.(i) A(a, 0), B(0, a) (ii) P(–6, –3), Q(–1, 9) (iii) R(–3a, a), S(a, –2a)
Answer» Find the distances between the following points. (i) A(a, 0), B(0, a) (ii) P(–6, –3), Q(–1, 9) (iii) R(–3a, a), S(a, –2a)

Discussion

5334.	The diameters of the lower and upper ends of a bucket in the form of a frustum of a cone are 10 cm and 30 cm respectively. If its height is 24 cm, then what is the area of the metal sheet used to make the bucket? (Use π = 3.14)
Answer» The diameters of the lower and upper ends of a bucket in the form of a frustum of a cone are 10 cm and 30 cm respectively. If its height is 24 cm, then what is the area of the metal sheet used to make the bucket? (Use $π$ = 3.14)

Discussion

5335.	The angle between a tangent and the radius at point of contact equals __.
Answer» The angle between a tangent and the radius at point of contact equals __.

5335.

The angle between a tangent and the radius at point of contact equals __.

Answer»

The angle between a tangent and the radius at point of contact equals

__.

Discussion

5336.	In the given figure, ABCD is a parallelogram in which P is the mid-point of DC and Q is a point on AC such that CQ = 14 AC. If PQ produced meets BC at R, prove that R is a mid-point of BC.
Answer» In the given figure, ABCD is a parallelogram in which P is the mid-point of DC and Q is a point on AC such that CQ = $\frac{1}{4}$ AC. If PQ produced meets BC at R, prove that R is a mid-point of BC.

Discussion

5337.	If 3x=cosecθ and 3x=cotθ, find the value of 3x2-1x2. [CBSE 2010]
Answer» If $3 x = cosec θ$ and $\frac{3}{x} = \cot θ$ , find the value of $3 (x^{2} - \frac{1}{x^{2}})$ . [CBSE 2010]

Discussion

5338.	If one this one is one of the zeros of the polynomial x square - X + k then find the value of k
Answer» If one this one is one of the zeros of the polynomial x square - X + k then find the value of k

Discussion

5339.	Three persons start a business and spend ₹ 25,000, ₹ 15,000 and ₹ 40,000 respectively. Find the share of each out of a profit of ₹ 14,400 in a year.
Answer» Three persons start a business and spend ₹ 25,000, ₹ 15,000 and ₹ 40,000 respectively. Find the share of each out of a profit of ₹ 14,400 in a year.

Discussion

5340.	Find the value of k for which the system 3x+5y=0,kx+10y=0 has a nonzero solution.
Answer» Find the value of k for which the system 3x+5y=0,kx+10y=0 has a nonzero solution.

Discussion

5341.	If the equation x2+2(k+2)x+9k=0 has real equal roots, then values of k are
Answer» If the equation $x^{2} + 2 (k + 2) x + 9 k = 0$ has real equal roots, then values of $k$ are

Discussion

5342.	Using the information given in fig. write the values of all trigonometric ratios of angle C.
Answer» Using the information given in fig. write the values of all trigonometric ratios of angle C.

5342.

Using the information given in fig. write the values of all trigonometric ratios of angle C.

Answer»

Using the information given in fig. write the values of all trigonometric ratios of angle C.

Discussion

5343.	Find the median of the following data distribution. Marks obtained2029283342384325Number of students62824152412028.5
Answer» Find the median of the following data distribution. $\begin{matrix} Marks obtained & 20 & 29 & 28 & 33 & 42 & 38 & 43 & 25 Number of students & 6 & 28 & 24 & 15 & 2 & 4 & 1 & 20 \end{matrix}$ 28.5

Discussion

5344.	A question was asked in a class”The points A(5, 5), B(4, 4) and C(3, 3) form which triangle?”.Unfortunately, no student could get it right.What type of triangle will be formed if the points are joined ?
Answer» A question was asked in a class ”The points A(5, 5), B(4, 4) and C(3, 3) form which triangle?”. Unfortunately, no student could get it right. What type of triangle will be formed if the points are joined ?

Discussion

5345.	Question 2(e) Write True (T) or False (F) against the following statement: 5.2:3.9::3:4
Answer» Question 2(e) Write True (T) or False (F) against the following statement: $5.2 : 3.9 :: 3 : 4$

5345.

Question 2(e) Write True (T) or False (F) against the following statement: 5.2:3.9::3:4

Answer»

Question 2(e)

Write True (T) or False (F) against the following statement:

$5.2 : 3.9 :: 3 : 4$

Discussion

5346.	The L.C.M. of v2−v, (v−1)2, and v3−1 is .
Answer» The L.C.M. of $v^{2} - v$ , $(v - 1)^{2}$ , and $v^{3} - 1$ is .

Discussion

5347.	The number of times a particular item occurs in a class interval is called its ________.
Answer» The number of times a particular item occurs in a class interval is called its ________.

Discussion

5348.	If α and β are the zeroes of a polynomial f(x) = x2 − 5x + k, such that α − β = 1, find the value of k.
Answer» If α and β are the zeroes of a polynomial f(x) = x² − 5x + k, such that α − β = 1, find the value of k.

Discussion

5349.	Write down the series whose rth term s 3.2r+1?
Answer» Write down the series whose $r^{t h} t e r m$ s ${3.2}^{r + 1} ?$

Discussion

5350.	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=227]
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. [Take $π = \frac{22}{7}$ ]

Discussion

Explore topic-wise InterviewSolutions in .

Two pipes running together can fill a cistern in 3113 minutes. If one pipe takes 3 minutes more than the other to fill it, find the time in which faster pipe would fill the cistern.

Which of the following equations have a unique solution?

AB is a chord of a circle with centre O. If ∠AOB=50∘ and AB = 18 cm, then find the diameter of the circle. sin 25∘=0.42

If a + b + c = 0 and a2 + b2 + c2 = 16, find the value of ab + bc + ca.

Solve each of the following equations by using the method of completing the square: √3x2+10x+7√3=0

Draw a circle of radius 6 cm. From a point 10 cm away from its centre, construct the pair of tangents to the circle and measure their lengths.

The range of f(x)=√x−4+√14−2x is

The sides of a right triangle are a, a+d, a+2d. a and d are both positive. The ratio of a to d is: a. 1:3 b.1:4 c. 2:1 d.3:1 e. 3:4

Mark the correct alternative in each of the following:By what number 435 be multiplied to get 237?(a) 39135 (b) 8591 (c) 9185 (d) None of these

Write down the equation of the line whose gradient is 32 and which passes through P, where P divides the line segment joining A(-2, 6) and B(3, -4) in the ratio 2 : 3.

Find the smallest number which leaves remainders 8 and 12 when divided by 28 and 32 respectively.

15. The difference between the semi-perimeter and the sides of a triangle ABC are 8cm , 7cm , 5cm respectively . The area of the triangle is

In the given figure O is the centre of the circle and AB is a tangent at B. If AB = 15 cm and AC =7.5 cm, find the radius of the circle.

A sphere of maximum volume is cut-out from a solid hemisphere of radius r, what is the ratio of the volume of the hemisphere to that of the cut-out sphere?

Each observation in a raw data is first multiplied by 3, then 6 is added. It is then divided by 3 and subsequently reduced by 6. Which of the following statements is true?

For what values of k, the kth terms of two APS given below are equal? ¡)1,7,113,19,....¡¡)64,63,62,61

Two lights flash at 3 minutes and 8 minutes respectively. If they flash together at 7:00 then at what time next they flash together?

In the given frequency distribution, which is the median term?Age in yearsNumber of people15316817101810195204

The value of x∈R for which vectors →a=(1,−2,3), →b=(−2,3,−4), →c=(1,−1,x) form a linearly dependent system is

Question 7Two sides and the perimeter of a triangle are respectively three times the corresponding sides and the perimeter of the other triangle. Are the two triangles similar? Why?

A square ABCD is inscribed in a circle of 10 units. The area of the circle not included in the square is

If diameter of a road roller is 0.9 m and its length is 1.4 m, how much area of a field will be pressed in its 500 rotations ?

A juice seller sells juice from a big cylindrical container of height 35.2 cm and radius 10 cm. He charges ₹ 10 for each cylindrical glass of juice whose height is 10 cm and radius is 4 cm. Find the total amount of money he earns by selling the juice.(Take π=227)

Solve the following quadratic equations by factorization:5x2 − 3x − 2 = 0

105.How to determine whether a curve is continuous or discontinuous?

If f(x)=x2+1, then find fof.

If x = 6 is a zero of quadratic polynomial 3x2–mx−24, then the value of m is __

Draw and describe the locus of a point in rhombus ABCD which is equidistant from AB and AD.

Prove the following trigonometric identities.11+sinA+11-sinA=2 sec2A

Construct a ∠ABC = 60∘ . Mark a point D on BC such that BD = 6 cm. Find the radius of the circle to touch AB at B and also pass through D.

ABC and DEF are similar triangles, identify the corresponding sides.

Find the distances between the following points.(i) A(a, 0), B(0, a) (ii) P(–6, –3), Q(–1, 9) (iii) R(–3a, a), S(a, –2a)

The diameters of the lower and upper ends of a bucket in the form of a frustum of a cone are 10 cm and 30 cm respectively. If its height is 24 cm, then what is the area of the metal sheet used to make the bucket? (Use π = 3.14)

The angle between a tangent and the radius at point of contact equals __.

In the given figure, ABCD is a parallelogram in which P is the mid-point of DC and Q is a point on AC such that CQ = 14 AC. If PQ produced meets BC at R, prove that R is a mid-point of BC.

If 3x=cosecθ and 3x=cotθ, find the value of 3x2-1x2. [CBSE 2010]

If one this one is one of the zeros of the polynomial x square - X + k then find the value of k

Three persons start a business and spend ₹ 25,000, ₹ 15,000 and ₹ 40,000 respectively. Find the share of each out of a profit of ₹ 14,400 in a year.

Find the value of k for which the system 3x+5y=0,kx+10y=0 has a nonzero solution.

If the equation x2+2(k+2)x+9k=0 has real equal roots, then values of k are

Using the information given in fig. write the values of all trigonometric ratios of angle C.

Find the median of the following data distribution. Marks obtained2029283342384325Number of students62824152412028.5

A question was asked in a class”The points A(5, 5), B(4, 4) and C(3, 3) form which triangle?”.Unfortunately, no student could get it right.What type of triangle will be formed if the points are joined ?

Question 2(e) Write True (T) or False (F) against the following statement: 5.2:3.9::3:4

The L.C.M. of v2−v, (v−1)2, and v3−1 is .

The number of times a particular item occurs in a class interval is called its ________.

If α and β are the zeroes of a polynomial f(x) = x2 − 5x + k, such that α − β = 1, find the value of k.

Write down the series whose rth term s 3.2r+1?