32581 + Interview Questions in Mathematics Page 52 InterviewSolution

2551.	An express train takes 1 hour less than a passenger train to travel 132km between Mysore and Bangalore (Without taking into consideration the time they stop at intermediate stations). If the average speed of the express train is 11km/hr more than that of the passenger train, find the average speeds of the two trains.
Answer» An express train takes 1 hour less than a passenger train to travel 132km between Mysore and Bangalore (Without taking into consideration the time they stop at intermediate stations). If the average speed of the express train is 11km/hr more than that of the passenger train, find the average speeds of the two trains.

Discussion

2552.	2.2 cu dm(decimeter cube) of brass is to be drawn into a cylindrical wire of diameter 0.50 cm. Find the length of the wire(in m). ___
Answer» 2.2 cu dm(decimeter cube) of brass is to be drawn into a cylindrical wire of diameter 0.50 cm. Find the length of the wire(in m). ___

Discussion

2553.	Question 8 (ii)A dome of a building is in the form of a hemisphere. From inside, it was whitewashed at the cost of ₹ 498.96. If the cost of whitewashing is ₹ 2 per square meter, find the:volume of the air inside the dome[Assume π=227]
Answer» Question 8 (ii) A dome of a building is in the form of a hemisphere. From inside, it was whitewashed at the cost of ₹ 498.96. If the cost of whitewashing is ₹ 2 per square meter, find the: volume of the air inside the dome $[A s s u m e π = \frac{22}{7}]$

Discussion

2554.	Find the values of p for which the quadratic equation 2x^2+px+8=0 has real roots.
Answer» Find the values of p for which the quadratic equation 2x^2+px+8=0 has real roots.

Discussion

2555.	A line intersecting a circle in two distinct points is called a __________.
Answer» A line intersecting a circle in two distinct points is called a __________.

Discussion

2556.	If the point (2k – 3, k + 2) lies on the line 2x + 3y + 15 = 0, find the value of k.
Answer» If the point (2k – 3, k + 2) lies on the line 2x + 3y + 15 = 0, find the value of k.

Discussion

2557.	In a right ΔABC right-angled at C, if D is the mid-point of BC, prove that BC2=4(AD2−AC2).
Answer» In a right $Δ A B C$ right-angled at C, if D is the mid-point of BC, prove that $B C^{2} = 4 (A D^{2} - A C^{2})$ .

Discussion

2558.	Determine the ratio in which line 3x+y-9=0 divides the line segment joining the points (1,3) and (2,7)
Answer» Determine the ratio in which line 3x+y-9=0 divides the line segment joining the points (1,3) and (2,7)

Discussion

2559.	The coordinates of the circumcentre of a triangle whose sides are x = 0, y = 0 and x + y = 1 are
Answer» The coordinates of the circumcentre of a triangle whose sides are x = 0, y = 0 and x + y = 1 are

Discussion

2560.	The volume of a hemispherical shell of outer radius 7cm and inner radius 3.5cm is
Answer» The volume of a hemispherical shell of outer radius 7cm and inner radius 3.5cm is

Discussion

2561.	Find the roots of the following quadratic equation by factorisation method. 2x2+53x−2=0
Answer» Find the roots of the following quadratic equation by factorisation method. $2 x^{2} + \frac{5}{3} x - 2 = 0$

Discussion

2562.	In ΔABC,AB=BC=6cm. A circle is drawn with center at B and radius 2 cm. What is the scale factor of the triangle formed by the point B and the points where the circle intersects △ABC?
Answer» In $Δ A B C, A B = B C = 6 c m$ . A circle is drawn with center at B and radius 2 cm. What is the scale factor of the triangle formed by the point B and the points where the circle intersects $△ A B C$ ?

Discussion

2563.	Ashin invested an amount of Rs. 13,900 divided into two different schemes A and B at the simple interest rate of 14% p.a. and 11% p.a. respectively. If the total amount of simple interest earned in 2 years be Rs. 3508, what was the amount invested in Scheme B (in rupees)? ___
Answer» Ashin invested an amount of Rs. 13,900 divided into two different schemes A and B at the simple interest rate of 14% p.a. and 11% p.a. respectively. If the total amount of simple interest earned in 2 years be Rs. 3508, what was the amount invested in Scheme B (in rupees)? ___

2563.

Ashin invested an amount of Rs. 13,900 divided into two different schemes A and B at the simple interest rate of 14% p.a. and 11% p.a. respectively. If the total amount of simple interest earned in 2 years be Rs. 3508, what was the amount invested in Scheme B (in rupees)? ___

Answer»

Ashin invested an amount of Rs. 13,900 divided into two different schemes A and B at the simple interest rate of 14% p.a. and 11% p.a. respectively. If the total amount of simple interest earned in 2 years be Rs. 3508, what was the amount invested in Scheme B (in rupees)?

___

Discussion

2564.	Which is better investment: 11% stock at 143 or 9.75% stock at 117?
Answer» Which is better investment: 11% stock at 143 or $9.75 %$ stock at 117?

Discussion

2565.	If a vertical pole of length 6m costs a shadow 4m long on the ground and at the same time a tower costs a shadow of 28m long then the height of the tower is?
Answer» If a vertical pole of length 6m costs a shadow 4m long on the ground and at the same time a tower costs a shadow of 28m long then the height of the tower is?

Discussion

2566.	Evaluate:(i) 3.21+2.34(ii) 0.0345+6.124(iii) 6.9+32.26
Answer» Evaluate: (i) $3.21 + 2.34$ (ii) $0.0345 + 6.124$ (iii) $6.9 + 32.26$

Discussion

2567.	A bag contains 5 red, 8 white and 7 black balls. A ball is drawn at random form the bag. Find the probability that the drawn ball is (i) red or white (ii) not black (iii) neither white nor black.
Answer» A bag contains 5 red, 8 white and 7 black balls. A ball is drawn at random form the bag. Find the probability that the drawn ball is (i) red or white (ii) not black (iii) neither white nor black.

Discussion

2568.	Check whether -150 is a term of the A.P. 11, 8, 5, 2, …
Answer» Check whether -150 is a term of the A.P. 11, 8, 5, 2, …

Discussion

2569.	A father is three times as old as his son. The product of the father's age 3 years hence and the the son's age three years ago is twenty times the present age of son. What is the age of the father
Answer» A father is three times as old as his son. The product of the father's age 3 years hence and the the son's age three years ago is twenty times the present age of son. What is the age of the father

Discussion

2570.	In the given figure, ABC is a triangle, a circle with diameter BC is drawn, intersecting AB and AC at D and E respectively. If the lengths of AB, AC and CD are 30 cm, 25 cm and 20 cm respectively, then the sum of lengths of AT and BE is(AT is tangent to the circle)
Answer» In the given figure, ABC is a triangle, a circle with diameter BC is drawn, intersecting AB and AC at D and E respectively. If the lengths of AB, AC and CD are 30 cm, 25 cm and 20 cm respectively, then the sum of lengths of AT and BE is (AT is tangent to the circle)

Discussion

2571.	The pairs of linear equations which have the unique solution x=2,y=–3 are,
Answer» The pairs of linear equations which have the unique solution $x = 2, y = - 3$ are,

Discussion

2572.	A cubical box has edge of measeure 2 cm. The surface area of the box is ____ cm2.
Answer» A cubical box has edge of measeure 2 cm. The surface area of the box is ____ $c m^{2}$ .

Discussion

2573.	Find the area of metal sheet required in making a closed hollow cone of base radius 7 cm and height 24 cm.
Answer» Find the area of metal sheet required in making a closed hollow cone of base radius 7 cm and height 24 cm.

Discussion

2574.	The 11th term and the 21st term of an A.P. are 16 and 29 respectively, then find the 41th term of that A.P.
Answer» The 11^th term and the 21^st term of an A.P. are 16 and 29 respectively, then find the 41^th term of that A.P.

Discussion

2575.	Two number differ by 3 and their product is 504. Find the numbers.
Answer» Two number differ by 3 and their product is 504. Find the numbers.

Discussion

2576.	Two different dice are thrown together. Find the probability that the numbers obtained(i) have a sum less than 7(ii) have a product less than 16(iii) is a doublet of odd numbers. [CBSE 2017]
Answer» Two different dice are thrown together. Find the probability that the numbers obtained (i) have a sum less than 7 (ii) have a product less than 16 (iii) is a doublet of odd numbers. [CBSE 2017]

Discussion

2577.	A man standing on the deck of a ship, which is 10 m above the water level, observes the angle of elevation of the top of a hill as 60∘, and the angle of depression of the base of the hill as 30∘. Find the distance of the hill from the ship and the height of the hill.
Answer» A man standing on the deck of a ship, which is 10 m above the water level, observes the angle of elevation of the top of a hill as $60^{\circ}$ , and the angle of depression of the base of the hill as $30^{\circ}$ . Find the distance of the hill from the ship and the height of the hill.

Discussion

2578.	If TP and TQ are two tangents to a circle with center O such that ∠POQ=110o, then ∠PTQ will be .
Answer» $If TP and TQ are two tangents to a circle with center O such that ∠ P O Q = 110^{o}, then ∠ P T Q will be$ .

Discussion

2579.	A(h, –6), B(2, 3) and C(–6, k) are the co–ordinates of vertices of a triangle whose centroid is G (1, 5). Find h and k.
Answer» A(h, –6), B(2, 3) and C(–6, k) are the co–ordinates of vertices of a triangle whose centroid is G (1, 5). Find h and k.

Discussion

2580.	69. Find the distance of the point from the origin which divides the line segment joining the points (5,-4) and (3,-2) in the ratio of 4:3
Answer» 69. Find the distance of the point from the origin which divides the line segment joining the points (5,-4) and (3,-2) in the ratio of 4:3

Discussion

2581.	Question 2 The following observed values of x and y are thought to satisfy a linear equation. Write the linear equation. X6−6Y−26 Draw the graph using the values of x, y as given in the above table. At what points the graph of the linear equation. (i) Cuts the x-axis? (ii) Cuts the y-axis?
Answer» Question 2 The following observed values of x and y are thought to satisfy a linear equation. Write the linear equation. $\begin{matrix} X & 6 & - 6 Y & - 2 & 6 \end{matrix}$ Draw the graph using the values of x, y as given in the above table. At what points the graph of the linear equation. (i) Cuts the x-axis? (ii) Cuts the y-axis?

Discussion

2582.	Question 3 In the given figure, ΔCDE is an equilateral triangle formed on a side CD of a square ABCD. Show that ΔADE≅ΔBCE
Answer» Question 3 In the given figure, $Δ CDE$ is an equilateral triangle formed on a side CD of a square ABCD. Show that $Δ ADE ≅ Δ BCE$

Discussion

2583.	In the given figure, point A is on the bisector of ∠XYZ. If AX = 2 cm then find AZ.
Answer» In the given figure, point A is on the bisector of $∠$ XYZ. If AX = 2 cm then find AZ.

Discussion

2584.	Albie is 4 years older than Morne. If Morne's present age is y years, then the algebraic expression for Albie's present age (in years) is
Answer» Albie is $4$ years older than Morne. If Morne's present age is $y$ years, then the algebraic expression for Albie's present age (in years) is

Discussion

2585.	Shri Shantilal has purchased 150 shares of FV Rs 100, for MV of Rs 120. Company has paid dividend at 7%. Find the rate of return on his investment.
Answer» Shri Shantilal has purchased 150 shares of FV Rs 100, for MV of Rs 120. Company has paid dividend at 7%. Find the rate of return on his investment.

Discussion

2586.	One zero of the polynomial 3x3+16x2+15x-18 is 23. Find the other zeroes of the polynomial.
Answer» One zero of the polynomial $3 x^{3} + 16 x^{2} + 15 x - 18$ is $\frac{2}{3}$ . Find the other zeroes of the polynomial.

Discussion

2587.	The circumference of a hemispherical dome is 44 m. Calculate the cost of painting at Rs 20 per sq. m.
Answer» The circumference of a hemispherical dome is 44 m. Calculate the cost of painting at Rs 20 per sq. m.

Discussion

2588.	A farmer has 3 storage units for rice. Each storage unit has the same capacity. Rice is available to the farmer in bags of 80 kg, 85 kg and 90 kg. Find the minimum storage capacity of each of the storage unit considering that he has to take rice in bags of 80 kg, 85 kg and 90 kg only.
Answer» A farmer has 3 storage units for rice. Each storage unit has the same capacity. Rice is available to the farmer in bags of 80 kg, 85 kg and 90 kg. Find the minimum storage capacity of each of the storage unit considering that he has to take rice in bags of 80 kg, 85 kg and 90 kg only.

Discussion

2589.	During a practice match, a softball pitcher throws a ball whose height can be modelled by the equation h=−16t2+24t+1, where h=height in feet and t=time in seconds. How long does it take for the ball to reach a height of 6 feet?
Answer» During a practice match, a softball pitcher throws a ball whose height can be modelled by the equation $h = - 16 t^{2} + 24 t + 1$ , where $h = height in feet and t = time in seconds$ . How long does it take for the ball to reach a height of 6 feet?

Discussion

2590.	Which of the following has the same value as the given expression? cot(90∘−θ)cosec2θ.secθ.cot3θsin2(90∘−θ)
Answer» Which of the following has the same value as the given expression? $\frac{c o t (90^{\circ} - θ)}{c o s e c^{2} θ}$ . $\frac{s e c θ . c o t^{3} θ}{s i n^{2} (90^{\circ} - θ)}$

2590.

Which of the following has the same value as the given expression? cot(90∘−θ)cosec2θ.secθ.cot3θsin2(90∘−θ)

Answer»

Which of the following has the same value as the given expression?

$\frac{c o t (90^{\circ} - θ)}{c o s e c^{2} θ}$ . $\frac{s e c θ . c o t^{3} θ}{s i n^{2} (90^{\circ} - θ)}$

Discussion

2591.	Three vertices of a parallelogram A(-2,3) B(6,7) C(8,3). Find fourth vertex D.
Answer» Three vertices of a parallelogram A(-2,3) B(6,7) C(8,3). Find fourth vertex D.

Discussion

2592.	is it necessary that if a rational number is non terminating, it should be repeating?
Answer» is it necessary that if a rational number is non terminating, it should be repeating?

Discussion

2593.	A hollow copper pipe of inner diameter 6 cm and outer diameter 10 cm is melted and changed into a solid circular cylinder of the same height as that of the pipe then the diameter of the solid sphere is
Answer» A hollow copper pipe of inner diameter 6 cm and outer diameter 10 cm is melted and changed into a solid circular cylinder of the same height as that of the pipe then the diameter of the solid sphere is

Discussion

2594.	If tangents PA and PB from a point P to a circle with centre O are inclined to each other at an angle of 80∘, then ∠POA is equal to
Answer» If tangents PA and PB from a point P to a circle with centre O are inclined to each other at an angle of $80^{\circ},$ then $∠ P O A$ is equal to

Discussion

2595.	In case of right angle triangle, circumradius is given by?
Answer» In case of right angle triangle, circumradius is given by?

Discussion

2596.	Question 2In the figure, find tan P – cot R.
Answer» Question 2 In the figure, find tan P – cot R.

Discussion

2597.	Find the values of x and y in the below given pair of equation, where x≠0 & y≠0.2x+3y=135x−4y=−2
Answer» Find the values of x and y in the below given pair of equation, where $x \neq 0 & y \neq 0$ . $\frac{2}{x} + \frac{3}{y} = 13$ $\frac{5}{x} - \frac{4}{y} = - 2$

Discussion

2598.	Verify by using euclid's division algorithm that the numbers 350 and 849 are coprime
Answer» Verify by using euclid's division algorithm that the numbers 350 and 849 are coprime

Discussion

2599.	Triangles ABC and DEF are similar.(i) If area (∆ABC) = 16 cm2, area (∆DEF) = 25 cm2 and BC = 2.3 cm, find EF.(ii) If area (∆ABC) = 9 cm2, area (∆DEF) = 64 cm2 and DE = 5.1 cm , find AB.(iii) If AC = 19 cm and DF = 8 cm, find the ratio of the area of two triangles.(iv) If area (∆ABC) = 36 cm2, area (∆DEF) = 64 cm2 and DE = 6.2 cm, find AB.(v) If AB = 1.2 cm and DE = 1.4 cm, find the ratio of the areas of ∆ABC and ∆DEF.
Answer» Triangles ABC and DEF are similar. (i) If area (∆ABC) = 16 cm², area (∆DEF) = 25 cm² and BC = 2.3 cm, find EF. (ii) If area (∆ABC) = 9 cm², area (∆DEF) = 64 cm² and DE = 5.1 cm , find AB. (iii) If AC = 19 cm and DF = 8 cm, find the ratio of the area of two triangles. (iv) If area (∆ABC) = 36 cm², area (∆DEF) = 64 cm² and DE = 6.2 cm, find AB. (v) If AB = 1.2 cm and DE = 1.4 cm, find the ratio of the areas of ∆ABC and ∆DEF.

Discussion

2600.	Two numbers are in the ratio 4 : 5. If 30 is subtracted from each of the numbers, the ratio becomes 1 : 2. Find the numbers.
Answer» Two numbers are in the ratio 4 : 5. If 30 is subtracted from each of the numbers, the ratio becomes 1 : 2. Find the numbers.

Discussion

Explore topic-wise InterviewSolutions in .

2.2 cu dm(decimeter cube) of brass is to be drawn into a cylindrical wire of diameter 0.50 cm. Find the length of the wire(in m). ___

Question 8 (ii)A dome of a building is in the form of a hemisphere. From inside, it was whitewashed at the cost of ₹ 498.96. If the cost of whitewashing is ₹ 2 per square meter, find the:volume of the air inside the dome[Assume π=227]

Find the values of p for which the quadratic equation 2x^2+px+8=0 has real roots.

A line intersecting a circle in two distinct points is called a __________.

If the point (2k – 3, k + 2) lies on the line 2x + 3y + 15 = 0, find the value of k.

In a right ΔABC right-angled at C, if D is the mid-point of BC, prove that BC2=4(AD2−AC2).

Determine the ratio in which line 3x+y-9=0 divides the line segment joining the points (1,3) and (2,7)

The coordinates of the circumcentre of a triangle whose sides are x = 0, y = 0 and x + y = 1 are

The volume of a hemispherical shell of outer radius 7cm and inner radius 3.5cm is

Find the roots of the following quadratic equation by factorisation method. 2x2+53x−2=0

In ΔABC,AB=BC=6cm. A circle is drawn with center at B and radius 2 cm. What is the scale factor of the triangle formed by the point B and the points where the circle intersects △ABC?

Ashin invested an amount of Rs. 13,900 divided into two different schemes A and B at the simple interest rate of 14% p.a. and 11% p.a. respectively. If the total amount of simple interest earned in 2 years be Rs. 3508, what was the amount invested in Scheme B (in rupees)? ___

Which is better investment: 11% stock at 143 or 9.75% stock at 117?

If a vertical pole of length 6m costs a shadow 4m long on the ground and at the same time a tower costs a shadow of 28m long then the height of the tower is?

Evaluate:(i) 3.21+2.34(ii) 0.0345+6.124(iii) 6.9+32.26

A bag contains 5 red, 8 white and 7 black balls. A ball is drawn at random form the bag. Find the probability that the drawn ball is (i) red or white (ii) not black (iii) neither white nor black.

Check whether -150 is a term of the A.P. 11, 8, 5, 2, …

A father is three times as old as his son. The product of the father's age 3 years hence and the the son's age three years ago is twenty times the present age of son. What is the age of the father

In the given figure, ABC is a triangle, a circle with diameter BC is drawn, intersecting AB and AC at D and E respectively. If the lengths of AB, AC and CD are 30 cm, 25 cm and 20 cm respectively, then the sum of lengths of AT and BE is(AT is tangent to the circle)

The pairs of linear equations which have the unique solution x=2,y=–3 are,

A cubical box has edge of measeure 2 cm. The surface area of the box is ____ cm2.

Find the area of metal sheet required in making a closed hollow cone of base radius 7 cm and height 24 cm.

The 11th term and the 21st term of an A.P. are 16 and 29 respectively, then find the 41th term of that A.P.

Two number differ by 3 and their product is 504. Find the numbers.

Two different dice are thrown together. Find the probability that the numbers obtained(i) have a sum less than 7(ii) have a product less than 16(iii) is a doublet of odd numbers. [CBSE 2017]

A man standing on the deck of a ship, which is 10 m above the water level, observes the angle of elevation of the top of a hill as 60∘, and the angle of depression of the base of the hill as 30∘. Find the distance of the hill from the ship and the height of the hill.

If TP and TQ are two tangents to a circle with center O such that ∠POQ=110o, then ∠PTQ will be .

A(h, –6), B(2, 3) and C(–6, k) are the co–ordinates of vertices of a triangle whose centroid is G (1, 5). Find h and k.

69. Find the distance of the point from the origin which divides the line segment joining the points (5,-4) and (3,-2) in the ratio of 4:3

Question 2 The following observed values of x and y are thought to satisfy a linear equation. Write the linear equation. X6−6Y−26 Draw the graph using the values of x, y as given in the above table. At what points the graph of the linear equation. (i) Cuts the x-axis? (ii) Cuts the y-axis?

Question 3 In the given figure, ΔCDE is an equilateral triangle formed on a side CD of a square ABCD. Show that ΔADE≅ΔBCE

In the given figure, point A is on the bisector of ∠XYZ. If AX = 2 cm then find AZ.

Albie is 4 years older than Morne. If Morne's present age is y years, then the algebraic expression for Albie's present age (in years) is

Shri Shantilal has purchased 150 shares of FV Rs 100, for MV of Rs 120. Company has paid dividend at 7%. Find the rate of return on his investment.

One zero of the polynomial 3x3+16x2+15x-18 is 23. Find the other zeroes of the polynomial.

The circumference of a hemispherical dome is 44 m. Calculate the cost of painting at Rs 20 per sq. m.

A farmer has 3 storage units for rice. Each storage unit has the same capacity. Rice is available to the farmer in bags of 80 kg, 85 kg and 90 kg. Find the minimum storage capacity of each of the storage unit considering that he has to take rice in bags of 80 kg, 85 kg and 90 kg only.

During a practice match, a softball pitcher throws a ball whose height can be modelled by the equation h=−16t2+24t+1, where h=height in feet and t=time in seconds. How long does it take for the ball to reach a height of 6 feet?

Which of the following has the same value as the given expression? cot(90∘−θ)cosec2θ.secθ.cot3θsin2(90∘−θ)

Three vertices of a parallelogram A(-2,3) B(6,7) C(8,3). Find fourth vertex D.

is it necessary that if a rational number is non terminating, it should be repeating?

A hollow copper pipe of inner diameter 6 cm and outer diameter 10 cm is melted and changed into a solid circular cylinder of the same height as that of the pipe then the diameter of the solid sphere is

If tangents PA and PB from a point P to a circle with centre O are inclined to each other at an angle of 80∘, then ∠POA is equal to

In case of right angle triangle, circumradius is given by?

Question 2In the figure, find tan P – cot R.

Find the values of x and y in the below given pair of equation, where x≠0 &amp; y≠0.2x+3y=135x−4y=−2

Verify by using euclid's division algorithm that the numbers 350 and 849 are coprime

Two numbers are in the ratio 4 : 5. If 30 is subtracted from each of the numbers, the ratio becomes 1 : 2. Find the numbers.

Find the values of x and y in the below given pair of equation, where x≠0 & y≠0.2x+3y=135x−4y=−2