32581 + Interview Questions in Mathematics Page 150 InterviewSolution

7451.	3.If a, b, c>0 , then prove that a/b + b/c + c/a > ab+bc+ca
Answer» 3.If a, b, c>0 , then prove that a/b + b/c + c/a > ab+bc+ca

Discussion

7452.	A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius. The total height of the toy is 15.5 cm. Find the totalsurface area of the toy. [CBSE 2012]
Answer» A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius. The total height of the toy is 15.5 cm. Find the total surface area of the toy. [CBSE 2012]

Discussion

7453.	Solve the following systems of equations: x3+y4=11 5x6−y3=−7
Answer» Solve the following systems of equations: $\frac{x}{3} + \frac{y}{4} = 11$ $\frac{5 x}{6} - \frac{y}{3} = - 7$

7453.

Solve the following systems of equations: x3+y4=11 5x6−y3=−7

Answer»

Solve the following systems of equations:

$\frac{x}{3} + \frac{y}{4} = 11$

$\frac{5 x}{6} - \frac{y}{3} = - 7$

Discussion

7454.	Two arithmetic progressions have the same common difference. Their first terms are A and B respectively. The difference between their nth terms is _________.
Answer» Two arithmetic progressions have the same common difference. Their first terms are A and B respectively. The difference between their n^th terms is _________.

Discussion

7455.	The sum of the squares of two consecutive odd numbers is 394. Find the numbers.
Answer» The sum of the squares of two consecutive odd numbers is 394. Find the numbers.

Discussion

7456.	The lengths of the diagonals of a rhombus are 40 cm and 42 cm. Find the length of each side of the rhombus.
Answer» The lengths of the diagonals of a rhombus are $40 c m$ and $42 c m .$ Find the length of each side of the rhombus.

Discussion

7457.	Factorise the following using appropriate identities: 9y2–6y+1
Answer» Factorise the following using appropriate identities: $9 y^{2} - 6 y + 1$

Discussion

7458.	Show that : cos θ (tan θ + 2 ) (2 tan θ +1 ) = 2 sec θ + 5 sin θ
Answer» Show that : cos $θ$ (tan $θ$ + 2 ) (2 tan $θ$ +1 ) = 2 sec $θ$ + 5 sin $θ$

Discussion

7459.	If the angle of elevation of a cloud from a point 200 m above a lake is 30∘ and the angle of depression of its reflection in the lake is 60∘, then the height of the cloud above the lake is ___.
Answer» If the angle of elevation of a cloud from a point 200 m above a lake is $30^{\circ}$ and the angle of depression of its reflection in the lake is $60^{\circ}$ , then the height of the cloud above the lake is ___.

Discussion

7460.	The angle of elevation of a jet fighter from a point A on the ground is 60∘. After a flight of 15 seconds, the angle of elevation changes to 30∘. If the jet is flying at a speed of 720 km/hour, find the constant height at which the jet is flying. [Use √3=1.732]
Answer» The angle of elevation of a jet fighter from a point A on the ground is $60^{\circ}$ . After a flight of 15 seconds, the angle of elevation changes to $30^{\circ}$ . If the jet is flying at a speed of 720 km/hour, find the constant height at which the jet is flying. [Use $\sqrt{3} = 1.732$ ]

Discussion

7461.	if the seventh term from the beginning and end in the binomial expansion of 23+133n are equal, find n.
Answer» if the seventh term from the beginning and end in the binomial expansion of ${(\sqrt[3]{2} + \frac{1}{\sqrt[3]{3}})}^{n}$ are equal, find n.

Discussion

7462.	Question 5If P(E) = 0.05, what is the probability of ‘not E’?
Answer» Question 5 If P(E) = 0.05, what is the probability of ‘not E’?

Discussion

7463.	If the lines y = 3 + 7 & 2y + p = 3 are \|\| to each other, find the value of p.
Answer» If the lines y = 3 + 7 & 2y + p = 3 are \|\| to each other, find the value of p.

Discussion

7464.	35. In YSDE let β be fringe width and I_o be intensity at the central bright fringe. At a distance x from the central bright fringe, the intensity will be
Answer» 35. In YSDE let β be fringe width and I_o be intensity at the central bright fringe. At a distance x from the central bright fringe, the intensity will be

Discussion

7465.	If one of the diagonal of a trapezium divides the other in the ratio 2:1 prove that one of the parallel sides is twice the other
Answer» If one of the diagonal of a trapezium divides the other in the ratio 2:1 prove that one of the parallel sides is twice the other

Discussion

7466.	Two circles touch externally at a point P. From a point T on the tangent at P, tangents TQ and TR are drawn to the circles with points of contact Q and R respectively. Prove that TQ = TR.
Answer» Two circles touch externally at a point P. From a point T on the tangent at P, tangents TQ and TR are drawn to the circles with points of contact Q and R respectively. Prove that TQ = TR.

Discussion

7467.	A solid iron pole consists of a cylinder of height 220 cm and base diameter 24 cm, which is surmounted by another cylinder of height 60 cm and radius 8 cm. Find the mass of the pole, given that 1cm3 of iron has approximately 8 g mass. (Use π=3.14) [3 MARKS]
Answer» A solid iron pole consists of a cylinder of height 220 cm and base diameter 24 cm, which is surmounted by another cylinder of height 60 cm and radius 8 cm. Find the mass of the pole, given that ${1 c m}^{3}$ of iron has approximately 8 g mass. (Use $π = 3.14$ ) [3 MARKS]

Discussion

7468.	Solve the following quadratic equations by factorization:25x (x + 1) = −4
Answer» Solve the following quadratic equations by factorization: 25x (x + 1) = −4

Discussion

7469.	The sum of the first 7 terms of an AP is 63 and the sum of it's next 7 terms is 161. Find the 28th term of this AP.
Answer» The sum of the first $7$ terms of an AP is $63$ and the sum of it's next $7$ terms is $161$ . Find the $28^{t h}$ term of this AP.

Discussion

7470.	Express 3825 as a product of its prime factors.
Answer» Express 3825 as a product of its prime factors.

Discussion

7471.	To solve the quadratic equation 9x2+34x-2=0 by the method of completing the square, without making making the coefficient of x2 unity, we must add and subtract _________.
Answer» To solve the quadratic equation $9 x^{2} + \frac{3}{4} x - \sqrt{2} = 0$ by the method of completing the square, without making making the coefficient of x² unity, we must add and subtract _________.

Discussion

7472.	If in a ΔABC,a2−b2a2+b2=sin(A−B)sin(A+B), prove that it is either a right-angled or an isosceles triangle.
Answer» If in a $Δ A B C, \frac{a^{2} - b^{2}}{a^{2} + b^{2}} = \frac{s i n (A - B)}{s} i n (A + B)$ , prove that it is either a right-angled or an isosceles triangle.

Discussion

7473.	For what value of k will the following pair of linear equation have no solution? 2x+3y=9,6x+(k−2)y=(3k−2).
Answer» For what value of k will the following pair of linear equation have no solution? $2 x + 3 y = 9, 6 x + (k - 2) y = (3 k - 2) .$

7473.

For what value of k will the following pair of linear equation have no solution? 2x+3y=9,6x+(k−2)y=(3k−2).

Answer»

For what value of k will the following pair of linear equation have no solution?

$2 x + 3 y = 9, 6 x + (k - 2) y = (3 k - 2) .$

Discussion

7474.

A life insurance agent found the following data for distribution of ages of 100 policy holders. Calculate the median age, if policies are only given to persons having age 18 years onward but less than 60 years. Age in years Number of policy holders Below 20 Below 25 Below 30 Below 35 Below 40 Below 45 Below 50 Below 55 Below 60 2 6 24 45 78 89 92 98 100

Answer» A life insurance agent found the following data for distribution of ages of 100 policy holders. Calculate the median age, if policies are only given to persons having age 18 years onward but less than 60 years.

Age in years	Number of policy holders
Below 20 Below 25 Below 30 Below 35 Below 40 Below 45 Below 50 Below 55 Below 60	2 6 24 45 78 89 92 98 100

Discussion

7475.	The sum of three non zero prime no.s is 100 . One of them exceedsthe other by 36. Find the largest number.
Answer» The sum of three non zero prime no.s is 100 . One of them exceedsthe other by 36. Find the largest number.

Discussion

7476.	The length of the hypotenuse of an isosceles right triangle whose one side is 42 cm is(a) 12 cm(b) 8 cm(c) 82 cm(d) 122 cm
Answer» The length of the hypotenuse of an isosceles right triangle whose one side is $4 \sqrt{2} cm$ is (a) 12 cm (b) 8 cm (c) $8 \sqrt{2} cm$ (d) $12 \sqrt{2} cm$

Discussion

7477.	If a vertex of a triangle be (1, 1) and the middle points of the sides through it be (−2,−3) and (5 2) find the other vertices.
Answer» If a vertex of a triangle be (1, 1) and the middle points of the sides through it be (−2,−3) and (5 2) find the other vertices.

Discussion

7478.	The difference between the outer and inner curved surface areas of a hollow right circular cylinder 14 cm long is 88 cm2. If the volume of metal used in making the cylinder is 176 cm3, find the outer and inner diameters of the cylinder. (Use π = 22/7)
Answer» The difference between the outer and inner curved surface areas of a hollow right circular cylinder 14 cm long is 88 cm². If the volume of metal used in making the cylinder is 176 cm³, find the outer and inner diameters of the cylinder. (Use π = 22/7)

Discussion

7479.	Prove by vector method that the internal bisectors of the angles of a triangle are concurrent.
Answer» Prove by vector method that the internal bisectors of the angles of a triangle are concurrent.

Discussion

7480.	In the given figure, PA and PB are two tangents to the circle with centre O. If ∠APB = 60∘ then ∠OAB is [CBSE 2011](a) 15∘(b) 30∘(c) 60∘(d) 90∘
Answer» In the given figure, PA and PB are two tangents to the circle with centre O. If ∠APB = 60^∘ then ∠OAB is [CBSE 2011] (a) 15^∘ (b) 30^∘ (c) 60^∘ (d) 90^∘

Discussion

7481.	How many tangents can be drawn through a point on a circle?
Answer» How many tangents can be drawn through a point on a circle?

7481.

How many tangents can be drawn through a point on a circle?

Answer»

How many tangents can be drawn through a point on a circle?

Discussion

7482.	What is the graph of a linear equation in 2 variables?
Answer» What is the graph of a linear equation in 2 variables?

Discussion

7483.	Let A be a square matrix such that A(adj A)=⎡⎢⎣400040004⎤⎥⎦. Then the value of \|adj(adj A)\|\|adj A\| is
Answer» Let $A$ be a square matrix such that $A (a d j A) = ⎡ ⎢ ⎣ \begin{matrix} 4 & 0 & 0 0 & 4 & 0 0 & 0 & 4 \end{matrix} ⎤ ⎥ ⎦ .$ Then the value of $\frac{\| a d j (a d j A) \|}{\| a d j A \|}$ is

Discussion

7484.	The pages of a book are numbered for 1 to 100 manually. How many times will be it is essential to write the number 5?
Answer» The pages of a book are numbered for 1 to 100 manually. How many times will be it is essential to write the number 5?

Discussion

7485.	Let abc be a right triangle in which ab=3cm , bc=4cm and angle b =90 degree . Bd is perpendicular from b on ac . The circle through b,c,d is drawn. Construct the tangents from a to this circle
Answer» Let abc be a right triangle in which ab=3cm , bc=4cm and angle b =90 degree . Bd is perpendicular from b on ac . The circle through b,c,d is drawn. Construct the tangents from a to this circle

Discussion

7486.	A cylinder with base radius of 8 cm and height of 2 cm is melted to form a cone of height 6 cm. The radius of the cone is(a) 4 cm(b) 5 cm(c) 6 cm(d) 8 cm
Answer» A cylinder with base radius of 8 cm and height of 2 cm is melted to form a cone of height 6 cm. The radius of the cone is (a) 4 cm (b) 5 cm (c) 6 cm (d) 8 cm

Discussion

7487.	A wooden toy is in the shape of a cone mounted on a cylinder as shown alongside. If the height of the cone is 24 cm, the total height of the toy is 60 cm and the radius of the base of the cone = twice the radius of the base of the cylinder = 10 cm; find the total surface area of the toy. [Take π=3.14]
Answer» A wooden toy is in the shape of a cone mounted on a cylinder as shown alongside. If the height of the cone is 24 cm, the total height of the toy is 60 cm and the radius of the base of the cone = twice the radius of the base of the cylinder = 10 cm; find the total surface area of the toy. [Take $π$ =3.14]

7487.

A wooden toy is in the shape of a cone mounted on a cylinder as shown alongside. If the height of the cone is 24 cm, the total height of the toy is 60 cm and the radius of the base of the cone = twice the radius of the base of the cylinder = 10 cm; find the total surface area of the toy. [Take π=3.14]

Answer»

A wooden toy is in the shape of a cone mounted on a cylinder as shown alongside. If the height of the cone is 24 cm, the total height of the toy is 60 cm and the radius of the base of the cone = twice the radius of the base of the cylinder = 10 cm; find the total surface area of the toy. [Take $π$ =3.14]

Discussion

7488.	If tan A=34 and A+B=90°, then what is the value of cot B?
Answer» If $\tan A = \frac{3}{4} and A + B = 90 °$ , then what is the value of cot B?

Discussion

7489.	Question 2Express the following linear equations in the form ax + by + c = 0 and indicate the values of a, b and c in each case:(i)2x+3y=9.35 (ii)x−y5−10=0 (iii)−2x+3y=6 (iv)x=3y(v)2x=−5y (vi)3x+2=0 (vii)y−2=0 (viii)5=2x
Answer» Question 2 Express the following linear equations in the form ax + by + c = 0 and indicate the values of a, b and c in each case: $(i) 2 x + 3 y = 9.35 (i i) x - \frac{y}{5} - 10 = 0 (i i i) - 2 x + 3 y = 6 (i v) x = 3 y$ $(v) 2 x = - 5 y (v i) 3 x + 2 = 0 (v i i) y - 2 = 0 (v i i i) 5 = 2 x$

Discussion

7490.	(s+1)−2 is the Laplace transform of
Answer» $(s + 1)^{- 2}$ is the Laplace transform of

Discussion

7491.	Question 2 In Figure, find tan P – cot R.
Answer» Question 2 In Figure, find tan P – cot R.

Discussion

7492.	AC and BD are two perpendicular diameters of a circle ABCD. Given that the area of the shaded portion is 308 cm2, calculate the circumference of the circle.
Answer» $A C$ and $B D$ are two perpendicular diameters of a circle $A B C D$ . Given that the area of the shaded portion is $308 c m^{2}$ , calculate the circumference of the circle.

7492.

AC and BD are two perpendicular diameters of a circle ABCD. Given that the area of the shaded portion is 308 cm2, calculate the circumference of the circle.

Answer»

$A C$ and $B D$ are two perpendicular diameters of a circle $A B C D$ . Given that the area of the shaded portion is $308 c m^{2}$ , calculate the circumference of the circle.

Discussion

7493.	Which among the following is irrational?
Answer» Which among the following is irrational?

Discussion

7494.	((x-2√6)(5√3+5√2)/5√3-5√2) = 1 then x = ?
Answer» ((x-2√6)(5√3+5√2)/5√3-5√2) = 1 then x = ?

Discussion

7495.	Two cubes each of volume 125 cm3 are joined end to end to form a solid. Find the surface area of the resulting cuboid.
Answer» Two cubes each of volume 125 $c m^{3}$ are joined end to end to form a solid. Find the surface area of the resulting cuboid.

Discussion

7496.	If an angle of a parallelogram is half of its adjacent angle, find the angles of the parallelogram. [2 MARKS]
Answer» If an angle of a parallelogram is half of its adjacent angle, find the angles of the parallelogram. [2 MARKS]

Discussion

7497.	The roots of x2 - 8x + 12 = 0, are
Answer» The roots of x² - 8x + 12 = 0, are

Discussion

7498.	Evaluate each of the followingsin2 30° + sin2 45° + sin2 60° + sin2 60° + sin2 90°
Answer» Evaluate each of the following sin² 30° + sin² 45° + sin²60° + sin² 60° + sin² 90°

Discussion

7499.	Solve the following pair of equations.5x−1+1y−2=2 6x−1−3y−2=1 Here, x ≠ 1 and y ≠ 2Choose the correct answer from the given options.
Answer» Solve the following pair of equations. $\frac{5}{x - 1} + \frac{1}{y - 2} = 2$ $\frac{6}{x - 1} - \frac{3}{y - 2} = 1$ Here, x $\neq$ 1 and y $\neq$ 2 Choose the correct answer from the given options.

Discussion

7500.	If the list price of a toy is reduced by Rs. 2, a person can buy 2 toys more for Rs. 360. Find the original price of the toy.
Answer» If the list price of a toy is reduced by Rs. 2, a person can buy 2 toys more for Rs. 360. Find the original price of the toy.

Discussion

Explore topic-wise InterviewSolutions in .

3.If a, b, c>0 , then prove that a/b + b/c + c/a > ab+bc+ca

A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius. The total height of the toy is 15.5 cm. Find the totalsurface area of the toy. [CBSE 2012]

Solve the following systems of equations: x3+y4=11 5x6−y3=−7

Two arithmetic progressions have the same common difference. Their first terms are A and B respectively. The difference between their nth terms is _________.

The sum of the squares of two consecutive odd numbers is 394. Find the numbers.

The lengths of the diagonals of a rhombus are 40 cm and 42 cm. Find the length of each side of the rhombus.

Factorise the following using appropriate identities: 9y2–6y+1

Show that : cos θ (tan θ + 2 ) (2 tan θ +1 ) = 2 sec θ + 5 sin θ

If the angle of elevation of a cloud from a point 200 m above a lake is 30∘ and the angle of depression of its reflection in the lake is 60∘, then the height of the cloud above the lake is ___.

The angle of elevation of a jet fighter from a point A on the ground is 60∘. After a flight of 15 seconds, the angle of elevation changes to 30∘. If the jet is flying at a speed of 720 km/hour, find the constant height at which the jet is flying. [Use √3=1.732]

if the seventh term from the beginning and end in the binomial expansion of 23+133n are equal, find n.

Question 5If P(E) = 0.05, what is the probability of ‘not E’?

If the lines y = 3 + 7 &amp; 2y + p = 3 are || to each other, find the value of p.

35. In YSDE let β be fringe width and I_o be intensity at the central bright fringe. At a distance x from the central bright fringe, the intensity will be

If one of the diagonal of a trapezium divides the other in the ratio 2:1 prove that one of the parallel sides is twice the other

Two circles touch externally at a point P. From a point T on the tangent at P, tangents TQ and TR are drawn to the circles with points of contact Q and R respectively. Prove that TQ = TR.

A solid iron pole consists of a cylinder of height 220 cm and base diameter 24 cm, which is surmounted by another cylinder of height 60 cm and radius 8 cm. Find the mass of the pole, given that 1cm3 of iron has approximately 8 g mass. (Use π=3.14) [3 MARKS]

Solve the following quadratic equations by factorization:25x (x + 1) = −4

The sum of the first 7 terms of an AP is 63 and the sum of it's next 7 terms is 161. Find the 28th term of this AP.

Express 3825 as a product of its prime factors.

To solve the quadratic equation 9x2+34x-2=0 by the method of completing the square, without making making the coefficient of x2 unity, we must add and subtract _________.

If in a ΔABC,a2−b2a2+b2=sin(A−B)sin(A+B), prove that it is either a right-angled or an isosceles triangle.

For what value of k will the following pair of linear equation have no solution? 2x+3y=9,6x+(k−2)y=(3k−2).

The sum of three non zero prime no.s is 100 . One of them exceedsthe other by 36. Find the largest number.

The length of the hypotenuse of an isosceles right triangle whose one side is 42 cm is(a) 12 cm(b) 8 cm(c) 82 cm(d) 122 cm

If a vertex of a triangle be (1, 1) and the middle points of the sides through it be (−2,−3) and (5 2) find the other vertices.

The difference between the outer and inner curved surface areas of a hollow right circular cylinder 14 cm long is 88 cm2. If the volume of metal used in making the cylinder is 176 cm3, find the outer and inner diameters of the cylinder. (Use π = 22/7)

Prove by vector method that the internal bisectors of the angles of a triangle are concurrent.

In the given figure, PA and PB are two tangents to the circle with centre O. If ∠APB = 60∘ then ∠OAB is [CBSE 2011](a) 15∘(b) 30∘(c) 60∘(d) 90∘

How many tangents can be drawn through a point on a circle?

What is the graph of a linear equation in 2 variables?

Let A be a square matrix such that A(adj A)=⎡⎢⎣400040004⎤⎥⎦. Then the value of |adj(adj A)||adj A| is

The pages of a book are numbered for 1 to 100 manually. How many times will be it is essential to write the number 5?

Let abc be a right triangle in which ab=3cm , bc=4cm and angle b =90 degree . Bd is perpendicular from b on ac . The circle through b,c,d is drawn. Construct the tangents from a to this circle

A cylinder with base radius of 8 cm and height of 2 cm is melted to form a cone of height 6 cm. The radius of the cone is(a) 4 cm(b) 5 cm(c) 6 cm(d) 8 cm

If tan A=34 and A+B=90°, then what is the value of cot B?

Question 2Express the following linear equations in the form ax + by + c = 0 and indicate the values of a, b and c in each case:(i)2x+3y=9.35 (ii)x−y5−10=0 (iii)−2x+3y=6 (iv)x=3y(v)2x=−5y (vi)3x+2=0 (vii)y−2=0 (viii)5=2x

(s+1)−2 is the Laplace transform of

Question 2 In Figure, find tan P – cot R.

AC and BD are two perpendicular diameters of a circle ABCD. Given that the area of the shaded portion is 308 cm2, calculate the circumference of the circle.

Which among the following is irrational?

((x-2√6)(5√3+5√2)/5√3-5√2) = 1 then x = ?

Two cubes each of volume 125 cm3 are joined end to end to form a solid. Find the surface area of the resulting cuboid.

If an angle of a parallelogram is half of its adjacent angle, find the angles of the parallelogram. [2 MARKS]

The roots of x2 - 8x + 12 = 0, are

Evaluate each of the followingsin2 30° + sin2 45° + sin2 60° + sin2 60° + sin2 90°

Solve the following pair of equations.5x−1+1y−2=2 6x−1−3y−2=1 Here, x ≠ 1 and y ≠ 2Choose the correct answer from the given options.

If the list price of a toy is reduced by Rs. 2, a person can buy 2 toys more for Rs. 360. Find the original price of the toy.

If the lines y = 3 + 7 & 2y + p = 3 are || to each other, find the value of p.