24740 + Interview Questions in Mathematics Page 95 InterviewSolution

4701.	Nazima is fly fishing in a stream. The tip of her fishing rod is 1.8 m above the surface of the water and the fly at the end of the string rests on the water 3.6 m away and 2.4 m from a point directly under the tip of the road. Assuming that her string (from the tip of her road to the fly) is taut, how much string does she have out (in the given figure)? If she pulls the string at the rate of 5 cm per second, what will the horizontal distance of the fly from her after 12 seconds.
Answer» Nazima is fly fishing in a stream. The tip of her fishing rod is 1.8 m above the surface of the water and the fly at the end of the string rests on the water 3.6 m away and 2.4 m from a point directly under the tip of the road. Assuming that her string (from the tip of her road to the fly) is taut, how much string does she have out (in the given figure)? If she pulls the string at the rate of 5 cm per second, what will the horizontal distance of the fly from her after 12 seconds.

Discussion

4702.	If each side of a triangle is doubled, then find percentage increase in its area.
Answer» If each side of a triangle is doubled, then find percentage increase in its area.

Discussion

4703.	76. Solve for x and y using substitution method: 2x+5y/xy=6,4x-5y/xy=-3 where x and y are not equal to zero.
Answer» 76. Solve for x and y using substitution method: 2x+5y/xy=6,4x-5y/xy=-3 where x and y are not equal to zero.

Discussion

4704.	In the adjoining figure, if BC = a, AC = b, AB = c and ∠CAB = 120∘, then the correct relation is-
Answer» In the adjoining figure, if BC = a, AC = b, AB = c and $∠ C A B$ = $120^{\circ}$ , then the correct relation is-

4704.

In the adjoining figure, if BC = a, AC = b, AB = c and ∠CAB = 120∘, then the correct relation is-

Answer»

In the adjoining figure, if BC = a, AC = b, AB = c and $∠ C A B$ = $120^{\circ}$ , then the correct relation is-

Discussion

4705.	Prove the following trigonometric identities.(i) cot θ-tan θ=2 cos2 θ-1sin θ cos θ(ii) tan θ-cot θ=2 sin2 θ-1sin θ cos θ(iii) sin A-2sin3 A2cos3 A-cos A=tan A
Answer» Prove the following trigonometric identities. (i) $\cot θ - \tan θ = \frac{2 \cos^{2} θ - 1}{\sin θ \cos θ}$ (ii) $\tan θ - \cot θ = \frac{2 \sin^{2} θ - 1}{\sin θ \cos θ}$ (iii) $\frac{\sin A - 2 \sin^{3} A}{2 \cos^{3} A - \cos A} = \tan A$

Discussion

4706.	S1 : The graph of a linear equation is a straight line S2 : The solution of a pair of linear equations is a point common to two lines.
Answer» S1 : The graph of a linear equation is a straight line S2 : The solution of a pair of linear equations is a point common to two lines.

4706.

S1 : The graph of a linear equation is a straight line S2 : The solution of a pair of linear equations is a point common to two lines.

Answer»

S1 : The graph of a linear equation is a straight line

S2 : The solution of a pair of linear equations is a point common to two lines.

Discussion

4707.	A round table cover has six equal designs as shown in figure. If the radius of the cover is 28 cm, find the cost of making the designs at the rate of ₹0.35 per cm2 . (Use √3=1.7)
Answer» A round table cover has six equal designs as shown in figure. If the radius of the cover is 28 cm, find the cost of making the designs at the rate of ₹0.35 per $c m^{2}$ . (Use $\sqrt{3} = 1.7$ )

4707.

A round table cover has six equal designs as shown in figure. If the radius of the cover is 28 cm, find the cost of making the designs at the rate of ₹0.35 per cm2 . (Use √3=1.7)

Answer»

A round table cover has six equal designs as shown in figure. If the radius of the cover is 28 cm, find the cost of making the designs at the rate of ₹0.35 per $c m^{2}$ . (Use $\sqrt{3} = 1.7$ )

Discussion

4708.	A hopscotch is formed by the same size of rectangles as shown. If the perimeter of this structure is 110 units. What is the value of 'k'?6
Answer» A hopscotch is formed by the same size of rectangles as shown. If the perimeter of this structure is 110 units. What is the value of 'k'? 6

Discussion

4709.	Question 132 The planet Uranus is approximately 2,896,819,200,000 metres away from the Sun. What is this distance in standard form?
Answer» Question 132 The planet Uranus is approximately 2,896,819,200,000 metres away from the Sun. What is this distance in standard form?

4709.

Question 132 The planet Uranus is approximately 2,896,819,200,000 metres away from the Sun. What is this distance in standard form?

Answer»

Question 132

The planet Uranus is approximately 2,896,819,200,000 metres away from the Sun. What is this distance in standard form?

Discussion

4710.	The sum of the radius of the base and height of a solid cylinder is 37 m. If the total surface area of the solid cylinder is 1628 m2. Find the volume of the cylinder.
Answer» The sum of the radius of the base and height of a solid cylinder is 37 m. If the total surface area of the solid cylinder is 1628 $m^{2}$ . Find the volume of the cylinder.

Discussion

4711.	The figure formed by joining the mid-points of the adjacent sides of a parallelogram is a(a) rectangle(b) parallelogram(c) rhombus(d) square
Answer» The figure formed by joining the mid-points of the adjacent sides of a parallelogram is a (a) rectangle (b) parallelogram (c) rhombus (d) square

Discussion

4712.	for what value of k x + 1 is a factor of k x^2- x-4
Answer» for what value of k x + 1 is a factor of k x^2- x-4

Discussion

4713.	If f(x) = x-1, what is f(1)?
Answer» If f(x) = x-1, what is f(1)?

Discussion

4714.	Which of the following is a factor of 5xy?
Answer» Which of the following is a factor of 5xy?

Discussion

4715.	If z1 and z2 are two complex numbers such that z1=z2 and arg(z1) + arg(z2) = π, then show that z1=-z2¯.
Answer» If z₁ and z₂ are two complex numbers such that $\|z_{1}\| = \|z_{2}\|$ and arg(z₁) + arg(z₂) = $π$ , then show that $z_{1} = - \bar{z_{2}}$ .

Discussion

4716.	Factorise:33a3-b3-55c3-315abc
Answer» Factorise: $3 \sqrt{3} a^{3} - b^{3} - 5 \sqrt{5} c^{3} - 3 \sqrt{15} a b c$

Discussion

4717.	Which of the following fraction is equal to 1√5−√7?
Answer» Which of the following fraction is equal to $\frac{1}{\sqrt{5} - \sqrt{7}}$ ?

Discussion

4718.	In figure, PQRS and MNRL are rectangles. If point M is the midpoint of side PR then prove that, (i)SL=LR, (ii)LN=12SQ.
Answer» In figure, PQRS and MNRL are rectangles. If point M is the midpoint of side PR then prove that, $(i) S L = L R, (i i) L N = \frac{1}{2} S Q .$

Discussion

4719.	What do we understand by the term statistics?
Answer» What do we understand by the term statistics?

Discussion

4720.	Find the value of: 1+sin30∘cos30∘+cos30∘1+sin30∘
Answer» Find the value of: $\frac{1 + s i n 30^{\circ}}{c o s 30^{\circ}} + \frac{c o s 30^{\circ}}{1 + s i n 30^{\circ}}$

4720.

Find the value of: 1+sin30∘cos30∘+cos30∘1+sin30∘

Answer»

Find the value of:

$\frac{1 + s i n 30^{\circ}}{c o s 30^{\circ}} + \frac{c o s 30^{\circ}}{1 + s i n 30^{\circ}}$

Discussion

4721.	Which of the following is a rational number between 4 and 4.5?
Answer» Which of the following is a rational number between 4 and 4.5?

Discussion

4722.	In ΔABC,∠C=60o and ∠C>∠B.Which is the longest side of the triangle?
Answer» In $Δ A B C, ∠ C = 60^{o}$ and $∠ C > ∠ B$ . Which is the longest side of the triangle?

Discussion

4723.	A non-terminating and non-recurring decimal number is known as a/an _________.
Answer» A non-terminating and non-recurring decimal number is known as a/an _________.

Discussion

4724.	In grouped frequency distribution, what is another name for class size? __
Answer» In grouped frequency distribution, what is another name for class size? __

Discussion

4725.	If the radius of a sphere is measured as 9 m with an error of 0.03 m, then find the approximate error in calculating in surface area.
Answer» If the radius of a sphere is measured as 9 m with an error of 0.03 m, then find the approximate error in calculating in surface area.

Discussion

4726.	Express 0.8+0.¯¯¯7+0.4¯¯¯3 in the form pq, where p and q are integers and q≠0.
Answer» Express $0.8 + 0. ¯ ¯ ¯ 7 + 0.4 ¯ ¯ ¯ 3$ in the form $\frac{p}{q},$ where p and q are integers and $q \neq 0$ .

Discussion

4727.	The equivalent fraction of 67 is __.
Answer» The equivalent fraction of $\frac{6}{7}$ is __.

Discussion

4728.	The area of parallelogram ABCD is:
Answer» The area of parallelogram ABCD is:

4728.

The area of parallelogram ABCD is:

Answer»

The area of parallelogram ABCD is:

Discussion

4729.	‘-p’ and ‘q’ are the zeroes of the polynomialx2–bx+c.The zeroes of the polynomial x2–bxy+cy2are
Answer» ‘-p’ and ‘q’ are the zeroes of the polynomial $x^{2} - b x + c$ . The zeroes of the polynomial $x^{2} - b x y + c y^{2}$ are

Discussion

4730.	(3x − 2y)3 + (2y − 4z)3 + (4z − 3x)3
Answer» (3x − 2y)³ + (2y − 4z)³ + (4z − 3x)³

Discussion

4731.	The distance of the point (-3, 4) from x-axis is (a) 3 (b) -3 (c) 4 (d) 5
Answer» The distance of the point (-3, 4) from x-axis is (a) 3 (b) -3 (c) 4 (d) 5

4731.

The distance of the point (-3, 4) from x-axis is (a) 3 (b) -3 (c) 4 (d) 5

Answer»

The distance of the point (-3, 4) from x-axis is

(a) 3 (b) -3 (c) 4 (d) 5

Discussion

4732.	Are the given dotted line segments parallel ?
Answer» Are the given dotted line segments parallel ?

Discussion

4733.	For constructing an angle of 75∘.Steps of construction:Step 1: Draw ray ABStep 2: Construct ∠BAC=60∘Step 3: Construct
Answer» For constructing an angle of $75^{\circ}$ . Steps of construction: Step 1: Draw ray AB Step 2: Construct $∠ B A C = 60^{\circ}$ Step 3: Construct

Discussion

4734.	If the diameter of a sphere decreased by 25% then how much percent it volume and surface area will increase.
Answer» If the diameter of a sphere decreased by 25% then how much percent it volume and surface area will increase.

Discussion

4735.	37. Sides of a rhombus are parallel to the lines x+y=1 and 7x-y=5 .it is given that diagonals of the rhombus intersect at (1,3) and one vertex,'A',of the rhombus lies on the line y=2x.Sum of all possible x coordinates of the vertex A is
Answer» 37. Sides of a rhombus are parallel to the lines x+y=1 and 7x-y=5 .it is given that diagonals of the rhombus intersect at (1,3) and one vertex,'A',of the rhombus lies on the line y=2x.Sum of all possible x coordinates of the vertex A is

Discussion

4736.	ABC is an isosceles triangle such that AB = AC and AD is the median to base BC. Then, ∠BAD =(a) 55°(b) 70°(c) 35°(d) 110°
Answer» ABC is an isosceles triangle such that AB = AC and AD is the median to base BC. Then, ∠BAD = (a) 55° (b) 70° (c) 35° (d) 110°

Discussion

4737.	The perimeter of an isosceles triangle is 42 cm and its base is 32 times each of the equal sides. Find the length of each side of the triangle, area of the triangle and the height of the triangle.
Answer» The perimeter of an isosceles triangle is 42 cm and its base is $\frac{3}{2}$ times each of the equal sides. Find the length of each side of the triangle, area of the triangle and the height of the triangle.

Discussion

4738.	Question 2It is required to make a closed cylindrical tank of height 1 m and base diameter 140 cm from a metal sheet. How many square meters of the sheet is required for the same?[Assume π=227]
Answer» Question 2 It is required to make a closed cylindrical tank of height 1 m and base diameter 140 cm from a metal sheet. How many square meters of the sheet is required for the same? $[A s s u m e π = \frac{22}{7}]$

Discussion

4739.	Identify the figures that do not lie on the same base and between the same parallels.
Answer» Identify the figures that do not lie on the same base and between the same parallels.

Discussion

4740.	Question 115State whether the statements are True or False.Every parallelogram is a rectangle.
Answer» Question 115 State whether the statements are True or False. Every parallelogram is a rectangle.

Discussion

4741.	Question 5 (ii) An organization selected 2400 families at random and surveyed them to determine a relationship between income level and the number of vehicles in a family. The information gathered is listed in the table below: Monthly income(inRs)Vehicles per family012Above 2Less than 7000101602507000−10000030527210000−13000153529113000−160002469592516000 or more15798288 Suppose a family is chosen, find the probability that the family chosen is (ii) earning Rs16000 or more per month and owning exactly 1vehicle.
Answer» Question 5 (ii) An organization selected 2400 families at random and surveyed them to determine a relationship between income level and the number of vehicles in a family. The information gathered is listed in the table below: $\begin{matrix} M o n t h l y i n c o m e (i n R s) & V e h i c l e s p e r f a m i l y 0 & 1 & 2 & A b o v e 2 L e s s t h a n 7000 & 10 & 160 & 25 & 0 7000 - 10000 & 0 & 305 & 27 & 2 10000 - 13000 & 1 & 535 & 29 & 1 13000 - 16000 & 2 & 469 & 59 & 25 16000 o r m o r e & 1 & 579 & 82 & 88 \end{matrix}$ Suppose a family is chosen, find the probability that the family chosen is (ii) earning Rs16000 or more per month and owning exactly 1vehicle.

Discussion

4742.	In the given figure, θ equals
Answer» In the given figure, $θ$ equals

Discussion

4743.	Question 6: Consider the following figure of line ←−→MN . Say whether following statement is true or false in the context of the given figure: (a) Ray −−→OP same as ray −−→OM.
Answer» Question 6: Consider the following figure of line $\leftarrow - \to M N$ . Say whether following statement is true or false in the context of the given figure: (a) Ray $- - \to O P$ same as ray $- - \to O M$ .

4743.

Question 6: Consider the following figure of line ←−→MN . Say whether following statement is true or false in the context of the given figure: (a) Ray −−→OP same as ray −−→OM.

Answer»

Question 6: Consider the following figure of line $\leftarrow - \to M N$ . Say whether following statement is true or false in the context of the given figure:

(a) Ray $- - \to O P$ same as ray $- - \to O M$ .

Discussion

4744.	A person will keep throwing dice until he get 6. If he get 6 then experiment will be stopped. The probability of experiment if every number should appear atleast once will be?
Answer» A person will keep throwing dice until he get 6. If he get 6 then experiment will be stopped. The probability of experiment if every number should appear atleast once will be?

Discussion

4745.	Show that the lines 2x+3y+19=0 and 9x+6y-17=0 cut the coordinate axes in concyclic points.
Answer» Show that the lines 2x+3y+19=0 and 9x+6y-17=0 cut the coordinate axes in concyclic points.

Discussion

4746.	A factory manufactures 120000 pencils daily. The pencils are cylindrical in shape each of length 25 cm and circumference of base as 1.5 cm. Determine the cost of colouring the curved surfaces of the pencils manufactured in one day at Rs 0.05 per dm2.
Answer» A factory manufactures 120000 pencils daily. The pencils are cylindrical in shape each of length 25 cm and circumference of base as 1.5 cm. Determine the cost of colouring the curved surfaces of the pencils manufactured in one day at $R s 0.05 p e r d m^{2}$ .

Discussion

4747.	If a +b +c =5 and ab +bc+ca =10,then prove that a cube +b cube+c cube -3abc =-25
Answer» If a +b +c =5 and ab +bc+ca =10,then prove that a cube +b cube+c cube -3abc =-25

Discussion

4748.	Burst the bubble if the rational number is terminating.
Answer» Burst the bubble if the rational number is terminating.

Discussion

4749.	Factorize: 6a2−a−15
Answer» Factorize: $6 a^{2} - a - 15$

Discussion

4750.	Find the value of A to make the fraction onthe right hand side equivalent to 34
Answer» $Find the value of A to make the fraction on$ $the right hand side equivalent to \frac{3}{4}$

Discussion

Explore topic-wise InterviewSolutions in .

If each side of a triangle is doubled, then find percentage increase in its area.

76. Solve for x and y using substitution method: 2x+5y/xy=6,4x-5y/xy=-3 where x and y are not equal to zero.

In the adjoining figure, if BC = a, AC = b, AB = c and ∠CAB = 120∘, then the correct relation is-

Prove the following trigonometric identities.(i) cot θ-tan θ=2 cos2 θ-1sin θ cos θ(ii) tan θ-cot θ=2 sin2 θ-1sin θ cos θ(iii) sin A-2sin3 A2cos3 A-cos A=tan A

S1 : The graph of a linear equation is a straight line S2 : The solution of a pair of linear equations is a point common to two lines.

A round table cover has six equal designs as shown in figure. If the radius of the cover is 28 cm, find the cost of making the designs at the rate of ₹0.35 per cm2 . (Use √3=1.7)

A hopscotch is formed by the same size of rectangles as shown. If the perimeter of this structure is 110 units. What is the value of 'k'?6

Question 132 The planet Uranus is approximately 2,896,819,200,000 metres away from the Sun. What is this distance in standard form?

The sum of the radius of the base and height of a solid cylinder is 37 m. If the total surface area of the solid cylinder is 1628 m2. Find the volume of the cylinder.

The figure formed by joining the mid-points of the adjacent sides of a parallelogram is a(a) rectangle(b) parallelogram(c) rhombus(d) square

for what value of k x + 1 is a factor of k x^2- x-4

If f(x) = x-1, what is f(1)?

Which of the following is a factor of 5xy?

If z1 and z2 are two complex numbers such that z1=z2 and arg(z1) + arg(z2) = π, then show that z1=-z2¯.

Factorise:33a3-b3-55c3-315abc

Which of the following fraction is equal to 1√5−√7?

In figure, PQRS and MNRL are rectangles. If point M is the midpoint of side PR then prove that, (i)SL=LR, (ii)LN=12SQ.

What do we understand by the term statistics?

Find the value of: 1+sin30∘cos30∘+cos30∘1+sin30∘

Which of the following is a rational number between 4 and 4.5?

In ΔABC,∠C=60o and ∠C&gt;∠B.Which is the longest side of the triangle?

A non-terminating and non-recurring decimal number is known as a/an _________.

In grouped frequency distribution, what is another name for class size? __

If the radius of a sphere is measured as 9 m with an error of 0.03 m, then find the approximate error in calculating in surface area.

Express 0.8+0.¯¯¯7+0.4¯¯¯3 in the form pq, where p and q are integers and q≠0.

The equivalent fraction of 67 is __.

The area of parallelogram ABCD is:

‘-p’ and ‘q’ are the zeroes of the polynomialx2–bx+c.The zeroes of the polynomial x2–bxy+cy2are

(3x − 2y)3 + (2y − 4z)3 + (4z − 3x)3

The distance of the point (-3, 4) from x-axis is (a) 3 (b) -3 (c) 4 (d) 5

Are the given dotted line segments parallel ?

For constructing an angle of 75∘.Steps of construction:Step 1: Draw ray ABStep 2: Construct ∠BAC=60∘Step 3: Construct

If the diameter of a sphere decreased by 25% then how much percent it volume and surface area will increase.

37. Sides of a rhombus are parallel to the lines x+y=1 and 7x-y=5 .it is given that diagonals of the rhombus intersect at (1,3) and one vertex,'A',of the rhombus lies on the line y=2x.Sum of all possible x coordinates of the vertex A is

ABC is an isosceles triangle such that AB = AC and AD is the median to base BC. Then, ∠BAD =(a) 55°(b) 70°(c) 35°(d) 110°

The perimeter of an isosceles triangle is 42 cm and its base is 32 times each of the equal sides. Find the length of each side of the triangle, area of the triangle and the height of the triangle.

Question 2It is required to make a closed cylindrical tank of height 1 m and base diameter 140 cm from a metal sheet. How many square meters of the sheet is required for the same?[Assume π=227]

Identify the figures that do not lie on the same base and between the same parallels.

Question 115State whether the statements are True or False.Every parallelogram is a rectangle.

In the given figure, θ equals

Question 6: Consider the following figure of line ←−→MN . Say whether following statement is true or false in the context of the given figure: (a) Ray −−→OP same as ray −−→OM.

A person will keep throwing dice until he get 6. If he get 6 then experiment will be stopped. The probability of experiment if every number should appear atleast once will be?

Show that the lines 2x+3y+19=0 and 9x+6y-17=0 cut the coordinate axes in concyclic points.

A factory manufactures 120000 pencils daily. The pencils are cylindrical in shape each of length 25 cm and circumference of base as 1.5 cm. Determine the cost of colouring the curved surfaces of the pencils manufactured in one day at Rs 0.05 per dm2.

If a +b +c =5 and ab +bc+ca =10,then prove that a cube +b cube+c cube -3abc =-25

Burst the bubble if the rational number is terminating.

Factorize: 6a2−a−15

Find the value of A to make the fraction onthe right hand side equivalent to 34

In ΔABC,∠C=60o and ∠C>∠B.Which is the longest side of the triangle?