32581 + Interview Questions in Mathematics Page 8 InterviewSolution

351.	137. If 1-tanθ = k, then prove that ( secθ + tanθ + cosecθ ) is equal to [(2-k)
Answer» 137. If 1-tanθ = k, then prove that ( secθ + tanθ + cosecθ ) is equal to [(2-k)

Discussion

352.	Question 6In the below figure, if ΔABE≅ΔACD, show that ΔADE∼ΔABC.
Answer» Question 6 In the below figure, if $Δ A B E ≅ Δ A C D$ , show that $Δ A D E \sim Δ A B C$ .

Discussion

353.	In fig., if OC = 9 cm and OB = 15 cm, then BC + BD is equal to:
Answer» In fig., if OC = 9 cm and OB = 15 cm, then BC + BD is equal to:

353.

In fig., if OC = 9 cm and OB = 15 cm, then BC + BD is equal to:

Answer»

In fig., if OC = 9 cm and OB = 15 cm, then BC + BD is equal to:

Discussion

354.	The value of cos2 17° − sin2 73° is(a) 1(b) 13(c) 0(d) −1
Answer» The value of cos² 17° − sin² 73° is (a) 1 (b) $\frac{1}{3}$ (c) 0 (d) −1

Discussion

355.	Find the sum of the following surds(1) (2) (3)
Answer» Find the sum of the following surds (1) (2) (3)

355.

Find the sum of the following surds(1) (2) (3)

Answer»

Find the sum of the following surds

(1)

(2)

(3)

Discussion

356.	A pit is dug in the shape of a cuboid with dimensions 10 m×8 m×3 m. The earth taken out is spread evenly on a rectangular plot of land with dimensions 40 m×30 m. What is the increase in the level of the plot?
Answer» A pit is dug in the shape of a cuboid with dimensions $10 m \times 8 m \times 3 m .$ The earth taken out is spread evenly on a rectangular plot of land with dimensions $40 m \times 30 m$ . What is the increase in the level of the plot?

Discussion

357.	Question 149 Repeater Machine Similarly, repeater machine is a hypothetical machine which automatically enlarges items several times. e.g. Sending a piece of wire through a (×24) machine is the same as putting it through a (×2) machine four times. So, if you send a 3 cm piece of wire thorugh a (×2)4 machine, its length becomes 3×2×2×2×2=48 cm. It can also be written that a base (2) machine is being applied 4 times. What will be the new length of a 4 cm strip inserted in the machine?
Answer» Question 149 Repeater Machine Similarly, repeater machine is a hypothetical machine which automatically enlarges items several times. e.g. Sending a piece of wire through a $(\times 2^{4})$ machine is the same as putting it through a $(\times 2)$ machine four times. So, if you send a 3 cm piece of wire thorugh a $(\times 2)^{4}$ machine, its length becomes $3 \times 2 \times 2 \times 2 \times 2 = 48 c m .$ It can also be written that a base (2) machine is being applied 4 times. What will be the new length of a 4 cm strip inserted in the machine?

357.

Question 149 Repeater Machine Similarly, repeater machine is a hypothetical machine which automatically enlarges items several times. e.g. Sending a piece of wire through a (×24) machine is the same as putting it through a (×2) machine four times. So, if you send a 3 cm piece of wire thorugh a (×2)4 machine, its length becomes 3×2×2×2×2=48 cm. It can also be written that a base (2) machine is being applied 4 times. What will be the new length of a 4 cm strip inserted in the machine?

Answer»

Question 149

Repeater Machine
Similarly, repeater machine is a hypothetical machine which automatically enlarges items several times. e.g. Sending a piece of wire through a $(\times 2^{4})$ machine is the same as putting it through a $(\times 2)$ machine four times.
So, if you send a 3 cm piece of wire thorugh a $(\times 2)^{4}$ machine, its length becomes $3 \times 2 \times 2 \times 2 \times 2 = 48 c m .$ It can also be written that a base (2) machine is being applied 4 times.

What will be the new length of a 4 cm strip inserted in the machine?

Discussion

358.	two spheres made up of same subs†an ce have radii in the ratio 2 is to 3 . their thermal heat capaties will be in the rat
Answer» two spheres made up of same subs†an ce have radii in the ratio 2 is to 3 . their thermal heat capaties will be in the rat

Discussion

359.	If the points A(x,y), B(3, 6) and C(−3,4) are collinear,show that x − 3y + 15 = 0
Answer» If the points A(x,y), B(3, 6) and C(−3,4) are collinear,show that x − 3y + 15 = 0

Discussion

360.	how to find less than ogive and more than ogive from the given frequency or cumulative frequency
Answer» how to find less than ogive and more than ogive from the given frequency or cumulative frequency

Discussion

361.	Question 38(i)In a game, the entry fee is of Rs 5. The game consists of a tossing a coin 3 times. If one or two heads show, Sweta gets her entry fee back. If she throws 3 heads, she receives double the entry fees. Otherwise, she will lose. For tossing a coin three times, find the probability that she loses the entry fee.
Answer» Question 38(i) In a game, the entry fee is of Rs 5. The game consists of a tossing a coin 3 times. If one or two heads show, Sweta gets her entry fee back. If she throws 3 heads, she receives double the entry fees. Otherwise, she will lose. For tossing a coin three times, find the probability that she loses the entry fee.

Discussion

362.	If tan θ=17, then cosec2 θ-sec2 θcosec2 θ+sec2 θ=(a) 57(b) 37(c) 112(d) 34
Answer» If $\tan θ = \frac{1}{\sqrt{7}}, then \frac{{cosec}^{2} θ - \sec^{2} θ}{{cosec}^{2} θ + \sec^{2} θ} =$ (a) $\frac{5}{7}$ (b) $\frac{3}{7}$ (c) $\frac{1}{12}$ (d) $\frac{3}{4}$

Discussion

363.	Find the area of the shaded region and also it's perimeter if the lengths of AB and BC is 28 and 21 cm respectively and BCD is a quadrant of a circle.AEC is a semicircle on AC as diameter.
Answer» Find the area of the shaded region and also it's perimeter if the lengths of AB and BC is 28 and 21 cm respectively and BCD is a quadrant of a circle.AEC is a semicircle on AC as diameter.

Discussion

364.	The diameter of a circle is a line, which joins two points on the circle and also passes through the centre of the circle. (In the adjoining figure AB is a diameter of the circle; C is its centre). Express the diameter of the circle (d) in terms of its radius (r).
Answer» The diameter of a circle is a line, which joins two points on the circle and also passes through the centre of the circle. (In the adjoining figure AB is a diameter of the circle; C is its centre). Express the diameter of the circle (d) in terms of its radius (r).

Discussion

365.	In the given inequation 2x > 6 ; which of the following cannot be the value of the x
Answer» In the given inequation 2x > 6 ; which of the following cannot be the value of the x

Discussion

366.	Find the coordinates of midpoint of the segment joining the points (22, 20) and (0, 16).
Answer» Find the coordinates of midpoint of the segment joining the points (22, 20) and (0, 16).

Discussion

367.	Twenty seven solid iron spheres each of radius 2cm are melted to form a new solid sphere. What will be the surface area of the new sphere?
Answer» Twenty seven solid iron spheres each of radius 2cm are melted to form a new solid sphere. What will be the surface area of the new sphere?

Discussion

368.	A wire can be bent in the form of a circle of radius 56 cm. If it is bent in the form fo a square, then its area will be(a) 3520 cm2(b) 6400 cm2(c) 7744 cm2(d) 8800 cm2
Answer» A wire can be bent in the form of a circle of radius 56 cm. If it is bent in the form fo a square, then its area will be (a) 3520 cm² (b) 6400 cm² (c) 7744 cm² (d) 8800 cm²

Discussion

369.	Find the depth of a cylindrical tank of radius 28 m, if its capacity is equal to that of a rectangular tank of size 28 m × 16 m × 11 m.
Answer» Find the depth of a cylindrical tank of radius 28 m, if its capacity is equal to that of a rectangular tank of size 28 m × 16 m × 11 m.

Discussion

370.	For what value of n, are the nth terms of two APs 63, 65, 67, and 3, 10, 17, … equal
Answer» For what value of n, are the n^th terms of two APs 63, 65, 67, and 3, 10, 17, … equal

Discussion

371.	Given that x - 5 is a factor of the cubic polynomial x3 - 35x2 + 13x - 35 , find all the zeroes of the polynomial .
Answer» Given that $x - \sqrt{5}$ is a factor of the cubic polynomial $x^{3} - 3 \sqrt{5} x^{2} + 13 x - 3 \sqrt{5}$ , find all the zeroes of the polynomial .

Discussion

372.	A fire in building B is reported on the telephone to two fire stations P and Q, 20 km apart from each other on a straight road. P observes that the fire is at an angle of 60∘ to the road and Q observes that it is at an angle of 45∘ to the road. Which station should send its team and how much will this team have to travel?
Answer» A fire in building B is reported on the telephone to two fire stations P and Q, 20 km apart from each other on a straight road. P observes that the fire is at an angle of $60^{\circ}$ to the road and Q observes that it is at an angle of $45^{\circ}$ to the road. Which station should send its team and how much will this team have to travel?

Discussion

373.	If the roots of the equation (csq-ab) xsq-2(asq-bc)x+bsq-ac=0 are equal prove that a=0 /a cube +b cube+c cube=3abc
Answer» If the roots of the equation (csq-ab) xsq-2(asq-bc)x+bsq-ac=0 are equal prove that a=0 /a cube +b cube+c cube=3abc

Discussion

374.	Krishnan bought chocolates for his brothers. When he grouped the chocolates in groups of 4, 1 chocolate was left, if grouped in 5, 4 chocolates were left, if grouped in 6, 1 chocolate was left and if grouped in 7, no chocolate was left ungrouped. If the total number of chocolates bought was less than 50, find the number of chocolates Krishnan bought.
Answer» Krishnan bought chocolates for his brothers. When he grouped the chocolates in groups of 4, 1 chocolate was left, if grouped in 5, 4 chocolates were left, if grouped in 6, 1 chocolate was left and if grouped in 7, no chocolate was left ungrouped. If the total number of chocolates bought was less than 50, find the number of chocolates Krishnan bought.

Discussion

375.	When x3 - 5x2 + 3x + 1 is divided by x - 1, find the remainder.\N
Answer» When x $^{3}$ - 5x $^{2}$ + 3x + 1 is divided by x - 1, find the remainder. \N

Discussion

376.	The diameter of a roller is 84 cm and its length is 120cm. It takes 500 complete revolution to move once over to level playground. Find the area of the playground in m2.
Answer» The diameter of a roller is 84 cm and its length is 120cm. It takes 500 complete revolution to move once over to level playground. Find the area of the playground in $m^{2}$ .

Discussion

377.	Question 1In the following question out of the four options only one is correct, write the correct answerThe solution of which of the following equations is neither a fraction nor an integer?(a) 3x + 2 = 5x + 2(b) 4x – 18 = 2(c) 4x + 7 = x + 2(d) 5x – 8 = x + 4
Answer» Question 1 In the following question out of the four options only one is correct, write the correct answer The solution of which of the following equations is neither a fraction nor an integer? (a) 3x + 2 = 5x + 2 (b) 4x – 18 = 2 (c) 4x + 7 = x + 2 (d) 5x – 8 = x + 4

377.

Question 1In the following question out of the four options only one is correct, write the correct answerThe solution of which of the following equations is neither a fraction nor an integer?(a) 3x + 2 = 5x + 2(b) 4x – 18 = 2(c) 4x + 7 = x + 2(d) 5x – 8 = x + 4

Answer»

Question 1

In the following question out of the four options only one is correct, write the correct answer

The solution of which of the following equations is neither a fraction nor an integer?

(a) 3x + 2 = 5x + 2

(b) 4x – 18 = 2

(c) 4x + 7 = x + 2

(d) 5x – 8 = x + 4

Discussion

378.	how to convert tan 0.986 to degrees ?
Answer» how to convert tan 0.986 to degrees ?

Discussion

379.	Find the condition that zeroes of the polynomial ax2 + bx + c are reciprocal of each other
Answer» Find the condition that zeroes of the polynomial ax²+ bx + c are reciprocal of each other

Discussion

380.	Which of the following pair of linear equations has infinite solutions?
Answer» Which of the following pair of linear equations has infinite solutions?

Discussion

381.	If the distance between A (1, 3) and B (x, 7) is 5 then which of the following can be the value of x?
Answer» If the distance between A (1, 3) and B (x, 7) is 5 then which of the following can be the value of x?

Discussion

382.	The diagonals of a trapezium ABCD with AB \|\| DC intersect each other at point O. If AB = 2 CD, find the ratio of the areas of triangles AOB and COD.
Answer» The diagonals of a trapezium ABCD with AB \|\| DC intersect each other at point O. If AB = 2 CD, find the ratio of the areas of triangles AOB and COD.

Discussion

383.	Question 9The point P(5,-3) is one of the two points of trisection of line segment joining the points A(7,-2) and B(1,-5).
Answer» Question 9 The point P(5,-3) is one of the two points of trisection of line segment joining the points A(7,-2) and B(1,-5).

Discussion

384.	Four points A, B, C, and D are given on circle.Line segment AB and CD are parallel. Find the distance between AB and CD.
Answer» Four points A, B, C, and D are given on circle. Line segment AB and CD are parallel. Find the distance between AB and CD.

384.

Four points A, B, C, and D are given on circle.Line segment AB and CD are parallel. Find the distance between AB and CD.

Answer»

Four points A, B, C, and D are given on circle.

Line segment AB and CD are parallel. Find the distance between AB and CD.

Discussion

385.	Look at the measures shown in the adjacent figure and find the area of ☐ PQRS.
Answer» Look at the measures shown in the adjacent figure and find the area of ☐ PQRS.

Discussion

386.	A 20 m deep well of diameter 7 m is dug and the earth taken out is evenly spread out to form a platform of 22 m by 14 m. Find the height of the platform.
Answer» A 20 m deep well of diameter 7 m is dug and the earth taken out is evenly spread out to form a platform of 22 m by 14 m. Find the height of the platform.

Discussion

387.	A factory manufactures 120,000 pencils daily . The pencil 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 ₹0.05 per dm2.
Answer» A factory manufactures 120,000 pencils daily . The pencil 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 ₹0.05 per dm².

Discussion

388.	Let p,q and r denote the lengths of the sides QR,PR and PQ of a triangle PQR respectively. Then pcos2(R2)+rcos2(P2)
Answer» Let $p, q$ and $r$ denote the lengths of the sides $Q R, P R$ and $P Q$ of a triangle $P Q R$ respectively. Then $p {cos}^{2} (\frac{R}{2}) + r {cos}^{2} (\frac{P}{2})$

Discussion

389.	If the sum of the roots of the equation x2-k+6x+22k-1=0 is equal to half of their product, then k =(a) 6(b) 7(c) 1(d) 5
Answer» If the sum of the roots of the equation $x^{2} - (k + 6) x + 2 (2 k - 1) = 0$ is equal to half of their product, then k = (a) 6 (b) 7 (c) 1 (d) 5

Discussion

390.	From a solid cylinder of height 2.8 cm and diameter 4.2 cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid. (Take π=227). [CBSE 2014]
Answer» From a solid cylinder of height 2.8 cm and diameter 4.2 cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid. (Take $π = \frac{22}{7}$ ). [CBSE 2014]

Discussion

391.	A cubical box can be open into a 2D shape as given below. How many edges is there in the 2D shape?12
Answer» A cubical box can be open into a 2D shape as given below. How many edges is there in the 2D shape? 12

Discussion

392.	What is the relation between sin θ and cos θ for any value of θ?
Answer» What is the relation between $s i n θ$ and $c o s θ$ for any value of $θ$ ?

Discussion

393.	A card is accidently dropped from a pack of 52 playing cards. The probability that it is an ace is(a) 14(b) 113(c) 152(d) 1213
Answer» A card is accidently dropped from a pack of 52 playing cards. The probability that it is an ace is (a) $\frac{1}{4}$ (b) $\frac{1}{13}$ (c) $\frac{1}{52}$ (d) $\frac{12}{13}$

Discussion

394.	Question 4 Show that the square of any positive integer cannot be of the form 6m + 2 or 6m + 5 for any integer m.
Answer» Question 4 Show that the square of any positive integer cannot be of the form 6m + 2 or 6m + 5 for any integer m.

Discussion

395.	If sin θ=1213, find the value of sin2 θ−cos2 θ2sin θ cos θ×1tan2θ
Answer» If sin $θ = \frac{12}{13}$ , find the value of $\frac{s i n^{2} θ - c o s^{2} θ}{2 s i n θ c o s θ} \times \frac{1}{t a n^{2} θ}$

Discussion

396.	what is algebraic sum?
Answer» what is algebraic sum?

Discussion

397.	A box contains 20 tickets which are numbered from 1 to 20. If one card is drawn at random from the box, find the probability that the drawn card bears a perfect square number.
Answer» A box contains 20 tickets which are numbered from 1 to 20. If one card is drawn at random from the box, find the probability that the drawn card bears a perfect square number.

Discussion

398.	Which term of the AP 20, 1914, 1812, 1734 is its first negative term?
Answer» Which term of the AP $20, 19 \frac{1}{4}, 18 \frac{1}{2}, 17 \frac{3}{4}$ is its first negative term?

Discussion

399.	Solve the following quadratic equations by factorization method: [2 MARKS] (i) x2−8x+16=0 (ii) x2+14x–32=0
Answer» Solve the following quadratic equations by factorization method: [2 MARKS] (i) $x^{2} - 8 x + 16 = 0$ (ii) $x^{2} + 14 x - 32 = 0$

Discussion

400.	(− 22) + 21 + (− 22) + 21 + ... + 20 terms is equal to .............
Answer» (− 22) + 21 + (− 22) + 21 + ... + 20 terms is equal to .............

Discussion

Explore topic-wise InterviewSolutions in .

137. If 1-tanθ = k, then prove that ( secθ + tanθ + cosecθ ) is equal to [(2-k)

Question 6In the below figure, if ΔABE≅ΔACD, show that ΔADE∼ΔABC.

In fig., if OC = 9 cm and OB = 15 cm, then BC + BD is equal to:

The value of cos2 17° − sin2 73° is(a) 1(b) 13(c) 0(d) −1

Find the sum of the following surds(1) (2) (3)

A pit is dug in the shape of a cuboid with dimensions 10 m×8 m×3 m. The earth taken out is spread evenly on a rectangular plot of land with dimensions 40 m×30 m. What is the increase in the level of the plot?

two spheres made up of same subs†an ce have radii in the ratio 2 is to 3 . their thermal heat capaties will be in the rat

If the points A(x,y), B(3, 6) and C(−3,4) are collinear,show that x − 3y + 15 = 0

how to find less than ogive and more than ogive from the given frequency or cumulative frequency

If tan θ=17, then cosec2 θ-sec2 θcosec2 θ+sec2 θ=(a) 57(b) 37(c) 112(d) 34

Find the area of the shaded region and also it's perimeter if the lengths of AB and BC is 28 and 21 cm respectively and BCD is a quadrant of a circle.AEC is a semicircle on AC as diameter.

The diameter of a circle is a line, which joins two points on the circle and also passes through the centre of the circle. (In the adjoining figure AB is a diameter of the circle; C is its centre). Express the diameter of the circle (d) in terms of its radius (r).

In the given inequation 2x &gt; 6 ; which of the following cannot be the value of the x

Find the coordinates of midpoint of the segment joining the points (22, 20) and (0, 16).

Twenty seven solid iron spheres each of radius 2cm are melted to form a new solid sphere. What will be the surface area of the new sphere?

A wire can be bent in the form of a circle of radius 56 cm. If it is bent in the form fo a square, then its area will be(a) 3520 cm2(b) 6400 cm2(c) 7744 cm2(d) 8800 cm2

Find the depth of a cylindrical tank of radius 28 m, if its capacity is equal to that of a rectangular tank of size 28 m × 16 m × 11 m.

For what value of n, are the nth terms of two APs 63, 65, 67, and 3, 10, 17, … equal

Given that x - 5 is a factor of the cubic polynomial x3 - 35x2 + 13x - 35 , find all the zeroes of the polynomial .

If the roots of the equation (csq-ab) xsq-2(asq-bc)x+bsq-ac=0 are equal prove that a=0 /a cube +b cube+c cube=3abc

When x3 - 5x2 + 3x + 1 is divided by x - 1, find the remainder.\N

The diameter of a roller is 84 cm and its length is 120cm. It takes 500 complete revolution to move once over to level playground. Find the area of the playground in m2.

Question 1In the following question out of the four options only one is correct, write the correct answerThe solution of which of the following equations is neither a fraction nor an integer?(a) 3x + 2 = 5x + 2(b) 4x – 18 = 2(c) 4x + 7 = x + 2(d) 5x – 8 = x + 4

how to convert tan 0.986 to degrees ?

Find the condition that zeroes of the polynomial ax2 + bx + c are reciprocal of each other

Which of the following pair of linear equations has infinite solutions?

If the distance between A (1, 3) and B (x, 7) is 5 then which of the following can be the value of x?

The diagonals of a trapezium ABCD with AB || DC intersect each other at point O. If AB = 2 CD, find the ratio of the areas of triangles AOB and COD.

Question 9The point P(5,-3) is one of the two points of trisection of line segment joining the points A(7,-2) and B(1,-5).

Four points A, B, C, and D are given on circle.Line segment AB and CD are parallel. Find the distance between AB and CD.

Look at the measures shown in the adjacent figure and find the area of ☐ PQRS.

A 20 m deep well of diameter 7 m is dug and the earth taken out is evenly spread out to form a platform of 22 m by 14 m. Find the height of the platform.

A factory manufactures 120,000 pencils daily . The pencil 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 ₹0.05 per dm2.

Let p,q and r denote the lengths of the sides QR,PR and PQ of a triangle PQR respectively. Then pcos2(R2)+rcos2(P2)

If the sum of the roots of the equation x2-k+6x+22k-1=0 is equal to half of their product, then k =(a) 6(b) 7(c) 1(d) 5

From a solid cylinder of height 2.8 cm and diameter 4.2 cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid. (Take π=227). [CBSE 2014]

A cubical box can be open into a 2D shape as given below. How many edges is there in the 2D shape?12

What is the relation between sin θ and cos θ for any value of θ?

A card is accidently dropped from a pack of 52 playing cards. The probability that it is an ace is(a) 14(b) 113(c) 152(d) 1213

Question 4 Show that the square of any positive integer cannot be of the form 6m + 2 or 6m + 5 for any integer m.

If sin θ=1213, find the value of sin2 θ−cos2 θ2sin θ cos θ×1tan2θ

what is algebraic sum?

A box contains 20 tickets which are numbered from 1 to 20. If one card is drawn at random from the box, find the probability that the drawn card bears a perfect square number.

Which term of the AP 20, 1914, 1812, 1734 is its first negative term?

Solve the following quadratic equations by factorization method: [2 MARKS] (i) x2−8x+16=0 (ii) x2+14x–32=0

(− 22) + 21 + (− 22) + 21 + ... + 20 terms is equal to .............

In the given inequation 2x > 6 ; which of the following cannot be the value of the x