32581 + Interview Questions in Mathematics Page 108 InterviewSolution

5351.	Using factor theorem, show that g(x) is a factor of p(x), whenpx=69+11x-x2+x3, gx=x+3
Answer» Using factor theorem, show that g(x) is a factor of p(x), when $p (x) = 69 + 11 x - x^{2} + x^{3}, g (x) = x + 3$

Discussion

5352.	A 1.2 m tall girl spots a balloon moving with the wind in a horizontal line at a height of 88.2 metres from the ground. The angle of elevation of the balloon from the eyes of the girl at any instant is 60∘. After some time, the angle of elevation reduces to 30∘. Find the distance traveled by the balloon during the interval. [4 MARKS]
Answer» A 1.2 m tall girl spots a balloon moving with the wind in a horizontal line at a height of 88.2 metres from the ground. The angle of elevation of the balloon from the eyes of the girl at any instant is $60^{\circ}$ . After some time, the angle of elevation reduces to $30^{\circ}$ . Find the distance traveled by the balloon during the interval. [4 MARKS]

Discussion

5353.	Question 2 Find the distance between the points (0, 0) and (36, 15). Can you now find the distance between the two towns A and B discussed in Section 7.2?
Answer» Question 2 Find the distance between the points (0, 0) and (36, 15). Can you now find the distance between the two towns A and B discussed in Section 7.2?

Discussion

5354.	Raghu had to make a cylindrical tube with an aluminium cover. What is the area of the aluminium sheet he needs to cover the tube if the tube has a length of 1m and base radius 3.5cm? (Take π=22/7)
Answer» Raghu had to make a cylindrical tube with an aluminium cover. What is the area of the aluminium sheet he needs to cover the tube if the tube has a length of 1m and base radius 3.5cm? (Take $π = \frac{22}{/} 7$ )

Discussion

5355.	Solve the following systems of equations:2x+3y=9xy4x+9y=21xy, x≠0, y≠0
Answer» Solve the following systems of equations: $\frac{2}{x} + \frac{3}{y} = \frac{9}{x y} \frac{4}{x} + \frac{9}{y} = \frac{21}{x y}, x \neq 0, y \neq 0$

Discussion

5356.	In figure, OB⊥OA, ∠AOC and ∠BOC are complementary angles . Find the value of x and hence find ∠AOC and ∠BOC.
Answer» In figure, $O B ⊥ O A, ∠ A O C$ and $∠ B O C$ are complementary angles . Find the value of $x$ and hence find $∠ A O C$ and $∠ B O C$ .

5356.

In figure, OB⊥OA, ∠AOC and ∠BOC are complementary angles . Find the value of x and hence find ∠AOC and ∠BOC.

Answer»

In figure, $O B ⊥ O A, ∠ A O C$ and $∠ B O C$ are complementary angles . Find the value of $x$ and hence find $∠ A O C$ and $∠ B O C$ .

Discussion

5357.	If 3a + 7b3a - 7b= 43 then find the value of the ratio 3a2 - 7b23a2 + 7b2
Answer» If $\frac{3 a + 7 b}{3 a - 7 b} = \frac{4}{3}$ then find the value of the ratio $\frac{3 a^{2} - 7 b^{2}}{3 a^{2} + 7 b^{2}}$

Discussion

5358.	Prove the following trigonometric identities.(1 − cos2 A) cosec2 A = 1
Answer» Prove the following trigonometric identities. (1 − cos² A) cosec² A = 1

Discussion

5359.	In an AP, the pth term is q, and the qth term is p. What is the nth term? ( Given p≠q)
Answer» In an AP, the $p^{t h}$ term is q, and the $q^{t h}$ term is p. What is the $n^{t h}$ term? ( Given $p \neq q$ )

Discussion

5360.	Let be a segment with C and D between them such that the order of points on the segment is A, C, D,B. Suppose AD = BC. Prove that AC = DB.
Answer» Let be a segment with C and D between them such that the order of points on the segment is A, C, D,B. Suppose AD = BC. Prove that AC = DB.

5360.

Let be a segment with C and D between them such that the order of points on the segment is A, C, D,B. Suppose AD = BC. Prove that AC = DB.

Answer»

Let be a segment with C and D between them such that the order of points on the segment is A, C, D,B. Suppose AD = BC. Prove that AC = DB.

Discussion

5361.	Solve 5y+2y+y−7y= ___
Answer» Solve $5 y + 2 y + y - 7 y =$ ___

Discussion

5362.	How many irrational numbers exist between two rational numbers?
Answer» How many irrational numbers exist between two rational numbers?

Discussion

5363.	33.If S is the circumcentre, O is the orthocentre of triangle ABC, then vector SA+SB+SC equals
Answer» 33.If S is the circumcentre, O is the orthocentre of triangle ABC, then vector SA+SB+SC equals

Discussion

5364.	A person rowing at the rate of 5 km/h in still water , takes thrice as much time in going 40 km upstream as in going 40 km downstream . Find the speed of the stream .
Answer» A person rowing at the rate of 5 km/h in still water , takes thrice as much time in going 40 km upstream as in going 40 km downstream . Find the speed of the stream .

Discussion

5365.	Consider the following statements and choose the correct option.1) A tangent is a line that touches the circle at one point.2) A tangent is an extreme case of the secant where the points of intersection coincide.
Answer» Consider the following statements and choose the correct option. 1) A tangent is a line that touches the circle at one point. 2) A tangent is an extreme case of the secant where the points of intersection coincide.

Discussion

5366.	Write first four terms of the AP, when the first term a and common difference d are given as follows: (i) a= -2, d=0 (ii) a=4, d=-3 (iii) a= -1.25, d= -0.25
Answer» Write first four terms of the AP, when the first term a and common difference d are given as follows: (i) a= -2, d=0 (ii) a=4, d=-3 (iii) a= -1.25, d= -0.25

Discussion

5367.	If nP4 = 24. nC5, then the value of n is ____________.
Answer» If ⁿP₄ = 24. ⁿC₅, then the value of n is ____________.

Discussion

5368.	why do PbBr_{4 }and PbI_4 not exist ?
Answer» why do PbBr_{4 }and PbI_4 not exist ?

Discussion

5369.	If →a is a vector of magnitude 50 and is collinear with the vector →b=6^i−8^j−152^k and makes an obtuse angle with the positive direction of z - axis, then →a is equal to
Answer» If $\to a$ is a vector of magnitude 50 and is collinear with the vector $\to b = 6^i - 8^j - \frac{15}{2}^k$ and makes an obtuse angle with the positive direction of z - axis, then $\to a$ is equal to

Discussion

5370.	In the given figure, AD ⊥ BC and CD > BD. Show that AC > AB.
Answer» In the given figure, AD ⊥ BC and CD > BD. Show that AC > AB.

Discussion

5371.	Question 81 Solve the following: The volume of water in a tank is twice of that in the other. If we draw out 25 litres from the first and add it to the other, the volumes of the water in each tank will be the same. Find the volumes of water in each tank.
Answer» Question 81 Solve the following: The volume of water in a tank is twice of that in the other. If we draw out 25 litres from the first and add it to the other, the volumes of the water in each tank will be the same. Find the volumes of water in each tank.

5371.

Question 81 Solve the following: The volume of water in a tank is twice of that in the other. If we draw out 25 litres from the first and add it to the other, the volumes of the water in each tank will be the same. Find the volumes of water in each tank.

Answer»

Question 81

Solve the following:

The volume of water in a tank is twice of that in the other. If we draw out 25 litres from the first and add it to the other, the volumes of the water in each tank will be the same. Find the volumes of water in each tank.

Discussion

5372.	If x=a sec A cos B, y=b sec A sin B and z=c tan A, then x2a2+y2b2−z2c2=
Answer» If $x = a sec A cos B$ , $y = b sec A sin B$ and $z = c tan A$ , then $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} - \frac{z^{2}}{c^{2}} =$

Discussion

5373.	Find:(i) 10th term of the A.P. 1, 4, 7, 10, ...(ii) 18th term of the A.P. 2, 32, 52...(iii) nth term of the A.P. 13, 8, 3, −2, ...(iv) 10th term of the A.P. −40, −15, 10, 35, ...(v) 8th term of the A.P. 117, 104, 91, 78, ...(vi) 11th term of the A.P. 10.0, 10.5, 11.0, 11.5, ...(vii) 9th term of the A.P. 34,54,74,94, ...
Answer» Find: (i) 10^th term of the A.P. 1, 4, 7, 10, ... (ii) 18^th term of the A.P. $\sqrt{2}, 3 \sqrt{2}, 5 \sqrt{2} . . .$ (iii) n^th term of the A.P. 13, 8, 3, −2, ... (iv) 10^th term of the A.P. −40, −15, 10, 35, ... (v) 8th term of the A.P. 117, 104, 91, 78, ... (vi) 11th term of the A.P. 10.0, 10.5, 11.0, 11.5, ... (vii) 9th term of the A.P. $\frac{3}{4}, \frac{5}{4}, \frac{7}{4}, \frac{9}{4}, . . .$

Discussion

5374.

In a class test, 50 students obtained marks as follows: Marks obtained 0−20 20−40 40−60 60−80 80−100 Number of students 4 6 25 10 5 Find the modal class and the median class. [CBSE 2014]

Answer» In a class test, 50 students obtained marks as follows:

Marks obtained	0−20	20−40	40−60	60−80	80−100
Number of students	4	6	25	10	5

Find the modal class and the median class. [CBSE 2014]

Discussion

5375.	37. Solve the following inequality Mod of [X + 3] + X / X + 2 greater than 1
Answer» 37. Solve the following inequality Mod of [X + 3] + X / X + 2 greater than 1

Discussion

5376.	Define an identity.
Answer» Define an identity.

Discussion

5377.	In the given figure, one side of the 30∘ inscribed angle is the diameter of a semicircle of radius 3 cm. What is the perimeter of the shaded region bounded by the inscribed angle and its intercepted arc?
Answer» In the given figure, one side of the $30^{\circ}$ inscribed angle is the diameter of a semicircle of radius 3 cm. What is the perimeter of the shaded region bounded by the inscribed angle and its intercepted arc?

Discussion

5378.	In the given figure, the circles with centres A and B touch each other at E. Line l is a common tangent which touches the circles at C and D respectively. Find the length of seg CD if the radii of the circles are 4 cm, 6 cm.
Answer» In the given figure, the circles with centres A and B touch each other at E. Line l is a common tangent which touches the circles at C and D respectively. Find the length of seg CD if the radii of the circles are 4 cm, 6 cm.

Discussion

5379.	If \|\|x−2\|−5\|≤ 10, then
Answer» If $\| \| x - 2 \| - 5 \| \leq$ 10, then

Discussion

5380.	Find the area of a triangle, two sides of which are 8 cm and 12 cm and the perimeter is 38 cm .
Answer» Find the area of a triangle, two sides of which are 8 cm and 12 cm and the perimeter is 38 cm .

Discussion

5381.	Separate the variables in the below given equation. 7x - 2y = 5xyAfter separating the variables equation is of the form7□ - 2□ = 5
Answer» Separate the variables in the below given equation. 7x - 2y = 5xy After separating the variables equation is of the form $\frac{7}{□}$ - $\frac{2}{□}$ = 5

5381.

Separate the variables in the below given equation. 7x - 2y = 5xyAfter separating the variables equation is of the form7□ - 2□ = 5

Answer»

Separate the variables in the below given equation.

7x - 2y = 5xy

After separating the variables equation is of the form

$\frac{7}{□}$ - $\frac{2}{□}$ = 5

Discussion

5382.	Vijay inherited his father's wealth and doubled it by starting a soft drinks company. He then started a company which manufactures airplane toys and incurred losses amounting to k(>0) times the wealth he inherited. If his total assets now stand at a debt of 4 crores, then ___.
Answer» Vijay inherited his father's wealth and doubled it by starting a soft drinks company. He then started a company which manufactures airplane toys and incurred losses amounting to $k (> 0)$ times the wealth he inherited. If his total assets now stand at a debt of 4 crores, then ___.

Discussion

5383.	Chris wants to order DVDs over the internet. Each DVD costs Rs. 15.99 and shipping the entire order costs Rs. 9.99. If he can spend no more than Rs. 100, how many DVD's could he buy?
Answer» Chris wants to order DVDs over the internet. Each DVD costs Rs. 15.99 and shipping the entire order costs Rs. 9.99. If he can spend no more than Rs. 100, how many DVD's could he buy?

Discussion

5384.	What is the value of PB if OP = 1 unit and ∠POQ=θ?
Answer» What is the value of PB if OP = 1 unit and $∠ P O Q = θ$ ?

Discussion

5385.	If ∠A and ∠P are acute angles such that tan A = tan P, then show that ∠A = ∠P.
Answer» If ∠A and ∠P are acute angles such that tan A = tan P, then show that ∠A = ∠P.

Discussion

5386.	Find the probability of 53 Friday in a leap year
Answer» Find the probability of 53 Friday in a leap year

Discussion

5387.	Fill In The Blanks A chord of a circle is equal to its radius. The angle subtended by this chord at a point in major segment is ___________.
Answer» Fill In The Blanks A chord of a circle is equal to its radius. The angle subtended by this chord at a point in major segment is ___________.

Discussion

5388.	If a cos θ + b sin θ = 4 and a sin θ − b sin θ = 3, then a2 + b2 =(a) 7(b) 12(c) 25(d) None of these
Answer» If a cos θ + b sin θ = 4 and a sin θ − b sin θ = 3, then a² + b² = (a) 7 (b) 12 (c) 25 (d) None of these

Discussion

5389.	Find a relation between x and y, if the points A(2, 1), B(x, y) and C(7, 5) are collinear. [CBSE 2009C]
Answer» Find a relation between x and y, if the points A(2, 1), B(x, y) and C(7, 5) are collinear. [CBSE 2009C]

Discussion

5390.	Question 14 An observer 1.5 m tall is 20.5 m away from a tower 22 m high. Determine the angle of elevation of the top of the tower from the eye of the observer.
Answer» Question 14 An observer 1.5 m tall is 20.5 m away from a tower 22 m high. Determine the angle of elevation of the top of the tower from the eye of the observer.

Discussion

5391.	If f: R → R is defined by f(x) =xx2+1find f(f(2))
Answer» If f: R $\to$ R is defined by f(x) $= \frac{x}{x^{2} + 1}$ find f(f(2))

Discussion

5392.	Write the expression an- ak for the A.P. a, a + d, a + 2d, ...Hence, find the common difference of the A.P. for which(i) 11th term is 5 and 13th term is 79.(ii) a10 −a5 = 200(iii) 20th term is 10 more than the 18th term.
Answer» Write the expression a_n- a_k for the A.P. a, a + d, a + 2d, ... Hence, find the common difference of the A.P. for which (i) 11^th term is 5 and 13^th term is 79. (ii) a₁₀ −a₅= 200 (iii) 20^th term is 10 more than the 18^th term.

Discussion

5393.	Question 17In an AP, if a = 1,an=20and Sn = 399,then n is equal to :A) 19B) 21C) 38D) 42
Answer» Question 17 In an AP, if a = 1, $a_{n} = 20$ $a n d S_{n}$ = 399, then n is equal to : A) 19 B) 21 C) 38 D) 42

Discussion

5394.	A vertical stick 10 cm long casts a shadow 8 cm long. At the same time, a tower casts a shadow 30 cm long. Determine the height of the tower?
Answer» A vertical stick 10 cm long casts a shadow 8 cm long. At the same time, a tower casts a shadow 30 cm long. Determine the height of the tower?

Discussion

5395.	The area of a rectangular plot is 528 m2. The length of the plot (in metres) is one more than twice its breadth. We need to find the length and breadth of the plot.
Answer» The area of a rectangular plot is $528 m^{2}$ . The length of the plot (in metres) is one more than twice its breadth. We need to find the length and breadth of the plot.

Discussion

5396.	Question 14 (iii)One card is drawn from a well–shuffled deck of 52 cards. Find the probability of getting a red face card.
Answer» Question 14 (iii) One card is drawn from a well–shuffled deck of 52 cards. Find the probability of getting a red face card.

Discussion

5397.	The angle of elevation of the top of a tower at a distance of 120 m from a point A on the ground is 45∘. If the angle of elevation of the top of a flagstaff fixed at the top of the tower, at A is 60∘, then find the height of the flagstaff. [Use \sqrt 3=1.732.]
Answer» The angle of elevation of the top of a tower at a distance of 120 m from a point A on the ground is $45^{\circ}$ . If the angle of elevation of the top of a flagstaff fixed at the top of the tower, at A is $60^{\circ}$ , then find the height of the flagstaff. [Use \sqrt 3=1.732.]

Discussion

5398.	Find the ratio in which the line segment joining the points (-3, 8) and (5, - 9) is divided by (0, 2).
Answer» Find the ratio in which the line segment joining the points (-3, 8) and (5, - 9) is divided by (0, 2).

Discussion

5399.	In the formula R=pL/A, how the value of A comes, πd2/4?
Answer» In the formula R=pL/A, how the value of A comes, πd²/4?

Discussion

5400.	In the given figure, ∠AMN = ∠MBC = 760 If p, q and r are the lengths of AM, MB and BC respectively, then express the length of MN in terms of p, q and r.
Answer» In the given figure, ∠AMN = ∠MBC = 76⁰ If p, q and r are the lengths of AM, MB and BC respectively, then express the length of MN in terms of p, q and r.

Discussion

Explore topic-wise InterviewSolutions in .

Using factor theorem, show that g(x) is a factor of p(x), whenpx=69+11x-x2+x3, gx=x+3

Question 2 Find the distance between the points (0, 0) and (36, 15). Can you now find the distance between the two towns A and B discussed in Section 7.2?

Raghu had to make a cylindrical tube with an aluminium cover. What is the area of the aluminium sheet he needs to cover the tube if the tube has a length of 1m and base radius 3.5cm? (Take π=22/7)

Solve the following systems of equations:2x+3y=9xy4x+9y=21xy, x≠0, y≠0

In figure, OB⊥OA, ∠AOC and ∠BOC are complementary angles . Find the value of x and hence find ∠AOC and ∠BOC.

If 3a + 7b3a - 7b= 43 then find the value of the ratio 3a2 - 7b23a2 + 7b2

Prove the following trigonometric identities.(1 − cos2 A) cosec2 A = 1

In an AP, the pth term is q, and the qth term is p. What is the nth term? ( Given p≠q)

Let be a segment with C and D between them such that the order of points on the segment is A, C, D,B. Suppose AD = BC. Prove that AC = DB.

Solve 5y+2y+y−7y= ___

How many irrational numbers exist between two rational numbers?

33.If S is the circumcentre, O is the orthocentre of triangle ABC, then vector SA+SB+SC equals

A person rowing at the rate of 5 km/h in still water , takes thrice as much time in going 40 km upstream as in going 40 km downstream . Find the speed of the stream .

Consider the following statements and choose the correct option.1) A tangent is a line that touches the circle at one point.2) A tangent is an extreme case of the secant where the points of intersection coincide.

Write first four terms of the AP, when the first term a and common difference d are given as follows: (i) a= -2, d=0 (ii) a=4, d=-3 (iii) a= -1.25, d= -0.25

If nP4 = 24. nC5, then the value of n is ____________.

why do PbBr_{4 }and PbI_4 not exist ?

If →a is a vector of magnitude 50 and is collinear with the vector →b=6^i−8^j−152^k and makes an obtuse angle with the positive direction of z - axis, then →a is equal to

In the given figure, AD ⊥ BC and CD > BD. Show that AC > AB.

Question 81 Solve the following: The volume of water in a tank is twice of that in the other. If we draw out 25 litres from the first and add it to the other, the volumes of the water in each tank will be the same. Find the volumes of water in each tank.

If x=a sec A cos B, y=b sec A sin B and z=c tan A, then x2a2+y2b2−z2c2=

In a class test, 50 students obtained marks as follows: Marks obtained 0−20 20−40 40−60 60−80 80−100 Number of students 4 6 25 10 5 Find the modal class and the median class. [CBSE 2014]

37. Solve the following inequality Mod of [X + 3] + X / X + 2 greater than 1

Define an identity.

In the given figure, one side of the 30∘ inscribed angle is the diameter of a semicircle of radius 3 cm. What is the perimeter of the shaded region bounded by the inscribed angle and its intercepted arc?

In the given figure, the circles with centres A and B touch each other at E. Line l is a common tangent which touches the circles at C and D respectively. Find the length of seg CD if the radii of the circles are 4 cm, 6 cm.

If ||x−2|−5|≤ 10, then

Find the area of a triangle, two sides of which are 8 cm and 12 cm and the perimeter is 38 cm .

Separate the variables in the below given equation. 7x - 2y = 5xyAfter separating the variables equation is of the form7□ - 2□ = 5

Vijay inherited his father's wealth and doubled it by starting a soft drinks company. He then started a company which manufactures airplane toys and incurred losses amounting to k(&gt;0) times the wealth he inherited. If his total assets now stand at a debt of 4 crores, then ___.

Chris wants to order DVDs over the internet. Each DVD costs Rs. 15.99 and shipping the entire order costs Rs. 9.99. If he can spend no more than Rs. 100, how many DVD's could he buy?

What is the value of PB if OP = 1 unit and ∠POQ=θ?

If ∠A and ∠P are acute angles such that tan A = tan P, then show that ∠A = ∠P.

Find the probability of 53 Friday in a leap year

Fill In The Blanks A chord of a circle is equal to its radius. The angle subtended by this chord at a point in major segment is ___________.

If a cos θ + b sin θ = 4 and a sin θ − b sin θ = 3, then a2 + b2 =(a) 7(b) 12(c) 25(d) None of these

Find a relation between x and y, if the points A(2, 1), B(x, y) and C(7, 5) are collinear. [CBSE 2009C]

Question 14 An observer 1.5 m tall is 20.5 m away from a tower 22 m high. Determine the angle of elevation of the top of the tower from the eye of the observer.

If f: R → R is defined by f(x) =xx2+1find f(f(2))

Write the expression an- ak for the A.P. a, a + d, a + 2d, ...Hence, find the common difference of the A.P. for which(i) 11th term is 5 and 13th term is 79.(ii) a10 −a5 = 200(iii) 20th term is 10 more than the 18th term.

Question 17In an AP, if a = 1,an=20and Sn = 399,then n is equal to :A) 19B) 21C) 38D) 42

A vertical stick 10 cm long casts a shadow 8 cm long. At the same time, a tower casts a shadow 30 cm long. Determine the height of the tower?

The area of a rectangular plot is 528 m2. The length of the plot (in metres) is one more than twice its breadth. We need to find the length and breadth of the plot.

Question 14 (iii)One card is drawn from a well–shuffled deck of 52 cards. Find the probability of getting a red face card.

The angle of elevation of the top of a tower at a distance of 120 m from a point A on the ground is 45∘. If the angle of elevation of the top of a flagstaff fixed at the top of the tower, at A is 60∘, then find the height of the flagstaff. [Use \sqrt 3=1.732.]

Find the ratio in which the line segment joining the points (-3, 8) and (5, - 9) is divided by (0, 2).

In the formula R=pL/A, how the value of A comes, πd​​​​​2/4?

In the given figure, ∠AMN = ∠MBC = 760 If p, q and r are the lengths of AM, MB and BC respectively, then express the length of MN in terms of p, q and r.

Vijay inherited his father's wealth and doubled it by starting a soft drinks company. He then started a company which manufactures airplane toys and incurred losses amounting to k(>0) times the wealth he inherited. If his total assets now stand at a debt of 4 crores, then ___.

In the formula R=pL/A, how the value of A comes, πd2/4?