32581 + Interview Questions in Mathematics Page 118 InterviewSolution

5851.	For which values of p and q, will the following pair of linear equations have infinitely many solutions? 4x + 5y = 2 , (2p + 7q) x + (p + 8q) y = 2q-p + 1
Answer» For which values of p and q, will the following pair of linear equations have infinitely many solutions? 4x + 5y = 2 , (2p + 7q) x + (p + 8q) y = 2q-p + 1

Discussion

5852.	Question 72 Solve the following: 3x+22x−3=−34
Answer» Question 72 Solve the following: $\frac{3 x + 2}{2 x - 3} = - \frac{3}{4}$

5852.

Question 72 Solve the following: 3x+22x−3=−34

Answer»

Question 72

Solve the following:

$\frac{3 x + 2}{2 x - 3} = - \frac{3}{4}$

Discussion

5853.	There is a six faced die. Ram wants to find the probability that the number that lands on the die is at least 3. What is the number of favourable outcomes?
Answer» There is a six faced die. Ram wants to find the probability that the number that lands on the die is at least 3. What is the number of favourable outcomes?

Discussion

5854.	The legth of a rectangle exceeds its breadth by 9cm. If the length and breadth are each increased by 3cm, the area of the new rectangle will be 84cm^2 more than that of the given rectangle. Find the length and breadth of the given rectangle.
Answer» The legth of a rectangle exceeds its breadth by 9cm. If the length and breadth are each increased by 3cm, the area of the new rectangle will be 84cm^2 more than that of the given rectangle. Find the length and breadth of the given rectangle.

Discussion

5855.	The areas of two similar triangles are 12 cm2 and 48 cm2. If the height of the smaller triangle is 2.1 cm, then the corresponding height of the bigger triangle is _____.
Answer» The areas of two similar triangles are 12 $c m^{2}$ and 48 $c m^{2}$ . If the height of the smaller triangle is 2.1 $c m$ , then the corresponding height of the bigger triangle is _____.

Discussion

5856.	The mean of 6, 8, 11, 13, 14 and x is 66. Find the value of the observation x.
Answer» The mean of 6, 8, 11, 13, 14 and x is 66. Find the value of the observation x.

Discussion

5857.	A pole stands in a park such that its shadow increases by 2 m when the angle of elevation of Sun changes from 45º to 30º. The height of the pole is
Answer» A pole stands in a park such that its shadow increases by 2 m when the angle of elevation of Sun changes from 45º to 30º. The height of the pole is

Discussion

5858.	Prove that x + 1 is a factor of xn − 1 for every even number n.
Answer» Prove that x + 1 is a factor of xⁿ − 1 for every even number n.

Discussion

5859.	In an isosceles ΔABC right angled at B, prove that AC2=2AB2.
Answer» In an isosceles $Δ A B C$ right angled at B, prove that $A C^{2} = 2 A B^{2} .$

Discussion

5860.	Out of the two concentric circles, the radius of the outer circle is 5 cm and the chord AC of length 8 cm is a tagnent to the inner circle. Find the radius of the inner circle.
Answer» Out of the two concentric circles, the radius of the outer circle is 5 cm and the chord AC of length 8 cm is a tagnent to the inner circle. Find the radius of the inner circle.

Discussion

5861.	In the given figure, ABCD is a rectangle with AB = 80 cm and BC = 70 cm, ∠AED = 90° and DE = 42 cm. A semicircle is drawn, taking BC as diameter. Find the area of the shaded region. [CBSE 2014]
Answer» In the given figure, ABCD is a rectangle with AB = 80 cm and BC = 70 cm, ∠AED = 90° and DE = 42 cm. A semicircle is drawn, taking BC as diameter. Find the area of the shaded region. [CBSE 2014]

Discussion

5862.	find the circumradius of the circle circumscribed get the triangle formed by vertices A (-a,0),B (0,b)and (a, 0)
Answer» find the circumradius of the circle circumscribed get the triangle formed by vertices A (-a,0),B (0,b)and (a, 0)

Discussion

5863.	Which of the following suffixes are used for people and their jobs?
Answer» Which of the following suffixes are used for people and their jobs?

Discussion

5864.	In fig., there are two concentric circles with center O and of radii 5 cm and 3 cm. From an external point P, tangents PA and PB are drawn to these circles. If AP = 12 cm, find the length of BP [3 MARKS]
Answer» In fig., there are two concentric circles with center O and of radii 5 cm and 3 cm. From an external point P, tangents PA and PB are drawn to these circles. If AP = 12 cm, find the length of BP [3 MARKS]

5864.

In fig., there are two concentric circles with center O and of radii 5 cm and 3 cm. From an external point P, tangents PA and PB are drawn to these circles. If AP = 12 cm, find the length of BP [3 MARKS]

Answer»

In fig., there are two concentric circles with center O and of radii 5 cm and 3 cm. From an external point P, tangents PA and PB are drawn to these circles. If AP = 12 cm, find the length of BP [3 MARKS]

Discussion

5865.	If sin2A + cos2A =1 then sin4A + cos4A will also be equal to 1. Or sinA +cosA will also be equal to 1.
Answer» If sin²A + cos²A =1 then sin⁴A + cos⁴A will also be equal to 1. Or sinA +cosA will also be equal to 1.

Discussion

5866.	What is the trigonometric ratio that connects the opposite side to adjacent side in a right-angled triangle?
Answer» What is the trigonometric ratio that connects the opposite side to adjacent side in a right-angled triangle?

Discussion

5867.	If the 4th, 7th and 10th terms of a G.P. be a, b, c respectively, then the relation between a, b, c is _______.
Answer» If the $4^{t h}$ , $7^{t h}$ and $10^{t h}$ terms of a G.P. be a, b, c respectively, then the relation between a, b, c is _______.

Discussion

5868.	How to visualize complex number subtraction.
Answer» How to visualize complex number subtraction.

Discussion

5869.	The minimum value of 4x + 41 – x, x ∈ R, is(a) 2(b) 4(c) 1(d) 0
Answer» The minimum value of 4^x + 4^{1 – x}, x ∈ R, is (a) 2 (b) 4 (c) 1 (d) 0

Discussion

5870.	Question 14 An event is very unlikely to happen. Its probability is closest to (a) 0.0001 (b) 0.001 (c) 0.01 (d) 0.1
Answer» Question 14 An event is very unlikely to happen. Its probability is closest to (a) 0.0001 (b) 0.001 (c) 0.01 (d) 0.1

Discussion

5871.	A ray of light coming from the point (1, 2) is reflected at a point A on the x - axis and then passes through the point (5, 3). The coordinates of the point A are
Answer» A ray of light coming from the point (1, 2) is reflected at a point A on the x - axis and then passes through the point (5, 3). The coordinates of the point A are

Discussion

5872.	Find the mean using step-deviation. Class IntervalFrequency0−1016010−2020020−3032030−4048040−5030050−60140
Answer» Find the mean using step-deviation. $\begin{matrix} C l a s s I n t e r v a l & F r e q u e n c y 0 - 10 & 160 10 - 20 & 200 20 - 30 & 320 30 - 40 & 480 40 - 50 & 300 50 - 60 & 140 \end{matrix}$

Discussion

5873.	Find the equation of circle which passes through (-1,2) & (3,-1) and whose centre lies on the straight line x-2y=0
Answer» Find the equation of circle which passes through (-1,2) & (3,-1) and whose centre lies on the straight line x-2y=0

Discussion

5874.	In an equilateral triangle ABC, D is the mid-point of AB and E is the mid point of AC. The ar(ΔABC) : ar (ΔADE) =
Answer» In an equilateral triangle ABC, D is the mid-point of AB and E is the mid point of AC. The ar(ΔABC) : ar (ΔADE) =

Discussion

5875.	how to multiply an irrational number to an rational number
Answer» how to multiply an irrational number to an rational number

Discussion

5876.	If G be the centroid of a triangle ABC, prove that : AB2+BC2+CA2=3(GA2+GB2+GC2)
Answer» If G be the centroid of a triangle ABC, prove that : $A B^{2} + B C^{2} + C A^{2} = 3 (G A^{2} + G B^{2} + G C^{2})$

5876.

If G be the centroid of a triangle ABC, prove that : AB2+BC2+CA2=3(GA2+GB2+GC2)

Answer»

If G be the centroid of a triangle ABC, prove that :

$A B^{2} + B C^{2} + C A^{2} = 3 (G A^{2} + G B^{2} + G C^{2})$

Discussion

5877.	In a ∆ABC right angled at B, ∠A = ∠C. Find the values of(i) sin A cos C + cos A sin C(ii) sin A sin B + cos A cos B
Answer» In a ∆ABC right angled at B, ∠A = ∠C. Find the values of (i) sin A cos C + cos A sin C (ii) sin A sin B + cos A cos B

Discussion

5878.	A person is noting down the number of accidents along a busy highway during a year. The appropriate sample space in the experiment is:
Answer» A person is noting down the number of accidents along a busy highway during a year. The appropriate sample space in the experiment is:

Discussion

5879.	An exhibition tent is in the form of a cylinder surmounted by a cone. The height of the tent above the ground is 85 m and the height of the cylindrical part is 50 m. If the diameter of base is168 m, find the quantity of canvas required to make the tent. Allow 20% extra for folds and for stitching. Give your answer to the nearest m2.
Answer» An exhibition tent is in the form of a cylinder surmounted by a cone. The height of the tent above the ground is 85 m and the height of the cylindrical part is 50 m. If the diameter of base is168 m, find the quantity of canvas required to make the tent. Allow 20% extra for folds and for stitching. Give your answer to the nearest m².

Discussion

5880.	A takes 10 days less than the time taken by B to finish a piece of work. If both A and B together can finish the work in 12 days, find the time taken by B to finish the work.
Answer» A takes 10 days less than the time taken by B to finish a piece of work. If both A and B together can finish the work in 12 days, find the time taken by B to finish the work.

Discussion

5881.	Given a G.P. with a = 729 and 7 th term 64, determine S 7 .
Answer» Given a G.P. with a = 729 and 7 th term 64, determine S 7 .

Discussion

5882.	Draw a right triangle ABC in which AB = 6 cm, BC = 8 cm and ∠B = 90º. Draw BD perpendicular from B on AC and draw a circle passing through the points B, C and D. Construct tangents from A to this circle. [CBSE 2014]
Answer» Draw a right triangle ABC in which AB = 6 cm, BC = 8 cm and $∠$ B = 90º. Draw BD perpendicular from B on AC and draw a circle passing through the points B, C and D. Construct tangents from A to this circle. [CBSE 2014]

Discussion

5883.	Find the area of a sector of a circle with radius 6cm if the angle of the sector is 60∘
Answer» Find the area of a sector of a circle with radius 6cm if the angle of the sector is $60^{\circ}$

Discussion

5884.	Question 1 (iii) Fill in the blanks using the correct word in the given bracket. (iii) All ___ triangles are similar. (isosceles, equilateral)
Answer» Question 1 (iii) Fill in the blanks using the correct word in the given bracket. (iii) All ___ triangles are similar. (isosceles, equilateral)

Discussion

5885.	Question 9The angle of elevation of the top of a building from the foot of the tower is 30∘ and the angle of elevation of the top of the tower from the foot of the building is 60∘. If the tower is 50 m high, find the height of the building.
Answer» Question 9 The angle of elevation of the top of a building from the foot of the tower is $30^{\circ}$ and the angle of elevation of the top of the tower from the foot of the building is $60^{\circ}$ . If the tower is 50 m high, find the height of the building.

Discussion

5886.	Question 11In figure, if ∠D=∠C, then is it true that ΔADE∼ΔACB,? Why?
Answer» Question 11 In figure, if $∠ D = ∠ C$ , then is it true that $Δ A D E \sim Δ A C B$ ,? Why?

Discussion

5887.	There is a circular swimming pool. There is a bob at the centre of the pool at a distance of 50π m from the pool’s wall. Shyam is standing next to thewall and holding a thread whose other end is connected to the heavy stationary bob at the centre. Holding the thread Shyam now moves along the wall for 20seconds and the angle between the initial and final positions of the thread is12∘. What is Shyam’s speed in metres/minute?
Answer» There is a circular swimming pool. There is a bob at the centre of the pool at a distance of $\frac{50}{π}$ m from the pool’s wall. Shyam is standing next to the wall and holding a thread whose other end is connected to the heavy stationary bob at the centre. Holding the thread Shyam now moves along the wall for 20 seconds and the angle between the initial and final positions of the thread is $12^{\circ}$ . What is Shyam’s speed in metres/minute?

5887.

There is a circular swimming pool. There is a bob at the centre of the pool at a distance of 50π m from the pool’s wall. Shyam is standing next to thewall and holding a thread whose other end is connected to the heavy stationary bob at the centre. Holding the thread Shyam now moves along the wall for 20seconds and the angle between the initial and final positions of the thread is12∘. What is Shyam’s speed in metres/minute?

Answer»

There is a circular swimming pool. There is a bob at the centre of the pool at a distance of $\frac{50}{π}$ m from the pool’s wall. Shyam is standing next to the

wall and holding a thread whose other end is connected to the heavy stationary bob at the centre. Holding the thread Shyam now moves along the wall for 20

seconds and the angle between the initial and final positions of the thread is

$12^{\circ}$ . What is Shyam’s speed in metres/minute?

Discussion

5888.	Express 0.235353535...........in p/q form
Answer» Express 0.235353535...........in p/q form

Discussion

5889.	In parallelogram ABCD, AB = 10 cm. The altitudes corresponding to the sides AB and AD are respectively 7 cm and 8 cm. Find AD. [2 MARKS]
Answer» In parallelogram ABCD, AB = 10 cm. The altitudes corresponding to the sides AB and AD are respectively 7 cm and 8 cm. Find AD. [2 MARKS]

Discussion

5890.	Find the zeroes of the quadratic polynomial and verify the relationship between zeroes and coefficients 6x2-3-7x
Answer» Find the zeroes of the quadratic polynomial and verify the relationship between zeroes and coefficients 6x²-3-7x

Discussion

5891.	Question: Find the smallest number which leaves remainders 8 and 12 when divided by 28 and 32 respectively.
Answer» Question: Find the smallest number which leaves remainders 8 and 12 when divided by 28 and 32 respectively.

Discussion

5892.	Question1 (ii)Answer the following and justifyWhat will the quotient and remainder be on division of ax2+bx+c by px3+qx2+rx+s,p≠0?
Answer» Question1 (ii) Answer the following and justify What will the quotient and remainder be on division of $a x^{2} + b x + c$ by $p x^{3} + q x^{2} + r x + s, p \neq 0$ ?

Discussion

5893.	6 arithmetic means are inserted between 1 and 9/2 then the fourth arithmetic mean is please answer
Answer» 6 arithmetic means are inserted between 1 and 9/2 then the fourth arithmetic mean is please answer

Discussion

5894.	In Δ ABC, right angled at B, expressions for sec C and cosec C is
Answer» In $Δ$ ABC, right angled at B, expressions for sec C and cosec C is

5894.

In Δ ABC, right angled at B, expressions for sec C and cosec C is

Answer»

In $Δ$ ABC, right angled at B, expressions for sec C and cosec C is

Discussion

5895.	Question 4If from an external point B of a circle with centre O, two tangents BC and BD are drawn such that ∠ DBC = 120∘, prove that BC+BD=BO i.e BO = 2BC.
Answer» Question 4 If from an external point B of a circle with centre O, two tangents BC and BD are drawn such that $∠$ DBC = $120^{\circ}$ , prove that BC+BD=BO i.e BO = 2BC.

Discussion

5896.	At the time of admission of a partner C, assets and liabilities of A and B were revalued as follows:(a) A Provision for Doubtful Debts 10% was made on Sundry Debtors (Sundry Debtors ₹ 50,000).(b) Creditors were written back by ₹ 5,000.(c) Building was appreciated by 20% (Book Value of Building ₹ 2,00,000).(d) Unrecorded Investments were valued at ₹ 15,000.(e) A Provision of ₹ 2,000 was made for an Outstanding Bill for repairs.(f) Unrecorded Liability towards suppliers was ₹ 3,000.Pass necessary Journal entries.
Answer» At the time of admission of a partner C, assets and liabilities of A and B were revalued as follows: (a) A Provision for Doubtful Debts 10% was made on Sundry Debtors (Sundry Debtors ₹ 50,000). (b) Creditors were written back by ₹ 5,000. (c) Building was appreciated by 20% (Book Value of Building ₹ 2,00,000). (d) Unrecorded Investments were valued at ₹ 15,000. (e) A Provision of ₹ 2,000 was made for an Outstanding Bill for repairs. (f) Unrecorded Liability towards suppliers was ₹ 3,000. Pass necessary Journal entries.

Discussion

5897.	how to solve euclid division lemma
Answer» how to solve euclid division lemma

Discussion

5898.	Question 5 (iv)Prove the following identities, where the angles involved are acute angles for which the expressions are defined.(iv) (1+secA)secA=sin2A(1−cosA)[Hint : Simplify L.H.S and R.H.S separately]
Answer» Question 5 (iv) Prove the following identities, where the angles involved are acute angles for which the expressions are defined. (iv) $\frac{(1 + s e c A)}{s e c A} = \frac{s i n^{2} A}{(1 - c o s A)}$ [Hint : Simplify L.H.S and R.H.S separately]

Discussion

5899.	Question 86 What number divided by 520 gives the same quotient as 85 divided by 0.625?
Answer» Question 86 What number divided by 520 gives the same quotient as 85 divided by 0.625?

5899.

Question 86 What number divided by 520 gives the same quotient as 85 divided by 0.625?

Answer»

Question 86

What number divided by 520 gives the same quotient as 85 divided by 0.625?

Discussion

5900.	Solve the following pair of linear equations 2√x + 3√y = 2 4√x - 9√y = -1
Answer» Solve the following pair of linear equations $\frac{2}{\sqrt{x}}$ + $\frac{3}{\sqrt{y}}$ = 2 $\frac{4}{\sqrt{x}}$ - $\frac{9}{\sqrt{y}}$ = -1

5900.

Solve the following pair of linear equations 2√x + 3√y = 2 4√x - 9√y = -1

Answer»

Solve the following pair of linear equations

$\frac{2}{\sqrt{x}}$ + $\frac{3}{\sqrt{y}}$ = 2

$\frac{4}{\sqrt{x}}$ - $\frac{9}{\sqrt{y}}$ = -1

Discussion

Explore topic-wise InterviewSolutions in .

For which values of p and q, will the following pair of linear equations have infinitely many solutions? 4x + 5y = 2 , (2p + 7q) x + (p + 8q) y = 2q-p + 1

Question 72 Solve the following: 3x+22x−3=−34

There is a six faced die. Ram wants to find the probability that the number that lands on the die is at least 3. What is the number of favourable outcomes?

The legth of a rectangle exceeds its breadth by 9cm. If the length and breadth are each increased by 3cm, the area of the new rectangle will be 84cm^2 more than that of the given rectangle. Find the length and breadth of the given rectangle.

The areas of two similar triangles are 12 cm2 and 48 cm2. If the height of the smaller triangle is 2.1 cm, then the corresponding height of the bigger triangle is _____.

The mean of 6, 8, 11, 13, 14 and x is 66. Find the value of the observation x.

A pole stands in a park such that its shadow increases by 2 m when the angle of elevation of Sun changes from 45º to 30º. The height of the pole is

Prove that x + 1 is a factor of xn − 1 for every even number n.

In an isosceles ΔABC right angled at B, prove that AC2=2AB2.

Out of the two concentric circles, the radius of the outer circle is 5 cm and the chord AC of length 8 cm is a tagnent to the inner circle. Find the radius of the inner circle.

In the given figure, ABCD is a rectangle with AB = 80 cm and BC = 70 cm, ∠AED = 90° and DE = 42 cm. A semicircle is drawn, taking BC as diameter. Find the area of the shaded region. [CBSE 2014]

find the circumradius of the circle circumscribed get the triangle formed by vertices A (-a,0),B (0,b)and (a, 0)

Which of the following suffixes are used for people and their jobs?

In fig., there are two concentric circles with center O and of radii 5 cm and 3 cm. From an external point P, tangents PA and PB are drawn to these circles. If AP = 12 cm, find the length of BP [3 MARKS]

If sin2A + cos2A =1 then sin4A + cos4A will also be equal to 1. Or sinA +cosA will also be equal to 1.

What is the trigonometric ratio that connects the opposite side to adjacent side in a right-angled triangle?

If the 4th, 7th and 10th terms of a G.P. be a, b, c respectively, then the relation between a, b, c is _______.

How to visualize complex number subtraction.

The minimum value of 4x + 41 – x, x ∈ R, is(a) 2(b) 4(c) 1(d) 0

Question 14 An event is very unlikely to happen. Its probability is closest to (a) 0.0001 (b) 0.001 (c) 0.01 (d) 0.1

A ray of light coming from the point (1, 2) is reflected at a point A on the x - axis and then passes through the point (5, 3). The coordinates of the point A are

Find the mean using step-deviation. Class IntervalFrequency0−1016010−2020020−3032030−4048040−5030050−60140

Find the equation of circle which passes through (-1,2) & (3,-1) and whose centre lies on the straight line x-2y=0

In an equilateral triangle ABC, D is the mid-point of AB and E is the mid point of AC. The ar(ΔABC) : ar (ΔADE) =

how to multiply an irrational number to an rational number

If G be the centroid of a triangle ABC, prove that : AB2+BC2+CA2=3(GA2+GB2+GC2)

In a ∆ABC right angled at B, ∠A = ∠C. Find the values of(i) sin A cos C + cos A sin C(ii) sin A sin B + cos A cos B

A person is noting down the number of accidents along a busy highway during a year. The appropriate sample space in the experiment is:

A takes 10 days less than the time taken by B to finish a piece of work. If both A and B together can finish the work in 12 days, find the time taken by B to finish the work.

Given a G.P. with a = 729 and 7 th term 64, determine S 7 .

Draw a right triangle ABC in which AB = 6 cm, BC = 8 cm and ∠B = 90º. Draw BD perpendicular from B on AC and draw a circle passing through the points B, C and D. Construct tangents from A to this circle. [CBSE 2014]

Find the area of a sector of a circle with radius 6cm if the angle of the sector is 60∘

Question 1 (iii) Fill in the blanks using the correct word in the given bracket. (iii) All ___ triangles are similar. (isosceles, equilateral)

Question 9The angle of elevation of the top of a building from the foot of the tower is 30∘ and the angle of elevation of the top of the tower from the foot of the building is 60∘. If the tower is 50 m high, find the height of the building.

Question 11In figure, if ∠D=∠C, then is it true that ΔADE∼ΔACB,? Why?

Express 0.235353535...........in p/q form

In parallelogram ABCD, AB = 10 cm. The altitudes corresponding to the sides AB and AD are respectively 7 cm and 8 cm. Find AD. [2 MARKS]

Find the zeroes of the quadratic polynomial and verify the relationship between zeroes and coefficients 6x2-3-7x

Question: Find the smallest number which leaves remainders 8 and 12 when divided by 28 and 32 respectively.

Question1 (ii)Answer the following and justifyWhat will the quotient and remainder be on division of ax2+bx+c by px3+qx2+rx+s,p≠0?

6 arithmetic means are inserted between 1 and 9/2 then the fourth arithmetic mean is please answer

In Δ ABC, right angled at B, expressions for sec C and cosec C is

Question 4If from an external point B of a circle with centre O, two tangents BC and BD are drawn such that ∠ DBC = 120∘, prove that BC+BD=BO i.e BO = 2BC.

how to solve euclid division lemma

Question 5 (iv)Prove the following identities, where the angles involved are acute angles for which the expressions are defined.(iv) (1+secA)secA=sin2A(1−cosA)[Hint : Simplify L.H.S and R.H.S separately]

Question 86 What number divided by 520 gives the same quotient as 85 divided by 0.625?

Solve the following pair of linear equations 2√x + 3√y = 2 4√x - 9√y = -1