32581 + Interview Questions in Mathematics Page 230 InterviewSolution

11451.	Justify whether it is true to say that the sequence having following nth term is an A.P.(i) an = 2n − 1 (ii) an = 3n2 + 5 (iii) an = 1 + n + n2
Answer» Justify whether it is true to say that the sequence having following n^th term is an A.P. (i) a_n = 2n − 1 (ii) a_n = 3n² + 5 (iii) a_n = 1 + n + n²

Discussion

11452.	If h, S and V be the height curved surface area and volume of a cone respectively, then 3πVh3 – S2h2 + 9V2 is equal to ________.
Answer» If h, S and V be the height curved surface area and volume of a cone respectively, then 3πVh³ – S²h²+ 9V² is equal to ________.

Discussion

11453.	Question 4 (i) ABC is a triangle in which altitudes BE and CF to sides AC and AB are equal (see the given figure). Show that (i)ΔABE≅ΔACF
Answer» Question 4 (i) ABC is a triangle in which altitudes BE and CF to sides AC and AB are equal (see the given figure). Show that (i) $Δ A B E ≅ Δ A C F$

Discussion

11454.	Without using trigonometric tables find the values of: cos70°/sin20° + cos57°cosec33°-2cos60°
Answer» Without using trigonometric tables find the values of: cos70°/sin20° + cos57°cosec33°-2cos60°

11454.

Without using trigonometric tables find the values of: cos70°/sin20° + cos57°cosec33°-2cos60°

Answer»

Without using trigonometric tables find the values of:

cos70°/sin20° + cos57°cosec33°-2cos60°

Discussion

11455.	Given that two of the zeroes of the cubic polynomial ax3 + bx2 + cx + d are 0 , the third zero is (a) - ba (b) ba (c) ca (d) -da
Answer» Given that two of the zeroes of the cubic polynomial $a x^{3} + b x^{2} + c x + d$ are 0 , the third zero is (a) $- \frac{b}{a}$ (b) $\frac{b}{a}$ (c) $\frac{c}{a}$ (d) $- \frac{d}{a}$

Discussion

11456.	A Goldsmith can choose between three metals A, B and C. The probability that he chooses C is .
Answer» A Goldsmith can choose between three metals A, B and C. The probability that he chooses C is .

Discussion

11457.	Sides of two similar triangles are in the ratio of 4: 9. Find the ratio of the areas of these triangles.
Answer» Sides of two similar triangles are in the ratio of 4: 9. Find the ratio of the areas of these triangles.

Discussion

11458.	In △ABC, ∠B=90∘. If tan A=1√3, then sin A.cos C+cos A.sin C = ___
Answer» In $△$ ABC, $∠ B = 90^{\circ}$ . If $t a n A = \frac{1}{\sqrt{3}}$ , then $s i n A . c o s C + c o s A . s i n C$ = ___

Discussion

11459.	Find the area under the given curves and given lines: (i) y = x 2 , x = 1, x = 2 and x -axis (ii) y = x 4 , x = 1, x = 5 and x –axis
Answer» Find the area under the given curves and given lines: (i) y = x 2 , x = 1, x = 2 and x -axis (ii) y = x 4 , x = 1, x = 5 and x –axis

Discussion

11460.	In ΔABC, with points P and Q on sides AB and AC, respectively such that APPB=AQQC. If PQ is extended to T such that PT = BC and PB = TC, then x is equal to
Answer» In $Δ A B C$ , with points P and Q on sides AB and AC, respectively such that $\frac{A P}{P B} = \frac{A Q}{Q C}$ . If PQ is extended to T such that PT = BC and PB = TC, then x is equal to

Discussion

11461.	What is the relationship between AR curves and MR curves?
Answer» What is the relationship between AR curves and MR curves?

Discussion

11462.	Which of the following equations has two distinct real roots?
Answer» Which of the following equations has two distinct real roots?

Discussion

11463.	Please solve the quadratic equation by factorisation method: x² + ( a/a+b + a+b/a)x + 1 =0
Answer» Please solve the quadratic equation by factorisation method: x² + ( a/a+b + a+b/a)x + 1 =0

Discussion

11464.	Question 5 The lengths of 62 leaves of a plant are measured in millimetres and the data is represented in the following table. Length(in mm)Number of leave118−1268127−13510136−14412145−15317154−1627163−1715172−1803 Draw a histogram to represent the data above.
Answer» Question 5 The lengths of 62 leaves of a plant are measured in millimetres and the data is represented in the following table. $\begin{matrix} Length(in mm) & Number of leave 118 - 126 & 8 127 - 135 & 10 136 - 144 & 12 145 - 153 & 17 154 - 162 & 7 163 - 171 & 5 172 - 180 & 3 \end{matrix}$ Draw a histogram to represent the data above.

Discussion

11465.	A roller of a cricket pitch takes 800 revolutions to completely roll out the pitch. Find the area covered by the roller if its diameter is 49 cm and length is 2 m.
Answer» A roller of a cricket pitch takes 800 revolutions to completely roll out the pitch. Find the area covered by the roller if its diameter is 49 cm and length is 2 m.

Discussion

11466.	If the points P(a, -11), Q(5, b), R(2, 15) andS(1 ,1) are the vertices of a parallelogram PQRS, find the values of a and b.
Answer» If the points P(a, -11), Q(5, b), R(2, 15) andS(1 ,1) are the vertices of a parallelogram PQRS, find the values of a and b.

Discussion

11467.	Show that 2−√3 is an irrational number.
Answer» Show that $2 - \sqrt{3}$ is an irrational number.

Discussion

11468.	Two identical cubes of side 4 cm are placed one above the other, forming a cuboid. The total surface area of the cuboid thus formed is .
Answer» Two identical cubes of side 4 cm are placed one above the other, forming a cuboid. The total surface area of the cuboid thus formed is .

Discussion

11469.	In the fromula for mode of a grouped data ,mode =l+[t1−t02f1−f0−f2]×h ,where symbols have their usual meaning f1 represents
Answer» In the fromula for mode of a grouped data , mode $= l + [\frac{t_{1} - t_{0}}{2 f_{1} - f_{0} - f_{2}}] \times h$ , where symbols have their usual meaning $f_{1}$ represents

Discussion

11470.	Find the area of a triangle whose vertices are(i) (6, 3) (−3, 5) and (4, −2)(ii) (at12, 2at1), (at22,2at2) and (at32,2at3)(iii) (a, c + a), (a, c) and (−a, c − a)
Answer» Find the area of a triangle whose vertices are (i) (6, 3) (−3, 5) and (4, −2) (ii) $(a t_{1}^{2}, 2 a t_{1}), (a t_{2}^{2}, 2 a t_{2}) a n d (a t_{3}^{2}, 2 a t_{3})$ (iii) (a, c + a), (a, c) and (−a, c − a)

Discussion

11471.	When a polynomial f(x) is divided by (x^2-5) and the quotient is x^2-2x-3 and remainsre is zero. Find the polynomial and all its zeroes.
Answer» When a polynomial f(x) is divided by (x^2-5) and the quotient is x^2-2x-3 and remainsre is zero. Find the polynomial and all its zeroes.

Discussion

11472.	If tan θ=247, find that sin θ + cos θ.
Answer» If $\tan θ = \frac{24}{7}$ , find that sin θ + cos θ.

Discussion

11473.	(x2+4x+3) can be visualised by the rectangle below. Identify the region depicting the constant term.
Answer» ( $x^{2} + 4 x + 3$ ) can be visualised by the rectangle below. Identify the region depicting the constant term.

Discussion

11474.	From the top of a lighthouse, the angles of depression of two ships on the opposite sides of it are observed to be α and β. If the height of the lighthouse be h metres and the line joining the ships passes through the foot of the lighthouse, find the distance between the ships is metres.
Answer» From the top of a lighthouse, the angles of depression of two ships on the opposite sides of it are observed to be $α$ and $β$ . If the height of the lighthouse be h metres and the line joining the ships passes through the foot of the lighthouse, find the distance between the ships is metres.

Discussion

11475.	In the figure given below, point D divides AB in the ratio 3 : 5 and DE is parallel toBC. If AE = 4.8 cm, then find thelength of AC.
Answer» $In the figure given below, point D divides AB in the ratio 3 : 5 and DE is parallel to BC. If AE = 4.8 cm, then find the length of AC.$

11475.

In the figure given below, point D divides AB in the ratio 3 : 5 and DE is parallel toBC. If AE = 4.8 cm, then find thelength of AC.

Answer»

$In the figure given below, point D divides AB in the ratio 3 : 5 and DE is parallel to BC. If AE = 4.8 cm, then find the length of AC.$

Discussion

11476.	A steel wire when bent in the form of a square encloses an area of 121 cm2. If the same wire is bent in the form of a circle, find the area of the circle.
Answer» A steel wire when bent in the form of a square encloses an area of 121 cm². If the same wire is bent in the form of a circle, find the area of the circle.

Discussion

11477.	Question 20When a die is thrown, the probability of getting an odd number less than 3 is(a) 16(b) 13(c) 12(d) 0
Answer» Question 20 When a die is thrown, the probability of getting an odd number less than 3 is (a) $\frac{1}{6}$ (b) $\frac{1}{3}$ (c) $\frac{1}{2}$ (d) 0

Discussion

11478.	In a quadrilateral ABCD, AB = 2 cm , BC = 3 cm , CD = 5 cm and AD = 4 cm. Which one of the following relationship is TRUE between angles B and D ? 1) angle B Is greater than angle D2) angle D is greater than angle B
Answer» In a quadrilateral ABCD, AB = 2 cm , BC = 3 cm , CD = 5 cm and AD = 4 cm. Which one of the following relationship is TRUE between angles B and D ? 1) angle B Is greater than angle D 2) angle D is greater than angle B

Discussion

11479.	A ladder 15 metres long just reaches the top of a vertical wall. If the ladder makes an angle of 60∘ with the wall, find the height of the wall.
Answer» A ladder 15 metres long just reaches the top of a vertical wall. If the ladder makes an angle of $60^{\circ}$ with the wall, find the height of the wall.

Discussion

11480.	If A=[1−32202] and B=[2−1−110−1], then the matrix C such that A+B+C is a zero matrix, is
Answer» If $A = [\begin{matrix} 1 & - 3 & 2 2 & 0 & 2 \end{matrix}]$ and $B = [\begin{matrix} 2 & - 1 & - 1 1 & 0 & - 1 \end{matrix}]$ , then the matrix $C$ such that $A + B + C$ is a zero matrix, is

Discussion

11481.	70 Let C be the circle that touches the X-axis and whose centre coincides with the circumcentre of the triangle dened by 4\|x\| + 3y = 12; y ≥ 0. How many points with both co-ordinates integers are there in the interior of C? A. 0. B. 1. C. 2. D. 3.
Answer» 70 Let C be the circle that touches the X-axis and whose centre coincides with the circumcentre of the triangle dened by 4\|x\| + 3y = 12; y ≥ 0. How many points with both co-ordinates integers are there in the interior of C? A. 0. B. 1. C. 2. D. 3.

Discussion

11482.	Question 51Two cylinders of equal volume have heights in the ratio 1 : 9. The ratio of their radii is ___.
Answer» Question 51 Two cylinders of equal volume have heights in the ratio 1 : 9. The ratio of their radii is ___.

11482.

Question 51Two cylinders of equal volume have heights in the ratio 1 : 9. The ratio of their radii is ___.

Answer»

Question 51

Two cylinders of equal volume have heights in the ratio 1 : 9. The ratio of their radii is ___.

Discussion

11483.

Journalise the following transactions:- 2019 ₹ March 1 Started business with cash 50,000 2 Purchased Machinery for cash 20,000 Paid installation charges on machinery 2,000 5 Purchased goods from X of the list price of ₹ 25,000, Trade Discount 20% and cash discount 5%. Payment was made in cash immediately. 10 Sold goods to Y costing ₹ 10,000 at 30% profit on cost less 10% trade discount. 15 Paid Rent 1,000 20 Goods stolen from business 2,000 22 Gave as charity : Cash 100 Goods 200 31 Purchased Post Cards and Envelopes 50 31 Purchased a Computer for business 25,000

Answer» Journalise the following transactions:-

2019		₹
March 1	Started business with cash	50,000
2	Purchased Machinery for cash	20,000
	Paid installation charges on machinery	2,000
5	Purchased goods from X of the list price of ₹ 25,000, Trade Discount 20% and cash discount 5%. Payment was made in cash immediately.
10	Sold goods to Y costing ₹ 10,000 at 30% profit on cost less 10% trade discount.
15	Paid Rent	1,000
20	Goods stolen from business	2,000
22	Gave as charity :
	Cash	100
	Goods	200
31	Purchased Post Cards and Envelopes	50
31	Purchased a Computer for business	25,000

Discussion

11484.	The sum of first 16 terms of the A.P.: 10, 6, 2, ..., is(a) –320(b) 320(c) –352(d) –400
Answer» The sum of first 16 terms of the A.P.: 10, 6, 2, ..., is (a) –320 (b) 320 (c) –352 (d) –400

Discussion

11485.	From the top of a 7 m high building, the angle of elevation of the top of a cable tower is 60∘ and the angle of depression of its foot is 45∘. Determine the height of the tower.
Answer» From the top of a 7 m high building, the angle of elevation of the top of a cable tower is $60^{\circ}$ and the angle of depression of its foot is $45^{\circ}$ . Determine the height of the tower.

Discussion

11486.	the floor is in the shape of rectangle of length 9.6m and breadth 4.2 m. find the measure of the sind of the largest square shaped tile that can be used in the whole to cover the floor completely how many such tiles are needed for this purpose?
Answer» the floor is in the shape of rectangle of length 9.6m and breadth 4.2 m. find the measure of the sind of the largest square shaped tile that can be used in the whole to cover the floor completely how many such tiles are needed for this purpose?

Discussion

11487.	First term and common difference of an A.P. are 6 and 3 respectively ; find S27.
Answer» First term and common difference of an A.P. are 6 and 3 respectively ; find S₂₇.

Discussion

11488.	Which term of the AP 18, 23, 28, 33, ……. is 98?
Answer» Which term of the AP 18, 23, 28, 33, ……. is 98?

Discussion

11489.	The mean of 10 numbers is 12.5. The mean of first six numbers is 15 and the mean of last five terms is 10. Find the sixth number l.
Answer» The mean of 10 numbers is 12.5. The mean of first six numbers is 15 and the mean of last five terms is 10. Find the sixth number l.

Discussion

11490.	Is it possible to cnstruct a triangle whose sides are 5cm, 5cm and 10 cm.
Answer» Is it possible to cnstruct a triangle whose sides are 5cm, 5cm and 10 cm.

Discussion

11491.	An aeroplane when flying at a height of 3000 metres from the ground passes vertically above another aeroplane at an instant when the angles of elevation of the two planes from the same point on the ground are 60∘ and 45∘ respectively. Find the vertical distance between the aeroplanes at that instant. [Take √3=1.73]
Answer» An aeroplane when flying at a height of 3000 metres from the ground passes vertically above another aeroplane at an instant when the angles of elevation of the two planes from the same point on the ground are $60^{\circ}$ and $45^{\circ}$ respectively. Find the vertical distance between the aeroplanes at that instant. [Take $\sqrt{3} = 1.73$ ]

Discussion

11492.	The given figure shows a hemisphere surmounted by a conical block of wood. The diameter of their bases is 6 cm each & the slant height of the cone is 5 cm. Calculate the volume of the solid.
Answer» The given figure shows a hemisphere surmounted by a conical block of wood. The diameter of their bases is 6 cm each & the slant height of the cone is 5 cm. Calculate the volume of the solid.

11492.

The given figure shows a hemisphere surmounted by a conical block of wood. The diameter of their bases is 6 cm each & the slant height of the cone is 5 cm. Calculate the volume of the solid.

Answer»

The given figure shows a hemisphere surmounted by a conical block of wood. The diameter of their bases is 6 cm each & the slant height of the cone is 5 cm. Calculate the volume of the solid.

Discussion

11493.	If A is a matrix of order 3 × 3, then the number of minors in A is ____________.
Answer» If A is a matrix of order 3 × 3, then the number of minors in A is ____________.

Discussion

11494.	In a game, a man wins Rs 5 for getting a number greater than 4 and loses Rs 1 otherwise, when a fair die is thrown. The man decided to thrown a die thrice but to quit as and when he gets a number greater than 4. Find the expected value of the amount he wins/loses.
Answer» In a game, a man wins Rs 5 for getting a number greater than 4 and loses Rs 1 otherwise, when a fair die is thrown. The man decided to thrown a die thrice but to quit as and when he gets a number greater than 4. Find the expected value of the amount he wins/loses.

Discussion

11495.	If α and β are the zeroes of the quadratic polynomial f(x)=ax^{2 }+bx+c ,then the value of α^4 +β^4 is
Answer» If α and β are the zeroes of the quadratic polynomial f(x)=ax^{2 }+bx+c ,then the value of α^4 +β^4 is

Discussion

11496.	ABCD is a square such that an equilateral Δ BCQ is formed on the side of the square and another equilateral Δ ACP is formed on the diagonal of the square as shown in the figure. Find Ar (Δ BCQ) : Ar (Δ APC) .
Answer» ABCD is a square such that an equilateral $Δ B C Q$ is formed on the side of the square and another equilateral $Δ A C P$ is formed on the diagonal of the square as shown in the figure. Find $A r (Δ B C Q)$ : $A r (Δ A P C)$ .

Discussion

11497.	The angle of elevation of a cloud from point h meters above the surface of a lake is b and angle of depression of its angle in lake is a.Prove that the height of the cloud above the lake is =h(tan α+tan β)tan β−tan α
Answer» The angle of elevation of a cloud from point h meters above the surface of a lake is b and angle of depression of its angle in lake is a.Prove that the height of the cloud above the lake is $= \frac{h (t a n α + t a n β)}{t a n β - t a n α}$

Discussion

11498.

The marks obtained by 90 students of a school in mathematics out of 100 are given as under: Marks 10-20 20-30 30-40 40-50 50-60 60-70 70-80 No. of students 7 8 12 25 19 10 9 From these students, a student is chosen at random.What is the probability that the chosen student(i) gets less than 20% marks?(ii) gets 60% or more marks?

Answer»

The marks obtained by 90 students of a school in mathematics out of 100 are given as under:

Marks	10-20	20-30	30-40	40-50	50-60	60-70	70-80
No. of students	7	8	12	25	19	10	9

From these students, a student is chosen at random.

What is the probability that the chosen student

(i) gets less than 20% marks?

(ii) gets 60% or more marks?

Discussion

11499.	From the top of a hill, the angles of depression of two consecutive kilometer stones, due east, are found to be 30∘ and 45∘ respectively. Find the distances of the two stones from the foot of the hill.
Answer» From the top of a hill, the angles of depression of two consecutive kilometer stones, due east, are found to be $30^{\circ} a n d 45^{\circ}$ respectively. Find the distances of the two stones from the foot of the hill.

Discussion

11500.	Question 5A cylindrical pillar is 50 cm in diameter and 3.5 m in height. Find the cost of painting the curved surface of the pillar at the rate of Rs. 12.50 per m2.[Assume π=227]
Answer» Question 5 A cylindrical pillar is 50 cm in diameter and 3.5 m in height. Find the cost of painting the curved surface of the pillar at the rate of Rs. 12.50 per $m^{2} . [A s s u m e π = \frac{22}{7}]$

Discussion

Explore topic-wise InterviewSolutions in .

Justify whether it is true to say that the sequence having following nth term is an A.P.(i) an = 2n − 1 (ii) an = 3n2 + 5 (iii) an = 1 + n + n2

If h, S and V be the height curved surface area and volume of a cone respectively, then 3πVh3 – S2h2 + 9V2 is equal to ________.

Question 4 (i) ABC is a triangle in which altitudes BE and CF to sides AC and AB are equal (see the given figure). Show that (i)ΔABE≅ΔACF

Without using trigonometric tables find the values of: cos70°/sin20° + cos57°cosec33°-2cos60°

Given that two of the zeroes of the cubic polynomial ax3 + bx2 + cx + d are 0 , the third zero is (a) - ba (b) ba (c) ca (d) -da

A Goldsmith can choose between three metals A, B and C. The probability that he chooses C is .

Sides of two similar triangles are in the ratio of 4: 9. Find the ratio of the areas of these triangles.

In △ABC, ∠B=90∘. If tan A=1√3, then sin A.cos C+cos A.sin C = ___

Find the area under the given curves and given lines: (i) y = x 2 , x = 1, x = 2 and x -axis (ii) y = x 4 , x = 1, x = 5 and x –axis

In ΔABC, with points P and Q on sides AB and AC, respectively such that APPB=AQQC. If PQ is extended to T such that PT = BC and PB = TC, then x is equal to

What is the relationship between AR curves and MR curves?

Which of the following equations has two distinct real roots?

Please solve the quadratic equation by factorisation method: x² + ( a/a+b + a+b/a)x + 1 =0

Question 5 The lengths of 62 leaves of a plant are measured in millimetres and the data is represented in the following table. Length(in mm)Number of leave118−1268127−13510136−14412145−15317154−1627163−1715172−1803 Draw a histogram to represent the data above.

A roller of a cricket pitch takes 800 revolutions to completely roll out the pitch. Find the area covered by the roller if its diameter is 49 cm and length is 2 m.

If the points P(a, -11), Q(5, b), R(2, 15) andS(1 ,1) are the vertices of a parallelogram PQRS, find the values of a and b.

Show that 2−√3 is an irrational number.

Two identical cubes of side 4 cm are placed one above the other, forming a cuboid. The total surface area of the cuboid thus formed is .

In the fromula for mode of a grouped data ,mode =l+[t1−t02f1−f0−f2]×h ,where symbols have their usual meaning f1 represents

Find the area of a triangle whose vertices are(i) (6, 3) (−3, 5) and (4, −2)(ii) (at12, 2at1), (at22,2at2) and (at32,2at3)(iii) (a, c + a), (a, c) and (−a, c − a)

When a polynomial f(x) is divided by (x^2-5) and the quotient is x^2-2x-3 and remainsre is zero. Find the polynomial and all its zeroes.

If tan θ=247, find that sin θ + cos θ.

(x2+4x+3) can be visualised by the rectangle below. Identify the region depicting the constant term.

From the top of a lighthouse, the angles of depression of two ships on the opposite sides of it are observed to be α and β. If the height of the lighthouse be h metres and the line joining the ships passes through the foot of the lighthouse, find the distance between the ships is metres.

In the figure given below, point D divides AB in the ratio 3 : 5 and DE is parallel toBC. If AE = 4.8 cm, then find thelength of AC.

A steel wire when bent in the form of a square encloses an area of 121 cm2. If the same wire is bent in the form of a circle, find the area of the circle.

Question 20When a die is thrown, the probability of getting an odd number less than 3 is(a) 16(b) 13(c) 12(d) 0

In a quadrilateral ABCD, AB = 2 cm , BC = 3 cm , CD = 5 cm and AD = 4 cm. Which one of the following relationship is TRUE between angles B and D ? 1) angle B Is greater than angle D2) angle D is greater than angle B

A ladder 15 metres long just reaches the top of a vertical wall. If the ladder makes an angle of 60∘ with the wall, find the height of the wall.

If A=[1−32202] and B=[2−1−110−1], then the matrix C such that A+B+C is a zero matrix, is

70 Let C be the circle that touches the X-axis and whose centre coincides with the circumcentre of the triangle dened by 4|x| + 3y = 12; y ≥ 0. How many points with both co-ordinates integers are there in the interior of C? A. 0. B. 1. C. 2. D. 3.

Question 51Two cylinders of equal volume have heights in the ratio 1 : 9. The ratio of their radii is ___.

The sum of first 16 terms of the A.P.: 10, 6, 2, ..., is(a) –320(b) 320(c) –352(d) –400

From the top of a 7 m high building, the angle of elevation of the top of a cable tower is 60∘ and the angle of depression of its foot is 45∘. Determine the height of the tower.

the floor is in the shape of rectangle of length 9.6m and breadth 4.2 m. find the measure of the sind of the largest square shaped tile that can be used in the whole to cover the floor completely how many such tiles are needed for this purpose?

First term and common difference of an A.P. are 6 and 3 respectively ; find S27.

Which term of the AP 18, 23, 28, 33, ……. is 98?

The mean of 10 numbers is 12.5. The mean of first six numbers is 15 and the mean of last five terms is 10. Find the sixth number l.

Is it possible to cnstruct a triangle whose sides are 5cm, 5cm and 10 cm.

The given figure shows a hemisphere surmounted by a conical block of wood. The diameter of their bases is 6 cm each &amp; the slant height of the cone is 5 cm. Calculate the volume of the solid.

If A is a matrix of order 3 × 3, then the number of minors in A is ____________.

In a game, a man wins Rs 5 for getting a number greater than 4 and loses Rs 1 otherwise, when a fair die is thrown. The man decided to thrown a die thrice but to quit as and when he gets a number greater than 4. Find the expected value of the amount he wins/loses.

If α and β are the zeroes of the quadratic polynomial f(x)=ax^{2 }+bx+c ,then the value of α^4 +β^4 is

ABCD is a square such that an equilateral Δ BCQ is formed on the side of the square and another equilateral Δ ACP is formed on the diagonal of the square as shown in the figure. Find Ar (Δ BCQ) : Ar (Δ APC) .

The angle of elevation of a cloud from point h meters above the surface of a lake is b and angle of depression of its angle in lake is a.Prove that the height of the cloud above the lake is =h(tan α+tan β)tan β−tan α

From the top of a hill, the angles of depression of two consecutive kilometer stones, due east, are found to be 30∘ and 45∘ respectively. Find the distances of the two stones from the foot of the hill.

Question 5A cylindrical pillar is 50 cm in diameter and 3.5 m in height. Find the cost of painting the curved surface of the pillar at the rate of Rs. 12.50 per m2.[Assume π=227]

The given figure shows a hemisphere surmounted by a conical block of wood. The diameter of their bases is 6 cm each & the slant height of the cone is 5 cm. Calculate the volume of the solid.