32581 + Interview Questions in Mathematics Page 151 InterviewSolution

7501.

The mean of the following frequency distribution is 50. Find the value of p. Classes 0−20 20−40 40−60 60−80 80−100 Frequency 17 28 32 p 19

Answer» The mean of the following frequency distribution is 50. Find the value of p.

Classes	0−20	20−40	40−60	60−80	80−100
Frequency	17	28	32	p	19

Discussion

7502.	If the height and base of the right triangle is 12 cm and 9 cm resp., the area of the triangle is __ cm2.
Answer» If the height and base of the right triangle is 12 cm and 9 cm resp., the area of the triangle is __ $c m^{2}$ .

7502.

If the height and base of the right triangle is 12 cm and 9 cm resp., the area of the triangle is __ cm2.

Answer»

If the height and base of the right triangle is 12 cm and 9 cm resp., the area of the triangle is __ $c m^{2}$ .

Discussion

7503.	In the given figure, l \|\| m(i) Name three pairs of similar triangles with proper correspondence; write similarities.(ii) Prove that ABPQ=ACPR=BCRQ
Answer» In the given figure, l \|\| m (i) Name three pairs of similar triangles with proper correspondence; write similarities. (ii) Prove that $\frac{AB}{PQ} = \frac{AC}{PR} = \frac{BC}{RQ}$

Discussion

7504.	In the given figure, O is the centre of the circle. Find x.
Answer» In the given figure, O is the centre of the circle. Find $x$ .

7504.

In the given figure, O is the centre of the circle. Find x.

Answer»

In the given figure, O is the centre of the circle. Find $x$ .

Discussion

7505.	Corresponding sides of two similar triangles are in the ratio 2 : 3. If the area of the smaller triangle is 48 cm2, then the area of the larger triangle is _________.
Answer» Corresponding sides of two similar triangles are in the ratio 2 : 3. If the area of the smaller triangle is 48 cm², then the area of the larger triangle is _________.

Discussion

7506.	Find the zero of a linear polynomial ax + b.
Answer» Find the zero of a linear polynomial ax + b.

Discussion

7507.	A fraction becomes 1/3 if 1 is subtracted from both its numerator and denominator. If 1 is added to both the numerator and denominator, it becomes 1/2. Find the fraction.
Answer» A fraction becomes 1/3 if 1 is subtracted from both its numerator and denominator. If 1 is added to both the numerator and denominator, it becomes 1/2. Find the fraction.

Discussion

7508.	The height and radius of the cone of which the frustum is a part are h1 and r1 respectively. If h2 and r2 are the heights and radius of the smaller base of the frustum respectively and h2 : h1 = 1 : 2, then r2 : r1 is equal to(a) 1 : 3(b) 1 : 2(c) 2 : 1(d) 3 : 1
Answer» The height and radius of the cone of which the frustum is a part are h₁ and r₁ respectively. If h₂ and r₂ are the heights and radius of the smaller base of the frustum respectively and h₂ : h₁ = 1 : 2, then r₂ : r₁ is equal to (a) 1 : 3 (b) 1 : 2 (c) 2 : 1 (d) 3 : 1

Discussion

7509.	If r1 and r2 be the radii of two solid metallic spheres and if they are melted into one solid sphere, prove that the radius of the new sphere is r13 + r23.13
Answer» If r₁ and r₂ be the radii of two solid metallic spheres and if they are melted into one solid sphere, prove that the radius of the new sphere is $(r_{1}^{3} + r_{2}^{3}) .^{\frac{1}{3}}$

Discussion

7510.	A plot is in the form of a rectangle ABCD having semi-circle on BC as shown in the following figure. If AB = 60 m and BC = 28 m, find the area of the plot.
Answer» A plot is in the form of a rectangle ABCD having semi-circle on BC as shown in the following figure. If AB = 60 m and BC = 28 m, find the area of the plot.

Discussion

7511.	Find the volume of the following figure in (cm3)
Answer» Find the volume of the following figure in ( $c m^{3}$ )

Discussion

7512.	In the given series, 1.5, 0.5, -0.5, -1.5, .... , -8.5 If nth term is -8.5, find n.
Answer» In the given series, 1.5, 0.5, -0.5, -1.5, .... , -8.5 If $n^{t h}$ term is -8.5, find n.

Discussion

7513.	Hello, Please help me with following problem : In a two digit no. , the unit's digit exceeds tens digit by 2. The product of the given number and the sum of digits is equal to 144. Find the number. regards, Nikita
Answer» Hello, Please help me with following problem : In a two digit no. , the unit's digit exceeds tens digit by 2. The product of the given number and the sum of digits is equal to 144. Find the number. regards, Nikita

Discussion

7514.	Question 1(a) Find the sum by suitable rearrangement: 837 + 208 + 363
Answer» Question 1(a) Find the sum by suitable rearrangement: 837 + 208 + 363

7514.

Question 1(a) Find the sum by suitable rearrangement: 837 + 208 + 363

Answer»

Question 1(a)

Find the sum by suitable rearrangement:
837 + 208 + 363

Discussion

7515.	Find the area bounded by y=3x²+2x+4 , x-axis, x=-1 , x=3 using integration. NOTE: How to draw the graph of y=3x²+2x+4
Answer» Find the area bounded by y=3x²+2x+4 , x-axis, x=-1 , x=3 using integration. NOTE: How to draw the graph of y=3x²+2x+4

Discussion

7516.	A building subtends a right angle at the top of a pole on the other side of the road. The line joining the top of the pole and the top of the building makes an angle of 60^° with thevertical. If the width of the road is 45 m, find the height of the building
Answer» A building subtends a right angle at the top of a pole on the other side of the road. The line joining the top of the pole and the top of the building makes an angle of 60^° with thevertical. If the width of the road is 45 m, find the height of the building

Discussion

7517.	Two buildings on a plane ground are 30 m apart. From the top of the smaller building, one sees the base of the other building at an angle of depression of 60∘ and its top at an elevation of 35∘. Find the height of the bigger building.[Tan 60∘=1.7Tan 35∘=0.7] Let CD & AB be the smaller and taller building respectively.DE = AC = 30 m
Answer» Two buildings on a plane ground are 30 m apart. From the top of the smaller building, one sees the base of the other building at an angle of depression of $60^{\circ}$ and its top at an elevation of $35^{\circ} .$ Find the height of the bigger building. $[\begin{matrix} T a n 60^{\circ} = 1.7 T a n 35^{\circ} = 0.7 \end{matrix}]$ Let CD $&$ AB be the smaller and taller building respectively. DE = AC = 30 m

7517.

Two buildings on a plane ground are 30 m apart. From the top of the smaller building, one sees the base of the other building at an angle of depression of 60∘ and its top at an elevation of 35∘. Find the height of the bigger building.[Tan 60∘=1.7Tan 35∘=0.7] Let CD & AB be the smaller and taller building respectively.DE = AC = 30 m

Answer»

Two buildings on a plane ground are 30 m apart. From the top of the smaller building, one sees the base of the other building at an angle of depression of $60^{\circ}$ and its top at an elevation of $35^{\circ} .$ Find the height of the bigger building.

$[\begin{matrix} T a n 60^{\circ} = 1.7 T a n 35^{\circ} = 0.7 \end{matrix}]$

Let CD $&$ AB be the smaller and taller building respectively.

DE = AC = 30 m

Discussion

7518.	Question 4Any solution of the linear equation 2x+0y+9=0 in two variables is of the form:A) (−92,m)B) (n,−92)C) (0,−92)D) (−9,0)
Answer» Question 4 Any solution of the linear equation 2x+0y+9=0 in two variables is of the form: A) $(- \frac{9}{2}, m)$ B) $(n, - \frac{9}{2})$ C) $(0, - \frac{9}{2})$ D) $(- 9, 0)$

Discussion

7519.	The following is the distribution of height of students of a certain class in a certain city: Height (in cms): 160-162 163-165 166-168 169-171 172-174 No. of students: 15 118 142 127 18 Find the average height of maximum number of students.
Answer» The following is the distribution of height of students of a certain class in a certain city: Height (in cms): 160-162 163-165 166-168 169-171 172-174 No. of students: 15 118 142 127 18 Find the average height of maximum number of students.

Discussion

7520.

The following table shows points on a number line and their co-ordinates. Decide whether the pair of segments given below the table are congruent or not. Point A B C D E Co-ordinate -3 5 2 -7 9 (i) seg DE and seg AB (ii) seg BC and seg AD (iii) seg BE and seg AD

Answer»

The following table shows points on a number line and their co-ordinates. Decide whether the pair of segments given below the table are congruent or not.

Point	A	B	C	D	E
Co-ordinate	$-$ 3	5	2	$-$ 7	9

(i) seg DE and seg AB (ii) seg BC and seg AD (iii) seg BE and seg AD

Discussion

7521.	If D-15,52, E(7,3) and F72,72 are the mid-points of sides of ∆ ABC , find the area of ∆ ABC .
Answer» If $D (- \frac{1}{5}, \frac{5}{2}), E (7, 3) and F (\frac{7}{2}, \frac{7}{2})$ are the mid-points of sides of $∆ A B C$ , find the area of $∆ A B C$ .

Discussion

7522.	In the adjoining figure, CE \|\| AD and CF \|\| BA. Prove that ar(∆CBG) = ar(∆AFG).
Answer» In the adjoining figure, CE \|\| AD and CF \|\| BA. Prove that ar(∆CBG) = ar(∆AFG).

Discussion

7523.	How to "proove that root 2 is irrational " from the topic proof of contradiction
Answer» How to "proove that root 2 is irrational " from the topic proof of contradiction

Discussion

7524.	In a triangle ABC, N is a point on AC such that BN ⊥ AC. If BN2 = AN . NC, prove that ∠B = 90°.
Answer» In a triangle ABC, N is a point on AC such that BN ⊥ AC. If BN² = AN . NC, prove that ∠B = 90°.

Discussion

7525.	Question 1 (iv) State whether the pair of triangles in the below figure is similar. Write the similarity criterion used by you for answering the question and also write the pair of similar triangles in the symbolic form:
Answer» Question 1 (iv) State whether the pair of triangles in the below figure is similar. Write the similarity criterion used by you for answering the question and also write the pair of similar triangles in the symbolic form:

Discussion

7526.	Draw a circle of radius 6 cm. From a point 10 cm away from its centre, construct a pair of tangents to the circle and measure their lengths.
Answer» Draw a circle of radius 6 cm. From a point 10 cm away from its centre, construct a pair of tangents to the circle and measure their lengths.

Discussion

7527.	On Jan 01, 2016 Rao sold goods Rs 10,000 to Reddy. Half of the payment was made immediately and for the remaining half Rao drew a bill of exchange upon Reddy payable after 30 days. Reddy accepted the bill and returned it to Rao. On the due date Rao presented the bill to Reddy and received the payment Journalise the above transactions in the books Rao and prepare of Rao’s account in the books of Reddy.
Answer» On Jan 01, 2016 Rao sold goods Rs 10,000 to Reddy. Half of the payment was made immediately and for the remaining half Rao drew a bill of exchange upon Reddy payable after 30 days. Reddy accepted the bill and returned it to Rao. On the due date Rao presented the bill to Reddy and received the payment Journalise the above transactions in the books Rao and prepare of Rao’s account in the books of Reddy.

Discussion

7528.	Let f:R→R be defined as f(x) = 10x + 7. The function g:R→R such that gof = fog =IR. Then g(2017) =
Answer» Let $f : R \to R$ be defined as f(x) = 10x + 7. The function $g : R \to R$ such that gof = fog = $I_{R}$ . Then g(2017) =

Discussion

7529.	For what values of p, the linear equation 3x+py=9 has equal values of x and y for its solution
Answer» For what values of p, the linear equation 3x+py=9 has equal values of x and y for its solution

Discussion

7530.	Sides of a triangular field are 15 m , 16 m , 17 m . With three corners of the field a cow , a buffalo and a horse are tied separately with ropes of length 7 m each to graze in the field . Find the area of the field which cannot be grazed by three animals.
Answer» Sides of a triangular field are 15 m , 16 m , 17 m . With three corners of the field a cow , a buffalo and a horse are tied separately with ropes of length 7 m each to graze in the field . Find the area of the field which cannot be grazed by three animals.

Discussion

7531.	The given figure shows a trapezium in which AB \|\| DC and diagonal AC and BD intersect at point P. If AP : CP = 3:5 and area of △APB is 27 m2, then the area of △CPD is ___.
Answer» The given figure shows a trapezium in which AB \|\| DC and diagonal AC and BD intersect at point P. If AP : CP = 3:5 and area of $△ A P B$ is $27 m^{2}$ , then the area of $△ C P D$ is ___.

7531.

The given figure shows a trapezium in which AB || DC and diagonal AC and BD intersect at point P. If AP : CP = 3:5 and area of △APB is 27 m2, then the area of △CPD is ___.

Answer»

The given figure shows a trapezium in which AB || DC and diagonal AC and BD intersect at point P. If AP : CP = 3:5 and area of $△ A P B$ is $27 m^{2}$ , then the area of $△ C P D$ is ___.

Discussion

7532.	Solve each of the following quadratic equations:37x+15x-3-45x-37x+1=11, x≠35, -17 [CBSE 2014]
Answer» Solve each of the following quadratic equations: $3 (\frac{7 x + 1}{5 x - 3}) - 4 (\frac{5 x - 3}{7 x + 1}) = 11, x \neq \frac{3}{5}, - \frac{1}{7}$ [CBSE 2014]

Discussion

7533.	The value of ∣∣∣24−12∣∣∣ is
Answer» The value of $∣ ∣ ∣ \begin{matrix} 2 & 4 - 1 & 2 \end{matrix} ∣ ∣ ∣$ is

Discussion

7534.	Question 3 (vi)Form the pair of linear equations for the following problems and find their solution by substitution method:Five years hence, the age of Jacob will be three times that of his son. Five years ago, Jacob's age was seven times that of his son. What are their present ages?
Answer» Question 3 (vi) Form the pair of linear equations for the following problems and find their solution by substitution method: Five years hence, the age of Jacob will be three times that of his son. Five years ago, Jacob's age was seven times that of his son. What are their present ages?

Discussion

7535.	Solve the following quadratic equation: 4x−3=52x+3,x≠0,−32
Answer» Solve the following quadratic equation: $\frac{4}{x} - 3 = \frac{5}{2 x + 3}, x \neq 0, \frac{- 3}{2}$

Discussion

7536.	If the zeroes of polynomial are, find a and b.
Answer» If the zeroes of polynomial are, find a and b.

Discussion

7537.	A bucket is in the form of a frustum of a cone of height 30 cm with radii of its lower and upper ends as 10 cm and 20 cm respectively. Find the capacity and surface area of the bucket. Also, find the cost of milk which can completely fill the cointainer, at the rate of Rs.25 per litre. (Use π = 3.14)
Answer» A bucket is in the form of a frustum of a cone of height 30 cm with radii of its lower and upper ends as 10 cm and 20 cm respectively. Find the capacity and surface area of the bucket. Also, find the cost of milk which can completely fill the cointainer, at the rate of Rs.25 per litre. (Use $π$ = 3.14)

Discussion

7538.	Solve each of the following systems of eqautions by the method of cross-multiplication: x+2y+1=0 2x−3y−12=0
Answer» Solve each of the following systems of eqautions by the method of cross-multiplication: $x + 2 y + 1 = 0$ $2 x - 3 y - 12 = 0$

7538.

Solve each of the following systems of eqautions by the method of cross-multiplication: x+2y+1=0 2x−3y−12=0

Answer»

Solve each of the following systems of eqautions by the method of cross-multiplication:

$x + 2 y + 1 = 0$

$2 x - 3 y - 12 = 0$

Discussion

7539.	If the plane xa+yb+zc=3 meets the coordinates axes at A, B and C, then the coordinates of the centroid of ∆ABC are ______________.
Answer» If the plane $\frac{x}{a} + \frac{y}{b} + \frac{z}{c} = 3$ meets the coordinates axes at A, B and C, then the coordinates of the centroid of ∆ABC are ______________.

Discussion

7540.	if f(x) is a polynomial such that f(a) f(b)
Answer» if f(x) is a polynomial such that f(a) f(b) <0, then what is the number of zeroes lying between a and b?

Discussion

7541.	On a horizontal plane there is a vertical tower with a flag pole on the top of the tower. At a point 9 metres away from the foot of the tower the angle of elevation of the top and bottom of the flag pole are 60∘ and 30∘ respectively. Find the height of the tower and the flag pole mounted on it.
Answer» On a horizontal plane there is a vertical tower with a flag pole on the top of the tower. At a point 9 metres away from the foot of the tower the angle of elevation of the top and bottom of the flag pole are $60^{\circ} a n d 30^{\circ}$ respectively. Find the height of the tower and the flag pole mounted on it.

Discussion

7542.	25. A man standing on the deck of a ship ,which is 10m above the water level,observes the angle of elevation of the top of a hill as 60^° and angle of depression of the base of the hill as 30^° .find the distance between ship and hill and height of the hill.
Answer» 25. A man standing on the deck of a ship ,which is 10m above the water level,observes the angle of elevation of the top of a hill as 60^° and angle of depression of the base of the hill as 30^° .find the distance between ship and hill and height of the hill.

Discussion

7543.	12 spheres of the same size are made from melting a solid cylinder of 16 cm diameter and 2 cm height. The diameter of each sphere is(a) 3 cm(b) 2 cm(c) 3 cm(d) 4 cm
Answer» 12 spheres of the same size are made from melting a solid cylinder of 16 cm diameter and 2 cm height. The diameter of each sphere is (a) $\sqrt{3}$ cm (b) 2 cm (c) 3 cm (d) 4 cm

Discussion

7544.	Write the zeros of the quadratic polynomial f(x)=4√3x2+5x−2√3.
Answer» Write the zeros of the quadratic polynomial $f (x) = 4 \sqrt{3} x^{2} + 5 x - 2 \sqrt{3}$ .

Discussion

7545.	The are of minor sector ofcircle (0,5) is 150 . The length of the corresponding arc is
Answer» The are of minor sector ofcircle (0,5) is 150 . The length of the corresponding arc is

Discussion

7546.	There are 50 numbers. Each number is subtracted from 53 and the mean of the numbers so obtained is found to be (-3.5). Find the mean of the given number
Answer» There are 50 numbers. Each number is subtracted from 53 and the mean of the numbers so obtained is found to be (-3.5). Find the mean of the given number

Discussion

7547.	For what n , are the nth terms of two APs: 63,65,67,.. and 3,10,17,.. equal?
Answer» For what n , are the nth terms of two APs: 63,65,67,.. and 3,10,17,.. equal?

Discussion

7548.	The angle of elevation of the top of a tower standing on a horizontal plane from a point A is α. After walking a distance d towards the foot of the tower the angle of elevation is found to be β. The height of the tower is(a) dcot α+cot β(b) dcot α-cot β(c) dtan β-tan α (d) dtan β+tan α
Answer» The angle of elevation of the top of a tower standing on a horizontal plane from a point A is α. After walking a distance d towards the foot of the tower the angle of elevation is found to be β. The height of the tower is (a) $\frac{d}{c o t α + c o t β}$ (b) $\frac{d}{c o t α - c o t β}$ (c) $\frac{d}{\tan β - \tan α}$ (d) $\frac{d}{\tan β + \tan α}$

Discussion

7549.

If an equilateral triangle ABC is drawn as shown below with A(0,0) and a side of 8 units then find the other two vertices of the triangle.

Answer»

If an equilateral triangle ABC is drawn as shown below with A(0,0) and a side of 8 units then find the other two vertices of the triangle.

Discussion

7550.	If the sum of zeros of the polynomial p(x) = kx3−5x2−11x−3 is 2, then k is equal to:
Answer» If the sum of zeros of the polynomial p(x) = $k x^{3} - 5 x^{2} - 11 x - 3$ is 2, then k is equal to:

Discussion

Explore topic-wise InterviewSolutions in .

The mean of the following frequency distribution is 50. Find the value of p. Classes 0−20 20−40 40−60 60−80 80−100 Frequency 17 28 32 p 19

If the height and base of the right triangle is 12 cm and 9 cm resp., the area of the triangle is __ cm2.

In the given figure, l || m(i) Name three pairs of similar triangles with proper correspondence; write similarities.(ii) Prove that ABPQ=ACPR=BCRQ

In the given figure, O is the centre of the circle. Find x.

Corresponding sides of two similar triangles are in the ratio 2 : 3. If the area of the smaller triangle is 48 cm2, then the area of the larger triangle is _________.

Find the zero of a linear polynomial ax + b.

A fraction becomes 1/3 if 1 is subtracted from both its numerator and denominator. If 1 is added to both the numerator and denominator, it becomes 1/2. Find the fraction.

The height and radius of the cone of which the frustum is a part are h1 and r1 respectively. If h2 and r2 are the heights and radius of the smaller base of the frustum respectively and h2 : h1 = 1 : 2, then r2 : r1 is equal to(a) 1 : 3(b) 1 : 2(c) 2 : 1(d) 3 : 1

If r1 and r2 be the radii of two solid metallic spheres and if they are melted into one solid sphere, prove that the radius of the new sphere is r13 + r23.13

A plot is in the form of a rectangle ABCD having semi-circle on BC as shown in the following figure. If AB = 60 m and BC = 28 m, find the area of the plot.

Find the volume of the following figure in (cm3)

In the given series, 1.5, 0.5, -0.5, -1.5, .... , -8.5 If nth term is -8.5, find n.

Hello, Please help me with following problem : In a two digit no. , the unit's digit exceeds tens digit by 2. The product of the given number and the sum of digits is equal to 144. Find the number. regards, Nikita

Question 1(a) Find the sum by suitable rearrangement: 837 + 208 + 363

Find the area bounded by y=3x²+2x+4 , x-axis, x=-1 , x=3 using integration. NOTE: How to draw the graph of y=3x²+2x+4

A building subtends a right angle at the top of a pole on the other side of the road. The line joining the top of the pole and the top of the building makes an angle of 60^° with thevertical. If the width of the road is 45 m, find the height of the building

Question 4Any solution of the linear equation 2x+0y+9=0 in two variables is of the form:A) (−92,m)B) (n,−92)C) (0,−92)D) (−9,0)​​​​​​​

The following is the distribution of height of students of a certain class in a certain city: Height (in cms): 160-162 163-165 166-168 169-171 172-174 No. of students: 15 118 142 127 18 Find the average height of maximum number of students.

The following table shows points on a number line and their co-ordinates. Decide whether the pair of segments given below the table are congruent or not. Point A B C D E Co-ordinate -3 5 2 -7 9 (i) seg DE and seg AB (ii) seg BC and seg AD (iii) seg BE and seg AD

If D-15,52, E(7,3) and F72,72 are the mid-points of sides of ∆ ABC , find the area of ∆ ABC .

In the adjoining figure, CE || AD and CF || BA. Prove that ar(∆CBG) = ar(∆AFG).

How to "proove that root 2 is irrational " from the topic proof of contradiction

In a triangle ABC, N is a point on AC such that BN ⊥ AC. If BN2 = AN . NC, prove that ∠B = 90°.

Question 1 (iv) State whether the pair of triangles in the below figure is similar. Write the similarity criterion used by you for answering the question and also write the pair of similar triangles in the symbolic form:

Draw a circle of radius 6 cm. From a point 10 cm away from its centre, construct a pair of tangents to the circle and measure their lengths.

Let f:R→R be defined as f(x) = 10x + 7. The function g:R→R such that gof = fog =IR. Then g(2017) =

For what values of p, the linear equation 3x+py=9 has equal values of x and y for its solution

Sides of a triangular field are 15 m , 16 m , 17 m . With three corners of the field a cow , a buffalo and a horse are tied separately with ropes of length 7 m each to graze in the field . Find the area of the field which cannot be grazed by three animals.

The given figure shows a trapezium in which AB || DC and diagonal AC and BD intersect at point P. If AP : CP = 3:5 and area of △APB is 27 m2, then the area of △CPD is ___.

Solve each of the following quadratic equations:37x+15x-3-45x-37x+1=11, x≠35, -17 [CBSE 2014]

The value of ∣∣∣24−12∣∣∣ is

Question 3 (vi)Form the pair of linear equations for the following problems and find their solution by substitution method:Five years hence, the age of Jacob will be three times that of his son. Five years ago, Jacob's age was seven times that of his son. What are their present ages?

Solve the following quadratic equation: 4x−3=52x+3,x≠0,−32

If the zeroes of polynomial are, find a and b.

Solve each of the following systems of eqautions by the method of cross-multiplication: x+2y+1=0 2x−3y−12=0

If the plane xa+yb+zc=3 meets the coordinates axes at A, B and C, then the coordinates of the centroid of ∆ABC are ______________.

if f(x) is a polynomial such that f(a) f(b)

On a horizontal plane there is a vertical tower with a flag pole on the top of the tower. At a point 9 metres away from the foot of the tower the angle of elevation of the top and bottom of the flag pole are 60∘ and 30∘ respectively. Find the height of the tower and the flag pole mounted on it.

25. A man standing on the deck of a ship ,which is 10m above the water level,observes the angle of elevation of the top of a hill as 60^° and angle of depression of the base of the hill as 30^° .find the distance between ship and hill and height of the hill.

12 spheres of the same size are made from melting a solid cylinder of 16 cm diameter and 2 cm height. The diameter of each sphere is(a) 3 cm(b) 2 cm(c) 3 cm(d) 4 cm

Write the zeros of the quadratic polynomial f(x)=4√3x2+5x−2√3.

The are of minor sector ofcircle (0,5) is 150 . The length of the corresponding arc is

There are 50 numbers. Each number is subtracted from 53 and the mean of the numbers so obtained is found to be (-3.5). Find the mean of the given number

For what n , are the nth terms of two APs: 63,65,67,.. and 3,10,17,.. equal?

The angle of elevation of the top of a tower standing on a horizontal plane from a point A is α. After walking a distance d towards the foot of the tower the angle of elevation is found to be β. The height of the tower is(a) dcot α+cot β(b) dcot α-cot β(c) dtan β-tan α (d) dtan β+tan α

If an equilateral triangle ABC is drawn as shown below with A(0,0) and a side of 8 units then find the other two vertices of the triangle.

If the sum of zeros of the polynomial p(x) = kx3−5x2−11x−3 is 2, then k is equal to:

Question 4Any solution of the linear equation 2x+0y+9=0 in two variables is of the form:A) (−92,m)B) (n,−92)C) (0,−92)D) (−9,0)