32581 + Interview Questions in Mathematics Page 129 InterviewSolution

6401.	Observe the following figure. The polynomial drawn in above graph has how many zeros?
Answer» Observe the following figure. The polynomial drawn in above graph has how many zeros?

6401.

Observe the following figure. The polynomial drawn in above graph has how many zeros?

Answer»

Observe the following figure.

The polynomial drawn in above graph has how many zeros?

6402.	A man invests ₹ 8000 in buying shares of a company of face value of rupees hundred each at a premium of 10%. If he earns ₹ 1200 at the end of the year as dividend, then find thei) number of shares he has in company andii) dividend percent per share
Answer» A man invests ₹ 8000 in buying shares of a company of face value of rupees hundred each at a premium of 10%. If he earns ₹ 1200 at the end of the year as dividend, then find the i) number of shares he has in company and ii) dividend percent per share

Discussion

6403.	consider an ellipse whose centre is at the origin and its major axis is along xaxis.If the ecentricity is 3/5 and distance b/w its foci is 6 then area of the quadrilateral inscribed in the ellipse with vertices as the vertices of the ellipse is:
Answer» consider an ellipse whose centre is at the origin and its major axis is along xaxis.If the ecentricity is 3/5 and distance b/w its foci is 6 then area of the quadrilateral inscribed in the ellipse with vertices as the vertices of the ellipse is:

Discussion

6404.	Harpreet tosses two different coins simultaneously (say, one is of Re 1 and other of Rs 2). What is the probability that he gets at least one head?
Answer» Harpreet tosses two different coins simultaneously (say, one is of Re 1 and other of Rs 2). What is the probability that he gets at least one head?

Discussion

6405.	A fraction becomes 1/3 if 1 is subtracted from both its numerator and denominator. It 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. It 1 is added to both the numerator and denominator, it becomes 1/2. Find the fraction.

Discussion

6406.	Construct a regular hexagon of side 4 cm. Also, construct a circle circumscribing the hexagon and measure its circumradius.
Answer» Construct a regular hexagon of side 4 cm. Also, construct a circle circumscribing the hexagon and measure its circumradius.

Discussion

6407.	(cosec θ − sin θ) (sec θ − cos θ) (tan θ + cot θ) is equal to(a) 0(b) 1(c) −1(d) None of these
Answer» (cosec θ − sin θ) (sec θ − cos θ) (tan θ + cot θ) is equal to (a) 0 (b) 1 (c) −1 (d) None of these

Discussion

6408.	If A is 3 × 4 matrix and B is a matrix such that ATB and BAT are both defined. Then the order of B is __________.
Answer» If A is 3 × 4 matrix and B is a matrix such that A^TB and BA^T are both defined. Then the order of B is __________.

Discussion

6409.	One card is randomly drawn from a deck of 52 playing cards. Find the probability that (i) the drawn card is red. (ii) the drawn card is an ace. (iii) the drawn card is red and a king. (iv) the drawn card is red or a king. [4 MARKS]
Answer» One card is randomly drawn from a deck of 52 playing cards. Find the probability that (i) the drawn card is red. (ii) the drawn card is an ace. (iii) the drawn card is red and a king. (iv) the drawn card is red or a king. [4 MARKS]

Discussion

6410.	Question 1A solid metallic hemisphere of radius 8 cm is melted and recasted into a right circular cone of base radius 6 cm. Determine the height of the cone.
Answer» Question 1 A solid metallic hemisphere of radius 8 cm is melted and recasted into a right circular cone of base radius 6 cm. Determine the height of the cone.

Discussion

6411.	The angle of the elevation of the top Q of vertical tower PQ from a point X on the ground is 60°. At a point Y , 40 m vertically above X, the angle of elevation is 45° . Find the height of the tower PQ and the distance XQ.
Answer» The angle of the elevation of the top Q of vertical tower PQ from a point X on the ground is 60°. At a point Y , 40 m vertically above X, the angle of elevation is 45° . Find the height of the tower PQ and the distance XQ.

Discussion

6412.	Given that P(x) and Q(x) are polynomials of degree 3 with real coefficients, which one of the following is not true? (i)deg[P(x)×Q(x)]=6(ii)deg[P(x)+Q(x)]=3(iii)deg[P(x)-Q(x)]≤3(iv)deg[[P(x)]square [Q(x)] square]=15
Answer» Given that P(x) and Q(x) are polynomials of degree 3 with real coefficients, which one of the following is not true? (i)deg[P(x)×Q(x)]=6 (ii)deg[P(x)+Q(x)]=3 (iii)deg[P(x)-Q(x)]≤3 (iv)deg[[P(x)]square [Q(x)] square]=15

Discussion

6413.	The midpoint P of the line segment joining the points A(−10, 4) and B(−2, 0) lies on the line segment joining the points C(−9, −4) and D(−4, y). Find the ratio in which P divides CD. Also find the value of y.
Answer» The midpoint P of the line segment joining the points A(−10, 4) and B(−2, 0) lies on the line segment joining the points C(−9, −4) and D(−4, y). Find the ratio in which P divides CD. Also find the value of y.

Discussion

6414.	11. Find the equation of the circle passing through the points (1,1), (0,-1) and (-2,0)
Answer» 11. Find the equation of the circle passing through the points (1,1), (0,-1) and (-2,0)

Discussion

6415.	In ∆ABC and ∆DEF, it is being given that: AB = 5 cm, BC = 4 cm and CA = 4.2 cm; DE = 10 cm, EF = 8 cm and FD = 8.4 cm. If AL ⊥ BC and DM ⊥ EF, find AL : DM.
Answer» In ∆ABC and ∆DEF, it is being given that: AB = 5 cm, BC = 4 cm and CA = 4.2 cm; DE = 10 cm, EF = 8 cm and FD = 8.4 cm. If AL ⊥ BC and DM ⊥ EF, find AL : DM.

Discussion

6416.	A ladder is resting on a wall of height 10√7m such that the foot of the ladder when placed 10√7m away from the wall, half of the ladder is extending above the wall. When the tip of the ladder is placed on the tip of the wall, how far is the foot of the ladder from the wall?
Answer» A ladder is resting on a wall of height 10 $\sqrt{7}$ m such that the foot of the ladder when placed 10 $\sqrt{7}$ m away from the wall, half of the ladder is extending above the wall. When the tip of the ladder is placed on the tip of the wall, how far is the foot of the ladder from the wall?

Discussion

6417.	Find the area of the shaded region in the following figure, if AC = 24 cm, BC = 10 cm and O is the centre of the circle. (Use π = 3.14)
Answer» Find the area of the shaded region in the following figure, if AC = 24 cm, BC = 10 cm and O is the centre of the circle. (Use π = 3.14)

Discussion

6418.	Check whether 7+3x is a factor of 3x3+7x. [2 MARKS]
Answer» Check whether $7 + 3 x$ is a factor of $3 x^{3} + 7 x$ . [2 MARKS]

Discussion

6419.	How many irrational numbers exist between two rational numbers?
Answer» How many irrational numbers exist between two rational numbers?

Discussion

6420.	Find the value of k for which the following system of equations has a unique solution: (5-8) 8x + 5y =9 kx + 10y = 18
Answer» Find the value of k for which the following system of equations has a unique solution: (5-8) 8x + 5y =9 kx + 10y = 18

6420.

Find the value of k for which the following system of equations has a unique solution: (5-8) 8x + 5y =9 kx + 10y = 18

Answer»

Find the value of k for which the following system of equations has a unique solution: (5-8)

8x + 5y =9

kx + 10y = 18

Discussion

6421.	A ball starts to move along straight line at a speed of 40 metres/second and the speed decreases at the rate of 4 metres/second every second. Then the algebra for the distance from the starting point to the ball after 't' seconds is
Answer» A ball starts to move along straight line at a speed of 40 metres/second and the speed decreases at the rate of 4 metres/second every second. Then the algebra for the distance from the starting point to the ball after 't' seconds is

Discussion

6422.	The probability of getting a value which is a not a factor of either 5 or 6, in a throw of a die is?
Answer» The probability of getting a value which is a not a factor of either 5 or 6, in a throw of a die is?

Discussion

6423.	The pair of tangents AP and AQ drawn from an external point to a circle with centre O are perpendicular to each other and length of each tangent is 5 cm. The radius of the circle is (a) 10 cm (b) 7.5 cm (c) 5cm (d) 2.5 cm
Answer» The pair of tangents AP and AQ drawn from an external point to a circle with centre O are perpendicular to each other and length of each tangent is 5 cm. The radius of the circle is (a) 10 cm (b) 7.5 cm (c) 5cm (d) 2.5 cm

Discussion

6424.	Calculate the Mean of the distribution given using Assumed mean Method.MarksNo. of Students10−20220−30630−401040−501250−60960−70870−80480−903
Answer» Calculate the Mean of the distribution given using Assumed mean Method. $\begin{matrix} Marks & No. of Students 10 - 20 & 2 20 - 30 & 6 30 - 40 & 10 40 - 50 & 12 50 - 60 & 9 60 - 70 & 8 70 - 80 & 4 80 - 90 & 3 \end{matrix}$

6424.

Calculate the Mean of the distribution given using Assumed mean Method.MarksNo. of Students10−20220−30630−401040−501250−60960−70870−80480−903

Answer»

Calculate the Mean of the distribution given using Assumed mean Method.

$\begin{matrix} Marks & No. of Students 10 - 20 & 2 20 - 30 & 6 30 - 40 & 10 40 - 50 & 12 50 - 60 & 9 60 - 70 & 8 70 - 80 & 4 80 - 90 & 3 \end{matrix}$

Discussion

6425.	Prove that tan10 tan15 tan75 tan80=1
Answer» Prove that tan10 tan15 tan75 tan80=1

Discussion

6426.	Question 6How many silver coins, 1.75 cm in diameter and of thickness 2 mm, must be melted to form a cuboid of dimensions 5.5cm×10cm×3.5cm?
Answer» Question 6 How many silver coins, 1.75 cm in diameter and of thickness 2 mm, must be melted to form a cuboid of dimensions $5.5 c m \times 10 c m \times 3.5 c m ?$

Discussion

6427.	For what values of p are the roots of the equation 4x2+px+3=0 real and equal? [CBSE 2014]
Answer» For what values of p are the roots of the equation $4 x^{2} + p x + 3 = 0$ real and equal? [CBSE 2014]

Discussion

6428.	A solid piece of iron in the form of a cuboid of dimensions (49 cm×33 cm×24 cm) is moulded to form a solid sphere. The radius of the sphere is (a) 19 cm (b) 21 cm (c) 23 cm (d) 25 cm
Answer» A solid piece of iron in the form of a cuboid of dimensions $(49 c m \times 33 c m \times 24 c m)$ is moulded to form a solid sphere. The radius of the sphere is (a) 19 cm (b) 21 cm (c) 23 cm (d) 25 cm

6428.

A solid piece of iron in the form of a cuboid of dimensions (49 cm×33 cm×24 cm) is moulded to form a solid sphere. The radius of the sphere is (a) 19 cm (b) 21 cm (c) 23 cm (d) 25 cm

Answer»

A solid piece of iron in the form of a cuboid of dimensions $(49 c m \times 33 c m \times 24 c m)$ is moulded to form a solid sphere. The radius of the sphere is

(a) 19 cm (b) 21 cm (c) 23 cm (d) 25 cm

Discussion

6429.	Show that the following sets of points are collinear.(a) (2, 5), (4, 6) and (8, 8)(b) (1, −1), (2, 1) and (4, 5)
Answer» Show that the following sets of points are collinear. (a) (2, 5), (4, 6) and (8, 8) (b) (1, −1), (2, 1) and (4, 5)

Discussion

6430.	If sin 3 θ = cos (θ − 6°), where 3 θ and θ − 6° are acute angles, find the value of θ.
Answer» If sin 3 θ = cos (θ − 6°), where 3 θ and θ − 6° are acute angles, find the value of θ.

Discussion

6431.	The sum of two positive numbers x and y (x> y) is 50 and the difference of their squares is 720. Find the numbers.
Answer» The sum of two positive numbers x and y (x> y) is 50 and the difference of their squares is 720. Find the numbers.

Discussion

6432.	Two isosceles triangles have equal angles and their areas are in the ratio 16 : 25. The ratio of their corresponding heights is(a) 4 : 5(b) 5 : 4(c) 3 : 2(d) 5 : 7
Answer» Two isosceles triangles have equal angles and their areas are in the ratio 16 : 25. The ratio of their corresponding heights is (a) 4 : 5 (b) 5 : 4 (c) 3 : 2 (d) 5 : 7

Discussion

6433.	For which of the following inputs, output Y is high (1)?
Answer» For which of the following inputs, output $Y$ is high $(1) ?$

Discussion

6434.

Median of the following data set is 10 12 6 5 2 13

Answer» Median of the following data set is

10

12

6

5

2

13

Discussion

6435.	Evaluate the following limits:limx→1x7-2x5+1x3-3x2+2
Answer» Evaluate the following limits: $\lim_{x \to 1} \frac{x^{7} - 2 x^{5} + 1}{x^{3} - 3 x^{2} + 2}$

Discussion

6436.	The sums of first n terms of three A.P. are S1,S2 and S3. The first term of each is 5 and their common differences are 2, 4 and 6 respectively. Prove that S1 + S3 = 2S2
Answer» The sums of first n terms of three A.P. are S₁,S₂and S₃. The first term of each is 5 and their common differences are 2, 4 and 6 respectively. Prove that S₁+ S₃= 2S₂

Discussion

6437.	A man saved ₹33000 in 10 months. In each month after the first, he saved ₹100 more than he did in the preceding month. How much did he save in the first month?
Answer» A man saved ₹33000 in 10 months. In each month after the first, he saved ₹100 more than he did in the preceding month. How much did he save in the first month?

Discussion

6438.	A fraction becomes 911 if 2 is added to both the numerator and the denominator. If 3 is added to both the numerator and the denominator, it becomes 56. Find the fraction.
Answer» A fraction becomes $\frac{9}{11}$ if $2$ is added to both the numerator and the denominator. If $3$ is added to both the numerator and the denominator, it becomes $\frac{5}{6}$ . Find the fraction.

Discussion

6439.	Giving reason comment on the shape of production possibilities curve based on the following schedule: Goods-X01234UnitsGoods-Y86420Units
Answer» Giving reason comment on the shape of production possibilities curve based on the following schedule: $\begin{matrix} Goods-X & 0 & 1 & 2 & 3 & 4 Units Goods-Y & 8 & 6 & 4 & 2 & 0 Units \end{matrix}$

6439.

Giving reason comment on the shape of production possibilities curve based on the following schedule: Goods-X01234UnitsGoods-Y86420Units

Answer»

Giving reason comment on the shape of production possibilities curve based on the following schedule:

$\begin{matrix} Goods-X & 0 & 1 & 2 & 3 & 4 Units Goods-Y & 8 & 6 & 4 & 2 & 0 Units \end{matrix}$

Discussion

6440.	Tell whether the statement is true or false :The data 6, 4, 3, 8, 9, 12, 13, 9 has mean 9.
Answer» Tell whether the statement is true or false : The data 6, 4, 3, 8, 9, 12, 13, 9 has mean 9.

Discussion

6441.	ddx1log10x=______________.
Answer» $\frac{d}{d x} (\frac{1}{\log_{10} x}) =______________.$

Discussion

6442.	State the type of the conditional clause in the sentence. If Mike had signed up for the competition he would have won it easily.
Answer» State the type of the conditional clause in the sentence. If Mike had signed up for the competition he would have won it easily.

6442.

State the type of the conditional clause in the sentence. If Mike had signed up for the competition he would have won it easily.

Answer»

State the type of the conditional clause in the sentence.

If Mike had signed up for the competition he would have won it easily.

Discussion

6443.	A tangent drawn at a point M on the circle is perpendicular to the
Answer» A tangent drawn at a point M on the circle is perpendicular to the

Discussion

6444.	In triangle ABC, AB=AC and AD is the median on BC which meets BC at D. If a circle with diameter AD is drawn then prove that BD is tangent of the circle.
Answer» In triangle ABC, AB=AC and AD is the median on BC which meets BC at D. If a circle with diameter AD is drawn then prove that BD is tangent of the circle.

Discussion

6445.	Metallic spheres of radii 6 cm, 8 cm and 10 cm, respectively are melted to form a single solid sphere. Find the radius of the resulting sphere. [CBSE 2012]
Answer» Metallic spheres of radii 6 cm, 8 cm and 10 cm, respectively are melted to form a single solid sphere. Find the radius of the resulting sphere. [CBSE 2012]

Discussion

6446.	What is the largest number that divides 245 and 1029, leaving remainder 5 in each case ?16
Answer» What is the largest number that divides 245 and 1029, leaving remainder 5 in each case ? 16

Discussion

6447.	Prove the following trignometric identities: (1−cos2 A) cosec2 A=1
Answer» Prove the following trignometric identities: $(1 - c o s^{2} A) c o s e c^{2} A = 1$

6447.

Prove the following trignometric identities: (1−cos2 A) cosec2 A=1

Answer»

Prove the following trignometric identities:

$(1 - c o s^{2} A) c o s e c^{2} A = 1$

Discussion

6448.	If the equation 1+m2x2+2 mcx+c2-a2=0 has equal roots, prove that c2 = a2(1 + m2).
Answer» If the equation $(1 + m^{2}) x^{2} + 2 m c x + (c^{2} - a^{2}) = 0$ has equal roots, prove that c² = a²(1 + m²).

Discussion

6449.	In Fig. 4, OABC is a square inscribed in a quadrant OPBQ. If OA = 20 cm, find the area of shaded region [Use π = 3.14]
Answer» In Fig. 4, OABC is a square inscribed in a quadrant OPBQ. If OA = 20 cm, find the area of shaded region [Use π = 3.14]

Discussion

6450.	A solid is in the form of a right circular cylinder with a hemisphere at one end and a cone at the other end. The radius of common base is 3.5cm and heights of the cylindrical and conical portions are 10cm and 6cm respectively. The total surface area of the solid is
Answer» A solid is in the form of a right circular cylinder with a hemisphere at one end and a cone at the other end. The radius of common base is 3.5cm and heights of the cylindrical and conical portions are 10cm and 6cm respectively. The total surface area of the solid is

Discussion

Explore topic-wise InterviewSolutions in .

Observe the following figure. The polynomial drawn in above graph has how many zeros?

A man invests ₹ 8000 in buying shares of a company of face value of rupees hundred each at a premium of 10%. If he earns ₹ 1200 at the end of the year as dividend, then find thei) number of shares he has in company andii) dividend percent per share

consider an ellipse whose centre is at the origin and its major axis is along xaxis.If the ecentricity is 3/5 and distance b/w its foci is 6 then area of the quadrilateral inscribed in the ellipse with vertices as the vertices of the ellipse is:

Harpreet tosses two different coins simultaneously (say, one is of Re 1 and other of Rs 2). What is the probability that he gets at least one head?

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

Construct a regular hexagon of side 4 cm. Also, construct a circle circumscribing the hexagon and measure its circumradius.

(cosec θ − sin θ) (sec θ − cos θ) (tan θ + cot θ) is equal to(a) 0(b) 1(c) −1(d) None of these

If A is 3 × 4 matrix and B is a matrix such that ATB and BAT are both defined. Then the order of B is __________.

One card is randomly drawn from a deck of 52 playing cards. Find the probability that (i) the drawn card is red. (ii) the drawn card is an ace. (iii) the drawn card is red and a king. (iv) the drawn card is red or a king. [4 MARKS]

Question 1A solid metallic hemisphere of radius 8 cm is melted and recasted into a right circular cone of base radius 6 cm. Determine the height of the cone.

The angle of the elevation of the top Q of vertical tower PQ from a point X on the ground is 60°. At a point Y , 40 m vertically above X, the angle of elevation is 45° . Find the height of the tower PQ and the distance XQ.

Given that P(x) and Q(x) are polynomials of degree 3 with real coefficients, which one of the following is not true? (i)deg[P(x)×Q(x)]=6(ii)deg[P(x)+Q(x)]=3(iii)deg[P(x)-Q(x)]≤3(iv)deg[[P(x)]square [Q(x)] square]=15

The midpoint P of the line segment joining the points A(−10, 4) and B(−2, 0) lies on the line segment joining the points C(−9, −4) and D(−4, y). Find the ratio in which P divides CD. Also find the value of y.

11. Find the equation of the circle passing through the points (1,1), (0,-1) and (-2,0)

In ∆ABC and ∆DEF, it is being given that: AB = 5 cm, BC = 4 cm and CA = 4.2 cm; DE = 10 cm, EF = 8 cm and FD = 8.4 cm. If AL ⊥ BC and DM ⊥ EF, find AL : DM.

A ladder is resting on a wall of height 10√7m such that the foot of the ladder when placed 10√7m away from the wall, half of the ladder is extending above the wall. When the tip of the ladder is placed on the tip of the wall, how far is the foot of the ladder from the wall?

Find the area of the shaded region in the following figure, if AC = 24 cm, BC = 10 cm and O is the centre of the circle. (Use π = 3.14)

Check whether 7+3x is a factor of 3x3+7x. [2 MARKS]

How many irrational numbers exist between two rational numbers?

Find the value of k for which the following system of equations has a unique solution: (5-8) 8x + 5y =9 kx + 10y = 18

A ball starts to move along straight line at a speed of 40 metres/second and the speed decreases at the rate of 4 metres/second every second. Then the algebra for the distance from the starting point to the ball after 't' seconds is

The probability of getting a value which is a not a factor of either 5 or 6, in a throw of a die is?

The pair of tangents AP and AQ drawn from an external point to a circle with centre O are perpendicular to each other and length of each tangent is 5 cm. The radius of the circle is (a) 10 cm (b) 7.5 cm (c) 5cm (d) 2.5 cm

Calculate the Mean of the distribution given using Assumed mean Method.MarksNo. of Students10−20220−30630−401040−501250−60960−70870−80480−903

Prove that tan10 tan15 tan75 tan80=1

Question 6How many silver coins, 1.75 cm in diameter and of thickness 2 mm, must be melted to form a cuboid of dimensions 5.5cm×10cm×3.5cm?

For what values of p are the roots of the equation 4x2+px+3=0 real and equal? [CBSE 2014]

A solid piece of iron in the form of a cuboid of dimensions (49 cm×33 cm×24 cm) is moulded to form a solid sphere. The radius of the sphere is (a) 19 cm (b) 21 cm (c) 23 cm (d) 25 cm

Show that the following sets of points are collinear.(a) (2, 5), (4, 6) and (8, 8)(b) (1, −1), (2, 1) and (4, 5)

If sin 3 θ = cos (θ − 6°), where 3 θ and θ − 6° are acute angles, find the value of θ.

The sum of two positive numbers x and y (x&gt; y) is 50 and the difference of their squares is 720. Find the numbers.

Two isosceles triangles have equal angles and their areas are in the ratio 16 : 25. The ratio of their corresponding heights is(a) 4 : 5(b) 5 : 4(c) 3 : 2(d) 5 : 7

For which of the following inputs, output Y is high (1)?

Median of the following data set is 10 12 6 5 2 13

Evaluate the following limits:limx→1x7-2x5+1x3-3x2+2

The sums of first n terms of three A.P. are S1,S2 and S3. The first term of each is 5 and their common differences are 2, 4 and 6 respectively. Prove that S1 + S3 = 2S2

A man saved ₹33000 in 10 months. In each month after the first, he saved ₹100 more than he did in the preceding month. How much did he save in the first month?

A fraction becomes 911 if 2 is added to both the numerator and the denominator. If 3 is added to both the numerator and the denominator, it becomes 56. Find the fraction.

Giving reason comment on the shape of production possibilities curve based on the following schedule: Goods-X01234UnitsGoods-Y86420Units

Tell whether the statement is true or false :The data 6, 4, 3, 8, 9, 12, 13, 9 has mean 9.

ddx1log10x=______________.

State the type of the conditional clause in the sentence. If Mike had signed up for the competition he would have won it easily.

A tangent drawn at a point M on the circle is perpendicular to the

In triangle ABC, AB=AC and AD is the median on BC which meets BC at D. If a circle with diameter AD is drawn then prove that BD is tangent of the circle.

Metallic spheres of radii 6 cm, 8 cm and 10 cm, respectively are melted to form a single solid sphere. Find the radius of the resulting sphere. [CBSE 2012]

What is the largest number that divides 245 and 1029, leaving remainder 5 in each case ?16

Prove the following trignometric identities: (1−cos2 A) cosec2 A=1

If the equation 1+m2x2+2 mcx+c2-a2=0 has equal roots, prove that c2 = a2(1 + m2).

In Fig. 4, OABC is a square inscribed in a quadrant OPBQ. If OA = 20 cm, find the area of shaded region [Use π = 3.14]

A solid is in the form of a right circular cylinder with a hemisphere at one end and a cone at the other end. The radius of common base is 3.5cm and heights of the cylindrical and conical portions are 10cm and 6cm respectively. The total surface area of the solid is

The sum of two positive numbers x and y (x> y) is 50 and the difference of their squares is 720. Find the numbers.