32581 + Interview Questions in Mathematics Page 109 InterviewSolution

5401.	A cone of height 12 cm and radius of base 10cm is divided by a plane parallel to the base into a cone and a frustum of equal volume. Find the ratio of height of the new cone and frustum formed
Answer» A cone of height 12 cm and radius of base 10cm is divided by a plane parallel to the base into a cone and a frustum of equal volume. Find the ratio of height of the new cone and frustum formed

Discussion

5402.	A man invested Rs 45,000 in 45% Rs 100 shares quoted at Rs 125. When the market value of these shares rose to Rs 140, he sold some shares, just enough to raise Rs 8,400. Calculate: (i) the number of shares he still holds. (ii) the dividend due to him on these remaining shares. [4 MARKS]
Answer» A man invested Rs 45,000 in $45 %$ Rs 100 shares quoted at Rs 125. When the market value of these shares rose to Rs 140, he sold some shares, just enough to raise Rs 8,400. Calculate: (i) the number of shares he still holds. (ii) the dividend due to him on these remaining shares. [4 MARKS]

Discussion

5403.	The value of expression mx-ny is 3 when x = 5 and y=6. And its value is 8 when x=6 and y=5. Find the value of m and n.
Answer» The value of expression mx-ny is 3 when x = 5 and y=6. And its value is 8 when x=6 and y=5. Find the value of m and n.

Discussion

5404.	A player who was playing video game was given 20 coins to begin with the game. To go to the next level, he needs to spend 4 coins and if he succeeds the particular level, he earns 6 coins. Find the number of coins he collects after clearing each level (assuming he clears every level).
Answer» A player who was playing video game was given 20 coins to begin with the game. To go to the next level, he needs to spend 4 coins and if he succeeds the particular level, he earns 6 coins. Find the number of coins he collects after clearing each level (assuming he clears every level).

Discussion

5405.	Let a,b,c and d be non-zero numbers such that x=c and x=d are the roots of the equation x2+ax+b=0 and x=a and x=b are the roots of the equation x2+cx+d=0. Then
Answer» Let $a, b, c$ and $d$ be non-zero numbers such that $x = c$ and $x = d$ are the roots of the equation $x^{2} + a x + b = 0$ and $x = a$ and $x = b$ are the roots of the equation $x^{2} + c x + d = 0.$ Then

Discussion

5406.	Prove that 1secA+tanA=secA−tanA
Answer» Prove that $\frac{1}{s e c A + t a n A} = s e c A - t a n A$

Discussion

5407.	During first half distance of journey the average speed is 40 km per hour and during remaining distance of journey average speed is 70 km per hour find average speed for the entire journey?
Answer» During first half distance of journey the average speed is 40 km per hour and during remaining distance of journey average speed is 70 km per hour find average speed for the entire journey?

Discussion

5408.	A Person Standing on a boat at point A sees a submarine at point B, making an angle of depression of 60∘. After sometime, the submarine travels 100 m and moves to point C. Now, the angle of depression becomes 30∘. Find the distance the boat has to travel to reach a point that is exactly above the submarine. [Tan 30∘=0.57, tan 60∘=1.73]
Answer» A Person Standing on a boat at point A sees a submarine at point B, making an angle of depression of $60^{\circ}$ . After sometime, the submarine travels 100 m and moves to point C. Now, the angle of depression becomes 30 $^{\circ}$ . Find the distance the boat has to travel to reach a point that is exactly above the submarine. $[T a n 30^{\circ} = 0.57, t a n 60^{\circ} = 1.73]$

5408.

A Person Standing on a boat at point A sees a submarine at point B, making an angle of depression of 60∘. After sometime, the submarine travels 100 m and moves to point C. Now, the angle of depression becomes 30∘. Find the distance the boat has to travel to reach a point that is exactly above the submarine. [Tan 30∘=0.57, tan 60∘=1.73]

Answer»

A Person Standing on a boat at point A sees a submarine at point B, making an angle of depression of $60^{\circ}$ . After sometime, the submarine travels 100 m and moves to point C. Now, the angle of depression becomes 30 $^{\circ}$ . Find the distance the boat has to travel to reach a point that is exactly above the submarine. $[T a n 30^{\circ} = 0.57, t a n 60^{\circ} = 1.73]$

Discussion

5409.	The quadratic equation which has D = 0 and a root as 110 is
Answer» The quadratic equation which has D = 0 and a root as $\frac{1}{10}$ is

Discussion

5410.	Nick tosses three coins simultaneously. What is the probability of getting at least two heads?
Answer» Nick tosses three coins simultaneously. What is the probability of getting at least two heads?

Discussion

5411.	If ∆ABC ∼ ∆DEF such that AB = 9.1 cm and DE = 6.5 cm. If the perimeter of ∆DEF is 25 cm, then the perimeter of ∆ABC is(a) 36 cm(b) 30 cm(c) 34 cm(d) 35 cm
Answer» If ∆ABC ∼ ∆DEF such that AB = 9.1 cm and DE = 6.5 cm. If the perimeter of ∆DEF is 25 cm, then the perimeter of ∆ABC is (a) 36 cm (b) 30 cm (c) 34 cm (d) 35 cm

Discussion

5412.	There is a coin. Ram attaches a conical attachment to one flat end of coin. The conical attachment has same radius as coin. What is the surface area of the combined solid?
Answer» There is a coin. Ram attaches a conical attachment to one flat end of coin. The conical attachment has same radius as coin. What is the surface area of the combined solid?

Discussion

5413.	What is a sector of a circle with a central angle greater than 180 degree called?
Answer» What is a sector of a circle with a central angle greater than $180$ degree called?

Discussion

5414.	Draw a circle of radius 2 cm with centre O and take a point P outside the circle such that OP = 6.5 cm. From P, draw two tangents to the circle. [3 MARKS]
Answer» Draw a circle of radius 2 cm with centre O and take a point P outside the circle such that OP = 6.5 cm. From P, draw two tangents to the circle. [3 MARKS]

Discussion

5415.	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° 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.

Discussion

5416.	In Figure, P is a point in the interior of a parallelogram ABCD. Show that(i) ar(APB)+ar(PCD)=12ar(ABCD) (ii) ar(APD)+ar(PBC)=ar(APB)+ar(PCD) [Hint : Through P, draw a line parallel to AB.]
Answer» In Figure, P is a point in the interior of a parallelogram ABCD. Show that $(i) a r (A P B) + a r (P C D) = \frac{1}{2} a r (A B C D)$ $(ii) a r (A P D) + a r (P B C) = a r (A P B) + a r (P C D)$ [Hint : Through P, draw a line parallel to AB.]

Discussion

5417.	If sec(4A) = cosec(A−20∘), where 4A is an acute angle, then what is the value of A?
Answer» If sec(4A) = cosec $(A - 20^{\circ})$ , where 4A is an acute angle, then what is the value of A?

Discussion

5418.	proof that the external bisectors of any two angles of a triangle are concurrent with the internal bisector of the third angle
Answer» proof that the external bisectors of any two angles of a triangle are concurrent with the internal bisector of the third angle

Discussion

5419.	In a triangle ABC right angled at B, ∠ACB=θ. If tanθ=512, then find the value of (1+cos θ)×(1−sinθ)(1+sinθ)×(1−cosθ).
Answer» In a triangle ABC right angled at B, $∠ A C B = θ .$ $If t a n θ = \frac{5}{12}$ , $then find the value of \frac{(1 + c o s θ) \times (1 - s i n θ)}{(1 + s i n θ) \times (1 - c o s θ)} .$

Discussion

5420.	In a medical examination of students of a class, the following blood groups are recorded.Blood groupA+AB−B−O+Number of1013125studentsA student is selected at random from the class. The probability that he/she has blood group B− is:
Answer» In a medical examination of students of a class, the following blood groups are recorded. $\begin{matrix} Blood group & A + & A B - & B - & O + Number of & 10 & 13 & 12 & 5 students \end{matrix}$ A student is selected at random from the class. The probability that he/she has blood group $B -$ is:

Discussion

5421.	When x4+x3−2x2+x+1 is divided by x-1, the remainder is 2 and the quotient is q(x). Find q(x).
Answer» $When x^{4} + x^{3} - 2 x^{2} + x + 1 is divided by x-1, the remainder is 2 and the quotient is q(x). Find q(x).$

Discussion

5422.	A 1.2m tall girl spots a balloon moving with the wind in a horizontal line at a height of 88.2m from the ground. The angle of elevation of the balloon from the eyes of the girl at any instant is 60∘. After sometime, the angle of elevation reduces to 30∘. Find the distance travelled by the balloon during the interval?
Answer» A 1.2m tall girl spots a balloon moving with the wind in a horizontal line at a height of 88.2m from the ground. The angle of elevation of the balloon from the eyes of the girl at any instant is $60^{\circ}$ . After sometime, the angle of elevation reduces to $30^{\circ}$ . Find the distance travelled by the balloon during the interval?

5422.

A 1.2m tall girl spots a balloon moving with the wind in a horizontal line at a height of 88.2m from the ground. The angle of elevation of the balloon from the eyes of the girl at any instant is 60∘. After sometime, the angle of elevation reduces to 30∘. Find the distance travelled by the balloon during the interval?

Answer»

A 1.2m tall girl spots a balloon moving with the wind in a horizontal line at a height of 88.2m from the ground. The angle of elevation of the balloon from the eyes of the girl at any instant is $60^{\circ}$ . After sometime, the angle of elevation reduces to $30^{\circ}$ . Find the distance travelled by the balloon during the interval?

Discussion

5423.	The outer and inner diameter of a circular path are 728 m and 700 m respectively. Find the width and the area of the circular path.
Answer» The outer and inner diameter of a circular path are 728 m and 700 m respectively. Find the width and the area of the circular path.

Discussion

5424.	The polynomial ax3 + 41x2 + x – 2 when divided by (4x – 1) leaves remainder Then, the value of a and the remainder when the given polynomial is divided by x + 2 are respectively
Answer» The polynomial ax3 + 41x2 + x – 2 when divided by (4x – 1) leaves remainder Then, the value of a and the remainder when the given polynomial is divided by x + 2 are respectively

Discussion

5425.	Coins of diameter 10cm are arranged in hexagonal close packing inside a square with side of 40 cm . Find the maximum number of coins that can be placed whose Centre lies on or inside the square.
Answer» Coins of diameter 10cm are arranged in hexagonal close packing inside a square with side of 40 cm . Find the maximum number of coins that can be placed whose Centre lies on or inside the square.

Discussion

5426.	If sinA = 1/2 , verify that 2 sinA cosA = 2tanA/(1+ tan2A)
Answer» If sinA = 1/2 , verify that 2 sinA cosA = 2tanA/(1+ tan2A)

Discussion

5427.	Find the value of p for which the numbers 2p-1, 3p+1,11 are in AP. Hence, find the numbers.
Answer» Find the value of p for which the numbers 2p-1, 3p+1,11 are in AP. Hence, find the numbers.

Discussion

5428.	The larger of two supplementary angles exceeds the smaller by 18 degrees. Find the angles. [3 MARKS]
Answer» The larger of two supplementary angles exceeds the smaller by 18 degrees. Find the angles. [3 MARKS]

Discussion

5429.	Draw a triangle ABC in which AB = 6 cm, BC= 4.5 cm and AC= 5 cm. Draw and label: (i) the locus of the centres of all circles which touch AB and AC, (ii) the locus of the centres of all circles of radius 2 cm which touch AB. Hence, construct the circle of radius 2 cm which touches AB and AC.
Answer» Draw a triangle ABC in which AB = 6 cm, BC= 4.5 cm and AC= 5 cm. Draw and label: (i) the locus of the centres of all circles which touch AB and AC, (ii) the locus of the centres of all circles of radius 2 cm which touch AB. Hence, construct the circle of radius 2 cm which touches AB and AC.

5429.

Draw a triangle ABC in which AB = 6 cm, BC= 4.5 cm and AC= 5 cm. Draw and label: (i) the locus of the centres of all circles which touch AB and AC, (ii) the locus of the centres of all circles of radius 2 cm which touch AB. Hence, construct the circle of radius 2 cm which touches AB and AC.

Answer»

Draw a triangle ABC in which AB = 6 cm, BC= 4.5 cm and AC= 5 cm.

Draw and label:

(i) the locus of the centres of all circles which touch AB and AC,

(ii) the locus of the centres of all circles of radius 2 cm which touch AB.

Hence, construct the circle of radius 2 cm which touches AB and AC.

Discussion

5430.	Find the next number in the following sequence: 42.00, 39.50, 37.00, 34.50...
Answer» Find the next number in the following sequence: 42.00, 39.50, 37.00, 34.50...

Discussion

5431.	Find the slope of a line passing through the following points:(i) (−3, 2) and (1, 4) (ii) (3, −5), and (1, 2)
Answer» Find the slope of a line passing through the following points: $(i) (- 3, 2) a n d (1, 4) (i i) (3, - 5), a n d (1, 2)$

5431.

Find the slope of a line passing through the following points:(i) (−3, 2) and (1, 4) (ii) (3, −5), and (1, 2)

Answer»

Find the slope of a line passing through the following points:

$(i) (- 3, 2) a n d (1, 4) (i i) (3, - 5), a n d (1, 2)$

Discussion

5432.	If cosec theta - cot theta=a ,then find 2 cosec ^2 theta +3 cot ^2 theta
Answer» If cosec theta - cot theta=a ,then find 2 cosec ^2 theta +3 cot ^2 theta

Discussion

5433.	Question 3 (ii) Evaluate: (ii) sin25∘cos65∘+cos25∘sin65∘
Answer» Question 3 (ii) Evaluate: (ii) $s i n 25^{\circ} c o s 65^{\circ} + c o s 25^{\circ} s i n 65^{\circ}$

Discussion

5434.	A metallic solid right circular cone is of height 84 cm and the radius of its base is 21 cm. It is melted and recast into a solid sphere. Find thediameter of the sphere. [CBSE 2014]
Answer» A metallic solid right circular cone is of height 84 cm and the radius of its base is 21 cm. It is melted and recast into a solid sphere. Find the diameter of the sphere. [CBSE 2014]

Discussion

5435.	The age of the employees in a startup company is shown below. AgeNo. of Employees18−263026−347034−425042−503050−581058−6610 Find the modal age of the employees of the company. [2 MARKS]
Answer» The age of the employees in a startup company is shown below. $\begin{matrix} Age & No. of Employees 18 - 26 & 30 26 - 34 & 70 34 - 42 & 50 42 - 50 & 30 50 - 58 & 10 58 - 66 & 10 \end{matrix}$ Find the modal age of the employees of the company. [2 MARKS]

Discussion

5436.	Find the circumcentre of the triangle whose vertices are (−2, −3), (−1, 0), (7, −6).
Answer» Find the circumcentre of the triangle whose vertices are (−2, −3), (−1, 0), (7, −6).

Discussion

5437.	Find the values of k for each of the following quadratic equations, so that they have two equal roots. (i)2x2+kx+3=0
Answer» Find the values of k for each of the following quadratic equations, so that they have two equal roots. $(i) 2 x^{2} + k x + 3 = 0$

Discussion

5438.	Draw the graph y=x2−9 and hence solve the equation x2−2x−8=0
Answer» Draw the graph $y = x^{2} - 9$ and hence solve the equation $x^{2} - 2 x - 8 = 0$

Discussion

5439.	In the given figure, AB is a tangent to the circle with centre O. If OP = PC, then ∠OCP = ___.
Answer» In the given figure, AB is a tangent to the circle with centre O. If OP = PC, then $∠ O C P$ = ___.

5439.

In the given figure, AB is a tangent to the circle with centre O. If OP = PC, then ∠OCP = ___.

Answer»

In the given figure, AB is a tangent to the circle with centre O. If OP = PC, then $∠ O C P$ = ___.

Discussion

5440.	A circus artist is climbing a 20 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole, if the angle made by the rope with the ground level is 30∘.
Answer» A circus artist is climbing a 20 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole, if the angle made by the rope with the ground level is $30^{\circ}$ .

Discussion

5441.	Place A and B are 160 km apart on a highway.One car starts from A and another from B at the same time.If they travel in the same direction,they meet in 8 hours.But,If they travel towards each other,they meet in 2 hours.Find the speed of each car.
Answer» Place A and B are 160 km apart on a highway.One car starts from A and another from B at the same time.If they travel in the same direction,they meet in 8 hours.But,If they travel towards each other,they meet in 2 hours.Find the speed of each car.

Discussion

5442.	Question 18 The sum of 4th and 8th terms of an A.P. is 24 and the sum of the 6th and 10th terms is 44. Find the first three terms of the A.P.
Answer» Question 18 The sum of $4^{t h}$ and $8^{t h}$ terms of an A.P. is 24 and the sum of the $6^{t h}$ and $10^{t h}$ terms is 44. Find the first three terms of the A.P.

Discussion

5443.	Solve the following systems of equations: 2(3u−v)=5uv 2(u+3v)=5uv
Answer» Solve the following systems of equations: $2 (3 u - v) = 5 u v$ $2 (u + 3 v) = 5 u v$

5443.

Solve the following systems of equations: 2(3u−v)=5uv 2(u+3v)=5uv

Answer»

Solve the following systems of equations:

$2 (3 u - v) = 5 u v$

$2 (u + 3 v) = 5 u v$

Discussion

5444.	In the given figure, OABC is a quadrant of a circle with centre O and radius 3.5 cm. If OD = 2 cm, find the area of thet shaded region.
Answer» In the given figure, OABC is a quadrant of a circle with centre O and radius 3.5 cm. If OD = 2 cm, find the area of thet shaded region.

5444.

In the given figure, OABC is a quadrant of a circle with centre O and radius 3.5 cm. If OD = 2 cm, find the area of thet shaded region.

Answer»

In the given figure, OABC is a quadrant of a circle with centre O and radius 3.5 cm. If OD = 2 cm, find the area of thet shaded region.

Discussion

5445.	In the following APs find the missing term in the boxesI. II. III. IV. V.
Answer» In the following APs find the missing term in the boxes I. II. III. IV. V.

5445.

In the following APs find the missing term in the boxesI. II. III. IV. V.

Answer»

In the following APs find the missing term in the boxes

I.

II.

III.

IV.

V.

Discussion

5446.	An A.P. consists of 50 terms of which 3rd term is 12 and the last term is 106. Find the 29th term
Answer» An A.P. consists of 50 terms of which 3^rd term is 12 and the last term is 106. Find the 29^th term

Discussion

5447.	Area of a sector of circle of radius 12 cm and subtending an angle of 60∘ at the centre is cm2.
Answer» Area of a sector of circle of radius 12 cm and subtending an angle of 60 $^{\circ}$ at the centre is $c m^{2}$ .

Discussion

5448.	The length, breadth and height of a room are 825 cm, 675 cm and 450 cm respectively. Find the longest tape which can measure the three dimensions of the room exactly.
Answer» The length, breadth and height of a room are 825 cm, 675 cm and 450 cm respectively. Find the longest tape which can measure the three dimensions of the room exactly.

Discussion

5449.	A jeweller has bars of 18-carat gold and 12-carat gold. How much of each must be melted together to obtain abar of 16-carat gold, weighing 120 g?
Answer» A jeweller has bars of 18-carat gold and 12-carat gold. How much of each must be melted together to obtain a bar of 16-carat gold, weighing 120 g?

Discussion

5450.	If f(x) is a polynomial of degree 4 with leading coefficient 4 and f(1)=2,f(2)=8,f(3)=18,f(5)=50, then f(4) is
Answer» If $f (x)$ is a polynomial of degree $4$ with leading coefficient $4$ and $f (1) = 2, f (2) = 8, f (3) = 18, f (5) = 50$ , then $f (4)$ is

Discussion

Explore topic-wise InterviewSolutions in .

A cone of height 12 cm and radius of base 10cm is divided by a plane parallel to the base into a cone and a frustum of equal volume. Find the ratio of height of the new cone and frustum formed

A man invested Rs 45,000 in 45% Rs 100 shares quoted at Rs 125. When the market value of these shares rose to Rs 140, he sold some shares, just enough to raise Rs 8,400. Calculate: (i) the number of shares he still holds. (ii) the dividend due to him on these remaining shares. [4 MARKS]

The value of expression mx-ny is 3 when x = 5 and y=6. And its value is 8 when x=6 and y=5. Find the value of m and n.

A player who was playing video game was given 20 coins to begin with the game. To go to the next level, he needs to spend 4 coins and if he succeeds the particular level, he earns 6 coins. Find the number of coins he collects after clearing each level (assuming he clears every level).

Let a,b,c and d be non-zero numbers such that x=c and x=d are the roots of the equation x2+ax+b=0 and x=a and x=b are the roots of the equation x2+cx+d=0. Then

Prove that 1secA+tanA=secA−tanA

During first half distance of journey the average speed is 40 km per hour and during remaining distance of journey average speed is 70 km per hour find average speed for the entire journey?

The quadratic equation which has D = 0 and a root as 110 is

Nick tosses three coins simultaneously. What is the probability of getting at least two heads?

If ∆ABC ∼ ∆DEF such that AB = 9.1 cm and DE = 6.5 cm. If the perimeter of ∆DEF is 25 cm, then the perimeter of ∆ABC is(a) 36 cm(b) 30 cm(c) 34 cm(d) 35 cm

There is a coin. Ram attaches a conical attachment to one flat end of coin. The conical attachment has same radius as coin. What is the surface area of the combined solid?

What is a sector of a circle with a central angle greater than 180 degree called?

Draw a circle of radius 2 cm with centre O and take a point P outside the circle such that OP = 6.5 cm. From P, draw two tangents to the circle. [3 MARKS]

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.

In Figure, P is a point in the interior of a parallelogram ABCD. Show that(i) ar(APB)+ar(PCD)=12ar(ABCD) (ii) ar(APD)+ar(PBC)=ar(APB)+ar(PCD) [Hint : Through P, draw a line parallel to AB.]

If sec(4A) = cosec(A−20∘), where 4A is an acute angle, then what is the value of A?

proof that the external bisectors of any two angles of a triangle are concurrent with the internal bisector of the third angle

In a triangle ABC right angled at B, ∠ACB=θ. If tanθ=512, then find the value of (1+cos θ)×(1−sinθ)(1+sinθ)×(1−cosθ).

In a medical examination of students of a class, the following blood groups are recorded.Blood groupA+AB−B−O+Number of1013125studentsA student is selected at random from the class. The probability that he/she has blood group B− is:

When x4+x3−2x2+x+1 is divided by x-1, the remainder is 2 and the quotient is q(x). Find q(x).

The outer and inner diameter of a circular path are 728 m and 700 m respectively. Find the width and the area of the circular path.

The polynomial ax3 + 41x2 + x – 2 when divided by (4x – 1) leaves remainder Then, the value of a and the remainder when the given polynomial is divided by x + 2 are respectively

Coins of diameter 10cm are arranged in hexagonal close packing inside a square with side of 40 cm . Find the maximum number of coins that can be placed whose Centre lies on or inside the square.

If sinA = 1/2 , verify that 2 sinA cosA = 2tanA/(1+ tan2A)

Find the value of p for which the numbers 2p-1, 3p+1,11 are in AP. Hence, find the numbers.

The larger of two supplementary angles exceeds the smaller by 18 degrees. Find the angles. [3 MARKS]

Draw a triangle ABC in which AB = 6 cm, BC= 4.5 cm and AC= 5 cm. Draw and label: (i) the locus of the centres of all circles which touch AB and AC, (ii) the locus of the centres of all circles of radius 2 cm which touch AB. Hence, construct the circle of radius 2 cm which touches AB and AC.

Find the next number in the following sequence: 42.00, 39.50, 37.00, 34.50...

Find the slope of a line passing through the following points:(i) (−3, 2) and (1, 4) (ii) (3, −5), and (1, 2)

If cosec theta - cot theta=a ,then find 2 cosec ^2 theta +3 cot ^2 theta

Question 3 (ii) Evaluate: (ii) sin25∘cos65∘+cos25∘sin65∘

A metallic solid right circular cone is of height 84 cm and the radius of its base is 21 cm. It is melted and recast into a solid sphere. Find thediameter of the sphere. [CBSE 2014]

The age of the employees in a startup company is shown below. AgeNo. of Employees18−263026−347034−425042−503050−581058−6610 Find the modal age of the employees of the company. [2 MARKS]

Find the circumcentre of the triangle whose vertices are (−2, −3), (−1, 0), (7, −6).

Find the values of k for each of the following quadratic equations, so that they have two equal roots. (i)2x2+kx+3=0

Draw the graph y=x2−9 and hence solve the equation x2−2x−8=0

In the given figure, AB is a tangent to the circle with centre O. If OP = PC, then ∠OCP = ___.

A circus artist is climbing a 20 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole, if the angle made by the rope with the ground level is 30∘.

Place A and B are 160 km apart on a highway.One car starts from A and another from B at the same time.If they travel in the same direction,they meet in 8 hours.But,If they travel towards each other,they meet in 2 hours.Find the speed of each car.

Question 18 The sum of 4th and 8th terms of an A.P. is 24 and the sum of the 6th and 10th terms is 44. Find the first three terms of the A.P.

Solve the following systems of equations: 2(3u−v)=5uv 2(u+3v)=5uv

In the given figure, OABC is a quadrant of a circle with centre O and radius 3.5 cm. If OD = 2 cm, find the area of thet shaded region.

In the following APs find the missing term in the boxesI. II. III. IV. V.

An A.P. consists of 50 terms of which 3rd term is 12 and the last term is 106. Find the 29th term

Area of a sector of circle of radius 12 cm and subtending an angle of 60∘ at the centre is cm2.

The length, breadth and height of a room are 825 cm, 675 cm and 450 cm respectively. Find the longest tape which can measure the three dimensions of the room exactly.

A jeweller has bars of 18-carat gold and 12-carat gold. How much of each must be melted together to obtain abar of 16-carat gold, weighing 120 g?

If f(x) is a polynomial of degree 4 with leading coefficient 4 and f(1)=2,f(2)=8,f(3)=18,f(5)=50, then f(4) is