32581 + Interview Questions in Mathematics Page 123 InterviewSolution

6101.	In a Roman numeral, explain with the help of examples whether the value of the symbols will get added or subtracted if(i) A symbol of smaller value is written to the right of a symbol of greater value?(ii) A symbol of smaller value is written to the left of a symbol of greater value?
Answer» In a Roman numeral, explain with the help of examples whether the value of the symbols will get added or subtracted if (i) A symbol of smaller value is written to the right of a symbol of greater value? (ii) A symbol of smaller value is written to the left of a symbol of greater value?

Discussion

6102.	Question 4Find the area of the segment of a circle of radius 12 cm whose corresponding sector has a central angle of 60∘. (use π=3.14)
Answer» Question 4 Find the area of the segment of a circle of radius 12 cm whose corresponding sector has a central angle of $60^{\circ}$ . (use $π = 3.14$ )

Discussion

6103.	A cylindrical container is filled with ice-cream, whose diameter is 12 cm and height is 15 cm. the whole ice-cream is distributed to 10 children in equal cones having hemispherical tops. If the height of the conical portion is twice the diameter of its base, find the diameter of the ice-cream.
Answer» A cylindrical container is filled with ice-cream, whose diameter is 12 cm and height is 15 cm. the whole ice-cream is distributed to 10 children in equal cones having hemispherical tops. If the height of the conical portion is twice the diameter of its base, find the diameter of the ice-cream.

Discussion

6104.

A, B and C are partners sharing profits and losses in the ratio of 2 : 3 : 5. On 31st March, 2019, their Balance Sheet was: Liabilities Amount (₹) Assets Amount (₹) Creditors 64,000 Cash 18,000 Bills Payable 22,000 Bills Receivable 14,000 General Reserve 14,000 Stock 44,000 Capital A/cs: Debtors 42,000 A 36,000 Machinery 94,000 B 44,000 Goodwill 20,000 C 52,000 1,32,000 2,32,000 2,32,000 They admit D into partnership on the following terms:(a) Machinery is to be depreciated by 15%.(b) Stock is to be revalued at ₹ 48,000.(c) It is found that the Creditors included a sum of ₹ 12,000 which was not to be paid.(d) Outstanding Rent is ₹ 1,900.(e) D is to bring in ₹ 6,000 as goodwill and sufficient capital for 2/5th share.(f) The partners decided to use 10% of the profits every year in providing drinking water in schools, where required.Prepare Revaluation Account, Partners' Capital Accounts, Cash Account and Balance Sheet of the new firm.

Answer» A, B and C are partners sharing profits and losses in the ratio of 2 : 3 : 5. On 31st March, 2019, their Balance Sheet was:


Liabilities		Amount (₹)	Assets	Amount (₹)
Creditors		64,000	Cash	18,000
Bills Payable		22,000	Bills Receivable	14,000
General Reserve		14,000	Stock	44,000
Capital A/cs:			Debtors	42,000
A	36,000		Machinery	94,000
B	44,000		Goodwill	20,000
C	52,000	1,32,000
		2,32,000		2,32,000

They admit D into partnership on the following terms:

(a) Machinery is to be depreciated by 15%.

(b) Stock is to be revalued at ₹ 48,000.

(c) It is found that the Creditors included a sum of ₹ 12,000 which was not to be paid.

(d) Outstanding Rent is ₹ 1,900.

(e) D is to bring in ₹ 6,000 as goodwill and sufficient capital for 2/5th share.

(f) The partners decided to use 10% of the profits every year in providing drinking water in schools, where required.

Prepare Revaluation Account, Partners' Capital Accounts, Cash Account and Balance Sheet of the new firm.

Discussion

6105.	If the sides of a right-angled triangle are in AP then what are the sines of the acute angles? [2 MARKS]
Answer» If the sides of a right-angled triangle are in AP then what are the sines of the acute angles? [2 MARKS]

Discussion

6106.	Find the equation of the straight line passing through the point of intersection of the lines 5x − 6y − 1 = 0 and 3x + 2y + 5 = 0 and perpendicular to the line 3x − 5y + 11 = 0 [NCERT EXAMPLE]
Answer» Find the equation of the straight line passing through the point of intersection of the lines 5x − 6y − 1 = 0 and 3x + 2y + 5 = 0 and perpendicular to the line 3x − 5y + 11 = 0 [NCERT EXAMPLE]

Discussion

6107.	Which two consecutive even numbers have an LCM of 180?
Answer» Which two consecutive even numbers have an LCM of 180?

Discussion

6108.	3. Prove that tanA/1-cotA+cotA/1-tanA=1+secA.cosecA
Answer» 3. Prove that tanA/1-cotA+cotA/1-tanA=1+secA.cosecA

Discussion

6109.	limx→02x+3tanx3x-2sinx is equal to_________________________.
Answer» $\lim_{x \to 0} \frac{2 x + 3 \tan x}{3 x - 2 \sin x}$ is equal to_________________________.

Discussion

6110.	Solve 47x+31y=63 , 31x+47y=15
Answer» Solve 47x+31y=63 , 31x+47y=15

Discussion

6111.	Does the point p(-2,4) lie on a circle of a radius 6 units and centre at c(3,5)?
Answer» Does the point p(-2,4) lie on a circle of a radius 6 units and centre at c(3,5)?

Discussion

6112.	The time taken by a person to cover 150km was 2.5hrs more than the time taken in the return journey. If the returned at a speed of 10km/hr more than the speed of going, what was the speed per hour in each direction?
Answer» The time taken by a person to cover 150km was 2.5hrs more than the time taken in the return journey. If the returned at a speed of 10km/hr more than the speed of going, what was the speed per hour in each direction?

Discussion

6113.	From the top of a 7-metre-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. [Use 3 = 1.732] [CBSE 2013C]
Answer» From the top of a 7-metre-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. [Use $\sqrt{3}$ = 1.732] [CBSE 2013C]

Discussion

6114.	In the given triangle ABC,∠A=50∘,∠c=50∘, AB =10 cm, then find the length of BC. [sin 60∘=0.86,sin 50∘=0.76]
Answer» In the given triangle $A B C, ∠ A = 50^{\circ}, ∠ c = 50^{\circ}$ , AB =10 cm, then find the length of BC. $[s i n 60^{\circ} = 0.86, s i n 50^{\circ} = 0.76]$

6114.

In the given triangle ABC,∠A=50∘,∠c=50∘, AB =10 cm, then find the length of BC. [sin 60∘=0.86,sin 50∘=0.76]

Answer»

In the given triangle $A B C, ∠ A = 50^{\circ}, ∠ c = 50^{\circ}$ , AB =10 cm, then find the length of BC. $[s i n 60^{\circ} = 0.86, s i n 50^{\circ} = 0.76]$

Discussion

6115.	Question 61 State whether the following statement is True or False. The actual width of a storeroom is 280 cm. If the scale chosen to make its drawing is 1 : 7, then the width of the room in the drawing will be 40 cm.
Answer» Question 61 State whether the following statement is True or False. The actual width of a storeroom is 280 cm. If the scale chosen to make its drawing is 1 : 7, then the width of the room in the drawing will be 40 cm.

Discussion

6116.	Draw a circle of radius 3 cm . Draw a tangent which making an angle of 30 with the line passing through centre
Answer» Draw a circle of radius 3 cm . Draw a tangent which making an angle of 30 with the line passing through centre

Discussion

6117.	The surface area of a right circular cylinder of height 26 cm and radius 14 cm is ____________ cm2.
Answer» The surface area of a right circular cylinder of height 26 cm and radius 14 cm is ____________ $c m^{2}$ .

Discussion

6118.	Show that the cube of any positive integer of the form 6q +r,q is an integer and r is equal to zero, 1, 2, 3, 4, 5 is also a form of 6m+r
Answer» Show that the cube of any positive integer of the form 6q +r,q is an integer and r is equal to zero, 1, 2, 3, 4, 5 is also a form of 6m+r

Discussion

6119.	How many possible orders can a matrix with 15 elements have?
Answer» How many possible orders can a matrix with 15 elements have?

Discussion

6120.	In the given figure, ∠ABC = 75°, ∠EDC = 75° state which two triangles are similar and by which test? Also write the similarity of these two triangles by a proper one to one correspondence.
Answer» In the given figure, ∠ABC = 75°, ∠EDC = 75° state which two triangles are similar and by which test? Also write the similarity of these two triangles by a proper one to one correspondence.

Discussion

6121.	From the top of a tower 100 m high, a man observes two cars on the opposite sides of the tower with angles of depression 30° and 45°, respectively. Find the distance between the cars. [Take 3= 1.73] [CBSE 2011]
Answer» From the top of a tower 100 m high, a man observes two cars on the opposite sides of the tower with angles of depression 30° and 45°, respectively. Find the distance between the cars. [Take $\sqrt{3}$ = 1.73] [CBSE 2011]

Discussion

6122.	If the first term of an A.P. is a and nth term is b, then its common difference is(a) b-an+1(b) b-an-1 (c) b-an(d) b+an-1
Answer» If the first term of an A.P. is a and nth term is b, then its common difference is (a) $\frac{b - a}{n + 1}$ (b) $\frac{b - a}{n - 1}$ (c) $\frac{b - a}{n}$ (d) $\frac{b + a}{n - 1}$

Discussion

6123.	If the heights of two right circular cones are in the ratio 1 : 2 and the perimeters of their bases are in the ratio 3 : 4, what is the ratio of their volumes?
Answer» If the heights of two right circular cones are in the ratio 1 : 2 and the perimeters of their bases are in the ratio 3 : 4, what is the ratio of their volumes?

Discussion

6124.	In the given figure, O is the centre of the circle and ∠ ABC=55∘. Calculate the values of x and y.
Answer» In the given figure, O is the centre of the circle and $∠ A B C = 55^{\circ}$ . Calculate the values of x and y.

6124.

In the given figure, O is the centre of the circle and ∠ ABC=55∘. Calculate the values of x and y.

Answer»

In the given figure, O is the centre of the circle and $∠ A B C = 55^{\circ}$ . Calculate the values of x and y.

Discussion

6125.	Question 10If y-Coordinate of a point is zero, then this point always liesA) In I quadrantB) In II quadrantC) On x-axisD) On y-axis
Answer» Question 10 If y-Coordinate of a point is zero, then this point always lies A) In I quadrant B) In II quadrant C) On x-axis D) On y-axis

Discussion

6126.	S and T are point on sides PR and QR of ΔPQR such that ∠P=∠RTS. Show that ΔRPQ∼ΔRTS.
Answer» S and T are point on sides PR and QR of $Δ P Q R$ such that $∠ P = ∠ R T S$ . Show that $Δ R P Q \sim Δ R T S$ .

Discussion

6127.	The probability of getting a perfect square number in a single throw of a dice is ____.
Answer» The probability of getting a perfect square number in a single throw of a dice is ____.

Discussion

6128.	If ∫x0 f(t)dt=x+∫1x tf(t) dt, then the value of f (1) is
Answer» $I f \int_{0}^{x} f (t) d t = x + \int_{x}^{1} t f (t) d t,$ then the value of f (1) is

Discussion

6129.	Find the roots of each of the following equations, if they exist, by applying the quadratic formula:2x2+63x-60=0 [CBSE 2011, 15]
Answer» Find the roots of each of the following equations, if they exist, by applying the quadratic formula: $2 x^{2} + 6 \sqrt{3} x - 60 = 0$ [CBSE 2011, 15]

Discussion

6130.	The radius of gyration of a ring of radius r about a †an gent perpendicular to its plane is Options:a-r/\sqrt2 b-r/2 c-\sqrt{2r} d- 2r
Answer» The radius of gyration of a ring of radius r about a †an gent perpendicular to its plane is Options:a-r/\sqrt2 b-r/2 c-\sqrt{2r} d- 2r

Discussion

6131.	Draw a triangle ABC with side BC = 7 cm, ∠B = 45°, ∠A = 105°. Then, construct a triangle whose sides are times the corresponding side of ΔABC. Give the justification of the construction.
Answer» Draw a triangle ABC with side BC = 7 cm, ∠B = 45°, ∠A = 105°. Then, construct a triangle whose sides are times the corresponding side of ΔABC. Give the justification of the construction.

Discussion

6132.	Mr. Anna Hazare, Padyatra Party wanted to go from Delhi to Dehradun. The Walkers travelled 150 km straight and then took a 45∘ turn towards Varanasi and walked straight for another 120 km. Approximately how far was the party from the starting point?
Answer» Mr. Anna Hazare, Padyatra Party wanted to go from Delhi to Dehradun. The Walkers travelled 150 km straight and then took a $45^{\circ}$ turn towards Varanasi and walked straight for another 120 km. Approximately how far was the party from the starting point?

Discussion

6133.	If the sums of n terms of two arithmetic progressions are in the ratio 3n+5:5n-7, then their nth terms are in the ratio(a) 3n-15:n-1(b) 3n+15:n+1(c) 5n+13:n+1(d) 5n-13:n-1
Answer» If the sums of n terms of two arithmetic progressions are in the ratio 3n+5:5n-7, then their n^th terms are in the ratio (a) 3n-15:n-1 (b) 3n+15:n+1 (c) 5n+13:n+1 (d) 5n-13:n-1

Discussion

6134.	A triangle has coordinates (1, 4), (3, 4), and (3, 2), the image of the triangle when reflected in the line x = 4 will have coordinates -
Answer» A triangle has coordinates (1, 4), (3, 4), and (3, 2), the image of the triangle when reflected in the line x = 4 will have coordinates -

Discussion

6135.	Cards bearing numbers 1, 3, 5, .... , 35 are kept in a bag. A card is drawn at random from the bag. Find the probability of getting a card bearing(i) a prime number less than 15,(ii) a number divisible by 3 and 5.
Answer» Cards bearing numbers 1, 3, 5, .... , 35 are kept in a bag. A card is drawn at random from the bag. Find the probability of getting a card bearing (i) a prime number less than 15, (ii) a number divisible by 3 and 5.

Discussion

6136.	If the mean of the squares of first n natural number is 130 then the median of the first n natural number is?
Answer» If the mean of the squares of first n natural number is 130 then the median of the first n natural number is?

Discussion

6137.	Mean proportional of 2√m and 2√m is _________.
Answer» Mean proportional of $2 \sqrt{m} a n d 2 \sqrt{m}$ is _________.

Discussion

6138.	The adjoint of the matrixA=⎡⎢⎣11121−3−123⎤⎥⎦ is:
Answer» The adjoint of the matrix $A = ⎡ ⎢ ⎣ \begin{matrix} 1 & 1 & 1 2 & 1 & - 3 - 1 & 2 & 3 \end{matrix} ⎤ ⎥ ⎦$ is:

Discussion

6139.	Using the frequency distribution table given below, draw 'less than ogive'. Then from the ogive, find interquartile range.Class intervalFrequency10−20220−30430−40640−50850−6010
Answer» Using the frequency distribution table given below, draw 'less than ogive'. Then from the ogive, find interquartile range. $\begin{matrix} C l a s s i n t e r v a l & F r e q u e n c y 10 - 20 & 2 20 - 30 & 4 30 - 40 & 6 40 - 50 & 8 50 - 60 & 10 \end{matrix}$

Discussion

6140.	if the roots of quadratic equation a[b-c]x^2+b[c-a]x+c[a-b]=0 are equal and a,b,c>0 then prove that a,b,c are in hp
Answer» if the roots of quadratic equation a[b-c]x^2+b[c-a]x+c[a-b]=0 are equal and a,b,c>0 then prove that a,b,c are in hp

Discussion

6141.	Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line-segment joining the points of contact at the centre.
Answer» Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line-segment joining the points of contact at the centre.

Discussion

6142.	26. The function f(x)=0 has eight distinct solutions and f also satisfy f(4+x)= f(4-x). The sum of all eight solutions of f(x)=0 is
Answer» 26. The function f(x)=0 has eight distinct solutions and f also satisfy f(4+x)= f(4-x). The sum of all eight solutions of f(x)=0 is

Discussion

6143.	Question 3A bucket is in the form of a frustum of a cone and holds 28.490 litres of water. The radii of the top and bottom are 28 cm and 21 cm, respectively. Find the height of the bucket.
Answer» Question 3 A bucket is in the form of a frustum of a cone and holds 28.490 litres of water. The radii of the top and bottom are 28 cm and 21 cm, respectively. Find the height of the bucket.

Discussion

6144.	Question 4An AP consists of 37 terms. The sum of the three middle most terms is 225 and the sum of the last three is 429. Find the AP.
Answer» Question 4 An AP consists of 37 terms. The sum of the three middle most terms is 225 and the sum of the last three is 429. Find the AP.

Discussion

6145.	Vivek invests ₹ 4500 in 8 % , ₹ 10 shares at ₹ 15. He sells the shares when the price rise to 30 and invests the proceeds in 12 %, ₹ 100 shares at ₹ 125. Calculate (i) the sale proceeds (ii) the number of ₹ 125 shares he buys (iii) the change in his annual income from dividend
Answer» Vivek invests ₹ 4500 in 8 % , ₹ 10 shares at ₹ 15. He sells the shares when the price rise to 30 and invests the proceeds in 12 %, ₹ 100 shares at ₹ 125. Calculate (i) the sale proceeds (ii) the number of ₹ 125 shares he buys (iii) the change in his annual income from dividend

6145.

Vivek invests ₹ 4500 in 8 % , ₹ 10 shares at ₹ 15. He sells the shares when the price rise to 30 and invests the proceeds in 12 %, ₹ 100 shares at ₹ 125. Calculate (i) the sale proceeds (ii) the number of ₹ 125 shares he buys (iii) the change in his annual income from dividend

Answer»

Vivek invests ₹ 4500 in 8 % , ₹ 10 shares at ₹ 15. He sells the shares when the price rise to 30 and invests the proceeds in 12 %, ₹ 100 shares at ₹ 125.

Calculate (i) the sale proceeds

(ii) the number of ₹ 125 shares he buys

(iii) the change in his annual income from dividend

Discussion

6146.	If the angle of the elevation of a cloud from a point &quoth" metres above a lake is &quotA" and the angle of depression of its reflection in the lake is &quotB", prove that the distance of the cloud from the points of observation is - 2hSecA/(tanB- tanA).
Answer» If the angle of the elevation of a cloud from a point "h" metres above a lake is "A" and the angle of depression of its reflection in the lake is "B", prove that the distance of the cloud from the points of observation is - 2hSecA/(tanB- tanA).

Discussion

6147.	Flora buys a suit-case costing Rs 749. The rate of sales tax is 7%. She tells the shopkeeper to reduce the price of suit case to such an extent that she has not to pay anything more than Rs 749 including sale tax. Find the reduction needed in the price of suit-case.
Answer» Flora buys a suit-case costing Rs 749. The rate of sales tax is 7%. She tells the shopkeeper to reduce the price of suit case to such an extent that she has not to pay anything more than Rs 749 including sale tax. Find the reduction needed in the price of suit-case.

Discussion

6148.	Construct a 2×2 matrix, A=[aij], whose elements are given by:(i) aij=(i+j)22(ii) aij=ij(iii) aij=(i+2j)22
Answer» Construct a $2 \times 2$ matrix, $A = [a_{i j}]$ , whose elements are given by: $(i)$ $a_{i j} = \frac{(i + j)^{2}}{2}$ $(i i)$ $a_{i j} = \frac{i}{j}$ $(i i i)$ $a_{i j} = \frac{(i + 2 j)^{2}}{2}$

Discussion

6149.	The radii of the circular ends of a solid frustum of a cone are 18 cm and 12 cm and its height is 8 cm. Find its total surface area.[Use π = 3.14] [CBSE 2011]
Answer» The radii of the circular ends of a solid frustum of a cone are 18 cm and 12 cm and its height is 8 cm. Find its total surface area. [Use $π$ = 3.14] [CBSE 2011]

Discussion

6150.	what is bconvex lenc
Answer» what is bconvex lenc

Discussion

Explore topic-wise InterviewSolutions in .

In a Roman numeral, explain with the help of examples whether the value of the symbols will get added or subtracted if(i) A symbol of smaller value is written to the right of a symbol of greater value?(ii) A symbol of smaller value is written to the left of a symbol of greater value?

Question 4Find the area of the segment of a circle of radius 12 cm whose corresponding sector has a central angle of 60∘. (use π=3.14)

A cylindrical container is filled with ice-cream, whose diameter is 12 cm and height is 15 cm. the whole ice-cream is distributed to 10 children in equal cones having hemispherical tops. If the height of the conical portion is twice the diameter of its base, find the diameter of the ice-cream.

If the sides of a right-angled triangle are in AP then what are the sines of the acute angles? [2 MARKS]

Find the equation of the straight line passing through the point of intersection of the lines 5x − 6y − 1 = 0 and 3x + 2y + 5 = 0 and perpendicular to the line 3x − 5y + 11 = 0 [NCERT EXAMPLE]

Which two consecutive even numbers have an LCM of 180?

3. Prove that tanA/1-cotA+cotA/1-tanA=1+secA.cosecA

limx→02x+3tanx3x-2sinx is equal to_________________________.

Solve 47x+31y=63 , 31x+47y=15

Does the point p(-2,4) lie on a circle of a radius 6 units and centre at c(3,5)?

The time taken by a person to cover 150km was 2.5hrs more than the time taken in the return journey. If the returned at a speed of 10km/hr more than the speed of going, what was the speed per hour in each direction?

From the top of a 7-metre-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. [Use 3 = 1.732] [CBSE 2013C]

In the given triangle ABC,∠A=50∘,∠c=50∘, AB =10 cm, then find the length of BC. [sin 60∘=0.86,sin 50∘=0.76]

Question 61 State whether the following statement is True or False. The actual width of a storeroom is 280 cm. If the scale chosen to make its drawing is 1 : 7, then the width of the room in the drawing will be 40 cm.

Draw a circle of radius 3 cm . Draw a tangent which making an angle of 30 with the line passing through centre

The surface area of a right circular cylinder of height 26 cm and radius 14 cm is ____________ cm2.

Show that the cube of any positive integer of the form 6q +r,q is an integer and r is equal to zero, 1, 2, 3, 4, 5 is also a form of 6m+r

How many possible orders can a matrix with 15 elements have?

In the given figure, ∠ABC = 75°, ∠EDC = 75° state which two triangles are similar and by which test? Also write the similarity of these two triangles by a proper one to one correspondence.

From the top of a tower 100 m high, a man observes two cars on the opposite sides of the tower with angles of depression 30° and 45°, respectively. Find the distance between the cars. [Take 3= 1.73] [CBSE 2011]

If the first term of an A.P. is a and nth term is b, then its common difference is(a) b-an+1(b) b-an-1 (c) b-an(d) b+an-1

If the heights of two right circular cones are in the ratio 1 : 2 and the perimeters of their bases are in the ratio 3 : 4, what is the ratio of their volumes?

In the given figure, O is the centre of the circle and ∠ ABC=55∘. Calculate the values of x and y.

Question 10If y-Coordinate of a point is zero, then this point always liesA) In I quadrantB) In II quadrantC) On x-axis​​​​​​​D) On y-axis

S and T are point on sides PR and QR of ΔPQR such that ∠P=∠RTS. Show that ΔRPQ∼ΔRTS.

The probability of getting a perfect square number in a single throw of a dice is ____.

If ∫x0 f(t)dt=x+∫1x tf(t) dt, then the value of f (1) is

Find the roots of each of the following equations, if they exist, by applying the quadratic formula:2x2+63x-60=0 [CBSE 2011, 15]

The radius of gyration of a ring of radius r about a †an gent perpendicular to its plane is Options:a-r/\sqrt2 b-r/2 c-\sqrt{2r} d- 2r

Draw a triangle ABC with side BC = 7 cm, ∠B = 45°, ∠A = 105°. Then, construct a triangle whose sides are times the corresponding side of ΔABC. Give the justification of the construction.

Mr. Anna Hazare, Padyatra Party wanted to go from Delhi to Dehradun. The Walkers travelled 150 km straight and then took a 45∘ turn towards Varanasi and walked straight for another 120 km. Approximately how far was the party from the starting point?

If the sums of n terms of two arithmetic progressions are in the ratio 3n+5:5n-7, then their nth terms are in the ratio(a) 3n-15:n-1(b) 3n+15:n+1(c) 5n+13:n+1(d) 5n-13:n-1

A triangle has coordinates (1, 4), (3, 4), and (3, 2), the image of the triangle when reflected in the line x = 4 will have coordinates -

Cards bearing numbers 1, 3, 5, .... , 35 are kept in a bag. A card is drawn at random from the bag. Find the probability of getting a card bearing(i) a prime number less than 15,(ii) a number divisible by 3 and 5.

If the mean of the squares of first n natural number is 130 then the median of the first n natural number is?

Mean proportional of 2√m and 2√m is _________.

The adjoint of the matrixA=⎡⎢⎣11121−3−123⎤⎥⎦ is:

Using the frequency distribution table given below, draw 'less than ogive'. Then from the ogive, find interquartile range.Class intervalFrequency10−20220−30430−40640−50850−6010

if the roots of quadratic equation a[b-c]x^2+b[c-a]x+c[a-b]=0 are equal and a,b,c>0 then prove that a,b,c are in hp

Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line-segment joining the points of contact at the centre.

26. The function f(x)=0 has eight distinct solutions and f also satisfy f(4+x)= f(4-x). The sum of all eight solutions of f(x)=0 is

Question 3A bucket is in the form of a frustum of a cone and holds 28.490 litres of water. The radii of the top and bottom are 28 cm and 21 cm, respectively. Find the height of the bucket.

Question 4An AP consists of 37 terms. The sum of the three middle most terms is 225 and the sum of the last three is 429. Find the AP.

Vivek invests ₹ 4500 in 8 % , ₹ 10 shares at ₹ 15. He sells the shares when the price rise to 30 and invests the proceeds in 12 %, ₹ 100 shares at ₹ 125. Calculate (i) the sale proceeds (ii) the number of ₹ 125 shares he buys (iii) the change in his annual income from dividend

If the angle of the elevation of a cloud from a point &quoth" metres above a lake is &quotA" and the angle of depression of its reflection in the lake is &quotB", prove that the distance of the cloud from the points of observation is - 2hSecA/(tanB- tanA).

Flora buys a suit-case costing Rs 749. The rate of sales tax is 7%. She tells the shopkeeper to reduce the price of suit case to such an extent that she has not to pay anything more than Rs 749 including sale tax. Find the reduction needed in the price of suit-case.

Construct a 2×2 matrix, A=[aij], whose elements are given by:(i) aij=(i+j)22(ii) aij=ij(iii) aij=(i+2j)22

The radii of the circular ends of a solid frustum of a cone are 18 cm and 12 cm and its height is 8 cm. Find its total surface area.[Use π = 3.14] [CBSE 2011]

what is bconvex lenc

Question 10If y-Coordinate of a point is zero, then this point always liesA) In I quadrantB) In II quadrantC) On x-axisD) On y-axis