32581 + Interview Questions in Mathematics

1.	in triangle pqr if pq =qr and L,M and,N are the mid points of the sides PQ, QR and RP respectively thanprove that LN=MN
Answer» in triangle pqr if pq =qr and L,M and,N are the mid points of the sides PQ, QR and RP respectively thanprove that LN=MN

Discussion

2.	A rectangular courtyard is 20m 16cm long and 15m 60cm broad. It is to be paved with square stones of the same size. Find the least possible number of such stones.
Answer» A rectangular courtyard is 20m 16cm long and 15m 60cm broad. It is to be paved with square stones of the same size. Find the least possible number of such stones.

Discussion

3.	Question 13 As observed from the top of a 75 m high lighthouse from the sea-level, the angles of depression of two ships are 30∘ and 45∘. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships.
Answer» Question 13 As observed from the top of a 75 m high lighthouse from the sea-level, the angles of depression of two ships are $30^{\circ}$ and $45^{\circ}$ . If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships.

Discussion

4.	Question 1 (vi)Find the roots of the quadratic equations by using the quadratic formula in the following question.x2−3√5x+10=0
Answer» Question 1 (vi) Find the roots of the quadratic equations by using the quadratic formula in the following question. $x^{2} - 3 \sqrt{5} x + 10 = 0$

4.

Question 1 (vi)Find the roots of the quadratic equations by using the quadratic formula in the following question.x2−3√5x+10=0

Answer»

Question 1 (vi)

Find the roots of the quadratic equations by using the quadratic formula in the following question.

$x^{2} - 3 \sqrt{5} x + 10 = 0$

Discussion

5.	Question 8From a solid cylinder whose height is 2.4 cm and diameter 1.4 cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid to the nearest cm2.
Answer» Question 8 From a solid cylinder whose height is 2.4 cm and diameter 1.4 cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid to the nearest $c m^{2}$ .

Discussion

6.	If x=-3 and x=23 are solutions of quadratic equation mx2+7x+n=0,find the values of m and n.
Answer» If x=-3 and $x = \frac{2}{3}$ are solutions of quadratic equation $m x^{2} + 7 x + n = 0$ ,find the values of m and n.

Discussion

7.	Two students, while solving a quadratic equation, committed the following mistakes: (i) One of them made a mistake in the constant term and got the roots as 5 and 9. (ii) Another one committed an error in the coefficient of x and got the roots as 12 and 4. But, in the meantime, they realised that they are wrong and they managed to get it right jointly. Find the correct quadratic equation.
Answer» Two students, while solving a quadratic equation, committed the following mistakes: (i) One of them made a mistake in the constant term and got the roots as $5$ and $9$ . (ii) Another one committed an error in the coefficient of $x$ and got the roots as $12$ and $4$ . But, in the meantime, they realised that they are wrong and they managed to get it right jointly. Find the correct quadratic equation.

7.

Two students, while solving a quadratic equation, committed the following mistakes: (i) One of them made a mistake in the constant term and got the roots as 5 and 9. (ii) Another one committed an error in the coefficient of x and got the roots as 12 and 4. But, in the meantime, they realised that they are wrong and they managed to get it right jointly. Find the correct quadratic equation.

Answer»

Two students, while solving a quadratic equation, committed the following mistakes:
(i) One of them made a mistake in the constant term and got the roots as $5$ and $9$ .
(ii) Another one committed an error in the coefficient of $x$ and got the roots as $12$ and $4$ .
But, in the meantime, they realised that they are wrong and they managed to get it right jointly.

Find the correct quadratic equation.

Discussion

8.	Nazama is a proprietor of a firm, registered under GST. She has paid GST of Rs 12,500 on purchase and collected Rs 14,750 on sale. What is the amount of ITC to be claimed ? What is the amount of GST payable ?
Answer» Nazama is a proprietor of a firm, registered under GST. She has paid GST of Rs 12,500 on purchase and collected Rs 14,750 on sale. What is the amount of ITC to be claimed ? What is the amount of GST payable ?

Discussion

9.	What rate gives ₹280 as interest on a sum of ₹ 56,000 in 2 years?
Answer» What rate gives ₹280 as interest on a sum of ₹ 56,000 in 2 years?

Discussion

10.	Find the ratio of the volumes of a cylinder, a cone and a sphere, if each has the same diameter and same height?
Answer» Find the ratio of the volumes of a cylinder, a cone and a sphere, if each has the same diameter and same height?

Discussion

11.	Find value of x,y in the below given pair of equation. 2x + 3y = 13 5x - 4y = -2
Answer» Find value of x,y in the below given pair of equation. $\frac{2}{x}$ + $\frac{3}{y}$ = 13 $\frac{5}{x}$ - $\frac{4}{y}$ = -2

11.

Find value of x,y in the below given pair of equation. 2x + 3y = 13 5x - 4y = -2

Answer»

Find value of x,y in the below given pair of equation.

$\frac{2}{x}$ + $\frac{3}{y}$ = 13

$\frac{5}{x}$ - $\frac{4}{y}$ = -2

Discussion

12.	State SSS similarity criterion.
Answer» State SSS similarity criterion.

Discussion

13.	A man swims across a 400 m wide river flowing with a speed of 3 m/s , such that he reaches the point just in front on the bank in 100 s. The angle made by the direction he swims and river flow direction is:
Answer» A man swims across a 400 m wide river flowing with a speed of 3 m/s , such that he reaches the point just in front on the bank in 100 s. The angle made by the direction he swims and river flow direction is:

Discussion

14.	The following real number has decimal expansion as given below. Decide whether rational or not. If rational, and of the form pq, what can you say about the prime factors of q? 43.123456789
Answer» The following real number has decimal expansion as given below. Decide whether rational or not. If rational, and of the form $\frac{p}{q}$ , what can you say about the prime factors of q? 43.123456789

Discussion

15.	what is E_2 elimination?
Answer» what is E_2 elimination?

Discussion

16.	If π is taken as 227, the distance (in metres) covered by a wheel of diameter 35 cm, in one revolution, is(a) 2.2(b) 1.1(c) 9.625(d) 96.25
Answer» If π is taken as $\frac{22}{7}$ , the distance (in metres) covered by a wheel of diameter 35 cm, in one revolution, is (a) 2.2 (b) 1.1 (c) 9.625 (d) 96.25

Discussion

17.	Samira has a recurring deposit account in a bank of RS.2000 per month at the rate of 10%p.a.If she gets RS.83100 at the time of maturity, find the total time for which the account was held.
Answer» Samira has a recurring deposit account in a bank of RS.2000 per month at the rate of 10%p.a.If she gets RS.83100 at the time of maturity, find the total time for which the account was held.

Discussion

18.	Find the area of the triangle in the given figure.
Answer» Find the area of the triangle in the given figure.

Discussion

19.	3. Find the three consecutive numbers whose sum is 45.
Answer» 3. Find the three consecutive numbers whose sum is 45.

Discussion

20.	In the given figure triangle ABC is circumscribed by a circle, AB =5 cm, ∠A=30∘,∠C=60∘. Find the length of side BC. [sin 60∘=0.86, sin 30∘=0.5]
Answer» In the given figure triangle ABC is circumscribed by a circle, AB =5 cm, $∠ A = 30^{\circ}, ∠ C = 60^{\circ}$ . Find the length of side BC. $[s i n 60^{\circ} = 0.86, s i n 30^{\circ} = 0.5]$

20.

In the given figure triangle ABC is circumscribed by a circle, AB =5 cm, ∠A=30∘,∠C=60∘. Find the length of side BC. [sin 60∘=0.86, sin 30∘=0.5]

Answer»

In the given figure triangle ABC is circumscribed by a circle, AB =5 cm, $∠ A = 30^{\circ}, ∠ C = 60^{\circ}$ . Find the length of side BC. $[s i n 60^{\circ} = 0.86, s i n 30^{\circ} = 0.5]$

Discussion

21.	In figure 3, APB and CQD are semi-circles of diameter 7 cm each, while ARC and BSD are semi - circles of diameter 14 cm each. Find the perimeter of the shaded region. [Use π =227] OR Find the area of a quadrant of a circle, where the circumference of circle is 44 cm.[Use π =227]
Answer» In figure 3, APB and CQD are semi-circles of diameter 7 cm each, while ARC and BSD are semi - circles of diameter 14 cm each. Find the perimeter of the shaded region. $[U s e π = \frac{22}{7}]$ OR Find the area of a quadrant of a circle, where the circumference of circle is 44 cm. $[U s e π = \frac{22}{7}]$

Discussion

22.	In Fig. 14.78, a circle is inscribed in a square ABCD and the square is circumscribed by a circle. If the radius of the smaller circle is r сm, then the area of the shaded region in cm2 is _________.
Answer» In Fig. 14.78, a circle is inscribed in a square ABCD and the square is circumscribed by a circle. If the radius of the smaller circle is r сm, then the area of the shaded region in cm² is _________.

Discussion

23.	If S1 is the sum of an arithmetic progression of 'n' odd number of terms and S2 the sum of the terms of the series in odd places, then S1S2=(a) 2nn+1(b) nn+1(c) n+12n(d) n+1n
Answer» If S₁ is the sum of an arithmetic progression of 'n' odd number of terms and S₂ the sum of the terms of the series in odd places, then $\frac{S_{1}}{S_{2}} =$ (a) $\frac{2 n}{n + 1}$ (b) $\frac{n}{n + 1}$ (c) $\frac{n + 1}{2 n}$ (d) $\frac{n + 1}{n}$

Discussion

24.	The length of a rectangular garden is 20m longer than its breadth.if its perimeter is 200m,find its length and breadth.
Answer» The length of a rectangular garden is 20m longer than its breadth.if its perimeter is 200m,find its length and breadth.

Discussion

25.	Harry walks from his house at A to his office at B, by taking the shortest path. Find the probability that he will take the highlighted path, given that he can move only Up or Right at every intersection of roads.
Answer» Harry walks from his house at A to his office at B, by taking the shortest path. Find the probability that he will take the highlighted path, given that he can move only Up or Right at every intersection of roads.

Discussion

26.	How many times the volume of a cone decreases if the radius of the base is reduced by half?
Answer» How many times the volume of a cone decreases if the radius of the base is reduced by half?

Discussion

27.	In the given figure, AX : XB = 3 : 5 and XY \|\| BC. Then, the ratio of the areas of trapezium XBCY and triangle ABC is
Answer» In the given figure, AX : XB = 3 : 5 and XY \|\| BC. Then, the ratio of the areas of trapezium XBCY and triangle ABC is

27.

In the given figure, AX : XB = 3 : 5 and XY || BC. Then, the ratio of the areas of trapezium XBCY and triangle ABC is

Answer»

In the given figure, AX : XB = 3 : 5 and XY || BC.

Then, the ratio of the areas of trapezium XBCY and triangle ABC is

Discussion

28.	Two tangents PA and PB are drawn from an external point P to a circle with centre O. Prove that AOBP is a cyclic quadrilateral.
Answer» Two tangents PA and PB are drawn from an external point P to a circle with centre O. Prove that AOBP is a cyclic quadrilateral.

Discussion

29.	Question 4 (iii)Which of the following pairs of linear equations are consistent/ inconsistent? If consistent, obtain the solution graphically:2x + y - 6 = 0, 4x - 2y - 4 = 0
Answer» Question 4 (iii) Which of the following pairs of linear equations are consistent/ inconsistent? If consistent, obtain the solution graphically: 2x + y - 6 = 0, 4x - 2y - 4 = 0

Discussion

30.	For what values of 'k' will the equation x2 - 2x(k-1) + (k+1)=0 will have equal real roots?
Answer» For what values of 'k' will the equation x² - 2x(k-1) + (k+1)=0 will have equal real roots?

Discussion

31.

Arushi Computers Ltd. issued 10,000 equity shares of Rs. 100 each at 10% premium. The net amount payable as follows: On application Rs. 20 On allotment Rs. 50 (Rs. 40 + premium Rs. 10) On first call Rs. 30 On final call Rs. 10 A shareholder holding 200 shares did not pay final call. His shares were forfeited. Out of these 150 shares were reissued to Ms. Sonia at Rs. 75 per share. Give journal entries in the books of the company.

Answer»

Arushi Computers Ltd. issued 10,000 equity shares of Rs. 100 each at 10% premium. The net amount payable as follows:

On application	Rs. 20
On allotment	Rs. 50 (Rs. 40 + premium Rs. 10)
On first call	Rs. 30
On final call	Rs. 10

A shareholder holding 200 shares did not pay final call. His shares were forfeited. Out of these 150 shares were reissued to Ms. Sonia at Rs. 75 per share.

Give journal entries in the books of the company.

Discussion

32.	The midpoint of the line segment A(2a, 4) and B(-2, 3b) is C(1, 2a+1). Find the values of a and b.
Answer» The midpoint of the line segment A(2a, 4) and B(-2, 3b) is C(1, 2a+1). Find the values of a and b.

Discussion

33.	The length of a rectangle is three times the breadth. If the minimum perimeter of the rectangle is 160 cm, then
Answer» The length of a rectangle is three times the breadth. If the minimum perimeter of the rectangle is 160 cm, then

Discussion

34.	Question 01. The median of an ungrouped data and the median calculated when the same data is grouped are always the same. Do you think that this is a correct statement ? Give reason.
Answer» Question 01. The median of an ungrouped data and the median calculated when the same data is grouped are always the same. Do you think that this is a correct statement ? Give reason.

Discussion

35.	Write whether the following statemensst are true or false .Justify your answers : 1.Every quadratic equation has at least one real root 2.If in a quadratic equation of ,the coeffecient of x is zero then the quadratic equation has no real roots . 3.If the coeffecient of x2 and the constant term of the quadratic equation have opposite signs ,then the quadratic equation has real roots . 4.A quadratic equation with integeral coeffecient has integral roots.
Answer» Write whether the following statemensst are true or false .Justify your answers : 1.Every quadratic equation has at least one real root 2.If in a quadratic equation of ,the coeffecient of x is zero then the quadratic equation has no real roots . 3.If the coeffecient of x2 and the constant term of the quadratic equation have opposite signs ,then the quadratic equation has real roots . 4.A quadratic equation with integeral coeffecient has integral roots.

35.

Write whether the following statemensst are true or false .Justify your answers : 1.Every quadratic equation has at least one real root 2.If in a quadratic equation of ,the coeffecient of x is zero then the quadratic equation has no real roots . 3.If the coeffecient of x2 and the constant term of the quadratic equation have opposite signs ,then the quadratic equation has real roots . 4.A quadratic equation with integeral coeffecient has integral roots.

Answer»

Write whether the following statemensst are true or false .Justify your answers :

1.Every quadratic equation has at least one real root

2.If in a quadratic equation of ,the coeffecient of x is zero then the quadratic equation has no real roots .

3.If the coeffecient of x2 and the constant term of the quadratic equation have opposite signs ,then the quadratic equation has real roots .

4.A quadratic equation with integeral coeffecient has integral roots.

Discussion

36.	Express 3825 as the product of prime factors
Answer» Express 3825 as the product of prime factors

Discussion

37.

The following table gives the marks obtained by 50 students in a class test: Marks 11−15 16−20 21−25 26−30 31−35 36−40 41−45 46−50 Number of students 2 3 6 7 14 12 4 2 Calculate the mean, median and mode for the above data.

Answer»

The following table gives the marks obtained by 50 students in a class test:

Marks	11−15	16−20	21−25	26−30	31−35	36−40	41−45	46−50
Number of students	2	3	6	7	14	12	4	2

Calculate the mean, median and mode for the above data.

Discussion

38.	In the figure given below, AOB is a diameter of the circle and ∠ AOC=110∘. Find ∠ BDC.
Answer» In the figure given below, AOB is a diameter of the circle and $∠ A O C = 110^{\circ}$ . Find $∠ B D C$ .

38.

In the figure given below, AOB is a diameter of the circle and ∠ AOC=110∘. Find ∠ BDC.

Answer»

In the figure given below, AOB is a diameter of the circle and $∠ A O C = 110^{\circ}$ . Find $∠ B D C$ .

Discussion

39.	Water level in a cylinder raises by 16 cm when three spheres are dropped in it. If the ratio of the radii of the spheres is 1:2:3 and the radius of the cylinder is 6 cm, what is the volume (in cm3) of the smallest sphere?
Answer» Water level in a cylinder raises by 16 cm when three spheres are dropped in it. If the ratio of the radii of the spheres is 1:2:3 and the radius of the cylinder is 6 cm, what is the volume (in cm $^{3}$ ) of the smallest sphere?

Discussion

40.	If ∠A and ∠B are acute angles such that sinA = sinB, then prove that ∠A = ∠B.
Answer» If $∠$ A and $∠$ B are acute angles such that sinA = sinB, then prove that $∠$ A = $∠$ B.

Discussion

41.	If m times the mth term of an A.P. is eqaul to n times nth term then show that the (m + n)th term of the A.P. is zero.
Answer» If m times the m^th term of an A.P. is eqaul to n times n^th term then show that the (m + n)^thterm of the A.P. is zero.

Discussion

42.	A conical vessel of radius 6 cm and height 8 cm is completely filled with water. A sphere is lowered into the water and its size is such that when it touches the sides, it is just immersed. What fraction of water overflows?
Answer» A conical vessel of radius 6 cm and height 8 cm is completely filled with water. A sphere is lowered into the water and its size is such that when it touches the sides, it is just immersed. What fraction of water overflows?

Discussion

43.	The common zeroes of the polynomials x3+5x2−9x−45 and x3+8x2+15x are:
Answer» The common zeroes of the polynomials $x^{3} + 5 x^{2} - 9 x - 45$ and $x^{3} + 8 x^{2} + 15 x$ are:

Discussion

44.	If the sum of the zeros of the quadratic polynomial f (x)=kt^2 +2t + 3k is equal to their product, find the value of k
Answer» If the sum of the zeros of the quadratic polynomial f (x)=kt^2 +2t + 3k is equal to their product, find the value of k

Discussion

45.	The exact value of cosec 10°+ cosec 50° - cosec 70° is__________
Answer» The exact value of cosec 10°+ cosec 50° - cosec 70° is__________

Discussion

46.	Question 14A chord of a circle is equal to its radius. Find the angle subtended by this chord at a point in major segment.
Answer» Question 14 A chord of a circle is equal to its radius. Find the angle subtended by this chord at a point in major segment.

Discussion

47.	A cylinder and a cone have equal bases. The height of the cylinder is 3 cm and the area of its base is 100 cm2 .The cone is placedupon the cylinder. Volume of the solid figure so formed is 500 cm3 . Find the total height of the figure.
Answer» A cylinder and a cone have equal bases. The height of the cylinder is 3 cm and the area of its base is 100 cm² .The cone is placed upon the cylinder. Volume of the solid figure so formed is 500 cm³. Find the total height of the figure.

Discussion

48.	the length and breadth of a rec†an gular plate is measured as 20.0 cm and 10.0 cm respectively.the absolute error in its area is
Answer» the length and breadth of a rec†an gular plate is measured as 20.0 cm and 10.0 cm respectively.the absolute error in its area is

Discussion

49.	Naresh and Sukesh are partners with capitals of ₹ 3,00,000 each as on 31st March, 2019. Naresh had withdrawn ₹ 50,000 against capital on 1st October, 2018 and also ₹ 1,00,000 besides the drawings against capital. Sukesh also had drawings of ₹ 1,00,000.Interest on capital is to be allowed 10% p.a.Net profit for the year was ₹ 2,00,000, which is yet to be distributed.Pass the Journal entries for interest on capital and distribution of profit.
Answer» Naresh and Sukesh are partners with capitals of ₹ 3,00,000 each as on 31st March, 2019. Naresh had withdrawn ₹ 50,000 against capital on 1st October, 2018 and also ₹ 1,00,000 besides the drawings against capital. Sukesh also had drawings of ₹ 1,00,000. Interest on capital is to be allowed 10% p.a. Net profit for the year was ₹ 2,00,000, which is yet to be distributed. Pass the Journal entries for interest on capital and distribution of profit.

Discussion

50.	The value of m, if the points (5,1) (-2,-3), and (8,2m) are collinear is:
Answer» The value of m, if the points (5,1) (-2,-3), and (8,2m) are collinear is:

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

in triangle pqr if pq =qr and L,M and,N are the mid points of the sides PQ, QR and RP respectively thanprove that LN=MN

A rectangular courtyard is 20m 16cm long and 15m 60cm broad. It is to be paved with square stones of the same size. Find the least possible number of such stones.

Question 13 As observed from the top of a 75 m high lighthouse from the sea-level, the angles of depression of two ships are 30∘ and 45∘. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships.

Question 1 (vi)Find the roots of the quadratic equations by using the quadratic formula in the following question.x2−3√5x+10=0

Question 8From a solid cylinder whose height is 2.4 cm and diameter 1.4 cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid to the nearest cm2.

If x=-3 and x=23 are solutions of quadratic equation mx2+7x+n=0,find the values of m and n.

Nazama is a proprietor of a firm, registered under GST. She has paid GST of Rs 12,500 on purchase and collected Rs 14,750 on sale. What is the amount of ITC to be claimed ? What is the amount of GST payable ?

What rate gives ₹280 as interest on a sum of ₹ 56,000 in 2 years?

Find the ratio of the volumes of a cylinder, a cone and a sphere, if each has the same diameter and same height?

Find value of x,y in the below given pair of equation. 2x + 3y = 13 5x - 4y = -2

State SSS similarity criterion.

A man swims across a 400 m wide river flowing with a speed of 3 m/s , such that he reaches the point just in front on the bank in 100 s. The angle made by the direction he swims and river flow direction is:

The following real number has decimal expansion as given below. Decide whether rational or not. If rational, and of the form pq, what can you say about the prime factors of q? 43.123456789

what is E_2 elimination?

If π is taken as 227, the distance (in metres) covered by a wheel of diameter 35 cm, in one revolution, is(a) 2.2(b) 1.1(c) 9.625(d) 96.25

Samira has a recurring deposit account in a bank of RS.2000 per month at the rate of 10%p.a.If she gets RS.83100 at the time of maturity, find the total time for which the account was held.

Find the area of the triangle in the given figure.

3. Find the three consecutive numbers whose sum is 45.

In the given figure triangle ABC is circumscribed by a circle, AB =5 cm, ∠A=30∘,∠C=60∘. Find the length of side BC. [sin 60∘=0.86, sin 30∘=0.5]

In figure 3, APB and CQD are semi-circles of diameter 7 cm each, while ARC and BSD are semi - circles of diameter 14 cm each. Find the perimeter of the shaded region. [Use π =227] OR Find the area of a quadrant of a circle, where the circumference of circle is 44 cm.[Use π =227]

In Fig. 14.78, a circle is inscribed in a square ABCD and the square is circumscribed by a circle. If the radius of the smaller circle is r сm, then the area of the shaded region in cm2 is _________.

If S1 is the sum of an arithmetic progression of 'n' odd number of terms and S2 the sum of the terms of the series in odd places, then S1S2=(a) 2nn+1(b) nn+1(c) n+12n(d) n+1n

The length of a rectangular garden is 20m longer than its breadth.if its perimeter is 200m,find its length and breadth.

Harry walks from his house at A to his office at B, by taking the shortest path. Find the probability that he will take the highlighted path, given that he can move only Up or Right at every intersection of roads.

How many times the volume of a cone decreases if the radius of the base is reduced by half?

In the given figure, AX : XB = 3 : 5 and XY || BC. Then, the ratio of the areas of trapezium XBCY and triangle ABC is

Two tangents PA and PB are drawn from an external point P to a circle with centre O. Prove that AOBP is a cyclic quadrilateral.

Question 4 (iii)Which of the following pairs of linear equations are consistent/ inconsistent? If consistent, obtain the solution graphically:2x + y - 6 = 0, 4x - 2y - 4 = 0

For what values of 'k' will the equation x2 - 2x(k-1) + (k+1)=0 will have equal real roots?

The midpoint of the line segment A(2a, 4) and B(-2, 3b) is C(1, 2a+1). Find the values of a and b.

The length of a rectangle is three times the breadth. If the minimum perimeter of the rectangle is 160 cm, then

Question 01. The median of an ungrouped data and the median calculated when the same data is grouped are always the same. Do you think that this is a correct statement ? Give reason.

Express 3825 as the product of prime factors

The following table gives the marks obtained by 50 students in a class test: Marks 11−15 16−20 21−25 26−30 31−35 36−40 41−45 46−50 Number of students 2 3 6 7 14 12 4 2 Calculate the mean, median and mode for the above data.

In the figure given below, AOB is a diameter of the circle and ∠ AOC=110∘. Find ∠ BDC.

Water level in a cylinder raises by 16 cm when three spheres are dropped in it. If the ratio of the radii of the spheres is 1:2:3 and the radius of the cylinder is 6 cm, what is the volume (in cm3) of the smallest sphere?

If ∠A and ∠B are acute angles such that sinA = sinB, then prove that ∠A = ∠B.

If m times the mth term of an A.P. is eqaul to n times nth term then show that the (m + n)th term of the A.P. is zero.

A conical vessel of radius 6 cm and height 8 cm is completely filled with water. A sphere is lowered into the water and its size is such that when it touches the sides, it is just immersed. What fraction of water overflows?

The common zeroes of the polynomials x3+5x2−9x−45 and x3+8x2+15x are:

If the sum of the zeros of the quadratic polynomial f (x)=kt^2 +2t + 3k is equal to their product, find the value of k

The exact value of cosec 10°+ cosec 50° - cosec 70° is__________

Question 14A chord of a circle is equal to its radius. Find the angle subtended by this chord at a point in major segment.

A cylinder and a cone have equal bases. The height of the cylinder is 3 cm and the area of its base is 100 cm2 .The cone is placedupon the cylinder. Volume of the solid figure so formed is 500 cm3 . Find the total height of the figure.

the length and breadth of a rec†an gular plate is measured as 20.0 cm and 10.0 cm respectively.the absolute error in its area is

The value of m, if the points (5,1) (-2,-3), and (8,2m) are collinear is: