32581 + Interview Questions in Mathematics

1.	Question 3The list of numbers -10, -6, -2, 2, ... isA) an AP with d = - 16B) anAP with d = 4C) an AP with d = - 4D) not an AP
Answer» Question 3 The list of numbers -10, -6, -2, 2, ... is A) an AP with d = - 16 B) anAP with d = 4 C) an AP with d = - 4 D) not an AP

Discussion

2.

Using an appropriate method, find the mean of following frequency distribution: Class interval 84−90 90−96 96−102 102−108 108−114 114−120 Frequency 8 10 16 23 12 11 Which method did you use, and why?

Answer» Using an appropriate method, find the mean of following frequency distribution:

Class interval	84−90	90−96	96−102	102−108	108−114	114−120
Frequency	8	10	16	23	12	11

Which method did you use, and why?

Discussion

3.	Graphically represent the following pair of linear equation in two variable:y-2x-4=0 and2y=6x+12also find there solution.
Answer» Graphically represent the following pair of linear equation in two variable: y-2x-4=0 and 2y=6x+12 also find there solution.

Discussion

4.	From the top of a vertical tower, the angles of depression of two cars in the same straight line with the base of the tower, at an instant are found to be 45° and 60°. If the cars are 100 m apart and are on the same side of the tower, find the height of the tower. [CBSE 2011]
Answer» From the top of a vertical tower, the angles of depression of two cars in the same straight line with the base of the tower, at an instant are found to be 45° and 60°. If the cars are 100 m apart and are on the same side of the tower, find the height of the tower. [CBSE 2011]

Discussion

5.	Question 1 (i)Which of the following pairs of linear equations has a unique solution, no solution or infinitely many solutions? In case there is a unique solution, find it by using cross multiplication method.x - 3y - 3 = 0 ; 3x - 9y - 2 =0
Answer» Question 1 (i) Which of the following pairs of linear equations has a unique solution, no solution or infinitely many solutions? In case there is a unique solution, find it by using cross multiplication method. x - 3y - 3 = 0 ; 3x - 9y - 2 =0

Discussion

6.	If a quadratic polynomial f(x) is factorizable into linear distinct factors, then what is the total number of real and distinct zeros of f(x)?
Answer» If a quadratic polynomial f(x) is factorizable into linear distinct factors, then what is the total number of real and distinct zeros of f(x)?

Discussion

7.	A kite is flying at a height of 30 m above the ground. The string attached to the kite is temporarily tied to a point on the ground. The inclination of the string with the ground is 60∘. Find the length of the string, assuming that there is no slack in the string.
Answer» A kite is flying at a height of 30 m above the ground. The string attached to the kite is temporarily tied to a point on the ground. The inclination of the string with the ground is $60^{\circ}$ . Find the length of the string, assuming that there is no slack in the string.

Discussion

8.	In an A.P. the first term is 8, nth term is 33 and the sum to first n terms is 123. Find n and d, the common differences.
Answer» In an A.P. the first term is 8, nth term is 33 and the sum to first n terms is 123. Find n and d, the common differences.

Discussion

9.	The value of sin(12cos−145) is
Answer» The value of $sin (\frac{1}{2} {cos}^{- 1} \frac{4}{5})$ is

Discussion

10.	If a cone of radius 10 cm is divided into two parts by drawing a plane through the mid-point of its axis, parallel to its base. Compare the volumes of the two parts.
Answer» If a cone of radius 10 cm is divided into two parts by drawing a plane through the mid-point of its axis, parallel to its base. Compare the volumes of the two parts.

Discussion

11.	If α,β are the zeros of the polynomial x2+6x+2 then (1α+1β) = ? (a) 3 (b) -3 (c) 12 (d) -12
Answer» If $α, β$ are the zeros of the polynomial $x^{2} + 6 x + 2$ then $(\frac{1}{α} + \frac{1}{β})$ = ? (a) 3 (b) -3 (c) 12 (d) -12

11.

If α,β are the zeros of the polynomial x2+6x+2 then (1α+1β) = ? (a) 3 (b) -3 (c) 12 (d) -12

Answer»

If $α, β$ are the zeros of the polynomial $x^{2} + 6 x + 2$ then $(\frac{1}{α} + \frac{1}{β})$ = ?

(a) 3 (b) -3 (c) 12 (d) -12

Discussion

12.	Question 2Determine the mean of the following distributionMarksNumber of studentsBelow 10 5Below 20 9Below 30 17Below 40 29Below 50 45Below 60 60Below 70 70Below 80 78Below 90 83Below 100 85
Answer» Question 2 Determine the mean of the following distribution $\begin{matrix} M a r k s & N u m b e r o f s t u d e n t s B e l o w 10 & 5 B e l o w 20 & 9 B e l o w 30 & 17 B e l o w 40 & 29 B e l o w 50 & 45 B e l o w 60 & 60 B e l o w 70 & 70 B e l o w 80 & 78 B e l o w 90 & 83 B e l o w 100 & 85 \end{matrix}$

Discussion

13.	The value of k for which the quadratic equation x2+k(2x+k+1)+4=0 has real and equal roots is
Answer» The value of $k$ for which the quadratic equation $x^{2} + k (2 x + k + 1) + 4 = 0$ has real and equal roots is

Discussion

14.	For what value of n, 2n ✕ 5n ends in 5.
Answer» For what value of n, 2ⁿ ✕ 5ⁿ ends in 5.

Discussion

15.	The variance of a data is 121.If the A.M is 11 then the C.V is
Answer» The variance of a data is 121.If the A.M is 11 then the C.V is

Discussion

16.

Find the missing value of p for the following distribution whose mean is 12.58 x: 5 8 10 12 p 20 25 f: 2 5 8 22 7 4 2

Answer» Find the missing value of p for the following distribution whose mean is 12.58

x:	5	8	10	12	p	20	25
f:	2	5	8	22	7	4	2

Discussion

17.	If the mean of x1 and x2 is M1 and that of x1, x2, x3, x4 is M2, then the mean of ax1, ax2, x3a, x4a is _____.
Answer» If the mean of $x_{1}$ and $x_{2}$ is $M_{1}$ and that of $x_{1}, x_{2}, x_{3}, x_{4}$ is $M_{2}$ , then the mean of $a x_{1}, a x_{2}, \frac{x_{3}}{a}, \frac{x_{4}}{a}$ is _____.

Discussion

18.	If A = {8, 16, 24, 32}, B = {5, 25, 125} a R b means a < b, a ∈ A, b ∈ B, a R b ∈ (a, b), find the relation a R b.
Answer» If A = {8, 16, 24, 32}, B = {5, 25, 125} a R b means a < b, a $\in$ A, b $\in$ B, a R b $\in$ (a, b), find the relation a R b.

Discussion

19.	In a village, out of 60 couples, 15 couples were married at the age of 21 to 23, 25 couples were married at the age of 24 to 27 and 16 couples were married at the age of 28 to 30. The rest, after the age of 30. What is the probability that a couple gets married after the age of 30?
Answer» In a village, out of 60 couples, 15 couples were married at the age of 21 to 23, 25 couples were married at the age of 24 to 27 and 16 couples were married at the age of 28 to 30. The rest, after the age of 30. What is the probability that a couple gets married after the age of 30?

Discussion

20.	Question 92 (xxix)Factorise the following using the identity a2−b2=(a+b)(a−b).8a3−2a
Answer» Question 92 (xxix) Factorise the following using the identity $a^{2} - b^{2} = (a + b) (a - b) .$ $8 a^{3} - 2 a$

20.

Question 92 (xxix)Factorise the following using the identity a2−b2=(a+b)(a−b).8a3−2a

Answer»

Question 92 (xxix)

Factorise the following using the identity $a^{2} - b^{2} = (a + b) (a - b) .$

$8 a^{3} - 2 a$

Discussion

21.	Prove that for any value of q, line AB and CD are always perpendicular. Given : A = (2,6) , B = (q,3) C = (-6,4) , D = (0,2q)
Answer» Prove that for any value of q, line AB and CD are always perpendicular. Given : A = (2,6) , B = (q,3) C = (-6,4) , D = (0,2q)

Discussion

22.	Prove that the area of rhombus on the hypotenuse of a right angled triangle with one of the angle as 60° is equal to the sum of areas of rhombuses with one of their angles as 60°,drawn on the other two sides.
Answer» Prove that the area of rhombus on the hypotenuse of a right angled triangle with one of the angle as 60° is equal to the sum of areas of rhombuses with one of their angles as 60°,drawn on the other two sides.

Discussion

23.	if ratio of the height of the two right circular cones is 5:2 and that of their base radii is 2:5,then the ratio of their volumes is
Answer» if ratio of the height of the two right circular cones is 5:2 and that of their base radii is 2:5,then the ratio of their volumes is

Discussion

24.	Find all the zeros of the polynomial 2x3 + x2 − 6x − 3, if two of its zeros are -3 and 3.
Answer» Find all the zeros of the polynomial 2x³ + x² − 6x − 3, if two of its zeros are $- \sqrt{3} and \sqrt{3}$ .

Discussion

25.	The radius of a circle is 20 cm. Three more concentric circles are drawn inside it in such a manner that it is divided into four parts of equal area. Find the radius of the largest of the three concentric circle in cm.
Answer» The radius of a circle is 20 cm. Three more concentric circles are drawn inside it in such a manner that it is divided into four parts of equal area. Find the radius of the largest of the three concentric circle in cm.

Discussion

26.	ABC is an isosceles triangle with AB = AC and BD, CE are its two medians. Show that BD = CE.
Answer» ABC is an isosceles triangle with AB = AC and BD, CE are its two medians. Show that BD = CE.

Discussion

27.	Prove that √2 is irrational
Answer» Prove that √2 is irrational

Discussion

28.	Question 13The father’s age is six times his son’s age. Four years hence, the age of the father will be four times his son’s age. The present ages (in year) of the son and the father are respectively(A) 4 and 24(B) 5 and 30(C) 6 and 36(D) 3 and 24
Answer» Question 13 The father’s age is six times his son’s age. Four years hence, the age of the father will be four times his son’s age. The present ages (in year) of the son and the father are respectively (A) 4 and 24 (B) 5 and 30 (C) 6 and 36 (D) 3 and 24

Discussion

29.	The vertices of a parallelogram are (1, 2), (4, y), (x, 6) and (3, 5). What are the values of x and y?
Answer» The vertices of a parallelogram are (1, 2), (4, y), (x, 6) and (3, 5). What are the values of x and y?

Discussion

30.	The equation of a plane passing through the line of intersection of the planes x+2y+3z=2 and x−y+z=3 and at a distance 2√3 from the point (3,1,−1) is
Answer» The equation of a plane passing through the line of intersection of the planes $x + 2 y + 3 z = 2$ and $x - y + z = 3$ and at a distance $\frac{2}{\sqrt{3}}$ from the point $(3, 1, - 1)$ is

Discussion

31.	Solve each of the following quadratic equations:16x-1=15x+1, x≠0, -1 [CBSE 2014]
Answer» Solve each of the following quadratic equations: $\frac{16}{x} - 1 = \frac{15}{x + 1}, x \neq 0, - 1$ [CBSE 2014]

Discussion

32.	Question 4 (iv) Which of the following are APs? If they form an A.P. find the common difference d and write three more terms. (iv) -10, - 6, - 2, 2 …
Answer» Question 4 (iv) Which of the following are APs? If they form an A.P. find the common difference d and write three more terms. (iv) -10, - 6, - 2, 2 …

Discussion

33.	Equations of the lines through the point (3, 2) and making an angle of 45° with line x – 2y – 3 = 0 are __________.
Answer» Equations of the lines through the point (3, 2) and making an angle of 45° with line x – 2y – 3 = 0 are __________.

Discussion

34.	CosecA/cosecA-1+cosecA/cosecA+1=secA
Answer» CosecA/cosecA-1+cosecA/cosecA+1=secA

Discussion

35.	In the given figure, ACB is the largest triangle that can be inscribed in a semicircle of radius r. If two semicircles are drawn considering AC and BC as diameters, then the area of the shaded region is
Answer» In the given figure, $A C B$ is the largest triangle that can be inscribed in a semicircle of radius $r$ . If two semicircles are drawn considering $A C$ and $B C$ as diameters, then the area of the shaded region is

Discussion

36.	If the median of the following frequency distribution is 40 and total frequency is 60, then find the missing frequencies.Marks0−1010−3030−6060−8080−90Number of students5f130f22
Answer» If the median of the following frequency distribution is 40 and total frequency is 60, then find the missing frequencies. $\begin{matrix} Marks & 0 - 10 & 10 - 30 & 30 - 60 & 60 - 80 & 80 - 90 Number of students & 5 & f_{1} & 30 & f_{2} & 2 \end{matrix}$

Discussion

37.	Solve each of the following systems of equations by the method of cross-multiplication :2ax-by+a+4b=02bx+ay+b-4a=0
Answer» Solve each of the following systems of equations by the method of cross-multiplication : $2 (a x - b y) + a + 4 b = 0 2 (b x + a y) + b - 4 a = 0$

Discussion

38.	Two circle with centres O and O' are drawn to intersect each other at points A and B. Centre O of one circle lies on the circumference of the other circle and CD is drawn tangent to the circle with centre O' at A. Prove that OA bisects ∠BAC
Answer» Two circle with centres O and O' are drawn to intersect each other at points A and B. Centre O of one circle lies on the circumference of the other circle and CD is drawn tangent to the circle with centre O' at A. Prove that OA bisects $∠ B A C$

38.

Two circle with centres O and O' are drawn to intersect each other at points A and B. Centre O of one circle lies on the circumference of the other circle and CD is drawn tangent to the circle with centre O' at A. Prove that OA bisects ∠BAC

Answer»

Two circle with centres O and O' are drawn to intersect each other at points A and B.

Centre O of one circle lies on the circumference of the other circle and CD is drawn tangent to the circle with centre O' at A. Prove that OA bisects $∠ B A C$

Discussion

39.	Find the nature of the roots of the following quadratic equations:(i) 2x2-8x+5=0(ii) 3x2-26x+2=0(iii) 5x2-4x+1=0(iv) 5xx-2+6=0(v) 12x2-415x+5=0(vi) x2-x+2=0
Answer» Find the nature of the roots of the following quadratic equations: (i) $2 x^{2} - 8 x + 5 = 0$ (ii) $3 x^{2} - 2 \sqrt{6} x + 2 = 0$ (iii) $5 x^{2} - 4 x + 1 = 0$ (iv) $5 x (x - 2) + 6 = 0$ (v) $12 x^{2} - 4 \sqrt{15} x + 5 = 0$ (vi) $x^{2} - x + 2 = 0$

Discussion

40.	Identify the correct equation for the given line.
Answer» Identify the correct equation for the given line.

Discussion

41.	As shown in the given figure, two poles of height 8 m and 4 m are perpendicular to the ground. If the length of shadow of smaller pole due to sunlight is 6 m then how long will be the shadow of the bigger pole at the same time ?
Answer» As shown in the given figure, two poles of height 8 m and 4 m are perpendicular to the ground. If the length of shadow of smaller pole due to sunlight is 6 m then how long will be the shadow of the bigger pole at the same time ?

Discussion

42.	Question 5Is 0 a term of the AP 31, 28, 25, …? Justify your answer.
Answer» Question 5 Is 0 a term of the AP 31, 28, 25, …? Justify your answer.

Discussion

43.	The following table shows data during a 1hr exam for a student. Time during exam(mins) Total number of questions solved in the exam 0−10210−20520−301030−401540−501750−6025Which of the following graphs comes closest to depicting the correct value of the median?
Answer» The following table shows data during a 1hr exam for a student. $\begin{matrix} T i m e d u r i n g e x a m (m i n s) & T o t a l n u m b e r o f q u e s t i o n s s o l v e d i n t h e e x a m 0 - 10 & 2 10 - 20 & 5 20 - 30 & 10 30 - 40 & 15 40 - 50 & 17 50 - 60 & 25 \end{matrix}$ Which of the following graphs comes closest to depicting the correct value of the median?

43.

The following table shows data during a 1hr exam for a student. Time during exam(mins) Total number of questions solved in the exam 0−10210−20520−301030−401540−501750−6025Which of the following graphs comes closest to depicting the correct value of the median?

Answer»

The following table shows data during a 1hr exam for a student.

$\begin{matrix} T i m e d u r i n g e x a m (m i n s) & T o t a l n u m b e r o f q u e s t i o n s s o l v e d i n t h e e x a m 0 - 10 & 2 10 - 20 & 5 20 - 30 & 10 30 - 40 & 15 40 - 50 & 17 50 - 60 & 25 \end{matrix}$

Which of the following graphs comes closest to depicting the correct value of the median?

Discussion

44.	If,show that
Answer» If, show that

Discussion

45.	Two tangents PA and PB are drawn to a circle with center O from an external point P. Prove that ∠APB=2∠OAB [3 MARKS]
Answer» Two tangents PA and PB are drawn to a circle with center O from an external point P. Prove that $∠ A P B = 2 ∠ O A B$ [3 MARKS]

45.

Two tangents PA and PB are drawn to a circle with center O from an external point P. Prove that ∠APB=2∠OAB [3 MARKS]

Answer»

Two tangents PA and PB are drawn to a circle with center O from an external point P. Prove that $∠ A P B = 2 ∠ O A B$ [3 MARKS]

Discussion

46.	The radii of the circular ends of a solid frustum of a cone are 33 cm and 27 cm and its slant height is 10 cm. Find its total surface area.
Answer» The radii of the circular ends of a solid frustum of a cone are 33 cm and 27 cm and its slant height is 10 cm. Find its total surface area.

Discussion

47.	The point C(–1, 2) divides the lines segment AB in the ratio 3:4, where the coordinates of A are (2,5). The coordinates of B is:
Answer» The point $C (- 1, 2)$ divides the lines segment $A B$ in the ratio 3:4, where the coordinates of $A$ are $(2, 5)$ . The coordinates of $B$ is:

Discussion

48.	ABCD is a cyclic quadrilateral. The diagonals of the quadrilateral intetsect at right angles. Prove that the perpendicular drawn from their point of intersection to one side when extended bisects he other side a
Answer» ABCD is a cyclic quadrilateral. The diagonals of the quadrilateral intetsect at right angles. Prove that the perpendicular drawn from their point of intersection to one side when extended bisects he other side a

Discussion

49.	The angle between two tangents drawn from an external point to a circle is _______ to the angle subtended by the line segments joining the points of contact at the centre.
Answer» The angle between two tangents drawn from an external point to a circle is _______ to the angle subtended by the line segments joining the points of contact at the centre.

Discussion

50.	If p is a prime number then find the LCM of p,p2 and p3
Answer» If p is a prime number then find the LCM of p,p²and p³

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Question 3The list of numbers -10, -6, -2, 2, ... isA) an AP with d = - 16B) anAP with d = 4C) an AP with d = - 4D) not an AP

Using an appropriate method, find the mean of following frequency distribution: Class interval 84−90 90−96 96−102 102−108 108−114 114−120 Frequency 8 10 16 23 12 11 Which method did you use, and why?

Graphically represent the following pair of linear equation in two variable:y-2x-4=0 and2y=6x+12also find there solution.

From the top of a vertical tower, the angles of depression of two cars in the same straight line with the base of the tower, at an instant are found to be 45° and 60°. If the cars are 100 m apart and are on the same side of the tower, find the height of the tower. [CBSE 2011]

Question 1 (i)Which of the following pairs of linear equations has a unique solution, no solution or infinitely many solutions? In case there is a unique solution, find it by using cross multiplication method.x - 3y - 3 = 0 ; 3x - 9y - 2 =0

If a quadratic polynomial f(x) is factorizable into linear distinct factors, then what is the total number of real and distinct zeros of f(x)?

A kite is flying at a height of 30 m above the ground. The string attached to the kite is temporarily tied to a point on the ground. The inclination of the string with the ground is 60∘. Find the length of the string, assuming that there is no slack in the string.

In an A.P. the first term is 8, nth term is 33 and the sum to first n terms is 123. Find n and d, the common differences.

The value of sin(12cos−145) is

If a cone of radius 10 cm is divided into two parts by drawing a plane through the mid-point of its axis, parallel to its base. Compare the volumes of the two parts.

If α,β are the zeros of the polynomial x2+6x+2 then (1α+1β) = ? (a) 3 (b) -3 (c) 12 (d) -12

Question 2Determine the mean of the following distributionMarksNumber of studentsBelow 10 5Below 20 9Below 30 17Below 40 29Below 50 45Below 60 60Below 70 70Below 80 78Below 90 83Below 100 85

The value of k for which the quadratic equation x2+k(2x+k+1)+4=0 has real and equal roots is

For what value of n, 2n ✕ 5n ends in 5.

The variance of a data is 121.If the A.M is 11 then the C.V is

Find the missing value of p for the following distribution whose mean is 12.58 x: 5 8 10 12 p 20 25 f: 2 5 8 22 7 4 2

If the mean of x1 and x2 is M1 and that of x1, x2, x3, x4 is M2, then the mean of ax1, ax2, x3a, x4a is _____.

If A = {8, 16, 24, 32}, B = {5, 25, 125} a R b means a &lt; b, a ∈ A, b ∈ B, a R b ∈ (a, b), find the relation a R b.

In a village, out of 60 couples, 15 couples were married at the age of 21 to 23, 25 couples were married at the age of 24 to 27 and 16 couples were married at the age of 28 to 30. The rest, after the age of 30. What is the probability that a couple gets married after the age of 30?

Question 92 (xxix)Factorise the following using the identity a2−b2=(a+b)(a−b).8a3−2a

Prove that for any value of q, line AB and CD are always perpendicular. Given : A = (2,6) , B = (q,3) C = (-6,4) , D = (0,2q)

Prove that the area of rhombus on the hypotenuse of a right angled triangle with one of the angle as 60° is equal to the sum of areas of rhombuses with one of their angles as 60°,drawn on the other two sides.

if ratio of the height of the two right circular cones is 5:2 and that of their base radii is 2:5,then the ratio of their volumes is

Find all the zeros of the polynomial 2x3 + x2 − 6x − 3, if two of its zeros are -3 and 3.

The radius of a circle is 20 cm. Three more concentric circles are drawn inside it in such a manner that it is divided into four parts of equal area. Find the radius of the largest of the three concentric circle in cm.

ABC is an isosceles triangle with AB = AC and BD, CE are its two medians. Show that BD = CE.

Prove that √2 is irrational

Question 13The father’s age is six times his son’s age. Four years hence, the age of the father will be four times his son’s age. The present ages (in year) of the son and the father are respectively(A) 4 and 24(B) 5 and 30(C) 6 and 36(D) 3 and 24

The vertices of a parallelogram are (1, 2), (4, y), (x, 6) and (3, 5). What are the values of x and y?

The equation of a plane passing through the line of intersection of the planes x+2y+3z=2 and x−y+z=3 and at a distance 2√3 from the point (3,1,−1) is

Solve each of the following quadratic equations:16x-1=15x+1, x≠0, -1 [CBSE 2014]

Question 4 (iv) Which of the following are APs? If they form an A.P. find the common difference d and write three more terms. (iv) -10, - 6, - 2, 2 …

Equations of the lines through the point (3, 2) and making an angle of 45° with line x – 2y – 3 = 0 are __________.

CosecA/cosecA-1+cosecA/cosecA+1=secA

In the given figure, ACB is the largest triangle that can be inscribed in a semicircle of radius r. If two semicircles are drawn considering AC and BC as diameters, then the area of the shaded region is

If the median of the following frequency distribution is 40 and total frequency is 60, then find the missing frequencies.Marks0−1010−3030−6060−8080−90Number of students5f130f22

Solve each of the following systems of equations by the method of cross-multiplication :2ax-by+a+4b=02bx+ay+b-4a=0

Two circle with centres O and O' are drawn to intersect each other at points A and B. Centre O of one circle lies on the circumference of the other circle and CD is drawn tangent to the circle with centre O' at A. Prove that OA bisects ∠BAC

Find the nature of the roots of the following quadratic equations:(i) 2x2-8x+5=0(ii) 3x2-26x+2=0(iii) 5x2-4x+1=0(iv) 5xx-2+6=0(v) 12x2-415x+5=0(vi) x2-x+2=0

Identify the correct equation for the given line.

As shown in the given figure, two poles of height 8 m and 4 m are perpendicular to the ground. If the length of shadow of smaller pole due to sunlight is 6 m then how long will be the shadow of the bigger pole at the same time ?

Question 5Is 0 a term of the AP 31, 28, 25, …? Justify your answer.

The following table shows data during a 1hr exam for a student. Time during exam(mins) Total number of questions solved in the exam 0−10210−20520−301030−401540−501750−6025Which of the following graphs comes closest to depicting the correct value of the median?

If,show that

Two tangents PA and PB are drawn to a circle with center O from an external point P. Prove that ∠APB=2∠OAB [3 MARKS]

The radii of the circular ends of a solid frustum of a cone are 33 cm and 27 cm and its slant height is 10 cm. Find its total surface area.

The point C(–1, 2) divides the lines segment AB in the ratio 3:4, where the coordinates of A are (2,5). The coordinates of B is:

ABCD is a cyclic quadrilateral. The diagonals of the quadrilateral intetsect at right angles. Prove that the perpendicular drawn from their point of intersection to one side when extended bisects he other side a

The angle between two tangents drawn from an external point to a circle is _______ to the angle subtended by the line segments joining the points of contact at the centre.

If p is a prime number then find the LCM of p,p​​​​​​2 and p​​​​​​3

If A = {8, 16, 24, 32}, B = {5, 25, 125} a R b means a < b, a ∈ A, b ∈ B, a R b ∈ (a, b), find the relation a R b.

If p is a prime number then find the LCM of p,p2 and p3