32581 + Interview Questions in Mathematics

1.	P and Q are points on the sides AB and AC respectively of △ABC such that PQ \|\| BC and divides △ABC into two parts, equal in area. Find PB : AB.
Answer» P and Q are points on the sides AB and AC respectively of $△$ ABC such that PQ \|\| BC and divides $△$ ABC into two parts, equal in area. Find PB : AB.

Discussion

2.	The value of the expression 16x2+24x+9 for x=0 is _____.
Answer» The value of the expression $16 x^{2} + 24 x + 9$ for $x = 0$ is _____.

Discussion

3.	XYZ Ltd. invited applications for 10,000 shares of ₹ 100 each payable as follows:₹ 20 on application, ₹ 30 on allotment, ₹ 20 on first call and the balance on final call.All the shares were applied and allotted. All the money was duly received.You are required to journalise these transactions.
Answer» XYZ Ltd. invited applications for 10,000 shares of ₹ 100 each payable as follows: ₹ 20 on application, ₹ 30 on allotment, ₹ 20 on first call and the balance on final call. All the shares were applied and allotted. All the money was duly received. You are required to journalise these transactions.

Discussion

4.	Prove that cot °+ √1-cos° by 1+cos° =cosec°
Answer» Prove that cot °+ √1-cos° by 1+cos° =cosec°

Discussion

5.	What value of k, 2k-1, 7 and 3K will form an AP.
Answer» What value of k, 2k-1, 7 and 3K will form an AP.

Discussion

6.	The ends of the hypotenuse of a right angled triangle are (5, 0) and (0, 5), then find the locus of third vertexof triangle.
Answer» The ends of the hypotenuse of a right angled triangle are (5, 0) and (0, 5), then find the locus of third vertex of triangle.

Discussion

7.	Fill In The Blanks Two congruent circle with centres O and O' intesect at two points P and Q. then then, ∠POQ :∠PO'Q = ____________.
Answer» Fill In The Blanks Two congruent circle with centres O and O' intesect at two points P and Q. then then, ∠POQ :∠PO'Q = ____________.

Discussion

8.	Choose the correct formula used to verify division.
Answer» Choose the correct formula used to verify division.

Discussion

9.	The distance of the point P(−2,3,−4) from the line x+23=2y+34=3z+45 measured parallel to the plane 4x+12y−3z+1=0 is d. Then the value of 2d−8 is
Answer» The distance of the point $P (- 2, 3, - 4)$ from the line $\frac{x + 2}{3} = \frac{2 y + 3}{4} = \frac{3 z + 4}{5}$ measured parallel to the plane $4 x + 12 y - 3 z + 1 = 0$ is $d .$ Then the value of $2 d - 8$ is

Discussion

10.	Sunshine Ltd. issued 20,000 shares of ₹ 100 each payable ₹ 25 per share on application , ₹ 25 per share on allotment and the balance in two calls of ₹ 25 each. The company did not make the final call of ₹ 25 per share. All the money was duly received with the exception of the amount due on the first call on 400 shares held by Mr. Modi. The Board of Directors forfeited these shares and subsequently reissued them ₹ 75 per share paid-up for a sum of ₹ 28,000.Journalise the above transactions and prepare Share Capital Account.
Answer» Sunshine Ltd. issued 20,000 shares of ₹ 100 each payable ₹ 25 per share on application , ₹ 25 per share on allotment and the balance in two calls of ₹ 25 each. The company did not make the final call of ₹ 25 per share. All the money was duly received with the exception of the amount due on the first call on 400 shares held by Mr. Modi. The Board of Directors forfeited these shares and subsequently reissued them ₹ 75 per share paid-up for a sum of ₹ 28,000. Journalise the above transactions and prepare Share Capital Account.

Discussion

11.	the number of all five digit numbers which are divisible by 4 that can be formed from the digits 0,1,2,3,4 (without repetition) is
Answer» the number of all five digit numbers which are divisible by 4 that can be formed from the digits 0,1,2,3,4 (without repetition) is

Discussion

12.	Two cards are drawn at random in succession with replacement from a deck of 52 well shuffled card. What is the probability of getting both 'Aces'?
Answer» Two cards are drawn at random in succession with replacement from a deck of 52 well shuffled card. What is the probability of getting both 'Aces'?

Discussion

13.	Which of the following is/are the solution(s) of the inequality 1(x\|−3≥12?
Answer» Which of the following is/are the solution(s) of the inequality $\frac{1}{(x \| - 3} \geq \frac{1}{2}$ ?

Discussion

14.	Question 5 (ix)Prove the following identities, where the angles involved are acute angles for which the expressions are defined.(ix) (cosecA−sinA)(secA−cosA)=1(tanA+cotA)[Hint : Simplify L.H.S and R.H.S separately]
Answer» Question 5 (ix) Prove the following identities, where the angles involved are acute angles for which the expressions are defined. $(i x) (c o s e c A - s i n A) (s e c A - c o s A) = \frac{1}{(t a n A + c o t A)}$ [Hint : Simplify L.H.S and R.H.S separately]

Discussion

15.	Solve the following inequation and write the solution set :13x - 5 < 15x + 4 < 7x + 12, x is a member of real number
Answer» Solve the following inequation and write the solution set : 13x - 5 < 15x + 4 < 7x + 12, x is a member of real number

Discussion

16.	Figure 15.18 shows a sector of a circle of radius r cm containing an angle θ°. The area of the sector is A cm2 and perimeter of the sector is 50 cm. Prove that(i) θ = 360θ25r-1(ii) A = 25r − r2
Answer» Figure 15.18 shows a sector of a circle of radius r cm containing an angle $θ °$ . The area of the sector is A cm² and perimeter of the sector is 50 cm. Prove that (i) $θ = \frac{360}{θ} (\frac{25}{r} - 1)$ (ii) A = 25r − r²

Discussion

17.	Question 58For fixed time period and rate of interest, the simple interest is directly proportional to the principal.
Answer» Question 58 For fixed time period and rate of interest, the simple interest is directly proportional to the principal.

17.

Question 58For fixed time period and rate of interest, the simple interest is directly proportional to the principal.

Answer»

Question 58

For fixed time period and rate of interest, the simple interest is directly proportional to the principal.

Discussion

18.	Question 18 State whether the given statement is true (T) or false (F). 0.2:5=2:0.5
Answer» Question 18 State whether the given statement is true (T) or false (F). $0.2 : 5 = 2 : 0.5$

18.

Question 18 State whether the given statement is true (T) or false (F). 0.2:5=2:0.5

Answer»

Question 18

State whether the given statement is true (T) or false (F).

$0.2 : 5 = 2 : 0.5$

Discussion

19.	In the figure below, ABC is a triangle, AC and BC are tangents to the circle of center O at two different points. The lengths of AM, AR and BC are equal to 6 cm, 12 cm and 18 cm respectively. Find the radius of the circle.
Answer» In the figure below, ABC is a triangle, AC and BC are tangents to the circle of center O at two different points. The lengths of AM, AR and BC are equal to 6 cm, 12 cm and 18 cm respectively. Find the radius of the circle.

19.

In the figure below, ABC is a triangle, AC and BC are tangents to the circle of center O at two different points. The lengths of AM, AR and BC are equal to 6 cm, 12 cm and 18 cm respectively. Find the radius of the circle.

Answer»

In the figure below, ABC is a triangle, AC and BC are tangents to the circle of center O at two different points. The lengths of AM, AR and BC are equal to 6 cm, 12 cm and 18 cm respectively. Find the radius of the circle.

Discussion

20.	find the perimeter of the triangle whose vertices are (\surd2,\surd3) , ( -\surd2,-\surd3) and (0,2)
Answer» find the perimeter of the triangle whose vertices are (\surd2,\surd3) , ( -\surd2,-\surd3) and (0,2)

Discussion

21.	How many people are there between D and C?
Answer» How many people are there between D and C?

Discussion

22.	If a and b are the zeroes of x2 -p(x+1)+c such that (a+1)(b+1)=0, then find the value of c
Answer» If a and b are the zeroes of x²-p(x+1)+c such that (a+1)(b+1)=0, then find the value of c

Discussion

23.	Question 1(ii) Check whether the following are quadratic equations: (ii)x2−2x=(−2)(3−x)
Answer» Question 1(ii) Check whether the following are quadratic equations: $(i i) x^{2} - 2 x = (- 2) (3 - x)$

Discussion

24.

Pass Journal entries in the books of Hari Shankar & Co. from the following: 2017 ₹ April 1 Commenced business with cash 50,000 2 Purchased goods from Subhash 20,000 4 Sold goods to Ramnath 15,000 6 Ramnath returned defective goods 1,000 10 Received cash from Ramnath and 13,800 Discount allowed 200 12 Gopal sold goods to us 10,000 14 Paid to Gopal in full settlement of his account after deducting 5% discount. 15 Paid Rent 10,000 16 Paid Rent of Hari Shankar's residence 5,000 18 Purchased goods for cash from Govind for ₹ 6,000 at 20% trade discount. 20 Purchased goods from Govind for ₹ 10,000 at 20% trade discount. 24 Paid to Govind ₹ 7,850 in full settlement of his account. 25 Paid to Subhash ₹ 4,750; discount received ₹ 250. 30 Paid Wages ₹ 400; Salaries ₹ 4,000; Advertisement expenses ₹ 800 and Trade expenses ₹ 1,000.

Answer» Pass Journal entries in the books of Hari Shankar & Co. from the following:

2017		₹
April 1	Commenced business with cash	50,000
2	Purchased goods from Subhash	20,000
4	Sold goods to Ramnath	15,000
6	Ramnath returned defective goods	1,000
10	Received cash from Ramnath and	13,800
	Discount allowed	200
12	Gopal sold goods to us	10,000
14	Paid to Gopal in full settlement of his account after deducting 5% discount.
15	Paid Rent	10,000
16	Paid Rent of Hari Shankar's residence	5,000
18	Purchased goods for cash from Govind for ₹ 6,000 at 20% trade discount.
20	Purchased goods from Govind for ₹ 10,000 at 20% trade discount.
24	Paid to Govind ₹ 7,850 in full settlement of his account.
25	Paid to Subhash ₹ 4,750; discount received ₹ 250.
30	Paid Wages ₹ 400; Salaries ₹ 4,000; Advertisement expenses ₹ 800 and Trade expenses ₹ 1,000.

Discussion

25.	{ 17. If the }10 th term of an }AP is }52 and the }17 th term is }20 more than the }13 th }} term, find the AP.
Answer» { 17. If the }10 th term of an }AP is }52 and the }17 th term is }20 more than the }13 th }} term, find the AP.

Discussion

26.	The ogive curve for less than type is a plot of
Answer» The ogive curve for less than type is a plot of

Discussion

27.	There is a circle on the coordinate plane with two tangent lines x - y = 3 and x - y = 0. The points of contacts of the lines with the circle are (32,32) and (0,- 3). Find the radius and the center of the circle.
Answer» There is a circle on the coordinate plane with two tangent lines x - y = 3 and x - y = 0. The points of contacts of the lines with the circle are ( $\frac{3}{2}$ , $\frac{3}{2}$ ) and (0,- 3). Find the radius and the center of the circle.

Discussion

28.	In a class of 58 students, 20 follow cricket, 38 follow hockey and 15 follow basketball. Three students follow all the three games. How many students follow exactly two of these three games? ___
Answer» In a class of 58 students, 20 follow cricket, 38 follow hockey and 15 follow basketball. Three students follow all the three games. How many students follow exactly two of these three games? ___

Discussion

29.	Find the value of k for which the following system of equations has a unique solution:5x-7y-5=02x+ky-1=0
Answer» Find the value of k for which the following system of equations has a unique solution: $5 x - 7 y - 5 = 0 2 x + k y - 1 = 0$

Discussion

30.	The sum of 0.3¯ and 0.4¯ is(a) 710(b) 79(c) 711(d) 799
Answer» The sum of $0 . \bar{3} and 0 . \bar{4}$ is (a) $\frac{7}{10}$ (b) $\frac{7}{9}$ (c) $\frac{7}{11}$ (d) $\frac{7}{99}$

Discussion

31.	A circus tent consist of a cylindrical base and a conical roof mounted on it. The radius of the cylinder is 40 m. The total height of the tent is 65 m and that of the cone is 30 m. Find the volume of the tent and the area of the cloth used for making it.
Answer» A circus tent consist of a cylindrical base and a conical roof mounted on it. The radius of the cylinder is 40 m. The total height of the tent is 65 m and that of the cone is 30 m. Find the volume of the tent and the area of the cloth used for making it.

Discussion

32.	The sum of first q terms of an A.P. is 63q − 3q2. If its pth term is −60, find the value of p. Also, find the 11th term of this A.P.
Answer» The sum of first q terms of an A.P. is 63q − 3q². If its pth term is −60, find the value of p. Also, find the 11th term of this A.P.

Discussion

33.	A boat goes 24 km upstream and 28 km downstream in 6 hrs. It goes 30 km upstream and 21 km downstream in 612 hrs. Find the speed of the boat in still water and also speed of the stream.
Answer» A boat goes 24 km upstream and 28 km downstream in 6 hrs. It goes 30 km upstream and 21 km downstream in $6 \frac{1}{2} hrs$ . Find the speed of the boat in still water and also speed of the stream.

Discussion

34.	A man 1.75 metres tall, standing at the foot of a tower sees the top of a hill 40 metres away at an elevation of 60°. On climbing to the top of the tower, he sees the top of the hill at an elevation of 50°. Compute the heights of the hill and the tower.
Answer» A man 1.75 metres tall, standing at the foot of a tower sees the top of a hill 40 metres away at an elevation of 60°. On climbing to the top of the tower, he sees the top of the hill at an elevation of 50°. Compute the heights of the hill and the tower.

Discussion

35.	22. Prove that why the remainder is always less than divisor in Euclid Division Lemma?
Answer» 22. Prove that why the remainder is always less than divisor in Euclid Division Lemma?

Discussion

36.	Question 5 In ΔPQR and ΔMST,∠P=55∘,∠Q=25∘,∠M=100∘ and ∠S=25∘.Is ΔQPR∼ΔTSM? Why?
Answer» Question 5 $I n Δ P Q R a n d Δ M S T, ∠ P = 55^{\circ}, ∠ Q = 25^{\circ}, ∠ M = 100^{\circ} a n d ∠ S = 25^{\circ} . I s Δ Q P R \sim Δ T S M ? W h y ?$

Discussion

37.	A hemispherical bowl fits exactly on the flat surface of a right circular cone whose height is 5 cm and radius is 3.5 cm. Find the volume of the solid formed.
Answer» A hemispherical bowl fits exactly on the flat surface of a right circular cone whose height is 5 cm and radius is 3.5 cm. Find the volume of the solid formed.

Discussion

38.	The incomes of X and Y are in the ratio of 8 : 7 and their expenditures are in the ratio 19 : 16. If each saves Rs 1250, find their incomes.
Answer» The incomes of X and Y are in the ratio of 8 : 7 and their expenditures are in the ratio 19 : 16. If each saves Rs 1250, find their incomes.

Discussion

39.	In triangle PQR, PM is perpendicular to RQ and N is a point on PM. Which of the following relations holds good?
Answer» In triangle PQR, PM is perpendicular to RQ and N is a point on PM. Which of the following relations holds good?

Discussion

40.	In the given figure, PS is a tangent and line PR is a secant to the circle. If PQ = 4.9 cm and QR = 5.1 cm, find the value of PS .
Answer» In the given figure, PS is a tangent and line PR is a secant to the circle. If PQ = 4.9 cm and QR = 5.1 cm, find the value of PS .

Discussion

41.	The ΔPQR is inscribed in the circle x2+y2=25 .If Q and R have coordiantes (3,4) and (-4,3) respectively,then ∠QPR is equal to
Answer» The $Δ P Q R$ is inscribed in the circle $x^{2} + y^{2} = 25$ .If Q and R have coordiantes (3,4) and (-4,3) respectively,then $∠ Q P R$ is equal to

Discussion

42.	Match the following:Column AColumn B1. {x: x ∈ R, -5 < x ≤ 15 } a. 1 2. A = ϕ, then the power set P(A) has ––––––elements b.8 3. Universal set of Rational Numbers & Irrational Numbersc.Real Numbers4. No. of elements in Power Set of A={a,b,c} d.Integers e.(−5,15] f.[−5,15)
Answer» Match the following: $\begin{matrix} Column A & Column B 1. {x: x \in R, -5 < x \leq 15 } & a. 1 2. A = ϕ, then the power set P(A) has - ---- - elements & b . 8 3. Universal set of Rational Numbers & Irrational Numbers & c . Real Numbers 4. No. of elements in Power Set of A = {a, b, c} & d . Integers e . (- 5, 15] f . [- 5, 15) \end{matrix}$

42.

Match the following:Column AColumn B1. {x: x ∈ R, -5 < x ≤ 15 } a. 1 2. A = ϕ, then the power set P(A) has ––––––elements b.8 3. Universal set of Rational Numbers & Irrational Numbersc.Real Numbers4. No. of elements in Power Set of A={a,b,c} d.Integers e.(−5,15] f.[−5,15)

Answer»

Match the following:

$\begin{matrix} Column A & Column B 1. {x: x \in R, -5 < x \leq 15 } & a. 1 2. A = ϕ, then the power set P(A) has - ---- - elements & b . 8 3. Universal set of Rational Numbers & Irrational Numbers & c . Real Numbers 4. No. of elements in Power Set of A = {a, b, c} & d . Integers e . (- 5, 15] f . [- 5, 15) \end{matrix}$

Discussion

43.	The angles of depression of the top and the bottom of a 10 m tall building from the top of a multi-storeyed building are 30∘ and 45∘, respectively. Find the height of the multi-storeyed building.
Answer» The angles of depression of the top and the bottom of a 10 m tall building from the top of a multi-storeyed building are $30^{\circ}$ and $45^{\circ}$ , respectively. Find the height of the multi-storeyed building.

Discussion

44.	Cardinal number of the set A = {x : x is an even prime number} is ____ .
Answer» Cardinal number of the set A = {x : x is an even prime number} is ____ .

Discussion

45.	A car moves north with a speed of 20ms−1. It changes its direction to east and moves with a speed of 20ms−1. What is its velocity now ?
Answer» A car moves north with a speed of $20 m s^{- 1}$ . It changes its direction to east and moves with a speed of $20 m s^{- 1}$ . What is its velocity now ?

Discussion

46.	The sum of the digits of a two-digit number is 9. If 27 is added to it, the digits of the number get reversed, then find the number.
Answer» The sum of the digits of a two-digit number is 9. If 27 is added to it, the digits of the number get reversed, then find the number.

Discussion

47.	In ∆ABC, AL and CM are the perpendiculars from the vertices A and C to BC and AB respectively. If AL and CM intersect at O, prove that:(i) ∆OMA ∼ ∆OLC(ii) OAOC=OMOL
Answer» In ∆ABC, AL and CM are the perpendiculars from the vertices A and C to BC and AB respectively. If AL and CM intersect at O, prove that: (i) ∆OMA ∼ ∆OLC (ii) $\frac{OA}{OC} = \frac{OM}{OL}$

Discussion

48.	Prove the following trigonometric identities: sec A(1−sin A)(sec A+tan A)=1
Answer» Prove the following trigonometric identities: $s e c A (1 - s i n A) (s e c A + t a n A) = 1$

48.

Prove the following trigonometric identities: sec A(1−sin A)(sec A+tan A)=1

Answer»

Prove the following trigonometric identities:

$s e c A (1 - s i n A) (s e c A + t a n A) = 1$

Discussion

49.	A selling agent gets Rs 10,200 in a month. This includes his monthly salary of Rs 6000 and 6% commission for the sales. Find the value of goods he sold.
Answer» A selling agent gets Rs 10,200 in a month. This includes his monthly salary of Rs 6000 and 6% commission for the sales. Find the value of goods he sold.

Discussion

50.	Question 1The sum of the first five terms of an AP and the sum of the first seven terms of the same AP is 167. If the sum of the first ten terms of this AP is 235, find the sum of its first twenty terms.
Answer» Question 1 The sum of the first five terms of an AP and the sum of the first seven terms of the same AP is 167. If the sum of the first ten terms of this AP is 235, find the sum of its first twenty terms.

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

P and Q are points on the sides AB and AC respectively of △ABC such that PQ || BC and divides △ABC into two parts, equal in area. Find PB : AB.

The value of the expression 16x2+24x+9 for x=0 is _____.

Prove that cot °+ √1-cos° by 1+cos° =cosec°

What value of k, 2k-1, 7 and 3K will form an AP.

The ends of the hypotenuse of a right angled triangle are (5, 0) and (0, 5), then find the locus of third vertexof triangle.

Fill In The Blanks Two congruent circle with centres O and O' intesect at two points P and Q. then then, ∠POQ :∠PO'Q = ____________.

Choose the correct formula used to verify division.

The distance of the point P(−2,3,−4) from the line x+23=2y+34=3z+45 measured parallel to the plane 4x+12y−3z+1=0 is d. Then the value of 2d−8 is

the number of all five digit numbers which are divisible by 4 that can be formed from the digits 0,1,2,3,4 (without repetition) is

Two cards are drawn at random in succession with replacement from a deck of 52 well shuffled card. What is the probability of getting both 'Aces'?

Which of the following is/are the solution(s) of the inequality 1(x|−3≥12?

Question 5 (ix)Prove the following identities, where the angles involved are acute angles for which the expressions are defined.(ix) (cosecA−sinA)(secA−cosA)=1(tanA+cotA)[Hint : Simplify L.H.S and R.H.S separately]

Solve the following inequation and write the solution set :13x - 5 < 15x + 4 < 7x + 12, x is a member of real number

Figure 15.18 shows a sector of a circle of radius r cm containing an angle θ°. The area of the sector is A cm2 and perimeter of the sector is 50 cm. Prove that(i) θ = 360θ25r-1(ii) A = 25r − r2

Question 58For fixed time period and rate of interest, the simple interest is directly proportional to the principal.

Question 18 State whether the given statement is true (T) or false (F). 0.2:5=2:0.5

In the figure below, ABC is a triangle, AC and BC are tangents to the circle of center O at two different points. The lengths of AM, AR and BC are equal to 6 cm, 12 cm and 18 cm respectively. Find the radius of the circle.

find the perimeter of the triangle whose vertices are (\surd2,\surd3) , ( -\surd2,-\surd3) and (0,2)

How many people are there between D and C?

If a and b are the zeroes of x​​​​​​2 -p(x+1)+c such that (a+1)(b+1)=0, then find the value of c

Question 1(ii) Check whether the following are quadratic equations: (ii)x2−2x=(−2)(3−x)

{ 17. If the }10 th term of an }AP is }52 and the }17 th term is }20 more than the }13 th }} term, find the AP.

The ogive curve for less than type is a plot of

There is a circle on the coordinate plane with two tangent lines x - y = 3 and x - y = 0. The points of contacts of the lines with the circle are (32,32) and (0,- 3). Find the radius and the center of the circle.

In a class of 58 students, 20 follow cricket, 38 follow hockey and 15 follow basketball. Three students follow all the three games. How many students follow exactly two of these three games? ___

Find the value of k for which the following system of equations has a unique solution:5x-7y-5=02x+ky-1=0

The sum of 0.3¯ and 0.4¯ is(a) 710(b) 79(c) 711(d) 799

A circus tent consist of a cylindrical base and a conical roof mounted on it. The radius of the cylinder is 40 m. The total height of the tent is 65 m and that of the cone is 30 m. Find the volume of the tent and the area of the cloth used for making it.

The sum of first q terms of an A.P. is 63q − 3q2. If its pth term is −60, find the value of p. Also, find the 11th term of this A.P.

A boat goes 24 km upstream and 28 km downstream in 6 hrs. It goes 30 km upstream and 21 km downstream in 612 hrs. Find the speed of the boat in still water and also speed of the stream.

A man 1.75 metres tall, standing at the foot of a tower sees the top of a hill 40 metres away at an elevation of 60°. On climbing to the top of the tower, he sees the top of the hill at an elevation of 50°. Compute the heights of the hill and the tower.

22. Prove that why the remainder is always less than divisor in Euclid Division Lemma?

Question 5 In ΔPQR and ΔMST,∠P=55∘,∠Q=25∘,∠M=100∘ and ∠S=25∘.Is ΔQPR∼ΔTSM? Why?

A hemispherical bowl fits exactly on the flat surface of a right circular cone whose height is 5 cm and radius is 3.5 cm. Find the volume of the solid formed.

The incomes of X and Y are in the ratio of 8 : 7 and their expenditures are in the ratio 19 : 16. If each saves Rs 1250, find their incomes.

In triangle PQR, PM is perpendicular to RQ and N is a point on PM. Which of the following relations holds good?

In the given figure, PS is a tangent and line PR is a secant to the circle. If PQ = 4.9 cm and QR = 5.1 cm, find the value of PS .

The ΔPQR is inscribed in the circle x2+y2=25 .If Q and R have coordiantes (3,4) and (-4,3) respectively,then ∠QPR is equal to

The angles of depression of the top and the bottom of a 10 m tall building from the top of a multi-storeyed building are 30∘ and 45∘, respectively. Find the height of the multi-storeyed building.

Cardinal number of the set A = {x : x is an even prime number} is ____ .

A car moves north with a speed of 20ms−1. It changes its direction to east and moves with a speed of 20ms−1. What is its velocity now ?

The sum of the digits of a two-digit number is 9. If 27 is added to it, the digits of the number get reversed, then find the number.

In ∆ABC, AL and CM are the perpendiculars from the vertices A and C to BC and AB respectively. If AL and CM intersect at O, prove that:(i) ∆OMA ∼ ∆OLC(ii) OAOC=OMOL

Prove the following trigonometric identities: sec A(1−sin A)(sec A+tan A)=1

A selling agent gets Rs 10,200 in a month. This includes his monthly salary of Rs 6000 and 6% commission for the sales. Find the value of goods he sold.

Question 1The sum of the first five terms of an AP and the sum of the first seven terms of the same AP is 167. If the sum of the first ten terms of this AP is 235, find the sum of its first twenty terms.

If a and b are the zeroes of x2 -p(x+1)+c such that (a+1)(b+1)=0, then find the value of c