32581 + Interview Questions in Mathematics

1.	Let x and y be two positive integers which satisfy the following two relations : (a) x^2 = y^3 (b) x = 2y The value of x + y is
Answer» Let x and y be two positive integers which satisfy the following two relations : (a) x^2 = y^3 (b) x = 2y The value of x + y is

Discussion

2.	Solve the differential equations - dy/dx = log x
Answer» Solve the differential equations - dy/dx = log x

Discussion

3.	Match the object in Column A to formulae in Column B. Choose the Option with correct matches.AB1. Surface area of cone1. 4πr22. Surface area of sphere2. 2πrh3. curved surface area of cylinder3. πrL
Answer» Match the object in Column A to formulae in Column B. Choose the Option with correct matches. $\begin{matrix} A & B 1. S u r f a c e a r e a o f c o n e & 1. 4 π r^{2} 2. S u r f a c e a r e a o f s p h e r e & 2. 2 π r h 3. c u r v e d s u r f a c e a r e a o f c y l i n d e r & 3. π r L \end{matrix}$

3.

Match the object in Column A to formulae in Column B. Choose the Option with correct matches.AB1. Surface area of cone1. 4πr22. Surface area of sphere2. 2πrh3. curved surface area of cylinder3. πrL

Answer»

Match the object in Column A to formulae in Column B. Choose the Option with correct matches.

$\begin{matrix} A & B 1. S u r f a c e a r e a o f c o n e & 1. 4 π r^{2} 2. S u r f a c e a r e a o f s p h e r e & 2. 2 π r h 3. c u r v e d s u r f a c e a r e a o f c y l i n d e r & 3. π r L \end{matrix}$

Discussion

4.

A, B and C are sharing profits and losses in the ratio of 2 : 2 : 1. They decided to share profit w.e.f. 1st April, 2019 in the ratio of 5 : 3 : 2. They also decided not to change the values of assets and liabilities in the books of account. The book values and revised values of assets and liabilities as on the date of change were as follows: Book values (₹) Revised values (₹) Machinery 2,50,000 3,00,000 Computers 2,00,000 1,75,000 Sundry Creditors 90,000 75,000 Outstanding Expenses 15,000 25,000 Pass an adjustment entry.

Answer» A, B and C are sharing profits and losses in the ratio of 2 : 2 : 1. They decided to share profit w.e.f. 1st April, 2019 in the ratio of 5 : 3 : 2. They also decided not to change the values of assets and liabilities in the books of account. The book values and revised values of assets and liabilities as on the date of change were as follows:

	Book values (₹)	Revised values (₹)
Machinery	2,50,000	3,00,000
Computers	2,00,000	1,75,000
Sundry Creditors	90,000	75,000
Outstanding Expenses	15,000	25,000

Pass an adjustment entry.

Discussion

5.	23. Find the distance of chord of length 10 cm from the centre of a circle pf radis 13 cm
Answer» 23. Find the distance of chord of length 10 cm from the centre of a circle pf radis 13 cm

Discussion

6.	In a right angled triangle ABC right angled at B, 5×sin A=3. Find the value of cos C+tan A+cosec C.
Answer» In a right angled triangle ABC right angled at B, $5 \times s i n A = 3$ . Find the value of $c o s C + t a n A + c o s e c C .$

Discussion

7.	The sum of any two distance is greater than third distance. Then it form a triangle. But how to choose ,which is sum of distance and which is third distance. Explain it by using example.
Answer» The sum of any two distance is greater than third distance. Then it form a triangle. But how to choose ,which is sum of distance and which is third distance. Explain it by using example.

Discussion

8.	If A (1, –1), B (0, 4), C (–5, 3) are vertices of a triangle then find the slope of each side.
Answer» If A (1, –1), B (0, 4), C (–5, 3) are vertices of a triangle then find the slope of each side.

Discussion

9.	ABCD is cyclic quadrilateral such that AB is a diameter of the circle circumscribing it and ∠ADC=140∘, then ∠BAC is equal to (A) 80∘ (B) 50∘ (C) 40∘ (D) 30∘
Answer» $A B C D$ is cyclic quadrilateral such that $A B$ is a diameter of the circle circumscribing it and $∠ A D C = 140^{\circ},$ then $∠ B A C$ is equal to (A) $80^{\circ}$ (B) $50^{\circ}$ (C) $40^{\circ}$ (D) $30^{\circ}$

9.

ABCD is cyclic quadrilateral such that AB is a diameter of the circle circumscribing it and ∠ADC=140∘, then ∠BAC is equal to (A) 80∘ (B) 50∘ (C) 40∘ (D) 30∘

Answer»

$A B C D$ is cyclic quadrilateral such that $A B$ is a diameter of the circle circumscribing it and $∠ A D C = 140^{\circ},$ then $∠ B A C$ is equal to

(A) $80^{\circ}$
(B) $50^{\circ}$
(C) $40^{\circ}$
(D) $30^{\circ}$

Discussion

10.	In the given figure, the point O is situated within the triangle PQR in such a way that ∠POQ=90∘, OP = 6 cm , OQ = 8 cm , If PR = 24 cm & ∠QPR=90∘, then find the length of QR.
Answer» In the given figure, the point O is situated within the triangle PQR in such a way that $∠ P O Q = 90^{\circ}$ , OP = 6 cm , OQ = 8 cm , If PR = 24 cm & $∠ Q P R = 90^{\circ}$ , then find the length of QR.

10.

In the given figure, the point O is situated within the triangle PQR in such a way that ∠POQ=90∘, OP = 6 cm , OQ = 8 cm , If PR = 24 cm & ∠QPR=90∘, then find the length of QR.

Answer»

In the given figure, the point O is situated within the triangle PQR in such a way that $∠ P O Q = 90^{\circ}$ , OP = 6 cm , OQ = 8 cm , If PR = 24 cm & $∠ Q P R = 90^{\circ}$ , then find the length of QR.

Discussion

11.	Aju was standing at the corner of a square field. He started walking towards North-East direction. When he was 10√2 m away from where he started, he took a left turn and started walking again. Considering the square field as the coordinate plane and starting point as the origin, find the equation of Aju’s current path.
Answer» Aju was standing at the corner of a square field. He started walking towards North-East direction. When he was $10 \sqrt{2}$ m away from where he started, he took a left turn and started walking again. Considering the square field as the coordinate plane and starting point as the origin, find the equation of Aju’s current path.

Discussion

12.	If y=√√7+7+√8+2√7−√7, then find the value of y.
Answer» If $y = \sqrt{\sqrt{7} + 7 + \sqrt{8 + 2 \sqrt{7}}} - \sqrt{7}$ , then find the value of $y$ .

Discussion

13.	In the given figure, if AD, AE and BC are tangents to the circle at D, E and F respectively, Then,(a) AD = AB + BC + CA(b) 2AD = AB + BC + CA(c) 3AD = AB + BC + CA(d) 4AD = AB + BC + CA
Answer» In the given figure, if AD, AE and BC are tangents to the circle at D, E and F respectively, Then, (a) AD = AB + BC + CA (b) 2AD = AB + BC + CA (c) 3AD = AB + BC + CA (d) 4AD = AB + BC + CA

Discussion

14.	In given figure, how many squares are there?
Answer» In given figure, how many squares are there?

14.

In given figure, how many squares are there?

Answer»

In given figure, how many squares are there?

Discussion

15.	38. The long and short hands of a clock are 6 cm and 4 cm long respectively. Find the sum of distances travelled by their tips in 24 hours .( Use pi = 3.14 ).
Answer» 38. The long and short hands of a clock are 6 cm and 4 cm long respectively. Find the sum of distances travelled by their tips in 24 hours .( Use pi = 3.14 ).

Discussion

16.	In a parallelogram ABCD, what should be the location of a point E on AB such that if a line parallel to BC = 3 cm is drawn from E, a rhombus is formed? (AB > BC)
Answer» In a parallelogram ABCD, what should be the location of a point E on AB such that if a line parallel to BC = 3 cm is drawn from E, a rhombus is formed? (AB > BC)

Discussion

17.	37. cosec theta - sin theta = a cube sec theta - cos theta = b cube Prove that (a sq. * b sq.) [a sq. + b sq.] = 1
Answer» 37. cosec theta - sin theta = a cube sec theta - cos theta = b cube Prove that (a sq. * b sq.) [a sq. + b sq.] = 1

Discussion

18.	If the distance between the points (4, p) and (1, 0) is 5, then the values of p are __________.
Answer» If the distance between the points (4, p) and (1, 0) is 5, then the values of p are __________.

Discussion

19.	At a point on level ground, the angle of elevation of a vertical tower is found to be such that its tangent is 512. On walking 192 metres towards the tower; the tangent of the angle is found to be 34. Find the height of the tower.
Answer» At a point on level ground, the angle of elevation of a vertical tower is found to be such that its tangent is $\frac{5}{12}$ . On walking 192 metres towards the tower; the tangent of the angle is found to be $\frac{3}{4}$ . Find the height of the tower.

Discussion

20.	Question 4One of the two digits of a two-digit number is three times the other digit. If you inter change the digits of this two-digit number and add the resulting number to the original number, you get 88. What is the original number?
Answer» Question 4 One of the two digits of a two-digit number is three times the other digit. If you inter change the digits of this two-digit number and add the resulting number to the original number, you get 88. What is the original number?

Discussion

21.	Find the zero of the polynomial in each of the following cases: (i) p(x)=x+5 (ii) p(x)=cx+d,c ≠0,c,d are real numbers.
Answer» Find the zero of the polynomial in each of the following cases: (i) p(x)=x+5 (ii) p(x)=cx+d,c $\neq$ 0,c,d are real numbers.

Discussion

22.	If 21560 cubic cm of a liquid is filled in some cylindrical shaped container of radius 7 cm and height 14 cm. Find the number of such containers.
Answer» If 21560 cubic cm of a liquid is filled in some cylindrical shaped container of radius 7 cm and height 14 cm. Find the number of such containers.

Discussion

23.	A man on the top of a vertical tower observes a car moving at a uniform speed towards the tower on a horizonatal road. If it takes 18 min. for the angle of depression of the car to change from 30° to 45° ; then after this, the time taken (in min.) by the car to reach the foot of the tower, is:
Answer» A man on the top of a vertical tower observes a car moving at a uniform speed towards the tower on a horizonatal road. If it takes $18$ min. for the angle of depression of the car to change from $30 ° t o 45 °$ ; then after this, the time taken (in min.) by the car to reach the foot of the tower, is:

Discussion

24.	Construct a triangle PQR with sides QR = 7 cm, PQ = 6 cm and ∠PQR = 60º. Then construct another triangle whose sides are 35 of the corresponiding sides of ∆PQR. [CBSE 2014, 2015]
Answer» Construct a triangle PQR with sides QR = 7 cm, PQ = 6 cm and $∠$ PQR = 60º. Then construct another triangle whose sides are $\frac{3}{5}$ of the corresponiding sides of ∆PQR. [CBSE 2014, 2015]

Discussion

25.	Which of the following is correct
Answer» Which of the following is correct

Discussion

26.	If the circles of radii 3.4 cm and 1.8 cm are drawn with their centres 1.6 cm apart, how do they touch each other? Why?
Answer» If the circles of radii 3.4 cm and 1.8 cm are drawn with their centres 1.6 cm apart, how do they touch each other? Why?

Discussion

27.	A conical vessel, with base radius 5 cm and height 24 cm, is full of water. This water is emptied into a cylindrical vessel of base radius 10 cm. Find the height to which the water will rise in the cylindrical vessel. (Use π=227)
Answer» A conical vessel, with base radius 5 cm and height 24 cm, is full of water. This water is emptied into a cylindrical vessel of base radius 10 cm. Find the height to which the water will rise in the cylindrical vessel. (Use $π = \frac{22}{7}$ )

Discussion

28.	Solve for x and y:2x+5yxy=64x-5yxy=-3
Answer» Solve for x and y: $\frac{2 x + 5 y}{x y} = 6 \frac{4 x - 5 y}{x y} = - 3$

Discussion

29.	A box contains 3 black balls, 4 red balls and 3 green balls. All the balls are identical in shape and size. Rohit takes out a ball from the bag without looking into it. What is the probability that the ball drawn is a black ball?
Answer» A box contains 3 black balls, 4 red balls and 3 green balls. All the balls are identical in shape and size. Rohit takes out a ball from the bag without looking into it. What is the probability that the ball drawn is a black ball?

Discussion

30.	The volume of the largest right circular cone that can be fitted in a cube whose edge is 2r equals to the volume of a hemisphere of radius __________.
Answer» The volume of the largest right circular cone that can be fitted in a cube whose edge is 2r equals to the volume of a hemisphere of radius __________.

Discussion

31.	If X,y,zare three consecutive term of Arithmetic Progression then find difference
Answer» If X,y,zare three consecutive term of Arithmetic Progression then find difference

Discussion

32.	For real numbers α,β,γ and δ, if∫(x2−1)+tan−1(x2+1x)(x4+3x2+1)tan−1(x2+1x)dx=α loge(tan−1(x2+1x))+β tan−1(γ(x2−1)x)+δ tan−1(x2+1x)+C where C is an arbitrary constant, then the value of 10(α+βγ+δ) is equal to
Answer» For real numbers $α, β, γ$ and $δ,$ if $\int \frac{(x^{2} - 1) + {tan}^{- 1} (\frac{x^{2} + 1}{x})}{(x^{4} + 3 x^{2} + 1) {tan}^{- 1} (\frac{x^{2} + 1}{x})} d x = α {log}_{e} ({tan}^{- 1} (\frac{x^{2} + 1}{x})) + β {tan}^{- 1} (\frac{γ (x^{2} - 1)}{x}) + δ {tan}^{- 1} (\frac{x^{2} + 1}{x}) + C$ where $C$ is an arbitrary constant, then the value of $10 (α + β γ + δ)$ is equal to

Discussion

33.	13. threedigit number sare formed using digits0,2,4,6 and8 .a number is chossen at random out of these numbers .what is probability that this numbers has same digits??
Answer» 13. threedigit number sare formed using digits0,2,4,6 and8 .a number is chossen at random out of these numbers .what is probability that this numbers has same digits??

Discussion

34.	Theoretical probability of an event A is given as AB where S1 : A is the number of outcomes favourable to E S2 : B is the total number of possible outcomes.
Answer» Theoretical probability of an event A is given as $\frac{A}{B}$ where S1 : A is the number of outcomes favourable to E S2 : B is the total number of possible outcomes.

34.

Theoretical probability of an event A is given as AB where S1 : A is the number of outcomes favourable to E S2 : B is the total number of possible outcomes.

Answer»

Theoretical probability of an event A is given as $\frac{A}{B}$ where

S1 : A is the number of outcomes favourable to E

S2 : B is the total number of possible outcomes.

Discussion

35.	Question 6From a solid cube of side 7 cm, a conical cavity of height 7 cm and radius 3 cm is hollowed out. Find the volume of the remaining solid.
Answer» Question 6 From a solid cube of side 7 cm, a conical cavity of height 7 cm and radius 3 cm is hollowed out. Find the volume of the remaining solid.

Discussion

36.	How many irrational numbers exist between two rational numbers?
Answer» How many irrational numbers exist between two rational numbers?

Discussion

37.	Find the comman difference of an AP whose first term is 5 and the sum of first four term is half the sum of next four terms
Answer» Find the comman difference of an AP whose first term is 5 and the sum of first four term is half the sum of next four terms

Discussion

38.	If the pth term of an A.P be qvand qth term be p, then rth term will be?
Answer» If the pth term of an A.P be qvand qth term be p, then rth term will be?

Discussion

39.	If sec A. sin (36 +A) =1 find A if A and 36+A are acute angle
Answer» If sec A. sin (36 +A) =1 find A if A and 36+A are acute angle

Discussion

40.	A well of diameter 2 m is dug 14 m deep, The earth taken out of it is spread evenly all around it to form an embankment of height 40 cm. Find the width of the embankment.
Answer» A well of diameter 2 m is dug 14 m deep, The earth taken out of it is spread evenly all around it to form an embankment of height 40 cm. Find the width of the embankment.

Discussion

41.	how to know where the number 46.5 will come between 46 and 48 on x axis
Answer» how to know where the number 46.5 will come between 46 and 48 on x axis

Discussion

42.	Find the value of k such that the quadratic equation 5x2+kx+4=0 has real and equal roots.
Answer» Find the value of k such that the quadratic equation $5 x^{2} + k x + 4 = 0$ has real and equal roots.

Discussion

43.	Write a quadratic polynomial, sum of whose zeros is 23 and their product is 2.
Answer» Write a quadratic polynomial, sum of whose zeros is $2 \sqrt{3}$ and their product is 2.

Discussion

44.	A die is thrown once. What is the probability that the
Answer» A die is thrown once. What is the probability that the

Discussion

45.	Write the value of 1+tan2θcos2θ.
Answer» Write the value of $(1 + \tan^{2} θ) \cos^{2} θ$ .

Discussion

46.

On 1st March, 2018, Shri Kailash Chand, Lucknow commenced business with cash ₹ 50,000. The following are his transactions for the month of March, 2018. Record them in proper books, post them to the Ledger and take out a Trial Balance: 2018 ₹ March 1 Bought goods for cash* 5,000 Purchased from Hari, Lucknow: 5 Laptops ₹ 35,000 each 5 Desktops ₹ 25,000 each Less: Trade Discount 15% March 2 Purchased computer & printer from M/s. Computer Mart against cash for office use 20,000 March 5 Deposited into bank 15,000 March 7 Sold goods to Shri Ramesh Chand, Kanpur: 2 Laptops ₹ 32,000 each 2 Desktops ₹ 24,000 each March 10 Received Cheque from Shri Ramesh Chand on account 75,000 March 14 Received another Cheque in full settlement from Ramesh Chand 49,440 March 15 Sold goods to Jagdish, Kolkata: 2 Laptops ₹ 35,000 each 2 Desktops ₹ 25,000 each Less: Trade Discount 5% March 18 Bought from Shyam Lal, Delhi: 10 Keyboards ₹ 1,000 each 10 Mouse ₹ 500 each March 20 Drew cash from bank for office 17,000 March 21 Paid to Shyam Lal in full settlement 16,500 March 23 Cash Sales 5 Keyboards ₹ 1,200 each and 5 Mouse ₹ 600 each March 25 Paid Salary 2,500 March 28 Paid Rent* 1,500 March 30 Paid into bank 5,000 March 31 Drew cash for private expenses 500 Transactions marked* are intra-state transactions subject to CGST and SGST 6% each.Transactions marked** are inter-state transactions subject to IGST 12%.

Answer» On 1st March, 2018, Shri Kailash Chand, Lucknow commenced business with cash ₹ 50,000. The following are his transactions for the month of March, 2018. Record them in proper books, post them to the Ledger and take out a Trial Balance:


2018		₹
March 1	Bought goods for cash*	5,000
	Purchased from Hari, Lucknow*:
	5 Laptops ₹ 35,000 each
	5 Desktops ₹ 25,000 each
	Less: Trade Discount 15%
March 2	Purchased computer & printer from M/s. Computer Mart against cash for office use*	20,000
March 5	Deposited into bank	15,000
March 7	Sold goods to Shri Ramesh Chand, Kanpur*:
	2 Laptops ₹ 32,000 each
	2 Desktops ₹ 24,000 each
March 10	Received Cheque from Shri Ramesh Chand on account	75,000
March 14	Received another Cheque in full settlement from Ramesh Chand	49,440
March 15	Sold goods to Jagdish, Kolkata**:
	2 Laptops ₹ 35,000 each
	2 Desktops ₹ 25,000 each
	Less: Trade Discount 5%
March 18	Bought from Shyam Lal, Delhi**:
	10 Keyboards ₹ 1,000 each
	10 Mouse ₹ 500 each
March 20	Drew cash from bank for office	17,000
March 21	Paid to Shyam Lal in full settlement	16,500
March 23	Cash Sales 5 Keyboards ₹ 1,200 each and 5 Mouse ₹ 600 each*
March 25	Paid Salary	2,500
March 28	Paid Rent*	1,500
March 30	Paid into bank	5,000
March 31	Drew cash for private expenses	500

Transactions marked* are intra-state transactions subject to CGST and SGST 6% each.

Transactions marked** are inter-state transactions subject to IGST 12%.

Discussion

47.	Question 1 (v)Evaluate the following:(v) 5cos260∘+4sec230∘−tan245∘sin230∘+cos230∘
Answer» Question 1 (v) Evaluate the following: (v) $\frac{5 c o s^{2} 60^{\circ} + 4 s e c^{2} 30^{\circ} - t a n^{2} 45^{\circ}}{s i n^{2} 30^{\circ} + c o s^{2} 30^{\circ}}$

Discussion

48.

In the following data the median of the runs scored by 60 top batsmen of the world in one-day international cricket matches is 5000. Find the missing frequencies x and y. Runs scored 2500−3500 3500−4500 4500−5500 5500−6500 6500−7500 7500−8500 Number of batsmen 5 x y 12 6 2

Answer» In the following data the median of the runs scored by 60 top batsmen of the world in one-day international cricket matches is 5000. Find the missing frequencies x and y.

Runs scored	2500−3500	3500−4500	4500−5500	5500−6500	6500−7500	7500−8500
Number of batsmen	5	x	y	12	6	2

Discussion

49.

Question 3(a) See the figure and find the ratio of: The number of triangles to the number of circles inside the rectangle.

Answer»

Question 3(a)

See the figure and find the ratio of:

The number of triangles to the number of circles inside the rectangle.

Discussion

50.	The length, breadth and height of a cuboid are 2 m, 5 m and 4m respectively.1) What is the difference between total surface area and curved surface area ?2) If a cube of side measuring 100cm is placed inside the cuboid, what is amount of void space in the cuboid?
Answer» The length, breadth and height of a cuboid are 2 m, 5 m and 4m respectively. 1) What is the difference between total surface area and curved surface area ? 2) If a cube of side measuring 100cm is placed inside the cuboid, what is amount of void space in the cuboid?

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Let x and y be two positive integers which satisfy the following two relations : (a) x^2 = y^3 (b) x = 2y The value of x + y is

Solve the differential equations - dy/dx = log x

Match the object in Column A to formulae in Column B. Choose the Option with correct matches.AB1. Surface area of cone1. 4πr22. Surface area of sphere2. 2πrh3. curved surface area of cylinder3. πrL

23. Find the distance of chord of length 10 cm from the centre of a circle pf radis 13 cm

In a right angled triangle ABC right angled at B, 5×sin A=3. Find the value of cos C+tan A+cosec C.

The sum of any two distance is greater than third distance. Then it form a triangle. But how to choose ,which is sum of distance and which is third distance. Explain it by using example.

If A (1, –1), B (0, 4), C (–5, 3) are vertices of a triangle then find the slope of each side.

ABCD is cyclic quadrilateral such that AB is a diameter of the circle circumscribing it and ∠ADC=140∘, then ∠BAC is equal to (A) 80∘ (B) 50∘ (C) 40∘ (D) 30∘

In the given figure, the point O is situated within the triangle PQR in such a way that ∠POQ=90∘, OP = 6 cm , OQ = 8 cm , If PR = 24 cm &amp; ∠QPR=90∘, then find the length of QR.

If y=√√7+7+√8+2√7−√7, then find the value of y.

In the given figure, if AD, AE and BC are tangents to the circle at D, E and F respectively, Then,(a) AD = AB + BC + CA(b) 2AD = AB + BC + CA(c) 3AD = AB + BC + CA(d) 4AD = AB + BC + CA

In given figure, how many squares are there?

38. The long and short hands of a clock are 6 cm and 4 cm long respectively. Find the sum of distances travelled by their tips in 24 hours .( Use pi = 3.14 ).

In a parallelogram ABCD, what should be the location of a point E on AB such that if a line parallel to BC = 3 cm is drawn from E, a rhombus is formed? (AB &gt; BC)

37. cosec theta - sin theta = a cube sec theta - cos theta = b cube Prove that (a sq. * b sq.) [a sq. + b sq.] = 1

If the distance between the points (4, p) and (1, 0) is 5, then the values of p are __________.

At a point on level ground, the angle of elevation of a vertical tower is found to be such that its tangent is 512. On walking 192 metres towards the tower; the tangent of the angle is found to be 34. Find the height of the tower.

Question 4One of the two digits of a two-digit number is three times the other digit. If you inter change the digits of this two-digit number and add the resulting number to the original number, you get 88. What is the original number?

Find the zero of the polynomial in each of the following cases: (i) p(x)=x+5 (ii) p(x)=cx+d,c ≠0,c,d are real numbers.

If 21560 cubic cm of a liquid is filled in some cylindrical shaped container of radius 7 cm and height 14 cm. Find the number of such containers.

A man on the top of a vertical tower observes a car moving at a uniform speed towards the tower on a horizonatal road. If it takes 18 min. for the angle of depression of the car to change from 30° to 45° ; then after this, the time taken (in min.) by the car to reach the foot of the tower, is:

Construct a triangle PQR with sides QR = 7 cm, PQ = 6 cm and ∠PQR = 60º. Then construct another triangle whose sides are 35 of the corresponiding sides of ∆PQR. [CBSE 2014, 2015]

Which of the following is correct

If the circles of radii 3.4 cm and 1.8 cm are drawn with their centres 1.6 cm apart, how do they touch each other? Why?

A conical vessel, with base radius 5 cm and height 24 cm, is full of water. This water is emptied into a cylindrical vessel of base radius 10 cm. Find the height to which the water will rise in the cylindrical vessel. (Use π=227)

Solve for x and y:2x+5yxy=64x-5yxy=-3

A box contains 3 black balls, 4 red balls and 3 green balls. All the balls are identical in shape and size. Rohit takes out a ball from the bag without looking into it. What is the probability that the ball drawn is a black ball?

The volume of the largest right circular cone that can be fitted in a cube whose edge is 2r equals to the volume of a hemisphere of radius __________.

If X,y,zare three consecutive term of Arithmetic Progression then find difference

For real numbers α,β,γ and δ, if∫(x2−1)+tan−1(x2+1x)(x4+3x2+1)tan−1(x2+1x)dx=α loge(tan−1(x2+1x))+β tan−1(γ(x2−1)x)+δ tan−1(x2+1x)+C where C is an arbitrary constant, then the value of 10(α+βγ+δ) is equal to

13. threedigit number sare formed using digits0,2,4,6 and8 .a number is chossen at random out of these numbers .what is probability that this numbers has same digits??

Theoretical probability of an event A is given as AB where S1 : A is the number of outcomes favourable to E S2 : B is the total number of possible outcomes.

Question 6From a solid cube of side 7 cm, a conical cavity of height 7 cm and radius 3 cm is hollowed out. Find the volume of the remaining solid.

How many irrational numbers exist between two rational numbers?

Find the comman difference of an AP whose first term is 5 and the sum of first four term is half the sum of next four terms

If the pth term of an A.P be qvand qth term be p, then rth term will be?

If sec A. sin (36 +A) =1 find A if A and 36+A are acute angle

A well of diameter 2 m is dug 14 m deep, The earth taken out of it is spread evenly all around it to form an embankment of height 40 cm. Find the width of the embankment.

how to know where the number 46.5 will come between 46 and 48 on x axis

Find the value of k such that the quadratic equation 5x2+kx+4=0 has real and equal roots.

Write a quadratic polynomial, sum of whose zeros is 23 and their product is 2.

A die is thrown once. What is the probability that the

Write the value of 1+tan2θcos2θ.

Question 1 (v)Evaluate the following:(v) 5cos260∘+4sec230∘−tan245∘sin230∘+cos230∘

In the following data the median of the runs scored by 60 top batsmen of the world in one-day international cricket matches is 5000. Find the missing frequencies x and y. Runs scored 2500−3500 3500−4500 4500−5500 5500−6500 6500−7500 7500−8500 Number of batsmen 5 x y 12 6 2

Question 3(a) See the figure and find the ratio of: The number of triangles to the number of circles inside the rectangle.

The length, breadth and height of a cuboid are 2 m, 5 m and 4m respectively.1) What is the difference between total surface area and curved surface area ?2) If a cube of side measuring 100cm is placed inside the cuboid, what is amount of void space in the cuboid?

In the given figure, the point O is situated within the triangle PQR in such a way that ∠POQ=90∘, OP = 6 cm , OQ = 8 cm , If PR = 24 cm & ∠QPR=90∘, then find the length of QR.

In a parallelogram ABCD, what should be the location of a point E on AB such that if a line parallel to BC = 3 cm is drawn from E, a rhombus is formed? (AB > BC)