32581 + Interview Questions in Mathematics Page 92 InterviewSolution

4551.	A person has 2 parents, 4 grandparents, 8 great grand parents, and so on. Find the number of his ancestors during the ten generations preceding his own.
Answer» A person has 2 parents, 4 grandparents, 8 great grand parents, and so on. Find the number of his ancestors during the ten generations preceding his own.

Discussion

4552.	Three circles touch each other externally. The distance between their centers is 5 cm, 6 cm and 7 cm. Find the radii of the circles.
Answer» Three circles touch each other externally. The distance between their centers is $5 c m$ , $6 c m$ and $7 c m$ . Find the radii of the circles.

Discussion

4553.	If Zeba were younger by 5 years than what she really is, then the square of her age (in years) would have been 11 more than five times her actual age. What is her age now?
Answer» If Zeba were younger by 5 years than what she really is, then the square of her age (in years) would have been 11 more than five times her actual age. What is her age now?

Discussion

4554.	U=x+y+z,v=xsquare+ysquare+zsquare,w=yz+zx+xy
Answer» U=x+y+z,v=xsquare+ysquare+zsquare,w=yz+zx+xy

Discussion

4555.	Prove the following trigonometric identities.cot A-cos Acot A+cos A=cosec A-1cosec A+1
Answer» Prove the following trigonometric identities. $\frac{\cot A - \cos A}{\cot A + \cos A} = \frac{cosec A - 1}{cosec A + 1}$

Discussion

4556.	If (x+a) is a factor of (2x2+2ax+5x+10), find the value of a.
Answer» If (x+a) is a factor of $(2 x^{2} + 2 a x + 5 x + 10)$ , find the value of a.

Discussion

4557.	The sum of the ratio of m and n th term is (m)2:(n)2 to show the ratio of mn th term is (2m-1):(2n-1)
Answer» The sum of the ratio of m and n th term is (m)2:(n)2 to show the ratio of mn th term is (2m-1):(2n-1)

Discussion

4558.	the number of significant figures in 0.02300
Answer» the number of significant figures in 0.02300

Discussion

4559.	1x=45 From the above equation Value of 45x can be found as__
Answer» $\frac{1}{x} = 45$ From the above equation Value of 45x can be found as__

4559.

1x=45 From the above equation Value of 45x can be found as__

Answer»

$\frac{1}{x} = 45$

From the above equation Value of 45x can be found as__

Discussion

4560.	A solid is in the shape of a cone surmounted on a hemisphere, the radius of each of them being 3.5 cm and the total height of the solid is9.5 cm. Find the volume of the solid. [CBSE 2012]
Answer» A solid is in the shape of a cone surmounted on a hemisphere, the radius of each of them being 3.5 cm and the total height of the solid is 9.5 cm. Find the volume of the solid. [CBSE 2012]

Discussion

4561.	In the given figure, two triangles PQR and SQR are on the same side of QR in which ∠P=∠S=900. If PR and QS meet each other at T, then which of the following is always true?
Answer» In the given figure, two triangles PQR and SQR are on the same side of QR in which $∠ P = ∠ S = 90^{0}$ . If PR and QS meet each other at T, then which of the following is always true?

Discussion

4562.	Which of the following is not a quadratic equation?
Answer» Which of the following is not a quadratic equation?

Discussion

4563.	The distance of the point (4, 7) from the x-axis is(a) 4(b) 7(c) 11(d) 65
Answer» The distance of the point (4, 7) from the x-axis is (a) 4 (b) 7 (c) 11 (d) $\sqrt{65}$

Discussion

4564.	2 tan2 45∘+3 cos2 30∘−sin2 60∘ = ________ .
Answer» $2 t a n^{2} 45^{\circ} + 3 c o s^{2} 30^{\circ} - s i n^{2} 60^{\circ}$ = ________ .

Discussion

4565.	Find the mean deviation about median for the following data Marks0−1010−2020−3030−4040−5050−60No. of girls4891075
Answer» Find the mean deviation about median for the following data $\begin{matrix} M a r k s & 0 - 10 & 10 - 20 & 20 - 30 & 30 - 40 & 40 - 50 & 50 - 60 N o . o f g i r l s & 4 & 8 & 9 & 10 & 7 & 5 \end{matrix}$

4565.

Find the mean deviation about median for the following data Marks0−1010−2020−3030−4040−5050−60No. of girls4891075

Answer»

Find the mean deviation about median for the following data

$\begin{matrix} M a r k s & 0 - 10 & 10 - 20 & 20 - 30 & 30 - 40 & 40 - 50 & 50 - 60 N o . o f g i r l s & 4 & 8 & 9 & 10 & 7 & 5 \end{matrix}$

Discussion

4566.	Volume of a sphere is directly proportional to __ of radius of the sphere.
Answer» Volume of a sphere is directly proportional to __ of radius of the sphere.

Discussion

4567.

C maintains his books according to Single Entry System. Following figures were available from the books for the six months ended 31st December 2017: Particulars 1st July, 2017 (₹) 31st Dec. 2017 (₹) Plant and Machinery 1,50,000 1,40,000 Debtors 65,000 60,000 Cash and Bank Balances 25,000 31,000 Stock 40,000 45,000 Creditors 9,000 10,000 Adjustments:(a) He had withdrawn ₹ 200 in the beginning of every month for household purposes.(b) Depreciation on Plant and Machinery 10% p.a.(c) Further Bad Debts ₹ 5,000 and Provision for Doubtful Debts to be created 2%.(d) During the period, salaries have been prepaid by ₹ 500 while wages outstanding were ₹ 1,000.(e) Interest on drawings to be reckoned 6% p.a.You are required to prepare the Statement of Profit or Loss for the half year ended 31st December, 2017, followed by Revised Statement of Affairs as on that date.

Answer»

C maintains his books according to Single Entry System. Following figures were available from the books for the six months ended 31^st December 2017:

Particulars	1st July, 2017 (₹)	31st Dec. 2017 (₹)
Plant and Machinery	1,50,000	1,40,000
Debtors	65,000	60,000
Cash and Bank Balances	25,000	31,000
Stock	40,000	45,000
Creditors	9,000	10,000

Adjustments:

(a) He had withdrawn ₹ 200 in the beginning of every month for household purposes.

(b) Depreciation on Plant and Machinery 10% p.a.

(c) Further Bad Debts ₹ 5,000 and Provision for Doubtful Debts to be created 2%.

(d) During the period, salaries have been prepaid by ₹ 500 while wages outstanding were ₹ 1,000.

(e) Interest on drawings to be reckoned 6% p.a.

You are required to prepare the Statement of Profit or Loss for the half year ended 31^st December, 2017, followed by Revised Statement of Affairs as on that date.

Discussion

4568.	A truck covers a distance of 150 km at a certain average speed and then covers another 200 km at an average speed which is 20 km per hour more than the first speed. If the truck covers the total distance in 5 hours, find the first speed of the truck. [CBSE 2015]
Answer» A truck covers a distance of 150 km at a certain average speed and then covers another 200 km at an average speed which is 20 km per hour more than the first speed. If the truck covers the total distance in 5 hours, find the first speed of the truck. [CBSE 2015]

Discussion

4569.	The shape obtained when circles are stacked one above the other is:
Answer» The shape obtained when circles are stacked one above the other is:

Discussion

4570.	In the following situations does the list of numbers involved make an arithmetic progression and why?The taxi fare after each km when the fare is Rs. 15 for the first km and Rs. 8 for each additional km.
Answer» In the following situations does the list of numbers involved make an arithmetic progression and why? The taxi fare after each km when the fare is Rs. 15 for the first km and Rs. 8 for each additional km.

Discussion

4571.

Eastern Company Limited , having an authorised capital of ₹ 10,00,000 divided into shares of ₹ 10 each , issued 50,000 shares at a premium of ₹ 3 per share payable as follows: On Application ₹ 3 per share; On Allotment (including premium) ₹ 5 per share; On first call (due three months after allotment )and the balance as when required. ₹ 3 per share; Applications were received for 60,000 shares and the directors allotted the shares as follows:(i) Applicants for 40,000 shares received in full.(ii) Applicants for 15,000 shares received an allotment of 8,000 shares.(iii) Applicants for 5,000 shares received 2,000 shares on allotment , excess money being returned.All amounts due on allotment were received.The first call was made and the money was received except on 100 shares.Give journal and cash book entries to record these transactions of the company . Also prepare the Balance Sheet of the company.

Answer» Eastern Company Limited , having an authorised capital of ₹ 10,00,000 divided into shares of ₹ 10 each , issued 50,000 shares at a premium of ₹ 3 per share payable as follows:

On Application	₹ 3 per share;
On Allotment (including premium)	₹ 5 per share;
On first call (due three months after allotment )and the balance as when required.	₹ 3 per share;

Applications were received for 60,000 shares and the directors allotted the shares as follows:

(i) Applicants for 40,000 shares received in full.

(ii) Applicants for 15,000 shares received an allotment of 8,000 shares.

(iii) Applicants for 5,000 shares received 2,000 shares on allotment , excess money being returned.

All amounts due on allotment were received.

The first call was made and the money was received except on 100 shares.

Give journal and cash book entries to record these transactions of the company . Also prepare the Balance Sheet of the company.

Discussion

4572.	FIND AREA OF TRIANGLE MADE BY LINE 3X+4Y=1
Answer» FIND AREA OF TRIANGLE MADE BY LINE 3X+4Y=1

Discussion

4573.	In the given figure, ∆ ABC is an equilateral traingle. Points F,D and E are midpoints of side AB, side BC, side AC respectively. Show that ∆FED is an equilateral traingle.
Answer» In the given figure, $∆$ ABC is an equilateral traingle. Points F,D and E are midpoints of side AB, side BC, side AC respectively. Show that $∆$ FED is an equilateral traingle.

Discussion

4574.	if the polynomial x^4-6x^3+11x^{2 }-25x+10 is divided by another polynomial x^2-2x+k, the remainder comes out to be x+a, then find the values of and a.
Answer» if the polynomial x^4-6x^3+11x^{2 }-25x+10 is divided by another polynomial x^2-2x+k, the remainder comes out to be x+a, then find the values of and a.

Discussion

4575.	The sum of three consecutive terms terms of an is 21 and the sum of the squares of these terms is 165. find these terms.
Answer» The sum of three consecutive terms terms of an is 21 and the sum of the squares of these terms is 165. find these terms.

Discussion

4576.	Question 3 (iv) Are the following pair of linear equations consistent? Justify your answer x + 3y = 11 and 2(2x + 6y) = 22
Answer» Question 3 (iv) Are the following pair of linear equations consistent? Justify your answer x + 3y = 11 and 2(2x + 6y) = 22

Discussion

4577.	Prove that in an equilateral triangle, the circumcentre and incentre are the same. What is the ratio of the circumradius and inradius?
Answer» Prove that in an equilateral triangle, the circumcentre and incentre are the same. What is the ratio of the circumradius and inradius?

Discussion

4578.	1. Construct a pair of tangents to a circle of radius 6cm where the two radii are inclined to each other at an angle of 120.2. Draw two concentric circles C1 and C2 (with common centre O) of radii 4cm and 7cm.From a point P in between two circles, draw tangents to the circle C1.
Answer» 1. Construct a pair of tangents to a circle of radius 6cm where the two radii are inclined to each other at an angle of 120. 2. Draw two concentric circles C1 and C2 (with common centre O) of radii 4cm and 7cm.From a point P in between two circles, draw tangents to the circle C1.

Discussion

4579.	The tops of two poles of height 14 m and 20 m are connected by a wire which makes an angle of 30° with the horizontal. What is the length of the wire?
Answer» The tops of two poles of height 14 m and 20 m are connected by a wire which makes an angle of 30° with the horizontal. What is the length of the wire?

Discussion

4580.	Replace the underlined word with a modal auxiliary showing permission. You are allowed to borrow your partner’s stationery.
Answer» Replace the underlined word with a modal auxiliary showing permission. You are allowed to borrow your partner’s stationery.

4580.

Replace the underlined word with a modal auxiliary showing permission. You are allowed to borrow your partner’s stationery.

Answer»

Replace the underlined word with a modal auxiliary showing permission.

You are allowed to borrow your partner’s stationery.

Discussion

4581.

Prepare Two-column Cash Book of Vinod, Delhi from the following transactions: 2017 ₹ Oct. 1 Cash in Hand 25,000 Oct. 1 Cash at Bank 75,000 Oct. 7 Bought goods for ₹ 15,000 plus IGST 12% against cheque Oct. 8 Bought goods for ₹ 5,000 plus CGST and SGST 6% each Oct. 10 Honoured our own acceptance by cheque 5,000 Oct. 14 Paid petty expenses 150 Oct. 18 Ramesh who owed ₹ 5,000 became bankrupt and paid us 50 paise in a rupee Oct. 20 Received cash from Manohar 7,500 Allowed discount 250 Oct. 23 Withdrew from bank 4,000 Oct. 24 Paid to Ghanshyamdas & Co. 3,000 Received discount 100 Oct. 25 Withdrew from bank for personal expenses 3,000 Oct. 27 Sold goods for ₹ 11,000 plus CGST and SGST 6% against cash Oct. 28 Received cheque for goods sold for ₹ 9,000 plus CGST and SGST 6% each Oct. 29 Received repayment of a loan of ₹ 5,000 and deposited ₹ 3,000 out of it

Answer» Prepare Two-column Cash Book of Vinod, Delhi from the following transactions:


2017		₹
Oct. 1	Cash in Hand	25,000
Oct. 1	Cash at Bank	75,000
Oct. 7	Bought goods for ₹ 15,000 plus IGST 12% against cheque
Oct. 8	Bought goods for ₹ 5,000 plus CGST and SGST 6% each
Oct. 10	Honoured our own acceptance by cheque	5,000
Oct. 14	Paid petty expenses	150
Oct. 18	Ramesh who owed ₹ 5,000 became bankrupt and paid us 50 paise in a rupee
Oct. 20	Received cash from Manohar	7,500
	Allowed discount	250
Oct. 23	Withdrew from bank	4,000
Oct. 24	Paid to Ghanshyamdas & Co.	3,000
	Received discount	100
Oct. 25	Withdrew from bank for personal expenses	3,000
Oct. 27	Sold goods for ₹ 11,000 plus CGST and SGST 6% against cash
Oct. 28	Received cheque for goods sold for ₹ 9,000 plus CGST and SGST 6% each
Oct. 29	Received repayment of a loan of ₹ 5,000 and deposited ₹ 3,000 out of it

Discussion

4582.	At a given price, every seller can sell any amount of output in the market. What will be the shape of the demand curve in perfect competition?
Answer» At a given price, every seller can sell any amount of output in the market. What will be the shape of the demand curve in perfect competition?

Discussion

4583.	Question 1 (vii)Find the roots of the quadratic equations by using the quadratic formula in the following question.12x2−√11x+1=0
Answer» Question 1 (vii) Find the roots of the quadratic equations by using the quadratic formula in the following question. $\frac{1}{2} x^{2} - \sqrt{11} x + 1 = 0$

4583.

Question 1 (vii)Find the roots of the quadratic equations by using the quadratic formula in the following question.12x2−√11x+1=0

Answer»

Question 1 (vii)

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

$\frac{1}{2} x^{2} - \sqrt{11} x + 1 = 0$

Discussion

4584.	(i) If the vertices of △ABC be A(1, -3), B(4, p) and C(-9, 7) and its area is 15 square units, find the values of p. (ii) The area of a triangle is 5 sq units. Two of its vertices are (2, 1) and (3, -2). If the third vertex is (72,y), find the value of y.
Answer» (i) If the vertices of $△ A B C$ be A(1, -3), B(4, p) and C(-9, 7) and its area is 15 square units, find the values of p. (ii) The area of a triangle is 5 sq units. Two of its vertices are (2, 1) and (3, -2). If the third vertex is $(\frac{7}{2}, y)$ , find the value of y.

4584.

(i) If the vertices of △ABC be A(1, -3), B(4, p) and C(-9, 7) and its area is 15 square units, find the values of p. (ii) The area of a triangle is 5 sq units. Two of its vertices are (2, 1) and (3, -2). If the third vertex is (72,y), find the value of y.

Answer»

(i) If the vertices of $△ A B C$ be A(1, -3), B(4, p) and C(-9, 7) and its area is 15 square units, find the values of p.

(ii) The area of a triangle is 5 sq units. Two of its vertices are (2, 1) and (3, -2). If the third vertex is $(\frac{7}{2}, y)$ , find the value of y.

Discussion

4585.	In the given figure, chords PQ=RS, ∠POQ=75∘ and ∠POS=150∘.Find the value of ∠QOR.
Answer» In the given figure, chords $P Q = R S, ∠ P O Q = 75^{\circ}$ and $∠ P O S = 150^{\circ}$ . Find the value of $∠ Q O R$ .

Discussion

4586.	d is the HCF of 65 and 117 expressed on the form of 65m + 117n.
Answer» d is the HCF of 65 and 117 expressed on the form of 65m + 117n.

Discussion

4587.	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

4588.	The rain water from a roof of dimensions 22 m×20 m drains into a cylindrical vessel having diameter of base 2m and height 3.5 m . If the rain water collected from the roof just fills the cylindrical vessel , then find the rainfall in cm .
Answer» The rain water from a roof of dimensions $22 m \times 20 m$ drains into a cylindrical vessel having diameter of base 2m and height 3.5 m . If the rain water collected from the roof just fills the cylindrical vessel , then find the rainfall in cm .

Discussion

4589.

The given distribution shows the number of runs scored by some top batsmen of the world in one-day international cricket matches. Runs scored Number of batsman Runs scored Number of Batsman 3000−4000 4000−5000 5000−6000 6000−7000 4 18 9 7 7000−8000 8000−9000 9000−10000 10000−11000 6 3 1 1 Find the mode of data.

Answer» The given distribution shows the number of runs scored by some top batsmen of the world in one-day international cricket matches.

Runs scored	Number of batsman	Runs scored	Number of Batsman
3000−4000 4000−5000 5000−6000 6000−7000	4 18 9 7	7000−8000 8000−9000 9000−10000 10000−11000	6 3 1 1

Find the mode of data.

Discussion

4590.	Prove that tan θ-cot θsin θ cos θ=tan2 θ-cot2 θ.
Answer» Prove that $\frac{\tan θ - \cot θ}{\sin θ \cos θ} = \tan^{2} θ - \cot^{2} θ$ .

Discussion

4591.	How many of the following are functions ? (i) f(x) = x5;{−1,0,1}→{0,1,2} (ii) f(x) = ±√x;{0,4,9}→{0,2,−2,3,−3} (iii) f(x) = √x;{0,4,9}→{0,2,−2,3,−3} (iv) f(x) = x2;{0,1,2}→{0,1,2,3,4}
Answer» How many of the following are functions ? (i) f(x) = $x^{5}; {- 1, 0, 1} \to {0, 1, 2}$ (ii) f(x) = $\pm \sqrt{x}; {0, 4, 9} \to {0, 2, - 2, 3, - 3}$ (iii) f(x) = $\sqrt{x}; {0, 4, 9} \to {0, 2, - 2, 3, - 3}$ (iv) f(x) = $x^{2}; {0, 1, 2} \to {0, 1, 2, 3, 4}$

4591.

How many of the following are functions ? (i) f(x) = x5;{−1,0,1}→{0,1,2} (ii) f(x) = ±√x;{0,4,9}→{0,2,−2,3,−3} (iii) f(x) = √x;{0,4,9}→{0,2,−2,3,−3} (iv) f(x) = x2;{0,1,2}→{0,1,2,3,4}

Answer»

How many of the following are functions ?

(i) f(x) = $x^{5}; {- 1, 0, 1} \to {0, 1, 2}$

(ii) f(x) = $\pm \sqrt{x}; {0, 4, 9} \to {0, 2, - 2, 3, - 3}$

(iii) f(x) = $\sqrt{x}; {0, 4, 9} \to {0, 2, - 2, 3, - 3}$

(iv) f(x) = $x^{2}; {0, 1, 2} \to {0, 1, 2, 3, 4}$

Discussion

4592.	If p²(a²sec²α-b²cosec²α)=(a²+b²)² then prove that the straight line xcosα+ysinα=p will be a normal of the parabola b²x²-a²y²=a²b². (Using calculus)
Answer» If p²(a²sec²α-b²cosec²α)=(a²+b²)² then prove that the straight line xcosα+ysinα=p will be a normal of the parabola b²x²-a²y²=a²b². (Using calculus)

Discussion

4593.	If the first, second and last terms of an A.P. are a, b and 2a respectively, then the sum of its terms is ___________.
Answer» If the first, second and last terms of an A.P. are a, b and 2a respectively, then the sum of its terms is ___________.

Discussion

4594.	20. A man observes that when he moves up a distance 'c' meters on a slope ,the angle of depression of a point on the horizontal plane from the base of the slope is 30^° ,and when he moves up further a distance 'c' meters the angle of depression of that is 45^°. The angle of inclination of the slope with the horzontal is (A)60^° (B)45^° (C) 75^°
Answer» 20. A man observes that when he moves up a distance 'c' meters on a slope ,the angle of depression of a point on the horizontal plane from the base of the slope is 30^° ,and when he moves up further a distance 'c' meters the angle of depression of that is 45^°. The angle of inclination of the slope with the horzontal is (A)60^° (B)45^° (C) 75^°

Discussion

4595.	Question 5 Show that the square of any odd integer is of the form 4m + 1, for some integer m.
Answer» Question 5 Show that the square of any odd integer is of the form 4m + 1, for some integer m.

Discussion

4596.	What is the market value of 4*1/2% (Rs 100) share, when an investment of Rs 1800 produces an income of Rs 72?
Answer» What is the market value of 4*1/2% (Rs 100) share, when an investment of Rs 1800 produces an income of Rs 72?

Discussion

4597.	26. If rwo straight lines intersect each other, proce that thr ray oppksite to the bisector of one of the angles thus foemed bisects the verrically opposite angles
Answer» 26. If rwo straight lines intersect each other, proce that thr ray oppksite to the bisector of one of the angles thus foemed bisects the verrically opposite angles

Discussion

4598.	Find the roots of each of the following equations, if they exist, by applying the quadratic formula:36x2-12ax+a2-b2=0
Answer» Find the roots of each of the following equations, if they exist, by applying the quadratic formula: $36 x^{2} - 12 a x + (a^{2} - b^{2}) = 0$

Discussion

4599.

All kings and queens are removed from a pack of 52 cards. The remaining cards are well-shuffled and then a card is randomly drawn from it. Find the probability that this card is (i) a red face card (ii) a black card.

Answer»

All kings and queens are removed from a pack of 52 cards. The remaining cards are well-shuffled and then a card is randomly drawn from it. Find the probability that this card is

(i) a red face card (ii) a black card.

Discussion

4600.	Choose the correct option of cutting a circle into 3 equal parts.
Answer» Choose the correct option of cutting a circle into 3 equal parts.

Discussion

Explore topic-wise InterviewSolutions in .

A person has 2 parents, 4 grandparents, 8 great grand parents, and so on. Find the number of his ancestors during the ten generations preceding his own.

Three circles touch each other externally. The distance between their centers is 5 cm, 6 cm and 7 cm. Find the radii of the circles.

If Zeba were younger by 5 years than what she really is, then the square of her age (in years) would have been 11 more than five times her actual age. What is her age now?​

U=x+y+z,v=xsquare+ysquare+zsquare,w=yz+zx+xy

Prove the following trigonometric identities.cot A-cos Acot A+cos A=cosec A-1cosec A+1

If (x+a) is a factor of (2x2+2ax+5x+10), find the value of a.

The sum of the ratio of m and n th term is (m)2:(n)2 to show the ratio of mn th term is (2m-1):(2n-1)

the number of significant figures in 0.02300

1x=45 From the above equation Value of 45x can be found as__

A solid is in the shape of a cone surmounted on a hemisphere, the radius of each of them being 3.5 cm and the total height of the solid is9.5 cm. Find the volume of the solid. [CBSE 2012]

In the given figure, two triangles PQR and SQR are on the same side of QR in which ∠P=∠S=900. If PR and QS meet each other at T, then which of the following is always true?

Which of the following is not a quadratic equation?

The distance of the point (4, 7) from the x-axis is(a) 4(b) 7(c) 11(d) 65

2 tan2 45∘+3 cos2 30∘−sin2 60∘ = ________ .

Find the mean deviation about median for the following data Marks0−1010−2020−3030−4040−5050−60No. of girls4891075

Volume of a sphere is directly proportional to __ of radius of the sphere.

A truck covers a distance of 150 km at a certain average speed and then covers another 200 km at an average speed which is 20 km per hour more than the first speed. If the truck covers the total distance in 5 hours, find the first speed of the truck. [CBSE 2015]

The shape obtained when circles are stacked one above the other is:

In the following situations does the list of numbers involved make an arithmetic progression and why?The taxi fare after each km when the fare is Rs. 15 for the first km and Rs. 8 for each additional km.

FIND AREA OF TRIANGLE MADE BY LINE 3X+4Y=1

In the given figure, ∆ ABC is an equilateral traingle. Points F,D and E are midpoints of side AB, side BC, side AC respectively. Show that ∆FED is an equilateral traingle.

if the polynomial x^4-6x^3+11x^{2 }-25x+10 is divided by another polynomial x^2-2x+k, the remainder comes out to be x+a, then find the values of and a.

The sum of three consecutive terms terms of an is 21 and the sum of the squares of these terms is 165. find these terms.

Question 3 (iv) Are the following pair of linear equations consistent? Justify your answer x + 3y = 11 and 2(2x + 6y) = 22

Prove that in an equilateral triangle, the circumcentre and incentre are the same. What is the ratio of the circumradius and inradius?

1. Construct a pair of tangents to a circle of radius 6cm where the two radii are inclined to each other at an angle of 120.2. Draw two concentric circles C1 and C2 (with common centre O) of radii 4cm and 7cm.From a point P in between two circles, draw tangents to the circle C1.

The tops of two poles of height 14 m and 20 m are connected by a wire which makes an angle of 30° with the horizontal. What is the length of the wire?

Replace the underlined word with a modal auxiliary showing permission. You are allowed to borrow your partner’s stationery.

At a given price, every seller can sell any amount of output in the market. What will be the shape of the demand curve in perfect competition?

Question 1 (vii)Find the roots of the quadratic equations by using the quadratic formula in the following question.12x2−√11x+1=0

(i) If the vertices of △ABC be A(1, -3), B(4, p) and C(-9, 7) and its area is 15 square units, find the values of p. (ii) The area of a triangle is 5 sq units. Two of its vertices are (2, 1) and (3, -2). If the third vertex is (72,y), find the value of y.

In the given figure, chords PQ=RS, ∠POQ=75∘ and ∠POS=150∘.Find the value of ∠QOR.

d is the HCF of 65 and 117 expressed on the form of 65m + 117n.

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

The rain water from a roof of dimensions 22 m×20 m drains into a cylindrical vessel having diameter of base 2m and height 3.5 m . If the rain water collected from the roof just fills the cylindrical vessel , then find the rainfall in cm .

Prove that tan θ-cot θsin θ cos θ=tan2 θ-cot2 θ.

How many of the following are functions ? (i) f(x) = x5;{−1,0,1}→{0,1,2} (ii) f(x) = ±√x;{0,4,9}→{0,2,−2,3,−3} (iii) f(x) = √x;{0,4,9}→{0,2,−2,3,−3} (iv) f(x) = x2;{0,1,2}→{0,1,2,3,4}

If p²(a²sec²α-b²cosec²α)=(a²+b²)² then prove that the straight line xcosα+ysinα=p will be a normal of the parabola b²x²-a²y²=a²b². (Using calculus)

If the first, second and last terms of an A.P. are a, b and 2a respectively, then the sum of its terms is ___________.

Question 5 Show that the square of any odd integer is of the form 4m + 1, for some integer m.

What is the market value of 4*1/2% (Rs 100) share, when an investment of Rs 1800 produces an income of Rs 72?

26. If rwo straight lines intersect each other, proce that thr ray oppksite to the bisector of one of the angles thus foemed bisects the verrically opposite angles

Find the roots of each of the following equations, if they exist, by applying the quadratic formula:36x2-12ax+a2-b2=0

All kings and queens are removed from a pack of 52 cards. The remaining cards are well-shuffled and then a card is randomly drawn from it. Find the probability that this card is (i) a red face card (ii) a black card.

Choose the correct option of cutting a circle into 3 equal parts.

If Zeba were younger by 5 years than what she really is, then the square of her age (in years) would have been 11 more than five times her actual age. What is her age now?