32581 + Interview Questions in Mathematics Page 44 InterviewSolution

2151.	If the product of two zeros of the polynomial f(x) = 2x3 + 6x2 - 4x + 9 is 3, then its third zero is
Answer» If the product of two zeros of the polynomial f(x) = 2x³ + 6x² - 4x + 9 is 3, then its third zero is

Discussion

2152.	Find the radius of a circle whose circumference is equal to the sum of the circumference of two circles of radii 15 cm and 18 cm .132974
Answer» Find the radius of a circle whose circumference is equal to the sum of the circumference of two circles of radii 15 cm and 18 cm .132974

Discussion

2153.	Find the values of x and y in the following rectangle.
Answer» Find the values of x and y in the following rectangle.

2153.

Find the values of x and y in the following rectangle.

Answer»

Find the values of x and y in the following rectangle.

Discussion

2154.	Arjun and Karna had an archery competition where they had to shoot a target board with 7 concurrent circles dividing the board into 8 concurrent circular strips. Score for each outcome decreases by unity with centermost circle having score of 8. Dronacharya had difficulty in deciding who the winner was after the scores were recorded. Calculate the mean deviation about the score of innermost circle so as to decide who the winner is assuming the winner is less deviated from the bulls eye. Points87654321Arjun(fi)571423111043karna(fi)58112414853
Answer» Arjun and Karna had an archery competition where they had to shoot a target board with 7 concurrent circles dividing the board into 8 concurrent circular strips. Score for each outcome decreases by unity with centermost circle having score of 8. Dronacharya had difficulty in deciding who the winner was after the scores were recorded. Calculate the mean deviation about the score of innermost circle so as to decide who the winner is assuming the winner is less deviated from the bulls eye. $\begin{matrix} P o i n t s & 8 & 7 & 6 & 5 & 4 & 3 & 2 & 1 A r j u n (f_{i}) & 5 & 7 & 14 & 23 & 11 & 10 & 4 & 3 k a r n a (f_{i}) & 5 & 8 & 11 & 24 & 14 & 8 & 5 & 3 \end{matrix}$

2154.

Arjun and Karna had an archery competition where they had to shoot a target board with 7 concurrent circles dividing the board into 8 concurrent circular strips. Score for each outcome decreases by unity with centermost circle having score of 8. Dronacharya had difficulty in deciding who the winner was after the scores were recorded. Calculate the mean deviation about the score of innermost circle so as to decide who the winner is assuming the winner is less deviated from the bulls eye. Points87654321Arjun(fi)571423111043karna(fi)58112414853

Answer»

Arjun and Karna had an archery competition where they had to shoot a target board with 7 concurrent circles dividing the board into 8 concurrent circular strips. Score for each outcome decreases by unity with centermost circle having score of 8. Dronacharya had difficulty in deciding who the winner was after the scores were recorded. Calculate the mean deviation about the score of innermost circle so as to decide who the winner is assuming the winner is less deviated from the bulls eye.

$\begin{matrix} P o i n t s & 8 & 7 & 6 & 5 & 4 & 3 & 2 & 1 A r j u n (f_{i}) & 5 & 7 & 14 & 23 & 11 & 10 & 4 & 3 k a r n a (f_{i}) & 5 & 8 & 11 & 24 & 14 & 8 & 5 & 3 \end{matrix}$

Discussion

2155.	Is it possible to design a rectangular mango grove whose length is twice its breadth, and the area is 800 m2? If so, find its length and breadth.
Answer» Is it possible to design a rectangular mango grove whose length is twice its breadth, and the area is $800 m^{2}$ ? If so, find its length and breadth.

Discussion

2156.	Show that △ABC, where A(-2, 0), B(0, 2), and C(2, 0) and △PQR where P(-4, 0), Q(4, 0), R(0, 4) are similar triangles.
Answer» Show that $△ A B C$ , where A(-2, 0), B(0, 2), and C(2, 0) and $△ P Q R$ where P(-4, 0), Q(4, 0), R(0, 4) are similar triangles.

Discussion

2157.

Following is the Trial Balance of Mr. S. Kapur on 31st March, 2018: Particulars Dr. (₹) Cr. (₹) Cash in Hand 10,800 Cash at Bank 2,32,600 Purchases 8,13,500 Sales 19,75,600 Returns Inward 13,600 Returns Outward 10,000 Wages 2,09,600 Fuel and Power 94,600 Carriage Outwards 64,000 Carriage on Purchases 40,800 Stock on 1st April, 2017 1,15,200 Building 6,00,000 Computer 2,00,000 Machinery 4,00,000 Salaries 3,00,000 Patents 1,50,000 Advertisement Expenses 60,000 Insurance 12,000 Capital 16,00,000 Drawings 1,04,900 Sundry Debtors 2,90,000 Sundry Creditors 1,31,000 Input CGST 7,500 Input SGST 7,500 Output IGST 10,000 Total 37,26,600 37,26,600 Taking into account the following adjustments, prepare Trading and Profit and Loss Account and Balance Sheet:(a) Stock in Hand on 31st March, 2018 is ₹1,36,000.(b) Machinery is to be depreciated 10% and patents 20%.(c) Salaries for the month of March, 2018 amounting to ₹30,000 were unpaid.(d) Insurance includes a premium of ₹1,700 for the year ending 31st March, 2019.(e) Wages include a sum of ₹40,000 spent on constructing a scooter shed for employees and customers.(f) Provision for Doubtful Debts is to be created to the extent of 5% on Sundry Debtors.

Answer» Following is the Trial Balance of Mr. S. Kapur on 31st March, 2018:


Particulars	Dr. (₹)	Cr. (₹)
Cash in Hand	10,800
Cash at Bank	2,32,600
Purchases	8,13,500
Sales		19,75,600
Returns Inward	13,600
Returns Outward		10,000
Wages	2,09,600
Fuel and Power	94,600
Carriage Outwards	64,000
Carriage on Purchases	40,800
Stock on 1st April, 2017	1,15,200
Building	6,00,000
Computer	2,00,000
Machinery	4,00,000
Salaries	3,00,000
Patents	1,50,000
Advertisement Expenses	60,000
Insurance	12,000
Capital		16,00,000
Drawings	1,04,900
Sundry Debtors	2,90,000
Sundry Creditors		1,31,000
Input CGST	7,500
Input SGST	7,500
Output IGST		10,000
Total	37,26,600	37,26,600

Taking into account the following adjustments, prepare Trading and Profit and Loss Account and Balance Sheet:

(a) Stock in Hand on 31st March, 2018 is ₹1,36,000.

(b) Machinery is to be depreciated 10% and patents 20%.

(c) Salaries for the month of March, 2018 amounting to ₹30,000 were unpaid.

(d) Insurance includes a premium of ₹1,700 for the year ending 31st March, 2019.

(e) Wages include a sum of ₹40,000 spent on constructing a scooter shed for employees and customers.

(f) Provision for Doubtful Debts is to be created to the extent of 5% on Sundry Debtors.

Discussion

2158.	If A and B are two events associated with a random experiment such that P(A) = 0.3, P(B) = 0.2 and P(A∩B) = 0.1, then of P(A∩B) =_______________.
Answer» If A and B are two events associated with a random experiment such that P(A) = 0.3, P(B) = 0.2 and P( $A \cap B$ ) = 0.1, then of P( $A \cap B$ ) =_______________.

Discussion

2159.	Is it possible to design a rectangular park of perimeter 80 m and area 400 m2 ? If so, find its length and breadth.
Answer» Is it possible to design a rectangular park of perimeter $80 m$ and area $400 m^{2}$ ? If so, find its length and breadth.

Discussion

2160.	If (a + b), (b – c) and (c + d) are in AP, then which of the following is in AP?
Answer» If (a + b), (b – c) and (c + d) are in AP, then which of the following is in AP?

Discussion

2161.	For an arithmetic sequence, what is the sum of three consecutive terms?
Answer» For an arithmetic sequence, what is the sum of three consecutive terms?

Discussion

2162.	Find a cubic polynomial whose zeroes are 12, 1 and −3.
Answer» Find a cubic polynomial whose zeroes are $\frac{1}{2}$ , 1 and −3.

Discussion

2163.	ntIf p = (16+83) -(21-123) , then find p -n ntA) 8n ntB) 6n ntC) 5n ntD) 4n
Answer» ntIf p = (16+83) -(21-123) , then find p -n ntA) 8n ntB) 6n ntC) 5n ntD) 4n

Discussion

2164.	3. The line joining the top of a hill to tje foot of the hill makes an angle of 30degree with the horizontal through the foot of the hill.there is one temple at the foot of the hill and a guest house halfway from the foot to the top .the top of the temple and of the guest house both make an elevation of 45 degree at the foot of the hill. If the guest house is 100 m away from the foot of the hill along the hill,find the height of the guest house and temple
Answer» 3. The line joining the top of a hill to tje foot of the hill makes an angle of 30degree with the horizontal through the foot of the hill.there is one temple at the foot of the hill and a guest house halfway from the foot to the top .the top of the temple and of the guest house both make an elevation of 45 degree at the foot of the hill. If the guest house is 100 m away from the foot of the hill along the hill,find the height of the guest house and temple

Discussion

2165.	A positive number is divided into 2 parts such that the sum of the squares of 2 parts is 208. The square of the larger part is 18 times the smaller part. Taking ‘’ as the smaller part of the 2 parts, find the numbers.
Answer» A positive number is divided into 2 parts such that the sum of the squares of 2 parts is 208. The square of the larger part is 18 times the smaller part. Taking ‘’ as the smaller part of the 2 parts, find the numbers.

Discussion

2166.	What is the area of rhombus
Answer» What is the area of rhombus

Discussion

2167.	The length an breadth of a rectangular garden are in the ratio 9:5.A path 3.5 m wide,running all around inside it has an area of 1911 m2.Find the dimensions of the garden.
Answer» The length an breadth of a rectangular garden are in the ratio 9:5.A path 3.5 m wide,running all around inside it has an area of 1911 $m^{2}$ .Find the dimensions of the garden.

Discussion

2168.	Find the value of k, if the point P (2, 4) is equidistant from the points A (5, k) and B (k, 7).
Answer» Find the value of k, if the point P (2, 4) is equidistant from the points A (5, k) and B (k, 7).

Discussion

2169.	A technician has to repair a light on a pole of height 10 m. She needs to reach a point 2 m below the top of the pole to undertake the repair work. The length of the ramp (in m) that she should use which, when inclined at an angle of 30∘ to the horizontal, would enable her to reach the required position is ___ m.
Answer» A technician has to repair a light on a pole of height 10 m. She needs to reach a point 2 m below the top of the pole to undertake the repair work. The length of the ramp (in m) that she should use which, when inclined at an angle of $30^{\circ}$ to the horizontal, would enable her to reach the required position is ___ m.

Discussion

2170.	Question 4 (ii) Which of the following are APs? If they form an A.P. find the common difference d and write three more terms. (ii) 2,52,3,72, …
Answer» Question 4 (ii) Which of the following are APs? If they form an A.P. find the common difference d and write three more terms. (ii) $2, \frac{5}{2}, 3, \frac{7}{2}, \dots$

Discussion

2171.	Fill In The Blanks Two congruent circles have centres at O and O'. Arc AXb of circle centred at O, subtends an angle of 75∘ at the centre O and arc PYQ ( or circle centred at O') subtends an angle 25∘ at the centre O'. The ratio of the arcs AXB and PYQ is ___________.
Answer» Fill In The Blanks Two congruent circles have centres at O and O'. Arc AXb of circle centred at O, subtends an angle of 75^∘ at the centre O and arc PYQ ( or circle centred at O') subtends an angle 25^∘ at the centre O'. The ratio of the arcs AXB and PYQ is ___________.

Discussion

2172.	ABC is a right angled triangle with ∠ ABC = 90∘. D is any point on AB and DE is perpendicular to AC. Prove that : (i) Δ ADE~Δ ACB. (ii) If AC = 13 cm, BC = 5 cm and AE = 4 cm. Find DE and AD. (iii) Find, area of Δ ADE : area of quadrilateral BCED.
Answer» ABC is a right angled triangle with $∠$ ABC = $90^{\circ}$ . D is any point on AB and DE is perpendicular to AC. Prove that : (i) $Δ$ ADE~ $Δ$ ACB. (ii) If AC = 13 cm, BC = 5 cm and AE = 4 cm. Find DE and AD. (iii) Find, area of $Δ$ ADE : area of quadrilateral BCED.

2172.

ABC is a right angled triangle with ∠ ABC = 90∘. D is any point on AB and DE is perpendicular to AC. Prove that : (i) Δ ADE~Δ ACB. (ii) If AC = 13 cm, BC = 5 cm and AE = 4 cm. Find DE and AD. (iii) Find, area of Δ ADE : area of quadrilateral BCED.

Answer»

ABC is a right angled triangle with $∠$ ABC = $90^{\circ}$ . D is any point on AB and DE is perpendicular to AC. Prove that : (i) $Δ$ ADE~ $Δ$ ACB. (ii) If AC = 13 cm, BC = 5 cm and AE = 4 cm. Find DE and AD. (iii) Find, area of $Δ$ ADE : area of quadrilateral BCED.

Discussion

2173.	Verify that points P(–2, 2), Q(2, 2) and R(2, 7) are vertices of a right angled triangle.
Answer» Verify that points P(–2, 2), Q(2, 2) and R(2, 7) are vertices of a right angled triangle.

Discussion

2174.	In the given figure, ∆ACB ∼ ∆APQ. If BC = 8 cm, PQ = 4 cm, BA = 6.5 cm and AP = 2.8 cm, find CA and AQ.
Answer» In the given figure, ∆ACB ∼ ∆APQ. If BC = 8 cm, PQ = 4 cm, BA = 6.5 cm and AP = 2.8 cm, find CA and AQ.

Discussion

2175.	If the discriminant of a quadratic equation is greater than 0, how many distinct real roots does it have?
Answer» If the discriminant of a quadratic equation is greater than 0, how many distinct real roots does it have?

Discussion

2176.	Find all the zeros of the polynomial x3 + 3x2 − 2x − 6, if two of its zeros are -2 and 2.
Answer» Find all the zeros of the polynomial x³ + 3x² − 2x − 6, if two of its zeros are $- \sqrt{2} and \sqrt{2}$ .

Discussion

2177.	38. The sum of dimensions of a cuboid is 21 m. if its diagonals are 7\sqrt{}5 cm, find its surface area.
Answer» 38. The sum of dimensions of a cuboid is 21 m. if its diagonals are 7\sqrt{}5 cm, find its surface area.

Discussion

2178.	Solve the following quadric equations by factorization method only x2+2x+5=0
Answer» Solve the following quadric equations by factorization method only $x^{2} + 2 x + 5 = 0$

Discussion

2179.	A man bought a certain number of toys for RS 180 ,he kept one for his own use and sold rest of it for one rupee each more than he gave for them , besides getting his own toy for nothing he made a profit of RS 10. Find no of toys.
Answer» A man bought a certain number of toys for RS 180 ,he kept one for his own use and sold rest of it for one rupee each more than he gave for them , besides getting his own toy for nothing he made a profit of RS 10. Find no of toys.

Discussion

2180.	A room is 16m long and 13.5 m broad.Find the cost of covering its floor with 75-m-wide carpet at Rs.60 per metre.
Answer» A room is 16m long and 13.5 m broad.Find the cost of covering its floor with 75-m-wide carpet at Rs.60 per metre.

Discussion

2181.	4. AB is a line segment of length 12 cm and M is its mid point . Semi circles are drawn with AM , MB and AB as diameters on same side of the line AB . A circle with centre O and radius r is drawn so that it touches all the 3 semi circles . It touches the circle with diameter AM at the point P , the circle with diameter MB at the point Q and the circle with diameter AB at the point R . Find the value of r if L and N are the mid points of AM and MB respectively and the points O , P , L ; the points O , Q , N and the points R , O , M are collinear .
Answer» 4. AB is a line segment of length 12 cm and M is its mid point . Semi circles are drawn with AM , MB and AB as diameters on same side of the line AB . A circle with centre O and radius r is drawn so that it touches all the 3 semi circles . It touches the circle with diameter AM at the point P , the circle with diameter MB at the point Q and the circle with diameter AB at the point R . Find the value of r if L and N are the mid points of AM and MB respectively and the points O , P , L ; the points O , Q , N and the points R , O , M are collinear .

Discussion

2182.	Find the Y coordinates for the points which lie on y = 2x + 1, whose X coordinates are 3, 4 and 6.
Answer» Find the Y coordinates for the points which lie on y = 2x + 1, whose X coordinates are 3, 4 and 6.

Discussion

2183.	Question 26 Encircle the odd one of the following: (a) (-3, 3) (b) (-5, 5) (c) (-6, 1) (d) (-8, 8)
Answer» Question 26 Encircle the odd one of the following: (a) (-3, 3) (b) (-5, 5) (c) (-6, 1) (d) (-8, 8)

2183.

Question 26 Encircle the odd one of the following: (a) (-3, 3) (b) (-5, 5) (c) (-6, 1) (d) (-8, 8)

Answer»

Question 26

Encircle the odd one of the following:

(a) (-3, 3)
(b) (-5, 5)
(c) (-6, 1)
(d) (-8, 8)

Discussion

2184.	Which of the following points does not lie in any quadrant?(a) (3, –6)(b) (–3, 4)(c) (5, 7)(d) (0, 3)
Answer» Which of the following points does not lie in any quadrant? (a) (3, –6) (b) (–3, 4) (c) (5, 7) (d) (0, 3)

Discussion

2185.	The conditions for ax+by+c=0 to be a linear equation in two variables (x,y) are
Answer» The conditions for $a x + b y + c = 0$ to be a linear equation in two variables $(x, y)$ are

Discussion

2186.	A card is drawn from a well-shuffled pack of 52 cards. Find the probability that the card drawn is neither a jack nor a queen.
Answer» A card is drawn from a well-shuffled pack of 52 cards. Find the probability that the card drawn is neither a jack nor a queen.

Discussion

2187.	Choose the correct answer of the following question:In the given figure, a tower AB is 20 m high and BC, its shadow on the ground is 203 m long. The sun's altitude is(a) 30° (b) 45° (c) 60° (d) none of these [CBSE 2015]
Answer» Choose the correct answer of the following question: In the given figure, a tower AB is 20 m high and BC, its shadow on the ground is $20 \sqrt{3}$ m long. The sun's altitude is (a) 30° (b) 45° (c) 60° (d) none of these [CBSE 2015]

Discussion

2188.	Factorise : (i) x3−2x2−x+2 (ii) 2y3+y2−2y−1
Answer» Factorise : (i) $x^{3}$ −2 $x^{2}$ −x+2 (ii) 2 $y^{3}$ + $y^{2}$ −2y−1

Discussion

2189.	If the zeroes of the quadratic polynomial ax2+bx+c, where a≠0 are equal then (A) c and a have opposite signs (B) c and b have opposite signs (C) c and a have the same sign (D) c and b have the same sign
Answer» If the zeroes of the quadratic polynomial $a x^{2} + b x + c, w h e r e a \neq 0$ are equal then (A) $c$ and $a$ have opposite signs (B) $c$ and $b$ have opposite signs (C) $c$ and $a$ have the same sign (D) $c$ and $b$ have the same sign

Discussion

2190.	Non-negative root of (3x−12x+3)2−5(3x−12x+3)+4=0 is _____.
Answer» Non-negative root of ${(\frac{3 x - 1}{2 x + 3})}^{2} - 5 (\frac{3 x - 1}{2 x + 3}) + 4 = 0$ is _____.

Discussion

2191.	If the polynomial (x4 + 2x3 + 8x2 + 12x + 18) is divided by another polynomial (x2 + 5), the remainder comes out to be (px + q). Find the values of p and q.
Answer» If the polynomial (x⁴ + 2x³+ 8x²+ 12x + 18) is divided by another polynomial (x² + 5), the remainder comes out to be (px + q). Find the values of p and q.

Discussion

2192.	Question 3Prove that, if a line is drawn parallel to one side of a triangle to intersect the other two sides, then the two sides are divided in the same ratio.
Answer» Question 3 Prove that, if a line is drawn parallel to one side of a triangle to intersect the other two sides, then the two sides are divided in the same ratio.

Discussion

2193.	56. Show that the line segment joining the mid point of the opposite sides of a quadrilateral bisect each other. Ag + I¯ → AgI + eˉ E^° = 0.152 V Ag → Ag+ + e¯ E^° = - 0.800 V What is the value of log Ksp for AgI (2.303RT/F = 0.059V )
Answer» 56. Show that the line segment joining the mid point of the opposite sides of a quadrilateral bisect each other. Ag + I¯ → AgI + eˉ E^° = 0.152 V Ag → Ag+ + e¯ E^° = - 0.800 V What is the value of log Ksp for AgI (2.303RT/F = 0.059V )

Discussion

2194.	The sum of the 2nd and the 7th terms of an AP is 30. If its 15th term is 1 less than twice its 8th term, find the AP. [CBSE 2014]
Answer» The sum of the 2nd and the 7th terms of an AP is 30. If its 15th term is 1 less than twice its 8th term, find the AP. [CBSE 2014]

Discussion

2195.	76 The value of x for which (5x + 2), (4x - 1) and (x + 2) are in arithmetic progression is
Answer» 76 The value of x for which (5x + 2), (4x - 1) and (x + 2) are in arithmetic progression is

Discussion

2196.	Shahrukh opened a Recurring Deposit Account in a bank and deposited Rs 800 per month for 112 years. If he received Rs 15,084 at the time of maturity, find the rate of interest per annum.
Answer» Shahrukh opened a Recurring Deposit Account in a bank and deposited Rs 800 per month for $1 \frac{1}{2}$ years. If he received Rs 15,084 at the time of maturity, find the rate of interest per annum.

Discussion

2197.	If the linex-32=y+2-1=z+43 lies in the plane lx+my-z=9, then find the value of l2+m2.
Answer» If the line $\frac{x - 3}{2} = \frac{y + 2}{- 1} = \frac{z + 4}{3}$ lies in the plane $l x + m y - z =$ 9, then find the value of $l^{2} + m^{2}$ .

Discussion

2198.	If px=2x3-11x2-4x+5 and gx=2x+1, show that g(x) is not a factor of p(x).
Answer» If $p (x) = 2 x^{3} - 11 x^{2} - 4 x + 5 and g (x) = 2 x + 1$ , show that g(x) is not a factor of p(x).

Discussion

2199.	The radius of the base of a right circular cone is 21 cm and its height is 20 cm. Find its volume.
Answer» The radius of the base of a right circular cone is 21 cm and its height is 20 cm. Find its volume.

Discussion

2200.	What will rupees 5000 amount to at 8% per annum for the period from April 6, 2017 to June 18, 2017
Answer» What will rupees 5000 amount to at 8% per annum for the period from April 6, 2017 to June 18, 2017

Discussion

Explore topic-wise InterviewSolutions in .

If the product of two zeros of the polynomial f(x) = 2x3 + 6x2 - 4x + 9 is 3, then its third zero is

Find the radius of a circle whose circumference is equal to the sum of the circumference of two circles of radii 15 cm and 18 cm .132974

Find the values of x and y in the following rectangle.

Is it possible to design a rectangular mango grove whose length is twice its breadth, and the area is 800 m2? If so, find its length and breadth.

Show that △ABC, where A(-2, 0), B(0, 2), and C(2, 0) and △PQR where P(-4, 0), Q(4, 0), R(0, 4) are similar triangles.

If A and B are two events associated with a random experiment such that P(A) = 0.3, P(B) = 0.2 and P(A∩B) = 0.1, then of P(A∩B) =_______________.

Is it possible to design a rectangular park of perimeter 80 m and area 400 m2 ? If so, find its length and breadth.

If (a + b), (b – c) and (c + d) are in AP, then which of the following is in AP?

For an arithmetic sequence, what is the sum of three consecutive terms?

Find a cubic polynomial whose zeroes are 12, 1 and −3.

ntIf p = (16+83) -(21-123) , then find p -n ntA) 8n ntB) 6n ntC) 5n ntD) 4n

A positive number is divided into 2 parts such that the sum of the squares of 2 parts is 208. The square of the larger part is 18 times the smaller part. Taking ‘’ as the smaller part of the 2 parts, find the numbers.

What is the area of rhombus

The length an breadth of a rectangular garden are in the ratio 9:5.A path 3.5 m wide,running all around inside it has an area of 1911 m2.Find the dimensions of the garden.

Find the value of k, if the point P (2, 4) is equidistant from the points A (5, k) and B (k, 7).

Question 4 (ii) Which of the following are APs? If they form an A.P. find the common difference d and write three more terms. (ii) 2,52,3,72, …

Fill In The Blanks Two congruent circles have centres at O and O'. Arc AXb of circle centred at O, subtends an angle of 75∘ at the centre O and arc PYQ ( or circle centred at O') subtends an angle 25∘ at the centre O'. The ratio of the arcs AXB and PYQ is ___________.

ABC is a right angled triangle with ∠ ABC = 90∘. D is any point on AB and DE is perpendicular to AC. Prove that : (i) Δ ADE~Δ ACB. (ii) If AC = 13 cm, BC = 5 cm and AE = 4 cm. Find DE and AD. (iii) Find, area of Δ ADE : area of quadrilateral BCED.

Verify that points P(–2, 2), Q(2, 2) and R(2, 7) are vertices of a right angled triangle.

In the given figure, ∆ACB ∼ ∆APQ. If BC = 8 cm, PQ = 4 cm, BA = 6.5 cm and AP = 2.8 cm, find CA and AQ.

If the discriminant of a quadratic equation is greater than 0, how many distinct real roots does it have?

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

38. The sum of dimensions of a cuboid is 21 m. if its diagonals are 7\sqrt{}5 cm, find its surface area.

Solve the following quadric equations by factorization method only x2+2x+5=0

A man bought a certain number of toys for RS 180 ,he kept one for his own use and sold rest of it for one rupee each more than he gave for them , besides getting his own toy for nothing he made a profit of RS 10. Find no of toys.

A room is 16m long and 13.5 m broad.Find the cost of covering its floor with 75-m-wide carpet at Rs.60 per metre.

Find the Y coordinates for the points which lie on y = 2x + 1, whose X coordinates are 3, 4 and 6.

Question 26 Encircle the odd one of the following: (a) (-3, 3) (b) (-5, 5) (c) (-6, 1) (d) (-8, 8)

Which of the following points does not lie in any quadrant?(a) (3, –6)(b) (–3, 4)(c) (5, 7)(d) (0, 3)

The conditions for ax+by+c=0 to be a linear equation in two variables (x,y) are

A card is drawn from a well-shuffled pack of 52 cards. Find the probability that the card drawn is neither a jack nor a queen.

Choose the correct answer of the following question:In the given figure, a tower AB is 20 m high and BC, its shadow on the ground is 203 m long. The sun's altitude is(a) 30° (b) 45° (c) 60° (d) none of these [CBSE 2015]

Factorise : (i) x3−2x2−x+2 (ii) 2y3+y2−2y−1

If the zeroes of the quadratic polynomial ax2+bx+c, where a≠0 are equal then (A) c and a have opposite signs (B) c and b have opposite signs (C) c and a have the same sign (D) c and b have the same sign

Non-negative root of (3x−12x+3)2−5(3x−12x+3)+4=0 is _____.

If the polynomial (x4 + 2x3 + 8x2 + 12x + 18) is divided by another polynomial (x2 + 5), the remainder comes out to be (px + q). Find the values of p and q.

Question 3Prove that, if a line is drawn parallel to one side of a triangle to intersect the other two sides, then the two sides are divided in the same ratio.

56. Show that the line segment joining the mid point of the opposite sides of a quadrilateral bisect each other. Ag + I¯ → AgI + eˉ E^° = 0.152 V Ag → Ag+ + e¯ E^° = - 0.800 V What is the value of log Ksp for AgI (2.303RT/F = 0.059V )

The sum of the 2nd and the 7th terms of an AP is 30. If its 15th term is 1 less than twice its 8th term, find the AP. [CBSE 2014]

76 The value of x for which (5x + 2), (4x - 1) and (x + 2) are in arithmetic progression is

Shahrukh opened a Recurring Deposit Account in a bank and deposited Rs 800 per month for 112 years. If he received Rs 15,084 at the time of maturity, find the rate of interest per annum.

If the linex-32=y+2-1=z+43 lies in the plane lx+my-z=9, then find the value of l2+m2.

If px=2x3-11x2-4x+5 and gx=2x+1, show that g(x) is not a factor of p(x).

The radius of the base of a right circular cone is 21 cm and its height is 20 cm. Find its volume.

What will rupees 5000 amount to at 8% per annum for the period from April 6, 2017 to June 18, 2017