32581 + Interview Questions in Mathematics Page 13 InterviewSolution

601.	Write the following by using ∑ notation(1) ab(a + b) + bc(b + c) + ca(c + a)(2) a2 + b2 + c2 − ab − bc − ca(3) x(y2 + z2) + y(z2 − x2) + z(x2 − y2)(4) ab2 − ac2 − a2b + bc2 − cb2 + ca2
Answer» Write the following by using ∑ notation (1) ab(a + b) + bc(b + c) + ca(c + a) (2) a² + b² + c² − ab − bc − ca (3) x(y² + z²) + y(z² − x²) + z(x² − y²) (4) ab² − ac² − a²b + bc² − cb² + ca²

601.

Write the following by using ∑ notation(1) ab(a + b) + bc(b + c) + ca(c + a)(2) a2 + b2 + c2 − ab − bc − ca(3) x(y2 + z2) + y(z2 − x2) + z(x2 − y2)(4) ab2 − ac2 − a2b + bc2 − cb2 + ca2

Answer»

Write the following by using ∑ notation

(1) ab(a + b) + bc(b + c) + ca(c + a)

(2) a² + b² + c² − ab − bc − ca

(3) x(y² + z²) + y(z² − x²) + z(x² − y²)

(4) ab² − ac² − a²b + bc² − cb² + ca²

Discussion

602.	In the given figure, O is the centre of two concentric circles of radii 5 cm and 3 cm. From an external point P tangents PA and PB are drawn to these circles. If PA = 12 cm then PB is equal to(a) 52 cm(b) 35 cm(c) 410 cm(d) 510 cm
Answer» In the given figure, O is the centre of two concentric circles of radii 5 cm and 3 cm. From an external point P tangents PA and PB are drawn to these circles. If PA = 12 cm then PB is equal to (a) $5 \sqrt{2} cm$ (b) $3 \sqrt{5} cm$ (c) $4 \sqrt{10} cm$ (d) $5 \sqrt{10} cm$

Discussion

603.	Which of the following is an essential function for a financial institution to become a bank?
Answer» Which of the following is an essential function for a financial institution to become a bank?

Discussion

604.	If α is the angle (in degrees) of a minor sector of a circle of radius r, then the area of the major sector is
Answer» If $α$ is the angle (in degrees) of a minor sector of a circle of radius $r$ , then the area of the major sector is

Discussion

605.	In the given figure, O is the centre of the circle and ∠DAB = 50° . Calculate the values of x and y.
Answer» In the given figure, O is the centre of the circle and ∠DAB = 50° . Calculate the values of x and y.

Discussion

606.	In ΔABC, BE ⊥ AC and CF ⊥ AB. BE and CF intersect at O. Show that
Answer» In ΔABC, BE ⊥ AC and CF ⊥ AB. BE and CF intersect at O. Show that

Discussion

607.	Solve the following systems of equations:11x+15y+23=07x-2y-20=0
Answer» Solve the following systems of equations: $11 x + 15 y + 23 = 0 7 x - 2 y - 20 = 0$

Discussion

608.	33. If m and n are the zeros of f(t)=9t2-9t+2.Find a quadratic polynomial whose zeros are (m+n)2 and (m-n)2
Answer» 33. If m and n are the zeros of f(t)=9t2-9t+2.Find a quadratic polynomial whose zeros are (m+n)2 and (m-n)2

Discussion

609.	The data of rainfall of 14 days recorded at a place is given.Draw a frequency table and find the average rainfall recored.70mm, 72mm, 77mm, 81mm, 83mm, 85mm, 83mm, 81mm, 84mm, 87mm, 89mm, 77mm, 81mm and 83mm.
Answer» The data of rainfall of 14 days recorded at a place is given.Draw a frequency table and find the average rainfall recored. 70mm, 72mm, 77mm, 81mm, 83mm, 85mm, 83mm, 81mm, 84mm, 87mm, 89mm, 77mm, 81mm and 83mm.

Discussion

610.	The Marked Price of an article is ₹50000. A wholeseller sells it to a dealer at 10% discount. The dealer further sells it to a customer at 20% profit. If the rate of GST at each stage is 18%, find the net tax liability of the dealer to the Government.
Answer» The Marked Price of an article is ₹50000. A wholeseller sells it to a dealer at 10% discount. The dealer further sells it to a customer at 20% profit. If the rate of GST at each stage is 18%, find the net tax liability of the dealer to the Government.

Discussion

611.	In the given figure, DE \|\| BC such that AE = (1/4) AC. If AB = 6 cm, find AD.
Answer» In the given figure, DE \|\| BC such that AE = (1/4) AC. If AB = 6 cm, find AD.

Discussion

612.	Thecylindrical tube of a spray pump has a cross-section of 8.0 cm2one end of which has 40 fine holes each of diameter 1.0 mm. If theliquid flow inside the tube is 1.5 m min–1,what is the speed of ejection of the liquid through the holes?
Answer» The cylindrical tube of a spray pump has a cross-section of 8.0 cm² one end of which has 40 fine holes each of diameter 1.0 mm. If the liquid flow inside the tube is 1.5 m min^–1, what is the speed of ejection of the liquid through the holes?

Discussion

613.	If sinθ=ab, show that secθ+tanθ=b+ab-a.
Answer» If $\sin θ = \frac{a}{b}$ , show that $(\sec θ + \tan θ) = \sqrt{\frac{b + a}{b - a}}$ .

Discussion

614.	Solve the following quadratic equations by factorization:1x+4-1x-7=1130, x≠4, 7
Answer» Solve the following quadratic equations by factorization: $\frac{1}{x + 4} - \frac{1}{x - 7} = \frac{11}{30}, x \neq 4, 7$

Discussion

615.	Question 8The value of c for which the pair of equations cx – y = 2 and 6x – 2y = 3 will have infinitely many solutions is(A) 3(B) – 3(C) –12(D) no value
Answer» Question 8 The value of c for which the pair of equations cx – y = 2 and 6x – 2y = 3 will have infinitely many solutions is (A) 3 (B) – 3 (C) –12 (D) no value

Discussion

616.	Write the first four terms of the sequence whose nth term is(a) Tn = 2n − 1(b) Tn = 5 − 2n(c) Tn = 3n2 + 1(d) Tn = 3n+1
Answer» Write the first four terms of the sequence whose nth term is (a) T_n = 2n − 1 (b) T_n = 5 − 2n (c) T_n = 3n² + 1 (d) T_n = 3ⁿ⁺¹

616.

Write the first four terms of the sequence whose nth term is(a) Tn = 2n − 1(b) Tn = 5 − 2n(c) Tn = 3n2 + 1(d) Tn = 3n+1

Answer»

Write the first four terms of the sequence whose nth term is

(a) T_n = 2n − 1

(b) T_n = 5 − 2n

(c) T_n = 3n² + 1

(d) T_n = 3ⁿ⁺¹

Discussion

617.	The probability of getting a composite number in a throw of an unbiased dice is___
Answer» The probability of getting a composite number in a throw of an unbiased dice is___

Discussion

618.	If x = r sin θ cos ϕ, y = r sin θ sin ϕ and z = r cos θ, then(a) x2+y2+z2=r2(b) x2+y2-z2=r2(c) x2-y2+z2=r2(d) z2+y2-x2=r2
Answer» If x = r sin θ cos ϕ, y = r sin θ sin ϕ and z = r cos θ, then (a) $x^{2} + y^{2} + z^{2} = r^{2}$ (b) $x^{2} + y^{2} - z^{2} = r^{2}$ (c) $x^{2} - y^{2} + z^{2} = r^{2}$ (d) $z^{2} + y^{2} - x^{2} = r^{2}$

Discussion

619.	If k is the ratio of the roots of polynomial x2+px−q, the value of k1+k2 is: [1 mark]
Answer» If k is the ratio of the roots of polynomial $x^{2} + p x - q$ , the value of $\frac{k}{1 + k^{2}}$ is: [1 mark]

Discussion

620.	If a≠b≠0, prove that the points (a,a2),(b,b2),(0,0) are never collinear.
Answer» If $a \neq b \neq 0,$ prove that the points $(a, a^{2}), (b, b^{2}), (0, 0)$ are never collinear.

Discussion

621.	37. From a point on B the ground 50 metres away from the tower the angle of elevation of the tower is 45^° and top a flag situated at the top of the tower is 60^° .Find height of the tower and flag
Answer» 37. From a point on B the ground 50 metres away from the tower the angle of elevation of the tower is 45^° and top a flag situated at the top of the tower is 60^° .Find height of the tower and flag

Discussion

622.	If A(–7, 5), B(–6, –7), C(–3, –8) and D(2, 3) are the vertices of a quadrilateral ABCD then find the area of the quadrilateral.
Answer» If A(–7, 5), B(–6, –7), C(–3, –8) and D(2, 3) are the vertices of a quadrilateral ABCD then find the area of the quadrilateral.

Discussion

623.	Two metallic spheres S1 and S2 are made of the same material and have got identical surface finish. The mass of S1 is thrice that of S2. Both the spheres are heated to the same high temperature and placed in the same room having lower temperature but are thermally insulated from each other. The ratio of the initial rate of cooling of S1 to that S2 is
Answer» Two metallic spheres $S_{1}$ and $S_{2}$ are made of the same material and have got identical surface finish. The mass of $S_{1}$ is thrice that of $S_{2}$ . Both the spheres are heated to the same high temperature and placed in the same room having lower temperature but are thermally insulated from each other. The ratio of the initial rate of cooling of $S_{1}$ to that $S_{2}$ is

Discussion

624.	In the given figure, \Delta ABC is right-angled at B such that BC = 6 cm and AB = 8 cm. A circle with centre O has been inscribed inside the triangle. OP ⊥ AB, OQ ⊥BC and OR ⊥ AC. if OP = OQ = OR = x cm then x = ? (a) 2 cm (b) 2.5 cm (c) 3 cm (d) 3.5 cm
Answer» In the given figure, \Delta ABC is right-angled at B such that BC = 6 cm and AB = 8 cm. A circle with centre O has been inscribed inside the triangle. OP $⊥$ AB, OQ $⊥$ BC and OR $⊥$ AC. if OP = OQ = OR = x cm then x = ? (a) 2 cm (b) 2.5 cm (c) 3 cm (d) 3.5 cm

624.

In the given figure, \Delta ABC is right-angled at B such that BC = 6 cm and AB = 8 cm. A circle with centre O has been inscribed inside the triangle. OP ⊥ AB, OQ ⊥BC and OR ⊥ AC. if OP = OQ = OR = x cm then x = ? (a) 2 cm (b) 2.5 cm (c) 3 cm (d) 3.5 cm

Answer»

In the given figure, \Delta ABC is right-angled at B such that BC = 6 cm and AB = 8 cm. A circle with centre O has been inscribed inside the triangle. OP $⊥$ AB, OQ $⊥$ BC and OR $⊥$ AC. if OP = OQ = OR = x cm then x = ?

(a) 2 cm (b) 2.5 cm

(c) 3 cm (d) 3.5 cm

Discussion

625.	The following table shows marks secured by 140 students in an examination:MarksNumber of students0−102010−202420−304030−403640−5020Calculate mean marks by the step deviation method.
Answer» The following table shows marks secured by 140 students in an examination: $\begin{matrix} Marks & Number of students 0 - 10 & 20 10 - 20 & 24 20 - 30 & 40 30 - 40 & 36 40 - 50 & 20 \end{matrix}$ Calculate mean marks by the step deviation method.

Discussion

626.	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 the number is ___.
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 the number is ___.

Discussion

627.	if the perimeter of a rectangle is 24 units and length exceeds the breadth by 4 units.find the are of the rectangle.
Answer» if the perimeter of a rectangle is 24 units and length exceeds the breadth by 4 units.find the are of the rectangle.

Discussion

628.	If tan x = 3 cot x then x = ? (a) 45o (b) 60o (c) 30o (d) 15o
Answer» If tan x = 3 cot x then x = ? (a) $45^{o}$ (b) $60^{o}$ (c) $30^{o}$ (d) $15^{o}$

628.

If tan x = 3 cot x then x = ? (a) 45o (b) 60o (c) 30o (d) 15o

Answer»

If tan x = 3 cot x then x = ?

(a) $45^{o}$ (b) $60^{o}$ (c) $30^{o}$ (d) $15^{o}$

Discussion

629.	The greatest four-digit number which is divisible by 15, 25, 40 and 75 is:
Answer» The greatest four-digit number which is divisible by 15, 25, 40 and 75 is:

Discussion

630.	If the number of square centimetres on the surface of a sphere is equal to the number of cubic centimetres in its volume,what is the diameter of the sphere?
Answer» If the number of square centimetres on the surface of a sphere is equal to the number of cubic centimetres in its volume,what is the diameter of the sphere?

Discussion

631.	A cylindrical tub radius 12 cm contains water to a depth of 20 cm. A spherical ball is dropped into the tub and the level of the water is raised by 6.75 cn. Find the radius of the ball.
Answer» A cylindrical tub radius 12 cm contains water to a depth of 20 cm. A spherical ball is dropped into the tub and the level of the water is raised by 6.75 cn. Find the radius of the ball.

Discussion

632.	If sin θ + cos θ = 2 cos 90°-θ, find cot θ.
Answer» If sin θ + cos θ = $\sqrt{2} \cos (90 ° - θ)$ , find cot θ.

Discussion

633.

Find the median of the following data: Class interval0−1010−2020−3030−4040−50TotalFrequency81636346100

Answer»

Find the median of the following data:

Class interval	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	Total
Frequency	$8$	$16$	$36$	$34$	$6$	$100$

Discussion

634.	Solve the following systems of equations: 22x+y+15x−y=5 55x+y+45x−y=14
Answer» Solve the following systems of equations: $\frac{22}{x + y} + \frac{15}{x - y} = 5$ $\frac{55}{x + y} + \frac{45}{x - y} = 14$

634.

Solve the following systems of equations: 22x+y+15x−y=5 55x+y+45x−y=14

Answer»

Solve the following systems of equations:

$\frac{22}{x + y} + \frac{15}{x - y} = 5$

$\frac{55}{x + y} + \frac{45}{x - y} = 14$

Discussion

635.

Find the following table gives the distribution of the life time of 400 neon lamps: Life time (in hours) Number of lamps 1500 − 2000 14 2000 − 2500 56 2500 − 3000 60 3000 − 3500 86 3500 − 4000 74 4000 − 4500 62 4500 − 5000 48 Find the median life time of a lamp.

Answer»

Find the following table gives the distribution of the life time of 400 neon lamps:

Life time (in hours)	Number of lamps
1500 − 2000	14
2000 − 2500	56
2500 − 3000	60
3000 − 3500	86
3500 − 4000	74
4000 − 4500	62
4500 − 5000	48

Find the median life time of a lamp.

Discussion

636.	If discriminant of a quadratic equation < 0, how many distinct real roots does it have?
Answer» If discriminant of a quadratic equation < 0, how many distinct real roots does it have?

Discussion

637.	________ of the data is the difference between the maximum and the minimum values of the observations.
Answer» ________ of the data is the difference between the maximum and the minimum values of the observations.

Discussion

638.	If a and b are the zeroes of a polynomial px2−5x+q,then find the values of p and q, if a + b = ab = 10.
Answer» $If a and b are the zeroes of a polynomial p x^{2} - 5 x + q, then find the values of p and q, if a + b = ab = 10.$

Discussion

639.	The number of tangents that can be drawn from a point outside a circle is ____.
Answer» The number of tangents that can be drawn from a point outside a circle is ____.

639.

The number of tangents that can be drawn from a point outside a circle is ____.

Answer»

The number of tangents that can be drawn from a point outside a circle is ____.

Discussion

640.	Question 9If bisectors of opposite angles of a cyclic quadrilateral ABCD intersect the circle, circumscribing it at the point P and Q, prove that PQ is a diameter of the circle.
Answer» Question 9 If bisectors of opposite angles of a cyclic quadrilateral ABCD intersect the circle, circumscribing it at the point P and Q, prove that PQ is a diameter of the circle.

Discussion

641.	In an equilateral triangleABC, D is a point on side BC such that BD=13BC. prove that 9AD=7AB.
Answer» In an equilateral triangleABC, D is a point on side BC such that $B D = \frac{1}{3}$ BC. prove that 9AD=7AB.

Discussion

642.	Find the median of the following data by making a 'less than ogive'. Marks0−1010−2020−3030−4040−5050−6060−7070−8080−9090−100Number of students5343347978
Answer» Find the median of the following data by making a 'less than ogive'. $\begin{matrix} M a r k s & 0 - 10 & 10 - 20 & 20 - 30 & 30 - 40 & 40 - 50 & 50 - 60 & 60 - 70 & 70 - 80 & 80 - 90 & 90 - 100 N u m b e r o f s t u d e n t s & 5 & 3 & 4 & 3 & 3 & 4 & 7 & 9 & 7 & 8 \end{matrix}$

642.

Find the median of the following data by making a 'less than ogive'. Marks0−1010−2020−3030−4040−5050−6060−7070−8080−9090−100Number of students5343347978

Answer»

Find the median of the following data by making a 'less than ogive'.

$\begin{matrix} M a r k s & 0 - 10 & 10 - 20 & 20 - 30 & 30 - 40 & 40 - 50 & 50 - 60 & 60 - 70 & 70 - 80 & 80 - 90 & 90 - 100 N u m b e r o f s t u d e n t s & 5 & 3 & 4 & 3 & 3 & 4 & 7 & 9 & 7 & 8 \end{matrix}$

Discussion

643.	If the cost of a bike x is twice the cost of a scooter y , Respresent it using equations in 2 variables in the form ax+by = 0
Answer» If the cost of a bike x is twice the cost of a scooter y , Respresent it using equations in 2 variables in the form ax+by = 0

Discussion

644.	Prove that If the sides of a parallelogram touch a circle, then the parallelogram is a rhombus.
Answer» Prove that If the sides of a parallelogram touch a circle, then the parallelogram is a rhombus.

Discussion

645.	Write the standard form of a cubic polynomial with real coefficients.
Answer» Write the standard form of a cubic polynomial with real coefficients.

Discussion

646.	If the points A (1,2) , O (0,0) and C (a,b) are collinear , then find a : b.
Answer» If the points A (1,2) , O (0,0) and C (a,b) are collinear , then find a : b.

Discussion

647.

Given below is the Balance Sheet of A and B, who are carrying on partnership business on 31st March, 2019. A and B share profits and losses in the ratio of 2 : 1. BALANCE SHEET OF A AND B as at 31st March, 2019 Liabilities ₹ Assets ₹ Bills Payable 10,000 Cash in Hand 10,000 Creditors 58,000 Cash at Bank 40,000 Outstanding Expenses 2,000 Sundry Debtors 60,000 Capital A/cs: Stock 40,000 A 1,80,000 Plant 1,00,000 B 1,50,000 3,30,000 Building 1,50,000 4,00,000 4,00,000 C is admitted as a partner on 1st April, 2019 on the following terms:(a) C will bring ₹ 1,00,000 as his capital and ₹ 60,000 as his share of goodwill for 1/4th share in the profits.(b) Plant is to be appreciated to ₹ 1,20,000 and the value of building is to be appreciated by 10%.(c) Stock is found overvalued by ₹ 4,000.(d) A provision for doubtful debts is to be created at 5% of sundry debtors.(e) Creditors were unrecorded to the extent of ₹ 1,000.Pass the necessary Journal entries, prepare the Revaluation Account and Partners' Capital Accounts, and show the Balance Sheet after the admission of C.

Answer» Given below is the Balance Sheet of A and B, who are carrying on partnership business on 31st March, 2019. A and B share profits and losses in the ratio of 2 : 1.

BALANCE SHEET OF A AND B

as at 31st March, 2019
Liabilities		₹	Assets	₹
Bills Payable		10,000	Cash in Hand	10,000
Creditors		58,000	Cash at Bank	40,000
Outstanding Expenses		2,000	Sundry Debtors	60,000
Capital A/cs:			Stock	40,000
A	1,80,000		Plant	1,00,000
B	1,50,000	3,30,000	Building	1,50,000
		4,00,000		4,00,000

C is admitted as a partner on 1st April, 2019 on the following terms:

(a) C will bring ₹ 1,00,000 as his capital and ₹ 60,000 as his share of goodwill for 1/4th share in the profits.

(b) Plant is to be appreciated to ₹ 1,20,000 and the value of building is to be appreciated by 10%.

(c) Stock is found overvalued by ₹ 4,000.

(d) A provision for doubtful debts is to be created at 5% of sundry debtors.

(e) Creditors were unrecorded to the extent of ₹ 1,000.

Pass the necessary Journal entries, prepare the Revaluation Account and Partners' Capital Accounts, and show the Balance Sheet after the admission of C.

Discussion

648.	The probability of selecting a green marble at random from a jar that contains only green, white and yellow marbles is 1/4. The probability of selecting a white marble at random from the same jar is 1/3. If this jar contains 10 yellow marbles. What is the total number of marbles in the jar?
Answer» The probability of selecting a green marble at random from a jar that contains only green, white and yellow marbles is 1/4. The probability of selecting a white marble at random from the same jar is 1/3. If this jar contains 10 yellow marbles. What is the total number of marbles in the jar?

Discussion

649.	Question: A mason has to fit a bathroom with square marble tiles of the largest possible size .The size of the bathroom is 10 ft.by 8ft.What would be the size in inches of the tile required that has to be cut and how many such tiles are required?
Answer» Question: A mason has to fit a bathroom with square marble tiles of the largest possible size .The size of the bathroom is 10 ft.by 8ft.What would be the size in inches of the tile required that has to be cut and how many such tiles are required?

Discussion

650.	A motor boat whose speed in still water is 18 km/hr takes 1 hour more to go 24 km up stream that to return down stream to the same spot. Find the speed of the stream.
Answer» A motor boat whose speed in still water is 18 km/hr takes 1 hour more to go 24 km up stream that to return down stream to the same spot. Find the speed of the stream.

Discussion

Explore topic-wise InterviewSolutions in .

Write the following by using ∑ notation(1) ab(a + b) + bc(b + c) + ca(c + a)(2) a2 + b2 + c2 − ab − bc − ca(3) x(y2 + z2) + y(z2 − x2) + z(x2 − y2)(4) ab2 − ac2 − a2b + bc2 − cb2 + ca2

In the given figure, O is the centre of two concentric circles of radii 5 cm and 3 cm. From an external point P tangents PA and PB are drawn to these circles. If PA = 12 cm then PB is equal to(a) 52 cm(b) 35 cm(c) 410 cm(d) 510 cm

Which of the following is an essential function for a financial institution to become a bank?

If α is the angle (in degrees) of a minor sector of a circle of radius r, then the area of the major sector is

In the given figure, O is the centre of the circle and ∠DAB = 50° . Calculate the values of x and y.

In ΔABC, BE ⊥ AC and CF ⊥ AB. BE and CF intersect at O. Show that

Solve the following systems of equations:11x+15y+23=07x-2y-20=0

33. If m and n are the zeros of f(t)=9t2-9t+2.Find a quadratic polynomial whose zeros are (m+n)2 and (m-n)2

The data of rainfall of 14 days recorded at a place is given.Draw a frequency table and find the average rainfall recored.70mm, 72mm, 77mm, 81mm, 83mm, 85mm, 83mm, 81mm, 84mm, 87mm, 89mm, 77mm, 81mm and 83mm.

The Marked Price of an article is ₹50000. A wholeseller sells it to a dealer at 10% discount. The dealer further sells it to a customer at 20% profit. If the rate of GST at each stage is 18%, find the net tax liability of the dealer to the Government.

In the given figure, DE || BC such that AE = (1/4) AC. If AB = 6 cm, find AD.

Thecylindrical tube of a spray pump has a cross-section of 8.0 cm2one end of which has 40 fine holes each of diameter 1.0 mm. If theliquid flow inside the tube is 1.5 m min–1,what is the speed of ejection of the liquid through the holes?

If sinθ=ab, show that secθ+tanθ=b+ab-a.

Solve the following quadratic equations by factorization:1x+4-1x-7=1130, x≠4, 7

Question 8The value of c for which the pair of equations cx – y = 2 and 6x – 2y = 3 will have infinitely many solutions is(A) 3(B) – 3(C) –12(D) no value

Write the first four terms of the sequence whose nth term is(a) Tn = 2n − 1(b) Tn = 5 − 2n(c) Tn = 3n2 + 1(d) Tn = 3n+1

The probability of getting a composite number in a throw of an unbiased dice is___

If x = r sin θ cos ϕ, y = r sin θ sin ϕ and z = r cos θ, then(a) x2+y2+z2=r2(b) x2+y2-z2=r2(c) x2-y2+z2=r2(d) z2+y2-x2=r2

If k is the ratio of the roots of polynomial x2+px−q, the value of k1+k2 is: [1 mark]

If a≠b≠0, prove that the points (a,a2),(b,b2),(0,0) are never collinear.

37. From a point on B the ground 50 metres away from the tower the angle of elevation of the tower is 45^° and top a flag situated at the top of the tower is 60^° .Find height of the tower and flag

If A(–7, 5), B(–6, –7), C(–3, –8) and D(2, 3) are the vertices of a quadrilateral ABCD then find the area of the quadrilateral.

In the given figure, \Delta ABC is right-angled at B such that BC = 6 cm and AB = 8 cm. A circle with centre O has been inscribed inside the triangle. OP ⊥ AB, OQ ⊥BC and OR ⊥ AC. if OP = OQ = OR = x cm then x = ? (a) 2 cm (b) 2.5 cm (c) 3 cm (d) 3.5 cm

The following table shows marks secured by 140 students in an examination:MarksNumber of students0−102010−202420−304030−403640−5020Calculate mean marks by the step deviation method.

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 the number is ___.

if the perimeter of a rectangle is 24 units and length exceeds the breadth by 4 units.find the are of the rectangle.

If tan x = 3 cot x then x = ? (a) 45o (b) 60o (c) 30o (d) 15o

The greatest four-digit number which is divisible by 15, 25, 40 and 75 is:

If the number of square centimetres on the surface of a sphere is equal to the number of cubic centimetres in its volume,what is the diameter of the sphere?

A cylindrical tub radius 12 cm contains water to a depth of 20 cm. A spherical ball is dropped into the tub and the level of the water is raised by 6.75 cn. Find the radius of the ball.

If sin θ + cos θ = 2 cos 90°-θ, find cot θ.

Find the median of the following data: Class interval0−1010−2020−3030−4040−50TotalFrequency81636346100

Solve the following systems of equations: 22x+y+15x−y=5 55x+y+45x−y=14

Find the following table gives the distribution of the life time of 400 neon lamps: Life time (in hours) Number of lamps 1500 − 2000 14 2000 − 2500 56 2500 − 3000 60 3000 − 3500 86 3500 − 4000 74 4000 − 4500 62 4500 − 5000 48 Find the median life time of a lamp.

If discriminant of a quadratic equation &lt; 0, how many distinct real roots does it have?

________ of the data is the difference between the maximum and the minimum values of the observations.

If a and b are the zeroes of a polynomial px2−5x+q,then find the values of p and q, if a + b = ab = 10.

The number of tangents that can be drawn from a point outside a circle is ____.

Question 9If bisectors of opposite angles of a cyclic quadrilateral ABCD intersect the circle, circumscribing it at the point P and Q, prove that PQ is a diameter of the circle.

In an equilateral triangleABC, D is a point on side BC such that BD=13BC. prove that 9AD=7AB.

Find the median of the following data by making a 'less than ogive'. Marks0−1010−2020−3030−4040−5050−6060−7070−8080−9090−100Number of students5343347978

If the cost of a bike x is twice the cost of a scooter y , Respresent it using equations in 2 variables in the form ax+by = 0

Prove that If the sides of a parallelogram touch a circle, then the parallelogram is a rhombus.

Write the standard form of a cubic polynomial with real coefficients.

If the points A (1,2) , O (0,0) and C (a,b) are collinear , then find a : b.

The probability of selecting a green marble at random from a jar that contains only green, white and yellow marbles is 1/4. The probability of selecting a white marble at random from the same jar is 1/3. If this jar contains 10 yellow marbles. What is the total number of marbles in the jar?

Question: A mason has to fit a bathroom with square marble tiles of the largest possible size .The size of the bathroom is 10 ft.by 8ft.What would be the size in inches of the tile required that has to be cut and how many such tiles are required?

A motor boat whose speed in still water is 18 km/hr takes 1 hour more to go 24 km up stream that to return down stream to the same spot. Find the speed of the stream.

If discriminant of a quadratic equation < 0, how many distinct real roots does it have?