32581 + Interview Questions in Mathematics Page 188 InterviewSolution

9351.	If the roots ofx^2 +mx + 12=0 are in the ratio 1:3. find 'm'
Answer» If the roots ofx^2 +mx + 12=0 are in the ratio 1:3. find 'm'

Discussion

9352.	10. Let abc be a right-angled triangle with /_B=90 degree. Let AD be the bisector of /_A with D on BC. Let the circumcircle of triangle ACD intersect AB again in E; and let the circumcircle of triangle ABD intersect AC again in F. Let K be the reflection of E in the line BC. Prove that FK=BC.
Answer» 10. Let abc be a right-angled triangle with /_B=90 degree. Let AD be the bisector of /_A with D on BC. Let the circumcircle of triangle ACD intersect AB again in E; and let the circumcircle of triangle ABD intersect AC again in F. Let K be the reflection of E in the line BC. Prove that FK=BC.

Discussion

9353.

Shyamlal and Sanjay were in partnership business sharing profits and losses in the ratio of 2 : 3 respectively. Their Balance Sheet as at 31st March, 2019 was: Liabilities ₹ Assets ₹ Sundry Creditors 12,435 Cash in Hand 710 Capital A/cs: Cash at Bank 11,925 Shyamlal 34,050 Sundry Debtors 5,500 Sanjay 34,050 68,100 Stock 18,000 Furniture 4,400 Building 40,000 80,535 80,535 On 1st April, 2019, they admitted Shanker into partnership for 1/3rd share in future profits on the following terms:(a) Shanker is to bring in ₹ 30,000 as his capital and ₹ 20,000 as goodwill which is to remain in the business.(b) Stock and Furniture are to be reduced in value by 10%.(c) Building is to be appreciated by ₹ 15,000.(d) Provision of 5% is to be made on Sundry Debtors for Doubtful Debts.(e) Unaccounted Accrued Income of ₹ 2,400 to be provided for. A debtor, whose dues of ₹ 4,800 were written off as bad debts, paid 50% in full settlement.(f) Outstanding Rent amounted to ₹ 4,800.Show Profit and Loss Adjustment Account (Revaluation Account), Capital Accounts of Partners and opening Balance Sheet of the new firm.

Answer» Shyamlal and Sanjay were in partnership business sharing profits and losses in the ratio of 2 : 3 respectively. Their Balance Sheet as at 31st March, 2019 was:


Liabilities		₹	Assets	₹
Sundry Creditors		12,435	Cash in Hand	710
Capital A/cs:			Cash at Bank	11,925
Shyamlal	34,050		Sundry Debtors	5,500
Sanjay	34,050	68,100	Stock	18,000
			Furniture	4,400
			Building	40,000


		80,535		80,535

On 1st April, 2019, they admitted Shanker into partnership for 1/3rd share in future profits on the following terms:

(a) Shanker is to bring in ₹ 30,000 as his capital and ₹ 20,000 as goodwill which is to remain in the business.

(b) Stock and Furniture are to be reduced in value by 10%.

(c) Building is to be appreciated by ₹ 15,000.

(d) Provision of 5% is to be made on Sundry Debtors for Doubtful Debts.

(e) Unaccounted Accrued Income of ₹ 2,400 to be provided for. A debtor, whose dues of ₹ 4,800 were written off as bad debts, paid 50% in full settlement.

(f) Outstanding Rent amounted to ₹ 4,800.

Show Profit and Loss Adjustment Account (Revaluation Account), Capital Accounts of Partners and opening Balance Sheet of the new firm.

Discussion

9354.	58.Given polynomial is exactly divisible by x+1 and when it is divided by 3x-1 ,the remainder is 4. The polynomial gives remainder hx+k when divided by 3xsquare+2x-1. Then find values of h and k.
Answer» 58.Given polynomial is exactly divisible by x+1 and when it is divided by 3x-1 ,the remainder is 4. The polynomial gives remainder hx+k when divided by 3xsquare+2x-1. Then find values of h and k.

Discussion

9355.	If A and B are independent events such that P(A)=0.3,P(B)=0.4, then the value of P(A and B) is:
Answer» If $A$ and $B$ are independent events such that $P (A) = 0.3, P (B) = 0.4$ , then the value of $P (A and B)$ is:

Discussion

9356.	Question 109 (ii) Observe the following patterns and fill in the blanks to make the statements true: 7×4=28 7×3= ___=28−7 7×2=___=___=−7 7×1=7=___−7 7×0=___ =___-___ 7×(−1)=−7=___-___ 7×(−2)=___=___-___ 7×(−3)___=___-___
Answer» Question 109 (ii) Observe the following patterns and fill in the blanks to make the statements true: $7 \times 4 = 28$ $7 \times 3 =$ ___ $= 28 - 7$ $7 \times 2 =$ ___=___ $= - 7$ $7 \times 1 = 7 =$ ___ $- 7$ $7 \times 0 =$ ___ =___-___ $7 \times (- 1) = - 7 =$ ___-___ $7 \times (- 2) =$ ___=___-___ $7 \times (- 3)$ ___=___-___

9356.

Question 109 (ii) Observe the following patterns and fill in the blanks to make the statements true: 7×4=28 7×3= _=28−7 7×2=_=_=−7 7×1=7=_−7 7×0=_ =_-_ 7×(−1)=−7=_-_ 7×(−2)=_=_-_ 7×(−3)_=_-___

Answer»

Question 109 (ii)

Observe the following patterns and fill in the blanks to make the statements true:
$7 \times 4 = 28$
$7 \times 3 =$ ___ $= 28 - 7$
$7 \times 2 =$ ___=___ $= - 7$
$7 \times 1 = 7 =$ ___ $- 7$
$7 \times 0 =$ ___ =___-___
$7 \times (- 1) = - 7 =$ ___-___
$7 \times (- 2) =$ ___=___-___
$7 \times (- 3)$ ___=___-___

Discussion

9357.	If arc tan(sin²Q - 2sinQ + 3) + arc cot(5^[sec²y] + 1) = pie/2 then find the value of cos²Q - sinQ is equal to _____.
Answer» If arc tan(sin²Q - 2sinQ + 3) + arc cot(5^[sec²y] + 1) = pie/2 then find the value of cos²Q - sinQ is equal to _____.

Discussion

9358.	Write the number of all possible matrices of order 2 × 2 with each entry 1, 2 or 3.
Answer» Write the number of all possible matrices of order 2 × 2 with each entry 1, 2 or 3.

Discussion

9359.	In △PQR, PQ = 12 cm and PR = 13 cm. ∠Q=90∘. Find tan P - cot R
Answer» In $△$ PQR, PQ = 12 cm and PR = 13 cm. $∠ Q = 90^{\circ}$ . Find tan P - cot R

Discussion

9360.

The daily wages of 40 workers of a factory are given in the following table. Wages in Rs. 30 – 34 34 – 38 38 – 42 42 – 46 46 – 50 50 – 54 No. of workers 4 7 9 11 6 3 Calculate (i) Mean (ii) Variance and (iii) Standard Deviation of wages and also interpret the findings.

Answer»

The daily wages of 40 workers of a factory are given in the following table.

Wages in Rs.	30 – 34	34 – 38	38 – 42	42 – 46	46 – 50	50 – 54
No. of workers	4	7	9	11	6	3

Calculate (i) Mean (ii) Variance and (iii) Standard Deviation of wages and also interpret the findings.

Discussion

9361.

Mukesh Khanna has not kept proper books. However, he gives you the following information relating to the year 2018-19: SUMMARY OF HIS CASH BOOK (₹) (₹) To Balance b/d 8,100 By Payment to Creditors 56,200 To Received from Debtors 75,000 By Carriage 1,270 To Cash Sales 52,000 By Salaries 24,000 To Sales of Old Newspapers 420 By Rent 16,000 To Loan from Mrs. Khanna 15% p.a. on 1st July, 2018 8,000 By Purchases of Cycle for his son 1,500 By Furniture Purchased 12,000 By Balance c/d 32,550 1,43,520 1,43,520 The following balances existed on 1st April, 2018 - Debtors ₹ 24,200; Furniture ₹ 18,000; Stock ₹ 30,000; Creditors ₹ 18,000.The following balances existed on 31st March, 2019 - Debtors ₹ 20,800; Furniture ₹ 30,000; Stock ₹ 35,950; Creditors ₹ 34,600.Adjustments:-(1) Depreciate Furniture by 10%.(2) Provide upto-date interest on Mrs. Khanna's Loan.Prepare Trading and Profit and Loss A/c for the year ending 31st March, 2019 and a Balance Sheet as at that date.

Answer» Mukesh Khanna has not kept proper books. However, he gives you the following information relating to the year 2018-19:

SUMMARY OF HIS CASH BOOK
	(₹)		(₹)
To Balance b/d	8,100	By Payment to Creditors	56,200
To Received from Debtors	75,000	By Carriage	1,270
To Cash Sales	52,000	By Salaries	24,000
To Sales of Old Newspapers	420	By Rent	16,000
To Loan from Mrs. Khanna 15% p.a. on 1st July, 2018	8,000	By Purchases of Cycle for his son	1,500
		By Furniture Purchased	12,000
		By Balance c/d	32,550

	1,43,520		1,43,520

The following balances existed on 1st April, 2018 - Debtors ₹ 24,200; Furniture ₹ 18,000; Stock ₹ 30,000; Creditors ₹ 18,000.

The following balances existed on 31st March, 2019 - Debtors ₹ 20,800; Furniture ₹ 30,000; Stock ₹ 35,950; Creditors ₹ 34,600.

Adjustments:-

(1) Depreciate Furniture by 10%.

(2) Provide upto-date interest on Mrs. Khanna's Loan.

Prepare Trading and Profit and Loss A/c for the year ending 31st March, 2019 and a Balance Sheet as at that date.

Discussion

9362.	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

9363.	Show that (p – 1) is a factor of (p10 – 1) and also of (p11 – 1).
Answer» Show that (p – 1) is a factor of (p¹⁰ – 1) and also of (p¹¹ – 1).

Discussion

9364.	Question 3Write ‘True’ or ‘False’ and justify your answer in each of the following:The value of the expression,(sin80∘−cos80∘) is negative.
Answer» Question 3 Write ‘True’ or ‘False’ and justify your answer in each of the following: The value of the expression, $(s i n 80^{\circ} - c o s 80^{\circ})$ is negative.

Discussion

9365.	In the given figure, ABCD is a rectangle of dimensions 21 cm × 14 cm. A semicircle is drawn with BC as diameter. Find the area and the perimeter of the shaded region in the figure. [CBSE 2017]
Answer» In the given figure, ABCD is a rectangle of dimensions 21 cm × 14 cm. A semicircle is drawn with BC as diameter. Find the area and the perimeter of the shaded region in the figure. [CBSE 2017]

Discussion

9366.	The first three terms of an A.P. respectively are 3y − 1, 3y + 5 and 5y + 1. Then, y equals(a) −3(b) 4(c) 5(d) 2
Answer» The first three terms of an A.P. respectively are 3y − 1, 3y + 5 and 5y + 1. Then, y equals (a) −3 (b) 4 (c) 5 (d) 2

Discussion

9367.	Convert the given decimals to percents. [2 MARKS] a) 0.65 b) 2.1
Answer» Convert the given decimals to percents. [2 MARKS] a) 0.65 b) 2.1

Discussion

9368.	If a and b are the zeroes of the quadratic polynomial f(x)=3x^2-7x-6, find a polynomial whose zeroes are (i) a^2 and b^2 (ii) 2a+3b and 3a+2b
Answer» If a and b are the zeroes of the quadratic polynomial f(x)=3x^2-7x-6, find a polynomial whose zeroes are (i) a^2 and b^2 (ii) 2a+3b and 3a+2b

Discussion

9369.	In the above figure, PB and PQ are tangents from point P, and MN and RN are tangents from the point N to the circle with centre O. Select the statemeents that are true:
Answer» In the above figure, PB and PQ are tangents from point P, and MN and RN are tangents from the point N to the circle with centre O. Select the statemeents that are true:

9369.

In the above figure, PB and PQ are tangents from point P, and MN and RN are tangents from the point N to the circle with centre O. Select the statemeents that are true:

Answer»

In the above figure, PB and PQ are tangents from point P, and MN and RN are tangents from the point N to the circle with centre O.

Select the statemeents that are true:

Discussion

9370.	The contrapositive of the statement p ⇒ ∼q is ________________________.
Answer» The contrapositive of the statement p ⇒ ∼q is ________________________.

Discussion

9371.

Find the mode, median and mean for the following data: [CBSE 2009] Marks obtained 25−35 35−45 45−55 55−65 65−75 75−85 Number of students 7 31 33 17 11 1

Answer»

Find the mode, median and mean for the following data: [CBSE 2009]

Marks obtained	25−35	35−45	45−55	55−65	65−75	75−85
Number of students	7	31	33	17	11	1

Discussion

9372.	Five identical cubes, each of edge 5 cm, are placed adjacent to each other. Find the volume of the resulting cuboid.
Answer» Five identical cubes, each of edge 5 cm, are placed adjacent to each other. Find the volume of the resulting cuboid.

Discussion

9373.	The distance between the points (a + b, b + c) and (a – b, c – b) is _________ .
Answer» The distance between the points (a + b, b + c) and (a – b, c – b) is _________ .

Discussion

9374.	given sec= 13/12, calculate all other trigonometric ratios
Answer» given sec= 13/12, calculate all other trigonometric ratios

Discussion

9375.	acosθ+bsinθ=m and asinθ−bcosθ=n, then a2+b2
Answer» $a cos θ + b sin θ = m a n d a sin θ - b cos θ = n, t h e n a^{2} + b^{2}$

Discussion

9376.	If 3 : 1 is the ratio of the roots of the quadratic equation 2x2 + 5x + m = 0, then the value of m is?
Answer» If 3 : 1 is the ratio of the roots of the quadratic equation 2x2 + 5x + m = 0, then the value of m is?

Discussion

9377.	The length of the tangent from an external point P on the circle with centre O is always ________ OP.
Answer» The length of the tangent from an external point P on the circle with centre O is always ________ OP.

Discussion

9378.	A cone and a cylinder have their heights in the ratio 4: 5 and their diameters are in the ratio 3: 2. The ratio of their volumes will be
Answer» A cone and a cylinder have their heights in the ratio 4: 5 and their diameters are in the ratio 3: 2. The ratio of their volumes will be

Discussion

9379.	Show that one and only one out of n, n + 4, n + 8, n + 12 and n + 16 is divisible by 5, where n is any positive integer.
Answer» Show that one and only one out of n, n + 4, n + 8, n + 12 and n + 16 is divisible by 5, where n is any positive integer.

Discussion

9380.	Find the mode of the following data. Class interval100−120120−140140−160160−180180−200Frequency10138712
Answer» Find the mode of the following data. $\begin{matrix} C l a s s i n t e r v a l & 100 - 120 & 120 - 140 & 140 - 160 & 160 - 180 & 180 - 200 F r e q u e n c y & 10 & 13 & 8 & 7 & 12 \end{matrix}$

Discussion

9381.	Find the coordinates of the midpoint of the line segment joining the points (2, 1) and (1, -3).
Answer» Find the coordinates of the midpoint of the line segment joining the points (2, 1) and (1, -3).

Discussion

9382.

Draw a 'more than' ogive for the data given below which gives the marks of 100 students. Marks 0−10 10−20 20−30 30−40 40−50 50−60 60−70 70−80 Number of students 4 6 10 10 25 22 18 5

Answer» Draw a 'more than' ogive for the data given below which gives the marks of 100 students.

Marks	0−10	10−20	20−30	30−40	40−50	50−60	60−70	70−80
Number of students	4	6	10	10	25	22	18	5

Discussion

9383.	A random survey of the number of children of various age groups playing in park was found as follows:Age (in years)Number of children1−252−333−565−7127−10910−151015−174Draw a histogram to represent the data above.
Answer» A random survey of the number of children of various age groups playing in park was found as follows: $\begin{matrix} Age (in years) & Number of children 1 - 2 & 5 2 - 3 & 3 3 - 5 & 6 5 - 7 & 12 7 - 10 & 9 10 - 15 & 10 15 - 17 & 4 \end{matrix}$ Draw a histogram to represent the data above.

Discussion

9384.	The degree of 4x+x3−x2 is
Answer» The degree of $4 x + x^{3} - x^{2}$ is

Discussion

9385.	Find the roots of each of the following equations, if they exist, by applying the quadratic formula: mnx2+nm=1−2x
Answer» Find the roots of each of the following equations, if they exist, by applying the quadratic formula: $\frac{m}{n} x^{2} + \frac{n}{m} = 1 - 2 x$

Discussion

9386.	ABCD is a quadrilateral in which AB = BC and AD = CD. Show that BD bisects both the angles ∠ABC and ∠ADC.
Answer» ABCD is a quadrilateral in which AB = BC and AD = CD. Show that BD bisects both the angles ∠ABC and ∠ADC.

Discussion

9387.	A hollow cylinder of radius r and height h is wrapped by an aluminium foil till its radius becomes R. The thickness of the foil wrapped around the cylinder is:
Answer» A hollow cylinder of radius r and height h is wrapped by an aluminium foil till its radius becomes R. The thickness of the foil wrapped around the cylinder is:

Discussion

9388.	Question 7If the lines given by 3x + 2ky = 2 and 3x + 5y = 1 are parallel, then the value of k is(a) −54(b) 12(c) 154(d) 32
Answer» Question 7 If the lines given by 3x + 2ky = 2 and 3x + 5y = 1 are parallel, then the value of k is (a) $- \frac{5}{4}$ (b) $\frac{1}{2}$ (c) $\frac{15}{4}$ (d) $\frac{3}{2}$

Discussion

9389.	The mean of first 673 natural numbers is _________.
Answer» The mean of first 673 natural numbers is _________.

Discussion

9390.	A small ant climbs 3 cm in 1 minute but slips down 2 cm. How much time will it take to climb to 2 cm?
Answer» A small ant climbs 3 cm in 1 minute but slips down 2 cm. How much time will it take to climb to 2 cm?

Discussion

9391.	If tan θ=17, show that cosec2 θ-sec2 θcosec2 θ+sec2 θ=34
Answer» If $\tan θ = \frac{1}{\sqrt{7}}$ , show that $\frac{{cosec}^{2} θ - \sec^{2} θ}{{cosec}^{2} θ + \sec^{2} θ} = \frac{3}{4}$

Discussion

9392.	Sign of abscissa and ordinate of a point in the third quadrant will be
Answer» Sign of abscissa and ordinate of a point in the third quadrant will be

Discussion

9393.	If the probability of an event happening is x, then the probability of event not happening is___
Answer» If the probability of an event happening is x, then the probability of event not happening is___

Discussion

9394.	If R is a relation from A = {11, 12, 13} to B = {8, 10 12} defined by y = x-3, then R-1 =_______________________.
Answer» If R is a relation from A = {11, 12, 13} to B = {8, 10 12} defined by y = x-3, then R^-1 =_______________________.

Discussion

9395.	The positive integers a, b, c are such that a²+ b² - ab = c². Then the quantity (a-c) (b-c) is necessarily A) < 0B) > 2C) > 1D) none of these
Answer» The positive integers a, b, c are such that a²+ b² - ab = c². Then the quantity (a-c) (b-c) is necessarily A) < 0 B) > 2 C) > 1 D) none of these

Discussion

9396.	Question 14The graph of the linear equation 2x + 3y = 6 is a line which meets the X-axis at the point:A) (0, 2)B) (2, 0)C) (3, 0)D) (0, 3)
Answer» Question 14 The graph of the linear equation 2x + 3y = 6 is a line which meets the X-axis at the point: A) (0, 2) B) (2, 0) C) (3, 0) D) (0, 3)

Discussion

9397.	Which of the following algebraic expressions/equations can represent a function?
Answer» Which of the following algebraic expressions/equations can represent a function?

Discussion

9398.	If the first, second and last term of an A.P. are a, b and 2a respectively, its sum is(a) ab2(b-a)(b) ab(b-a)(c) 3ab2(b-a)(d) none of these
Answer» If the first, second and last term of an A.P. are a, b and 2a respectively, its sum is (a) $\frac{a b}{2 (b - a)}$ (b) $\frac{a b}{(b - a)}$ (c) $\frac{3 a b}{2 (b - a)}$ (d) none of these

Discussion

9399.

In a triangle ABC, O is the center of incircle PQR, ∠BAC = 65∘, ∠BCA = 75∘, find ∠ ROQ:

Answer»

In a triangle ABC, O is the center of incircle PQR, $∠$ BAC = $65^{\circ}$ , $∠$ BCA = $75^{\circ}$ , find $∠$ ROQ:

Discussion

9400.	If the median of x5,x4,x2,x,and,x3,where x>0,is 8, find the value of x.
Answer» If the median of $\frac{x}{5}, \frac{x}{4}, \frac{x}{2}, x, a n d, \frac{x}{3}, w h e r e x > 0, i s 8,$ find the value of x.

Discussion

Explore topic-wise InterviewSolutions in .

If the roots ofx^2 +mx + 12=0 are in the ratio 1:3. find 'm'

10. Let abc be a right-angled triangle with /_B=90 degree. Let AD be the bisector of /_A with D on BC. Let the circumcircle of triangle ACD intersect AB again in E; and let the circumcircle of triangle ABD intersect AC again in F. Let K be the reflection of E in the line BC. Prove that FK=BC.

58.Given polynomial is exactly divisible by x+1 and when it is divided by 3x-1 ,the remainder is 4. The polynomial gives remainder hx+k when divided by 3xsquare+2x-1. Then find values of h and k.

If A and B are independent events such that P(A)=0.3,P(B)=0.4, then the value of P(A and B) is:

Question 109 (ii) Observe the following patterns and fill in the blanks to make the statements true: 7×4=28 7×3= ___=28−7 7×2=___=___=−7 7×1=7=___−7 7×0=___ =___-___ 7×(−1)=−7=___-___ 7×(−2)=___=___-___ 7×(−3)___=___-___

If arc tan(sin²Q - 2sinQ + 3) + arc cot(5^[sec²y] + 1) = pie/2 then find the value of cos²Q - sinQ is equal to _____.

Write the number of all possible matrices of order 2 × 2 with each entry 1, 2 or 3.

In △PQR, PQ = 12 cm and PR = 13 cm. ∠Q=90∘. Find tan P - cot R

The daily wages of 40 workers of a factory are given in the following table. Wages in Rs. 30 – 34 34 – 38 38 – 42 42 – 46 46 – 50 50 – 54 No. of workers 4 7 9 11 6 3 Calculate (i) Mean (ii) Variance and (iii) Standard Deviation of wages and also interpret the findings.

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:

Show that (p – 1) is a factor of (p10 – 1) and also of (p11 – 1).

Question 3Write ‘True’ or ‘False’ and justify your answer in each of the following:​​​​​​​The value of the expression,(sin80∘−cos80∘) is negative.

In the given figure, ABCD is a rectangle of dimensions 21 cm × 14 cm. A semicircle is drawn with BC as diameter. Find the area and the perimeter of the shaded region in the figure. [CBSE 2017]

The first three terms of an A.P. respectively are 3y − 1, 3y + 5 and 5y + 1. Then, y equals(a) −3(b) 4(c) 5(d) 2

Convert the given decimals to percents. [2 MARKS] a) 0.65 b) 2.1

If a and b are the zeroes of the quadratic polynomial f(x)=3x^2-7x-6, find a polynomial whose zeroes are (i) a^2 and b^2 (ii) 2a+3b and 3a+2b

In the above figure, PB and PQ are tangents from point P, and MN and RN are tangents from the point N to the circle with centre O. Select the statemeents that are true:

The contrapositive of the statement p ⇒ ∼q is ________________________.

Find the mode, median and mean for the following data: [CBSE 2009] Marks obtained 25−35 35−45 45−55 55−65 65−75 75−85 Number of students 7 31 33 17 11 1

Five identical cubes, each of edge 5 cm, are placed adjacent to each other. Find the volume of the resulting cuboid.

The distance between the points (a + b, b + c) and (a – b, c – b) is _________ .

given sec= 13/12, calculate all other trigonometric ratios

acosθ+bsinθ=m and asinθ−bcosθ=n, then a2+b2

If 3 : 1 is the ratio of the roots of the quadratic equation 2x2 + 5x + m = 0, then the value of m is?

The length of the tangent from an external point P on the circle with centre O is always ________ OP.

A cone and a cylinder have their heights in the ratio 4: 5 and their diameters are in the ratio 3: 2. The ratio of their volumes will be

Show that one and only one out of n, n + 4, n + 8, n + 12 and n + 16 is divisible by 5, where n is any positive integer.

Find the mode of the following data. Class interval100−120120−140140−160160−180180−200Frequency10138712

Find the coordinates of the midpoint of the line segment joining the points (2, 1) and (1, -3).

Draw a 'more than' ogive for the data given below which gives the marks of 100 students. Marks 0−10 10−20 20−30 30−40 40−50 50−60 60−70 70−80 Number of students 4 6 10 10 25 22 18 5

A random survey of the number of children of various age groups playing in park was found as follows:Age (in years)Number of children1−252−333−565−7127−10910−151015−174Draw a histogram to represent the data above.

The degree of 4x+x3−x2 is

Find the roots of each of the following equations, if they exist, by applying the quadratic formula: mnx2+nm=1−2x

ABCD is a quadrilateral in which AB = BC and AD = CD. Show that BD bisects both the angles ∠ABC and ∠ADC.

A hollow cylinder of radius r and height h is wrapped by an aluminium foil till its radius becomes R. The thickness of the foil wrapped around the cylinder is:

Question 7If the lines given by 3x + 2ky = 2 and 3x + 5y = 1 are parallel, then the value of k is(a) −54(b) 12(c) 154(d) 32

The mean of first 673 natural numbers is _________.

A small ant climbs 3 cm in 1 minute but slips down 2 cm. How much time will it take to climb to 2 cm?

If tan θ=17, show that cosec2 θ-sec2 θcosec2 θ+sec2 θ=34

Sign of abscissa and ordinate of a point in the third quadrant will be

If the probability of an event happening is x, then the probability of event not happening is___

If R is a relation from A = {11, 12, 13} to B = {8, 10 12} defined by y = x-3, then R-1 =_______________________.

The positive integers a, b, c are such that a²+ b² - ab = c². Then the quantity (a-c) (b-c) is necessarily A) < 0B) > 2C) > 1D) none of these

Question 14The graph of the linear equation 2x + 3y = 6 is a line which meets the X-axis at the point:A) (0, 2)B) (2, 0)C) (3, 0)D) (0, 3)

Which of the following algebraic expressions/equations can represent a function?

If the first, second and last term of an A.P. are a, b and 2a respectively, its sum is(a) ab2(b-a)(b) ab(b-a)(c) 3ab2(b-a)(d) none of these

In a triangle ABC, O is the center of incircle PQR, ∠BAC = 65∘, ∠BCA = 75∘, find ∠ ROQ:

If the median of x5,x4,x2,x,and,x3,where x&gt;0,is 8, find the value of x.

Question 109 (ii) Observe the following patterns and fill in the blanks to make the statements true: 7×4=28 7×3= _=28−7 7×2=_=_=−7 7×1=7=_−7 7×0=_ =_-_ 7×(−1)=−7=_-_ 7×(−2)=_=_-_ 7×(−3)_=_-___

Question 3Write ‘True’ or ‘False’ and justify your answer in each of the following:The value of the expression,(sin80∘−cos80∘) is negative.

If the median of x5,x4,x2,x,and,x3,where x>0,is 8, find the value of x.