32581 + Interview Questions in Mathematics

1.	The point A(4, 6) is first reflected in the origin to point A'. Point A' is then reflected in the y-axis to point A'', then find the coordinates of A'' .
Answer» The point A(4, 6) is first reflected in the origin to point A'. Point A' is then reflected in the y-axis to point A'', then find the coordinates of A'' .

Discussion

2.

Find the mode of the following distribution of marks obtained by 80 students: Marks obtained 0-10 10-20 20-30 30-40 40-50 Number of students 6 10 12 32 20

Answer» Find the mode of the following distribution of marks obtained by 80 students:

Marks obtained	0-10	10-20	20-30	30-40	40-50
Number of students	6	10	12	32	20

Discussion

3.	Give possible expressions for the length and the breadth of the rectangle whose area is 12x2−35x+25
Answer» Give possible expressions for the length and the breadth of the rectangle whose area is $12 x^{2} - 35 x + 25$

Discussion

4.	A kite is flying at a height of 45 m above the ground. The string attached to the kite is temporarily tide to a point on the ground. The inclination of the string with the ground is 60∘. Find the length of the string assuming that there is no slack in the string.
Answer» A kite is flying at a height of 45 m above the ground. The string attached to the kite is temporarily tide to a point on the ground. The inclination of the string with the ground is $60^{\circ}$ . Find the length of the string assuming that there is no slack in the string.

Discussion

5.	What is the condition for the equation x2+bx−c=0 to have real roots?
Answer» What is the condition for the equation $x^{2} + b x - c = 0$ to have real roots?

Discussion

6.	Each question consists of two statements, namely, Assertion (A) and Reason (R). For selecting the correct answer, use the following code: (a) Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A). (b) Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A). (c) Assertion (A) is true and Reason (R) is false. (d) Assertion (A) is false and Reason (R) is true. Assertion (A) Reason (R)The curved surface area of aVolume of a cone =πr2h.cone of base radius 3 cm andheight 4 cm is (15π) cm2. The correct answer is (a) / (b) / (c) / (d).
Answer» Each question consists of two statements, namely, Assertion (A) and Reason (R). For selecting the correct answer, use the following code: (a) Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A). (b) Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A). (c) Assertion (A) is true and Reason (R) is false. (d) Assertion (A) is false and Reason (R) is true. $\begin{matrix} A s s e r t i o n (A) & R e a s o n (R) T h e c u r v e d s u r f a c e a r e a o f a & V o l u m e o f a c o n e = π r^{2} h . c o n e o f b a s e r a d i u s 3 c m a n d h e i g h t 4 c m i s (15 π) c m^{2} . \end{matrix}$ The correct answer is (a) / (b) / (c) / (d).

6.

Each question consists of two statements, namely, Assertion (A) and Reason (R). For selecting the correct answer, use the following code: (a) Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A). (b) Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A). (c) Assertion (A) is true and Reason (R) is false. (d) Assertion (A) is false and Reason (R) is true. Assertion (A) Reason (R)The curved surface area of aVolume of a cone =πr2h.cone of base radius 3 cm andheight 4 cm is (15π) cm2. The correct answer is (a) / (b) / (c) / (d).

Answer»

Each question consists of two statements, namely, Assertion (A) and Reason (R). For selecting the correct answer, use the following code:

(a) Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).

(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).

(c) Assertion (A) is true and Reason (R) is false.

(d) Assertion (A) is false and Reason (R) is true.

$\begin{matrix} A s s e r t i o n (A) & R e a s o n (R) T h e c u r v e d s u r f a c e a r e a o f a & V o l u m e o f a c o n e = π r^{2} h . c o n e o f b a s e r a d i u s 3 c m a n d h e i g h t 4 c m i s (15 π) c m^{2} . \end{matrix}$

The correct answer is (a) / (b) / (c) / (d).

Discussion

7.	Which of the following errors will affect the Trial Balance? (i) The total of the Sales Book has not been posted to the Sales Account. (ii) ₹ 1,000 paid as installation charges of a new machine has been debited to Repairs Account.(iii) Goods costing ₹ 4,000 taken by the proprietor for personal use have been debited to Debtors’ Account.(iv) ₹ 1,000 paid for repairs to building have been debited to Building Account.
Answer» Which of the following errors will affect the Trial Balance? (i) The total of the Sales Book has not been posted to the Sales Account. (ii) ₹ 1,000 paid as installation charges of a new machine has been debited to Repairs Account. (iii) Goods costing ₹ 4,000 taken by the proprietor for personal use have been debited to Debtors’ Account. (iv) ₹ 1,000 paid for repairs to building have been debited to Building Account.

Discussion

8.	Prove the following trigonometric identities: sin2A+11+tan2A=1
Answer» Prove the following trigonometric identities: $s i n^{2} A + \frac{1}{1 + t a n^{2} A} = 1$

8.

Prove the following trigonometric identities: sin2A+11+tan2A=1

Answer»

Prove the following trigonometric identities:

$s i n^{2} A + \frac{1}{1 + t a n^{2} A} = 1$

Discussion

9.	Ruler and compasses may be used in this question.All construction lines and arcs must be clearly shown and be of sufficient length and clarity to permit assessment. (i) Construct a △ ABC,in which BC=6 cm,AB=9 cm and angle ABC=60o. (ii) Construct the locus of all points inside triangle ABC, which are equidistant from B and C. (iii) Construct the locus of the vertices of the triangles with BC as base and which are equal in area to triangle ABC. (iv) Mark the point Q, in your construction.which would make △ QBC equal in are to △ ABC, and isosceles. (v) Measure and record the length of CQ.
Answer» Ruler and compasses may be used in this question.All construction lines and arcs must be clearly shown and be of sufficient length and clarity to permit assessment. (i) Construct a $△ A B C$ ,in which BC=6 cm,AB=9 cm and angle ABC= $60^{o}$ . (ii) Construct the locus of all points inside triangle ABC, which are equidistant from B and C. (iii) Construct the locus of the vertices of the triangles with BC as base and which are equal in area to triangle ABC. (iv) Mark the point Q, in your construction.which would make $△ Q B C$ equal in are to $△ A B C$ , and isosceles. (v) Measure and record the length of CQ.

9.

Ruler and compasses may be used in this question.All construction lines and arcs must be clearly shown and be of sufficient length and clarity to permit assessment. (i) Construct a △ ABC,in which BC=6 cm,AB=9 cm and angle ABC=60o. (ii) Construct the locus of all points inside triangle ABC, which are equidistant from B and C. (iii) Construct the locus of the vertices of the triangles with BC as base and which are equal in area to triangle ABC. (iv) Mark the point Q, in your construction.which would make △ QBC equal in are to △ ABC, and isosceles. (v) Measure and record the length of CQ.

Answer»

Ruler and compasses may be used in this question.All construction lines and arcs must be clearly shown and be of sufficient length and clarity to permit assessment.

(i) Construct a $△ A B C$ ,in which BC=6 cm,AB=9 cm and angle ABC= $60^{o}$ .

(ii) Construct the locus of all points inside triangle ABC, which are equidistant from B and C.

(iii) Construct the locus of the vertices of the triangles with BC as base and which are equal in area to triangle ABC.

(iv) Mark the point Q, in your construction.which would make $△ Q B C$ equal in are to $△ A B C$ , and isosceles.

(v) Measure and record the length of CQ.

Discussion

10.	A car has two wipers which do not overlap. Each wiper has blade of length 25 cm sweeping through an angle of 115°. Find the total area cleaned at each sweep of the blades.
Answer» A car has two wipers which do not overlap. Each wiper has blade of length 25 cm sweeping through an angle of 115°. Find the total area cleaned at each sweep of the blades.

Discussion

11.

Bhavya and Sakshi are partners in a firm, sharing profits and losses in the ratio of 3 : 2. On 31st March, 2018 their Balance Sheet was as under: BALANCE SHEET OF BHAVYA AND SAKSHI as at 31st March, 2018 Liabilities Amount (₹) Assets Amount (₹) Sundry Creditors 13,800 Furniture 16,000 General Reserve 23,400 Land and Building 56,000 Investment Fluctuation Fund 20,000 Investments 30,000 Bhavya's Capital 50,000 Trade Receivables 18,500 Sakshi's Capital 40,000 Cash in Hand 26,700 1,47,200 1,47,200 The partners have decided to change their profit sharing ratio to 1 : 1 with immediate effect. For the purpose, they decided that:(i) Investments to be valued at ₹ 20,000.(ii) Goodwill of the firm be valued at ₹ 24,000.(iii) General Reserve not to be distributed between the partners.You are required to pass necessary Journal entries in the books of the firm. Show workings.

Answer» Bhavya and Sakshi are partners in a firm, sharing profits and losses in the ratio of 3 : 2. On 31st March, 2018 their Balance Sheet was as under:

BALANCE SHEET OF BHAVYA AND SAKSHI

as at 31st March, 2018
Liabilities	Amount (₹)	Assets	Amount (₹)
Sundry Creditors	13,800	Furniture	16,000
General Reserve	23,400	Land and Building	56,000
Investment Fluctuation Fund	20,000	Investments	30,000
Bhavya's Capital	50,000	Trade Receivables	18,500
Sakshi's Capital	40,000	Cash in Hand	26,700
	1,47,200		1,47,200

The partners have decided to change their profit sharing ratio to 1 : 1 with immediate effect. For the purpose, they decided that:

(i) Investments to be valued at ₹ 20,000.

(ii) Goodwill of the firm be valued at ₹ 24,000.

(iii) General Reserve not to be distributed between the partners.

You are required to pass necessary Journal entries in the books of the firm. Show workings.

Discussion

12.	(1+tanA tanB)2+(tanA − tanB)2sec2A sec2B= ___
Answer» $\frac{(1 + t a n A t a n B)^{2} + (t a n A - t a n B)^{2}}{{s e c}^{2} A {s e c}^{2} B} =$ ___

Discussion

13.	Écoutez l'enregistrement et associez au drapeau. Puis trouvez le pays correspondant.
Answer» Écoutez l'enregistrement et associez au drapeau. Puis trouvez le pays correspondant.

Discussion

14.	Water is flowing at the rate of 5km per hour through a pipe of diameter 14cm into a rectangular tank which is 25m long and 22m wide.Find the time in which the level of water in the tank will rise by 30cm.
Answer» Water is flowing at the rate of 5km per hour through a pipe of diameter 14cm into a rectangular tank which is 25m long and 22m wide.Find the time in which the level of water in the tank will rise by 30cm.

Discussion

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

Discussion

16.	Question 18The sum of 4th and 8th terms of an A.P. is 24 and the sum of the 6th and 10th terms is 44. Find the first three terms of the A.P.
Answer» Question 18 The sum of $4^{t h}$ and $8^{t h}$ terms of an A.P. is 24 and the sum of the $6^{t h}$ and $10^{t h}$ terms is 44. Find the first three terms of the A.P.

Discussion

17.	Find the value of k, if the points A(7, −2), B (5, 1) and C (3, 2k) are collinear.
Answer» Find the value of k, if the points A(7, −2), B (5, 1) and C (3, 2k) are collinear.

Discussion

18.	An wooden toy is made by scooping out a hemisphere of same radius from each end of a cylinder. If the height of the cylinder is 10 cm and its base is of radius 3.5 cm, find the volume of wood in the toy. (Use π=227)
Answer» An wooden toy is made by scooping out a hemisphere of same radius from each end of a cylinder. If the height of the cylinder is $10$ cm and its base is of radius $3.5$ cm, find the volume of wood in the toy. $(U s e π = \frac{22}{7})$

Discussion

19.	Find the sum of all three digit numbers which are multiples of 9.
Answer» Find the sum of all three digit numbers which are multiples of 9.

Discussion

20.	Match with the correct value of tanC×sinA in each case.
Answer» Match with the correct value of $tan C \times s i n A$ in each case.

Discussion

21.	If two equal chords of a circle intersect within the circle, prove that the segments of one chord are equal to corresponding segments of the other chord.
Answer» If two equal chords of a circle intersect within the circle, prove that the segments of one chord are equal to corresponding segments of the other chord.

Discussion

22.	The ratio of two numbers is 2 : 3. If two is subtracted from the first number and 8 from the second, the ratio becomes the reciprocal of the original ratio. Find the numbers.
Answer» The ratio of two numbers is 2 : 3. If two is subtracted from the first number and 8 from the second, the ratio becomes the reciprocal of the original ratio. Find the numbers.

Discussion

23.	for polynomial x2-2x-root 5, find (alpha2-beta2)-(alpha-beta)2+(alpha+beta)2
Answer» for polynomial x2-2x-root 5, find (alpha2-beta2)-(alpha-beta)2+(alpha+beta)2

Discussion

24.	If tan θ=125, find the value of 1+sin θ1-sin θ.
Answer» If $\tan θ = \frac{12}{5}$ , find the value of $\frac{1 + \sin θ}{1 - \sin θ}$ .

Discussion

25.	Question 1 (d) Write all the factors of the given number: 27
Answer» Question 1 (d) Write all the factors of the given number: 27

25.

Question 1 (d) Write all the factors of the given number: 27

Answer»

Question 1 (d)

Write all the factors of the given number:
27

Discussion

26.	In a trapezium ABCD, it is given that AB∥CD and AB = 2 CD. Its diagonals AC and BD intersect at a point O such that ar(△AOB) = 84 cm2Find ar(△COD)
Answer» In a trapezium ABCD, it is given that AB∥CD and AB = 2 CD. Its diagonals AC and BD intersect at a point O such that ar(△AOB) = 84 cm² Find ar(△COD)

Discussion

27.	Find the GCD of (a3−4a2+7a−6) and (a3−5a2+10a−8) by using the division method.
Answer» Find the GCD of $(a^{3} - 4 a^{2} + 7 a - 6)$ and $(a^{3} - 5 a^{2} + 10 a - 8)$ by using the division method.

Discussion

28.	find a necessary and sufficient condition involving onlythe coefficients in the order that one of the roots of ax^2+bx+c=0 is square of another
Answer» find a necessary and sufficient condition involving onlythe coefficients in the order that one of the roots of ax^2+bx+c=0 is square of another

Discussion

29.	A box contains cords numbered from 1 to 20. A card is drawn at random from the box. Find the probability that the number on the drawn card is (i) a prime number, (ii) a composite number, (iii) a number divisible by 3.
Answer» A box contains cords numbered from 1 to 20. A card is drawn at random from the box. Find the probability that the number on the drawn card is (i) a prime number, (ii) a composite number, (iii) a number divisible by 3.

Discussion

30.	In the given figure, the circles touch the lines at X , Y , Z , B , C and D.If PQ = 8cm , QA = 9cm and PA = 7cm, find the length PX , AZ and QY.
Answer» In the given figure, the circles touch the lines at X , Y , Z , B , C and D. If PQ = 8cm , QA = 9cm and PA = 7cm, find the length PX , AZ and QY.

30.

In the given figure, the circles touch the lines at X , Y , Z , B , C and D.If PQ = 8cm , QA = 9cm and PA = 7cm, find the length PX , AZ and QY.

Answer»

In the given figure, the circles touch the lines at X , Y , Z , B , C and D.

If PQ = 8cm , QA = 9cm and PA = 7cm, find the length PX , AZ and QY.

Discussion

31.	The x-axis divides the line segment joining the points (–4, –6) and (–1, 7) in the ratio _________.
Answer» The x-axis divides the line segment joining the points (–4, –6) and (–1, 7) in the ratio _________.

Discussion

32.

Charu do not keep proper books of accounts. Prepare the statement of profit or loss for the year ending 31-3-2017 from the following information: 1-4-2016 31-3-2017 ₹ ₹ Cash in hand 10,000 36,000 Debtors 20,000 80,000 Creditors 10,000 46,000 Bills Receivable 20,000 24,000 Bills Payable 4,000 42,000 Car – 80,000 Stock 40,000 30,000 Furniture 8,000 48,000 Investment 40,000 50,000 Bank balance 1,00,000 90,000 The following adjustments are to be made:(a) Proprietor withdrew cash ₹ 5,000 per month for private use.(b) Depreciation 5% on Car and 10% on furniture.(c) Outstanding Rent ₹ 6,000.(d) Fresh Capital introduced during the year ₹ 30,000.

Answer» Charu do not keep proper books of accounts. Prepare the statement of profit or loss for the year ending 31-3-2017 from the following information:

	1-4-2016	31-3-2017
	₹	₹
Cash in hand	10,000	36,000
Debtors	20,000	80,000
Creditors	10,000	46,000
Bills Receivable	20,000	24,000
Bills Payable	4,000	42,000
Car	–	80,000
Stock	40,000	30,000
Furniture	8,000	48,000
Investment	40,000	50,000
Bank balance	1,00,000	90,000

The following adjustments are to be made:

(a) Proprietor withdrew cash ₹ 5,000 per month for private use.

(b) Depreciation 5% on Car and 10% on furniture.

(c) Outstanding Rent ₹ 6,000.

(d) Fresh Capital introduced during the year ₹ 30,000.

Discussion

33.	Question 39 While dividing a fraction by another fraction, we ___ of the other fraction.
Answer» Question 39 While dividing a fraction by another fraction, we ___ of the other fraction.

33.

Question 39 While dividing a fraction by another fraction, we ___ of the other fraction.

Answer»

Question 39

While dividing a fraction by another fraction, we ___ of the other fraction.

Discussion

34.	In which of the following frequency distributions, the class intervals overlap?
Answer» In which of the following frequency distributions, the class intervals overlap?

Discussion

35.	The numerator of a fraction is 3 less than its denominator. If 1 is added to the denominator, the fraction is decreased by 115. Find the fraction. [CBSE 2012]
Answer» The numerator of a fraction is 3 less than its denominator. If 1 is added to the denominator, the fraction is decreased by $\frac{1}{15}$ . Find the fraction. [CBSE 2012]

Discussion

36.	A regular hexagon is inscribed in a circle. If the area of hexagon is 243 cm2, find the area of the circle. (Use π = 3.14)
Answer» A regular hexagon is inscribed in a circle. If the area of hexagon is $24 \sqrt{3}$ cm², find the area of the circle. (Use π = 3.14)

Discussion

37.	A circular garden of radius 10 m is divided into two parts by a straight line fence. Smaller part is the walking area and flowers are planted in the larger part. The fence is at a distance of 6 m from the centre of the garden. What is the walking area in m2? It is given that cos 53°= 35.
Answer» A circular garden of radius 10 m is divided into two parts by a straight line fence. Smaller part is the walking area and flowers are planted in the larger part. The fence is at a distance of 6 m from the centre of the garden. What is the walking area in $m^{2}$ ? It is given that cos 53°= $\frac{3}{5} .$

Discussion

38.	When two triangles are similar, their corresponding sides are ___.
Answer» When two triangles are similar, their corresponding sides are ___.

Discussion

39.	if two equal chords of a circle intersect within the circle, prove that the segements of one chord are equal to corresponding segments og the ot
Answer» if two equal chords of a circle intersect within the circle, prove that the segements of one chord are equal to corresponding segments og the ot

Discussion

40.	16. Find graphically the coordinate of vertices of triangle whose sides have the equation y=x-3,2y=x-4andx-4=0
Answer» 16. Find graphically the coordinate of vertices of triangle whose sides have the equation y=x-3,2y=x-4andx-4=0

Discussion

41.	38. Find the equation of a line that cuts off equal intercepts on the coordinate axes and passes through the point (2,3).
Answer» 38. Find the equation of a line that cuts off equal intercepts on the coordinate axes and passes through the point (2,3).

Discussion

42.	In a football match, a goalkeeper can stop the goal 24 times out of 30 attempts tried by the opponent team. What is the probability that the opponent team can convert the attempt into a goal?
Answer» In a football match, a goalkeeper can stop the goal 24 times out of 30 attempts tried by the opponent team. What is the probability that the opponent team can convert the attempt into a goal?

Discussion

43.	In figure, AT is a tangent to the circle with centre O such that OT = 4 cm and ∠OTA=30∘ . Then , AT is equal to
Answer» In figure, AT is a tangent to the circle with centre O such that OT = 4 cm and $∠ O T A = 30^{\circ}$ . Then , AT is equal to

Discussion

44.	Simplify the expression:sinA−sinBcosA+cosB+cosA−cosBsinA+sinB
Answer» Simplify the expression: $\frac{s i n A - s i n B}{c o s A + c o s B} + \frac{c o s A - c o s B}{s i n A + s i n B}$

Discussion

45.	Choose the wrong number in the series given below :25,32,37,40,58,71
Answer» Choose the wrong number in the series given below : $25, 32, 37, 40, 58, 71$

Discussion

46.	{ If }(5x^2+14x+2)^2-(4x^2-5x+7)^2 is divided by }(x^2+x+1), then quotient " }q 'and remainder " r' }} are given by
Answer» { If }(5x^2+14x+2)^2-(4x^2-5x+7)^2 is divided by }(x^2+x+1), then quotient " }q 'and remainder " r' }} are given by

Discussion

47.	(a) Tn = n find (i) Tn+1 (ii) T n−1(b) If Tn = n2 − 1 find (i) Tn−2 (ii) Tn+1(c) If Tn = 2n2 + 1 find the value of n if Tn = 73(d) In a sequence Tn = 5 − 3n find (i) Tn+1 (ii) Tn+2
Answer» (a) T_n = n find (i) T_n₊₁ (ii) T _n−1 (b) If T_n = n² − 1 find (i) T_n−2 (ii) T_n₊₁ (c) If T_n = 2n² + 1 find the value of n if T_n = 73 (d) In a sequence T_n= 5 − 3n find (i) T_n₊₁ (ii) T_n₊₂

47.

(a) Tn = n find (i) Tn+1 (ii) T n−1(b) If Tn = n2 − 1 find (i) Tn−2 (ii) Tn+1(c) If Tn = 2n2 + 1 find the value of n if Tn = 73(d) In a sequence Tn = 5 − 3n find (i) Tn+1 (ii) Tn+2

Answer»

(a) T_n = n find (i) T_n₊₁ (ii) T _n−1

(b) If T_n = n² − 1 find (i) T_n−2 (ii) T_n₊₁

(c) If T_n = 2n² + 1 find the value of n if T_n = 73

(d) In a sequence T_n= 5 − 3n find (i) T_n₊₁ (ii) T_n₊₂

Discussion

48.

Journalise the following: (i) Received a V.P.P. from Mohan Lal for ₹ 25,000. Sent a peon to collect it who paid ₹ 200 as cartage. (ii) Received ₹ 1,000 from sales of old newspapers and ₹ 5,000 from sales of old chairs. (iii) Goods given away as charity goods costing ₹ 7,000. (iv) Received Cash from a debtor written off as bad-debt last year ₹ 20,000. (v) Sold goods costing ₹ 50,000 to Ashok on credit at a profit of 20% on cost. (vi) Sold goods costing ₹ 1,00,000 for ₹ 1,40,000. (vii) Provide ₹ 50,000 as interest on Capital. (viii) Paid rent of building ₹ 60,000 by cheque. Half the building is used by the proprietor for residential purpose. (ix) Outstanding salary at the end of the year ₹ 30,000.

Answer»

Journalise the following:

(i)	Received a V.P.P. from Mohan Lal for ₹ 25,000. Sent a peon to collect it who paid ₹ 200 as cartage.
(ii)	Received ₹ 1,000 from sales of old newspapers and ₹ 5,000 from sales of old chairs.
(iii)	Goods given away as charity goods costing ₹ 7,000.
(iv)	Received Cash from a debtor written off as bad-debt last year ₹ 20,000.
(v)	Sold goods costing ₹ 50,000 to Ashok on credit at a profit of 20% on cost.
(vi)	Sold goods costing ₹ 1,00,000 for ₹ 1,40,000.
(vii)	Provide ₹ 50,000 as interest on Capital.
(viii)	Paid rent of building ₹ 60,000 by cheque. Half the building is used by the proprietor for residential purpose.
(ix)	Outstanding salary at the end of the year ₹ 30,000.

Discussion

49.	Find the value of a if 3 is one of the solution of the equation 2x2+ax+6=0.
Answer» Find the value of a if 3 is one of the solution of the equation $2 x^{2} + a x + 6 = 0$ .

Discussion

50.	In the figure given below, PA and PB are tangents to the circle from point P. When the centre of the circle O and the point P are joined, how are the values of x and y related?
Answer» In the figure given below, PA and PB are tangents to the circle from point P. When the centre of the circle O and the point P are joined, how are the values of $x$ and $y$ related?

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

The point A(4, 6) is first reflected in the origin to point A'. Point A' is then reflected in the y-axis to point A'', then find the coordinates of A'' .

Find the mode of the following distribution of marks obtained by 80 students: Marks obtained 0-10 10-20 20-30 30-40 40-50 Number of students 6 10 12 32 20

Give possible expressions for the length and the breadth of the rectangle whose area is 12x2−35x+25

A kite is flying at a height of 45 m above the ground. The string attached to the kite is temporarily tide to a point on the ground. The inclination of the string with the ground is 60∘. Find the length of the string assuming that there is no slack in the string.

What is the condition for the equation x2+bx−c=0 to have real roots?

Prove the following trigonometric identities: sin2A+11+tan2A=1

A car has two wipers which do not overlap. Each wiper has blade of length 25 cm sweeping through an angle of 115°. Find the total area cleaned at each sweep of the blades.

(1+tanA tanB)2+(tanA − tanB)2sec2A sec2B= ___

Écoutez l'enregistrement et associez au drapeau. Puis trouvez le pays correspondant.

Water is flowing at the rate of 5km per hour through a pipe of diameter 14cm into a rectangular tank which is 25m long and 22m wide.Find the time in which the level of water in the tank will rise by 30cm.

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

Question 18The sum of 4th and 8th terms of an A.P. is 24 and the sum of the 6th and 10th terms is 44. Find the first three terms of the A.P.

Find the value of k, if the points A(7, −2), B (5, 1) and C (3, 2k) are collinear.

An wooden toy is made by scooping out a hemisphere of same radius from each end of a cylinder. If the height of the cylinder is 10 cm and its base is of radius 3.5 cm, find the volume of wood in the toy. (Use π=227)

Find the sum of all three digit numbers which are multiples of 9.

Match with the correct value of tanC×sinA in each case.

If two equal chords of a circle intersect within the circle, prove that the segments of one chord are equal to corresponding segments of the other chord.

The ratio of two numbers is 2 : 3. If two is subtracted from the first number and 8 from the second, the ratio becomes the reciprocal of the original ratio. Find the numbers.

for polynomial x2-2x-root 5, find (alpha2-beta2)-(alpha-beta)2+(alpha+beta)2

If tan θ=125, find the value of 1+sin θ1-sin θ.

Question 1 (d) Write all the factors of the given number: 27

In a trapezium ABCD, it is given that AB∥CD and AB = 2 CD. Its diagonals AC and BD intersect at a point O such that ar(△AOB) = 84 cm2Find ar(△COD)

Find the GCD of (a3−4a2+7a−6) and (a3−5a2+10a−8) by using the division method.

find a necessary and sufficient condition involving onlythe coefficients in the order that one of the roots of ax^2+bx+c=0 is square of another

A box contains cords numbered from 1 to 20. A card is drawn at random from the box. Find the probability that the number on the drawn card is (i) a prime number, (ii) a composite number, (iii) a number divisible by 3.

In the given figure, the circles touch the lines at X , Y , Z , B , C and D.If PQ = 8cm , QA = 9cm and PA = 7cm, find the length PX , AZ and QY.

The x-axis divides the line segment joining the points (–4, –6) and (–1, 7) in the ratio _________.

Question 39 While dividing a fraction by another fraction, we ___ of the other fraction.

In which of the following frequency distributions, the class intervals overlap?

The numerator of a fraction is 3 less than its denominator. If 1 is added to the denominator, the fraction is decreased by 115. Find the fraction. [CBSE 2012]

A regular hexagon is inscribed in a circle. If the area of hexagon is 243 cm2, find the area of the circle. (Use π = 3.14)

A circular garden of radius 10 m is divided into two parts by a straight line fence. Smaller part is the walking area and flowers are planted in the larger part. The fence is at a distance of 6 m from the centre of the garden. What is the walking area in m2? It is given that cos 53°= 35.

When two triangles are similar, their corresponding sides are ___.

if two equal chords of a circle intersect within the circle, prove that the segements of one chord are equal to corresponding segments og the ot

16. Find graphically the coordinate of vertices of triangle whose sides have the equation y=x-3,2y=x-4andx-4=0

38. Find the equation of a line that cuts off equal intercepts on the coordinate axes and passes through the point (2,3).

In a football match, a goalkeeper can stop the goal 24 times out of 30 attempts tried by the opponent team. What is the probability that the opponent team can convert the attempt into a goal?

In figure, AT is a tangent to the circle with centre O such that OT = 4 cm and ∠OTA=30∘ . Then , AT is equal to

Simplify the expression:sinA−sinBcosA+cosB+cosA−cosBsinA+sinB

Choose the wrong number in the series given below :25,32,37,40,58,71

{ If }(5x^2+14x+2)^2-(4x^2-5x+7)^2 is divided by }(x^2+x+1), then quotient " }q 'and remainder " r' }} are given by

(a) Tn = n find (i) Tn+1 (ii) T n−1(b) If Tn = n2 − 1 find (i) Tn−2 (ii) Tn+1(c) If Tn = 2n2 + 1 find the value of n if Tn = 73(d) In a sequence Tn = 5 − 3n find (i) Tn+1 (ii) Tn+2

Find the value of a if 3 is one of the solution of the equation 2x2+ax+6=0.

In the figure given below, PA and PB are tangents to the circle from point P. When the centre of the circle O and the point P are joined, how are the values of x and y related?