32581 + Interview Questions in Mathematics

1.	Find the LCM and HCF of 8, 9 and 25 by applying the prime factorization method.
Answer» Find the LCM and HCF of 8, 9 and 25 by applying the prime factorization method.

Discussion

2.	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 m². If so, find its length and breadth.

Discussion

3.	A shopkeeper gives books on rent for reading . She takes a fixed charge for the first two days, and an additional charge for each day thereafter . Latika paid ₹22 for a book kept for 6 days, while Anand paid ₹16 for the book kept for four days . Find the fixed charges and charge for each extraday.
Answer» A shopkeeper gives books on rent for reading . She takes a fixed charge for the first two days, and an additional charge for each day thereafter . Latika paid ₹22 for a book kept for 6 days, while Anand paid ₹16 for the book kept for four days . Find the fixed charges and charge for each extraday.

Discussion

4.	Which measure of central tendency will a shoe manufacturer make use of to determine the size(s) which he should manufacture in maximum quantity?
Answer» Which measure of central tendency will a shoe manufacturer make use of to determine the size(s) which he should manufacture in maximum quantity?

Discussion

5.	A rectangular courtyard is 20m 16cm long and 15m 60cm broad. It is to be paved with square stones of the same size. Find the least possible number of such stones.
Answer» A rectangular courtyard is 20m 16cm long and 15m 60cm broad. It is to be paved with square stones of the same size. Find the least possible number of such stones.

Discussion

6.	The parallel sides of an isosceles trapezium are 12 cm and 8 cm respectively and the non-parallel side measures 10 cm and makes an angle of 120∘ with the parallel side. Then the distance between the parallel sides is [sin 60∘=0.86]
Answer» The parallel sides of an isosceles trapezium are 12 cm and 8 cm respectively and the non-parallel side measures 10 cm and makes an angle of $120^{\circ}$ with the parallel side. Then the distance between the parallel sides is $[s i n 60^{\circ} = 0.86]$

Discussion

7.

From the following figures prepare the Trading and Profit and Loss Account for the year ended 31st March, 2019 and the Balance Sheet as at that date:- Particulars (₹) Particulars (₹) Stock (1st April, 2018) 75,000 Sundry Debtors 82,000 Purchases 8,00,000 Loan from X 10,000 Sales 12,00,000 Interest on X Loan 1,500 Motor Car 1,50,000 Furniture 20,000 Car Expenses 42,000 Land and Building 2,00,000 Rent 5,500 Capital 2,50,000 Salaries 35,200 Sundry Creditors 91,300 Bad Debts 1,500 Returns Inward 7,500 Provision for bad debts 8,100 Returns Outward 6,000 Commission (Cr.) 4,600 Cash in hand 16,400 Wages 1,25,000 Insurance 8,400 Adjustments:-(i) Commission include ₹ 1,600 being commission received in advance.(ii) Write off ₹ 2,000 as further Bad-debts and maintain Bad-debts provision at 5% on debtors.(iii) Expenses paid in advance are: Wages ₹ 5,000 and Insurance ₹ 1,200.(iv) Rent and Salaries have been paid for 11 months.(v) Loan from X has been taken at 18% p.a. interest.(vi) Depreciate furniture by 15% p.a. and Motor Car by 20% p.a.(vii) Closing Stock was valued at ₹ 60,000.

Answer» From the following figures prepare the Trading and Profit and Loss Account for the year ended 31st March, 2019 and the Balance Sheet as at that date:-

Particulars	(₹)	Particulars	(₹)
Stock (1st April, 2018)	75,000	Sundry Debtors	82,000
Purchases	8,00,000	Loan from X	10,000
Sales	12,00,000	Interest on X Loan	1,500
Motor Car	1,50,000	Furniture	20,000
Car Expenses	42,000	Land and Building	2,00,000
Rent	5,500	Capital	2,50,000
Salaries	35,200	Sundry Creditors	91,300
Bad Debts	1,500	Returns Inward	7,500
Provision for bad debts	8,100	Returns Outward	6,000
Commission (Cr.)	4,600	Cash in hand	16,400
Wages	1,25,000
Insurance	8,400

Adjustments:-

(i) Commission include ₹ 1,600 being commission received in advance.

(ii) Write off ₹ 2,000 as further Bad-debts and maintain Bad-debts provision at 5% on debtors.

(iii) Expenses paid in advance are: Wages ₹ 5,000 and Insurance ₹ 1,200.

(iv) Rent and Salaries have been paid for 11 months.

(v) Loan from X has been taken at 18% p.a. interest.

(vi) Depreciate furniture by 15% p.a. and Motor Car by 20% p.a.

(vii) Closing Stock was valued at ₹ 60,000.

Discussion

8.	If a sequence whose nth term is given bytn = 3.23 n2– 4.81 n + 37, then which of the following is true?
Answer» If a sequence whose $n^{t h}$ term is given by $t_{n}$ = 3.23 $n^{2}$ – 4.81 n + 37, then which of the following is true?

Discussion

9.	Sum of the ages of 5 children born at the intervals of 3 years each is 50. What is the age of the middle child?
Answer» Sum of the ages of 5 children born at the intervals of 3 years each is 50. What is the age of the middle child?

Discussion

10.	Find the polynomial which when divided by (x+2) gives (2x-1) as the quotient and 3 as the remainder
Answer» Find the polynomial which when divided by (x+2) gives (2x-1) as the quotient and 3 as the remainder

Discussion

11.	Determine the degree of each of the following polynomials.(i) 4x−5x2+6x32x(ii) y2(y−y3)(iii) (3x−2)(2x3+3x2)
Answer» Determine the degree of each of the following polynomials. (i) $\frac{4 x - 5 x^{2} + 6 x^{3}}{2 x}$ (ii) $y^{2} (y - y^{3})$ (iii) $(3 x - 2) (2 x^{3} + 3 x^{2})$

11.

Determine the degree of each of the following polynomials.(i) 4x−5x2+6x32x(ii) y2(y−y3)(iii) (3x−2)(2x3+3x2)

Answer»

Determine the degree of each of the following polynomials.

(i) $\frac{4 x - 5 x^{2} + 6 x^{3}}{2 x}$

(ii) $y^{2} (y - y^{3})$

(iii) $(3 x - 2) (2 x^{3} + 3 x^{2})$

Discussion

12.	If S1 is the sum of an arithmetic progression of 'n' odd number of terms and S2 the sum of the terms of the series in odd places, then S1S2=
Answer» If $S_{1}$ is the sum of an arithmetic progression of 'n' odd number of terms and $S_{2}$ the sum of the terms of the series in odd places, then $\frac{S_{1}}{S_{2}} =$

Discussion

13.	Construct two chords of length 6 cm and 7 cm on either sides of the centre of a circle of radius 4.5 cm. Measure the distance between the centre and the chords.
Answer» Construct two chords of length 6 cm and 7 cm on either sides of the centre of a circle of radius 4.5 cm. Measure the distance between the centre and the chords.

Discussion

14.	(i) Prove that there is a value of c(≠ 0) for which the system6x + 3y = c − 312x + cy = c has infinitely many solutions. Find this value.(ii) Find c if the system of equations cx + 3y + 3 – c = 0, 12x + cy – c = 0 has infinitely many solutions?
Answer» (i) Prove that there is a value of c(≠ 0) for which the system 6x + 3y = c − 3 12x + cy = c has infinitely many solutions. Find this value. (ii) Find c if the system of equations cx + 3y + 3 – c = 0, 12x + cy – c = 0 has infinitely many solutions?

Discussion

15.	If two tangents PT and PS are drawn to a circle with centre O and radius 'r' from an external point P and OP=2r then ∠TOP is ____.
Answer» If two tangents PT and PS are drawn to a circle with centre O and radius 'r' from an external point P and OP=2r then $∠$ TOP is ____.

Discussion

16.	In a triangle, two exterior angles are given by 56∘ and 136∘. Find the third exterior angle.
Answer» In a triangle, two exterior angles are given by $56^{\circ}$ and $136^{\circ}$ . Find the third exterior angle.

Discussion

17.	Question 88 (xi)Factorise the following expression.a3+a2+a+1
Answer» Question 88 (xi) Factorise the following expression. $a^{3} + a^{2} + a + 1$

Discussion

18.	A 6 feet tall man sees an apple on the ground, 6√3 feet away from him. What is the angle of depression (in degrees) when he is looking at the apple?60
Answer» A 6 feet tall man sees an apple on the ground, $6 \sqrt{3}$ feet away from him. What is the angle of depression (in degrees) when he is looking at the apple? 60

Discussion

19.	The speed of a boat in still water is 19 km/hr. Find the upstream speed of the boat ?
Answer» The speed of a boat in still water is 19 km/hr. Find the upstream speed of the boat ?

19.

The speed of a boat in still water is 19 km/hr. Find the upstream speed of the boat ?

Answer»

The speed of a boat in still water is 19 km/hr. Find the upstream speed of the boat ?

Discussion

20.	If α & β are the zeroes of a quadratic polynomial p(x), and k is any constant, then what is the general form of the polynomial?
Answer» If $α & β$ are the zeroes of a quadratic polynomial $p (x)$ , and $k$ is any constant, then what is the general form of the polynomial?

Discussion

21.	Question 10Which of the following equations has no real roots?(A) x2−4x+3√2=0(B) x2+4x−3√2=0(C) x2−4x−3√2=0(D) 3x2− 4√3x+4=0
Answer» Question 10 Which of the following equations has no real roots? (A) $x^{2} - 4 x + 3 \sqrt{2} = 0$ (B) $x^{2} + 4 x - 3 \sqrt{2} = 0$ (C) $x^{2} - 4 x - 3 \sqrt{2} = 0$ (D) $3 x^{2} - 4 \sqrt{3} x + 4 = 0$

Discussion

22.	Evaluate each of the following 4(sin4 60o+cos4 30o)−3(tan2 60o−tan2 45o)+5 cos2 45o
Answer» Evaluate each of the following $4 (s i n^{4} 60^{o} + c o s^{4} 30^{o}) - 3 (t a n^{2} 60^{o} - t a n^{2} 45^{o}) + 5 c o s^{2} 45^{o}$

22.

Evaluate each of the following 4(sin4 60o+cos4 30o)−3(tan2 60o−tan2 45o)+5 cos2 45o

Answer»

Evaluate each of the following

$4 (s i n^{4} 60^{o} + c o s^{4} 30^{o}) - 3 (t a n^{2} 60^{o} - t a n^{2} 45^{o}) + 5 c o s^{2} 45^{o}$

Discussion

23.	If tan θ=34, find the value of 1-cos θ1+cos θ.
Answer» If $\tan θ = \frac{3}{4}$ , find the value of $\frac{1 - \cos θ}{1 + \cos θ}$ .

Discussion

24.	The inner circumference of a circular track is 440m, and the track is 14m wide. The cost of levelling the track at 25 paise/m2 will be
Answer» The inner circumference of a circular track is 440m, and the track is 14m wide. The cost of levelling the track at 25 paise/m² will be

Discussion

25.	Question 30(i)All the jacks, queens and kings are removed from a deck of 52 playing cards. The remaining cards are well shuffled and then one card is drawn at random. Giving ace a value 1 similar value for other cards, find the probability that the card has a value 7.
Answer» Question 30(i) All the jacks, queens and kings are removed from a deck of 52 playing cards. The remaining cards are well shuffled and then one card is drawn at random. Giving ace a value 1 similar value for other cards, find the probability that the card has a value 7.

Discussion

26.	40. Find the zeros of the quadratic polynomial 4u2+8u and verify the relationship between the zeros and the coefficient
Answer» 40. Find the zeros of the quadratic polynomial 4u2+8u and verify the relationship between the zeros and the coefficient

Discussion

27.	The digit of positive integers having 3-digit number are in AP and their sum is 15 . Number obtained by reversing the digit is 594 less than the original number. Find the number.
Answer» The digit of positive integers having 3-digit number are in AP and their sum is 15 . Number obtained by reversing the digit is 594 less than the original number. Find the number.

Discussion

28.

The loans sanctioned by a bank for construction of farm ponds are shown in the following table. Find the mean of the loans. Loan (Thousand Rupees) 40 - 50 50 - 60 60 - 70 70 - 80 80 - 90 No. of farm ponds 13 20 24 36 7

Answer» The loans sanctioned by a bank for construction of farm ponds are shown in the following table. Find the mean of the loans.

Loan (Thousand Rupees)	40 - 50	50 - 60	60 - 70	70 - 80	80 - 90
No. of farm ponds	13	20	24	36	7

Discussion

29.	26 The value of k for which the system of linear equation x+ (k+2)y =3, (k+2)x+25y = 5k has infinite number of solutions, is
Answer» 26 The value of k for which the system of linear equation x+ (k+2)y =3, (k+2)x+25y = 5k has infinite number of solutions, is

Discussion

30.	Find the sum of all integers between 50 and 500 which are divisible by 7.
Answer» Find the sum of all integers between 50 and 500 which are divisible by 7.

Discussion

31.	Find the 17th term from the end of the ap 1,6,11,16... 211,216
Answer» Find the 17th term from the end of the ap 1,6,11,16... 211,216

Discussion

32.	Question 38(ii)In a game, the entry fee is of Rs 5. The game consists of a tossing a coin 3 times. If one or two heads show, Sweta gets her entry fee back. If she throws 3 heads, she receives double the entry fees. Otherwise, she will lose. For tossing a coin three times, find the probability that shegets double entry fee.
Answer» Question 38(ii) In a game, the entry fee is of Rs 5. The game consists of a tossing a coin 3 times. If one or two heads show, Sweta gets her entry fee back. If she throws 3 heads, she receives double the entry fees. Otherwise, she will lose. For tossing a coin three times, find the probability that she gets double entry fee.

Discussion

33.	Dipro Electrical company sells a Desert cooler to a dealer A for Rs 8100 including sales tax (under VAT). The dealer A sells it to a dealer B for Rs 8500 plus sales tax and the dealer B sells it to a consumer at a profit of Rs 600. If the rate of sales tax (under VAT) is 8%, find. i) the cost price of the cooler for the dealer A. ii) the amount of tax received by the Government. iii) the amount which the consumer pays for the cooler.
Answer» Dipro Electrical company sells a Desert cooler to a dealer A for Rs 8100 including sales tax (under VAT). The dealer A sells it to a dealer B for Rs 8500 plus sales tax and the dealer B sells it to a consumer at a profit of Rs 600. If the rate of sales tax (under VAT) is 8%, find. i) the cost price of the cooler for the dealer A. ii) the amount of tax received by the Government. iii) the amount which the consumer pays for the cooler.

33.

Dipro Electrical company sells a Desert cooler to a dealer A for Rs 8100 including sales tax (under VAT). The dealer A sells it to a dealer B for Rs 8500 plus sales tax and the dealer B sells it to a consumer at a profit of Rs 600. If the rate of sales tax (under VAT) is 8%, find. i) the cost price of the cooler for the dealer A. ii) the amount of tax received by the Government. iii) the amount which the consumer pays for the cooler.

Answer»

Dipro Electrical company sells a Desert cooler to a dealer A for Rs 8100 including sales tax (under VAT). The dealer A sells it to a dealer B for Rs 8500 plus sales tax and the dealer B sells it to a consumer at a profit of Rs 600. If the rate of sales tax (under VAT) is 8%, find.

i) the cost price of the cooler for the dealer A.

ii) the amount of tax received by the Government.

iii) the amount which the consumer pays for the cooler.

Discussion

34.	If x = 3+8, find the value of x2+1x2
Answer» If x = 3+ $\sqrt{8}$ , find the value of $x^{2} + \frac{1}{x^{2}}$

Discussion

35.	Two pipes running together can fill a tank in 1119 minutes. If one pipe takes 5 minutes more than the other to fill the tank separately, find the time in which each pipe would fill the tank separately. [CBSE 2010]
Answer» Two pipes running together can fill a tank in $11 \frac{1}{9}$ minutes. If one pipe takes 5 minutes more than the other to fill the tank separately, find the time in which each pipe would fill the tank separately. [CBSE 2010]

Discussion

36.	In △ PQR, if ST \parallel QR, then RT(PQ+PS) equals (1) PR+SQ+PT (2) SQ(PR+PT) (3) 2(PR+PT) (4) PR(SQ+2PT)
Answer» In △ PQR, if ST \parallel QR, then RT(PQ+PS) equals (1) PR+SQ+PT (2) SQ(PR+PT) (3) 2(PR+PT) (4) PR(SQ+2PT)

Discussion

37.	Question 14 (i)One card is drawn from a well–shuffled deck of 52 cards. Find the probability of getting a king of red colour.
Answer» Question 14 (i) One card is drawn from a well–shuffled deck of 52 cards. Find the probability of getting a king of red colour.

Discussion

38.	The minimized expression for Boolean expressionf(A,B,C,D)=∑m(0,2,4,9,11)+∑d(1,5,13) can be expressed as
Answer» The minimized expression for Boolean expression $f (A, B, C, D) = \sum m (0, 2, 4, 9, 11) + \sum d (1, 5, 13)$ can be expressed as

Discussion

39.	Question 1 (iii) Two customers Shyam and Ekta are visiting a particular shop in the same week (Tuesday to Saturday). Each is equally likely to visit the shop on any day as on another day. What is the probability that both will visit the shop on different days?
Answer» Question 1 (iii) Two customers Shyam and Ekta are visiting a particular shop in the same week (Tuesday to Saturday). Each is equally likely to visit the shop on any day as on another day. What is the probability that both will visit the shop on different days?

Discussion

40.	Solve the following inequations: 7x+3≥3x−5 and x4−5≤54−x,xϵR. Also graph the solution set on the number line. [4 MARKS]
Answer» Solve the following inequations: $7 x + 3 \geq 3 x - 5$ and $\frac{x}{4} - 5 \leq \frac{5}{4} - x, x ϵ R$ . Also graph the solution set on the number line. [4 MARKS]

Discussion

41.	The probability of guessing the correct answer to a certain test questions is x12. If the probability of not guessing the correct answer to this question is 23, then x =(a) 2(b) 3(c) 4(d) 6
Answer» The probability of guessing the correct answer to a certain test questions is $\frac{x}{12}$ . If the probability of not guessing the correct answer to this question is $\frac{2}{3}$ , then x = (a) 2 (b) 3 (c) 4 (d) 6

Discussion

42.	A line intersects the y-axis and x-axis at P and Q , respectively. If (2, -5) is the mid-point of PQ, then the coordinates of P and Q are, respectively(a) (0, -5) and (2, 0) (b) (0, 10) and (-4, 0)(c) (0, 4) and (-10, 0 ) (d) (0, -10) and (4 , 0)
Answer» A line intersects the y-axis and x-axis at P and Q , respectively. If (2, $-$ 5) is the mid-point of PQ, then the coordinates of P and Q are, respectively (a) (0, $-$ 5) and (2, 0) (b) (0, 10) and ( $-$ 4, 0) (c) (0, 4) and ( $-$ 10, 0 ) (d) (0, $-$ 10) and (4 , 0)

Discussion

43.	If the points A(k+1,2k),B(3k,2k+3) and C(5k-1,5k) are collinear, then find the value of k.
Answer» If the points A(k+1,2k),B(3k,2k+3) and C(5k-1,5k) are collinear, then find the value of k.

Discussion

44.	Question 1 (viii)Find the zeroes of the following polynomials by factorization method and verify the relations between the zeroes and the coefficient of the polynomials(viii) v2+4√3v−15
Answer» Question 1 (viii) Find the zeroes of the following polynomials by factorization method and verify the relations between the zeroes and the coefficient of the polynomials (viii) $v^{2} + 4 \sqrt{3} v - 15$

Discussion

45.	Frequency of a variable is always:
Answer» Frequency of a variable is always:

Discussion

46.	In Q.No. 1, if PB = 10 cm, what is the perimeter of Δ PCD?
Answer» In Q.No. 1, if PB = 10 cm, what is the perimeter of Δ PCD?

Discussion

47.	Match the APs to their nth terms.
Answer» Match the APs to their $n^{th}$ terms.

Discussion

48.	Identify the odd one out from the following
Answer» Identify the odd one out from the following

Discussion

49.

From the following Trial Balance extracted from the books of Sh. Pawan Kumar, prepare a Trading Account, Profit & Loss Account for the year ended 31st March, 2019 and a Balance Sheet as at that date : Dr. Balances (₹) Cr. Balances (₹) Drawings 1,20,000 Capital 16,00,000 Plant and Machinery 12,00,000 Creditors 2,60,000 Horses and Carts 2,60,000 Sales 8,20,000 Debtors 3,40,000 Bills Payable 2,21,200 Purchases 2,00,000 Interest on Ram's Loan 1,800 Wages 80,000 Rent Received 12,000 Cash at Bank 2,60,000 Salaries 80,000 Repairs 5,000 Stock (1-4-2018) 70,000 Stock (31-3-2019) 92,000 Rent 45,000 Manufacturing expenses 15,000 Bad-Debts 50,000 Carriage 15,000 Income Tax 20,000 Life Insurance Premium 30,000 Loan to Ram at 12% p.a. 20,000 Insurance 12,000 Insurance Prepaid 1,000 29,15,000 29,15,000 Adjustments:- 1. Plant and Machinery includes a new machinery purchased on 1st October, 2018 for ₹ 2,00,000.2. Depreciate Plant and Machinery by 10% p.a. and Horses and Carts by 20% p.a.3. Salaries for the month of February and March 2019 are outstanding.4. Goods worth ₹ 15,000 were sold and despatched on 27th March but no entry was passed to this effect.5. Make a provision for Doubtful Debts at 5% on Debtors.

Answer» From the following Trial Balance extracted from the books of Sh. Pawan Kumar, prepare a Trading Account, Profit & Loss Account for the year ended 31st March, 2019 and a Balance Sheet as at that date :

Dr. Balances	(₹)	Cr. Balances	(₹)
Drawings	1,20,000	Capital	16,00,000
Plant and Machinery	12,00,000	Creditors	2,60,000
Horses and Carts	2,60,000	Sales	8,20,000
Debtors	3,40,000	Bills Payable	2,21,200
Purchases	2,00,000	Interest on Ram's Loan	1,800
Wages	80,000	Rent Received	12,000
Cash at Bank	2,60,000
Salaries	80,000
Repairs	5,000
Stock (1-4-2018)	70,000
Stock (31-3-2019)	92,000
Rent	45,000
Manufacturing expenses	15,000
Bad-Debts	50,000
Carriage	15,000
Income Tax	20,000
Life Insurance Premium	30,000
Loan to Ram at 12% p.a.	20,000
Insurance	12,000
Insurance Prepaid	1,000
	29,15,000		29,15,000

Adjustments:-

1. Plant and Machinery includes a new machinery purchased on 1st October, 2018 for ₹ 2,00,000.

2. Depreciate Plant and Machinery by 10% p.a. and Horses and Carts by 20% p.a.

3. Salaries for the month of February and March 2019 are outstanding.

4. Goods worth ₹ 15,000 were sold and despatched on 27th March but no entry was passed to this effect.

5. Make a provision for Doubtful Debts at 5% on Debtors.

Discussion

50.	Find the co-ordinates of the centroid of the triangle whose vertices are (4,7) , (8,4) & (7,11).
Answer» Find the co-ordinates of the centroid of the triangle whose vertices are (4,7) , (8,4) & (7,11).

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Find the LCM and HCF of 8, 9 and 25 by applying the prime factorization method.

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

Which measure of central tendency will a shoe manufacturer make use of to determine the size(s) which he should manufacture in maximum quantity?

A rectangular courtyard is 20m 16cm long and 15m 60cm broad. It is to be paved with square stones of the same size. Find the least possible number of such stones.

The parallel sides of an isosceles trapezium are 12 cm and 8 cm respectively and the non-parallel side measures 10 cm and makes an angle of 120∘ with the parallel side. Then the distance between the parallel sides is [sin 60∘=0.86]

If a sequence whose nth term is given bytn = 3.23 n2– 4.81 n + 37, then which of the following is true?

Sum of the ages of 5 children born at the intervals of 3 years each is 50. What is the age of the middle child?

Find the polynomial which when divided by (x+2) gives (2x-1) as the quotient and 3 as the remainder

Determine the degree of each of the following polynomials.(i) 4x−5x2+6x32x(ii) y2(y−y3)(iii) (3x−2)(2x3+3x2)

If S1 is the sum of an arithmetic progression of 'n' odd number of terms and S2 the sum of the terms of the series in odd places, then S1S2=

Construct two chords of length 6 cm and 7 cm on either sides of the centre of a circle of radius 4.5 cm. Measure the distance between the centre and the chords.

(i) Prove that there is a value of c(≠ 0) for which the system6x + 3y = c − 312x + cy = c has infinitely many solutions. Find this value.(ii) Find c if the system of equations cx + 3y + 3 – c = 0, 12x + cy – c = 0 has infinitely many solutions?

If two tangents PT and PS are drawn to a circle with centre O and radius 'r' from an external point P and OP=2r then ∠TOP is ____.

In a triangle, two exterior angles are given by 56∘ and 136∘. Find the third exterior angle.

Question 88 (xi)Factorise the following expression.a3+a2+a+1

A 6 feet tall man sees an apple on the ground, 6√3 feet away from him. What is the angle of depression (in degrees) when he is looking at the apple?60

The speed of a boat in still water is 19 km/hr. Find the upstream speed of the boat ?

If α &amp; β are the zeroes of a quadratic polynomial p(x), and k is any constant, then what is the general form of the polynomial?

Question 10Which of the following equations has no real roots?(A) x2−4x+3√2=0(B) x2+4x−3√2=0(C) x2−4x−3√2=0(D) 3x2− 4√3x+4=0

Evaluate each of the following 4(sin4 60o+cos4 30o)−3(tan2 60o−tan2 45o)+5 cos2 45o

If tan θ=34, find the value of 1-cos θ1+cos θ.

The inner circumference of a circular track is 440m, and the track is 14m wide. The cost of levelling the track at 25 paise/m2 will be

Question 30(i)All the jacks, queens and kings are removed from a deck of 52 playing cards. The remaining cards are well shuffled and then one card is drawn at random. Giving ace a value 1 similar value for other cards, find the probability that the card has a value 7.

40. Find the zeros of the quadratic polynomial 4u2+8u and verify the relationship between the zeros and the coefficient

The digit of positive integers having 3-digit number are in AP and their sum is 15 . Number obtained by reversing the digit is 594 less than the original number. Find the number.

The loans sanctioned by a bank for construction of farm ponds are shown in the following table. Find the mean of the loans. Loan (Thousand Rupees) 40 - 50 50 - 60 60 - 70 70 - 80 80 - 90 No. of farm ponds 13 20 24 36 7

26 The value of k for which the system of linear equation x+ (k+2)y =3, (k+2)x+25y = 5k has infinite number of solutions, is

Find the sum of all integers between 50 and 500 which are divisible by 7.

Find the 17th term from the end of the ap 1,6,11,16... 211,216

If x = 3+8, find the value of x2+1x2

Two pipes running together can fill a tank in 1119 minutes. If one pipe takes 5 minutes more than the other to fill the tank separately, find the time in which each pipe would fill the tank separately. [CBSE 2010]

In △ PQR, if ST \parallel QR, then RT(PQ+PS) equals (1) PR+SQ+PT (2) SQ(PR+PT) (3) 2(PR+PT) (4) PR(SQ+2PT)

Question 14 (i)One card is drawn from a well–shuffled deck of 52 cards. Find the probability of getting a king of red colour.

The minimized expression for Boolean expressionf(A,B,C,D)=∑m(0,2,4,9,11)+∑d(1,5,13) can be expressed as

Question 1 (iii) Two customers Shyam and Ekta are visiting a particular shop in the same week (Tuesday to Saturday). Each is equally likely to visit the shop on any day as on another day. What is the probability that both will visit the shop on different days?

Solve the following inequations: 7x+3≥3x−5 and x4−5≤54−x,xϵR. Also graph the solution set on the number line. [4 MARKS]

The probability of guessing the correct answer to a certain test questions is x12. If the probability of not guessing the correct answer to this question is 23, then x =(a) 2(b) 3(c) 4(d) 6

A line intersects the y-axis and x-axis at P and Q , respectively. If (2, -5) is the mid-point of PQ, then the coordinates of P and Q are, respectively(a) (0, -5) and (2, 0) (b) (0, 10) and (-4, 0)(c) (0, 4) and (-10, 0 ) (d) (0, -10) and (4 , 0)

If the points A(k+1,2k),B(3k,2k+3) and C(5k-1,5k) are collinear, then find the value of k.

Question 1 (viii)Find the zeroes of the following polynomials by factorization method and verify the relations between the zeroes and the coefficient of the polynomials(viii) v2+4√3v−15

Frequency of a variable is always:

In Q.No. 1, if PB = 10 cm, what is the perimeter of Δ PCD?

Match the APs to their nth terms.

Identify the odd one out from the following

Find the co-ordinates of the centroid of the triangle whose vertices are (4,7) , (8,4) &amp; (7,11).

If α & β are the zeroes of a quadratic polynomial p(x), and k is any constant, then what is the general form of the polynomial?

Find the co-ordinates of the centroid of the triangle whose vertices are (4,7) , (8,4) & (7,11).