32581 + Interview Questions in Mathematics

1.	Which is the side opposite to the angle θ?
Answer» Which is the side opposite to the angle $θ$ ?

1.

Which is the side opposite to the angle θ?

Answer»

Which is the side opposite to the angle $θ$ ?

2.	The area of triangle whose vertices are the incentre, centroid and circumcentre of a triangle with sides 14,50,48 is
Answer» The area of triangle whose vertices are the incentre, centroid and circumcentre of a triangle with sides 14,50,48 is

Discussion

3.	Question 1 (v) Write211 in decimal form and say what kind of decimal expansion it has.
Answer» Question 1 (v) Write $\frac{2}{11}$ in decimal form and say what kind of decimal expansion it has.

Discussion

4.	The construction of triangle ΔA'C'B similar to triangle ΔACB is shown in the figure below. Then
Answer» The construction of triangle ΔA'C'B similar to triangle ΔACB is shown in the figure below. Then

Discussion

5.	is the cubic polynomial whose zeroes are 2, - 3 and 4.
Answer» is the cubic polynomial whose zeroes are 2, - 3 and 4.

Discussion

6.	The sum of all two digit odd numbers is:
Answer» The sum of all two digit odd numbers is:

Discussion

7.	In a right angle triangle ΔABC, a perpendicular BD is drawn on to the largest side from the vertex B. Which of the following does NOT give the ratios of the areas of ΔABD and ΔBCD ?
Answer» In a right angle triangle $Δ A B C$ , a perpendicular BD is drawn on to the largest side from the vertex B. Which of the following does NOT give the ratios of the areas of $Δ A B D$ and $Δ B C D$ ?

Discussion

8.	Solve each of the following quadratic equations: (i) 1x+1+2x+2=5x+4,x≠−1,−2,−4 (ii) 1x+1+35x+1=5x+4,x≠−115,−4
Answer» Solve each of the following quadratic equations: (i) $\frac{1}{x + 1} + \frac{2}{x + 2} = \frac{5}{x + 4}, x \neq - 1, - 2, - 4$ (ii) $\frac{1}{x + 1} + \frac{3}{5 x + 1} = \frac{5}{x + 4}, x \neq - 1 \frac{1}{5}, - 4$

Discussion

9.	Question 1 Find the surface area of a sphere of radius: (i) 10.5 cm (ii) 5.6 cm (iii) 14 cm [Assume π=227]
Answer» Question 1 Find the surface area of a sphere of radius: (i) 10.5 cm (ii) 5.6 cm (iii) 14 cm $[A s s u m e π = \frac{22}{7}]$

9.

Question 1 Find the surface area of a sphere of radius: (i) 10.5 cm (ii) 5.6 cm (iii) 14 cm [Assume π=227]

Answer»

Question 1
Find the surface area of a sphere of radius:

(i) 10.5 cm

(ii) 5.6 cm

(iii) 14 cm

$[A s s u m e π = \frac{22}{7}]$

Discussion

10.	Journalise the following transactions in the books of M/s. R.K. & Co.:(i) Purchased goods of list price of ₹ 20,000 from Vishal at 20% trade discount against cheque payment.(ii) Purchased goods of list price of ₹ 20,000 from Naman at 15% trade discount against cash.(iii) Purchased goods of list price of ₹ 30,000 from Amrit at 20% trade discount.(iv) Purchased goods of list price of ₹ 40,000 for ₹ 35,000 for cash.(v) Goods returned of list price ₹ 10,000 purchased from Amrit.(vi) Sold goods to Parul of list price of ₹ 40,000 at 10% trade discount against cheque payment.(vii) Sold goods to Aman of list price of ₹ 30,000 at 10% trade discount against cash.(viii) Sold goods to Pawan of list price of ₹ 20,000 at 10% trade discount.(ix) Sold goods to Yamini of list price of ₹ 25,000 for ₹ 23,000.(x) Sold goods costing ₹ 10,000 at cost plus 20% less 10% trade discount to Bhupesh.(xi) Sold goods purchased at list price of ₹ 50,000 less 15% trade discount sold at a profit of 25% less 10% trade discount against cheque.(xii) Aman returned goods of list price of ₹ 10,000 sold to him at 10% trade discount.
Answer» Journalise the following transactions in the books of M/s. R.K. & Co.: (i) Purchased goods of list price of ₹ 20,000 from Vishal at 20% trade discount against cheque payment. (ii) Purchased goods of list price of ₹ 20,000 from Naman at 15% trade discount against cash. (iii) Purchased goods of list price of ₹ 30,000 from Amrit at 20% trade discount. (iv) Purchased goods of list price of ₹ 40,000 for ₹ 35,000 for cash. (v) Goods returned of list price ₹ 10,000 purchased from Amrit. (vi) Sold goods to Parul of list price of ₹ 40,000 at 10% trade discount against cheque payment. (vii) Sold goods to Aman of list price of ₹ 30,000 at 10% trade discount against cash. (viii) Sold goods to Pawan of list price of ₹ 20,000 at 10% trade discount. (ix) Sold goods to Yamini of list price of ₹ 25,000 for ₹ 23,000. (x) Sold goods costing ₹ 10,000 at cost plus 20% less 10% trade discount to Bhupesh. (xi) Sold goods purchased at list price of ₹ 50,000 less 15% trade discount sold at a profit of 25% less 10% trade discount against cheque. (xii) Aman returned goods of list price of ₹ 10,000 sold to him at 10% trade discount.

Discussion

11.	Kumar and Kavya together have 45 marbles. Both of them lost 5 marbles each, and the product of the number of marbles they now have is 124. Representing the problem mathematically gives the quadratic equation _____.
Answer» Kumar and Kavya together have 45 marbles. Both of them lost 5 marbles each, and the product of the number of marbles they now have is 124. Representing the problem mathematically gives the quadratic equation _____.

Discussion

12.	Question 5Two identical cubes each of volume 64 cm3 are joined together end to end. What is the surface area of the resulting cuboid?
Answer» Question 5 Two identical cubes each of volume $64 c m^{3}$ are joined together end to end. What is the surface area of the resulting cuboid?

Discussion

13.	Show graphically that each one of the following systems of equations has infinitely many solutions:2x + 3y = 64x + 6y = 12
Answer» Show graphically that each one of the following systems of equations has infinitely many solutions: 2x + 3y = 6 4x + 6y = 12

Discussion

14.	Write ‘True’ or ‘False’ and justify your answer in each of the following :(i) The length of tangents from an external point P on a circle is always greater than the radius of the circle.(ii) The length of tangents from an external point P on a circle with centre O is always less than OP.
Answer» Write ‘True’ or ‘False’ and justify your answer in each of the following : (i) The length of tangents from an external point P on a circle is always greater than the radius of the circle. (ii) The length of tangents from an external point P on a circle with centre O is always less than OP.

Discussion

15.	A polynomial g(x) of degree zero is added to the polynomial 2x^3 + 5x^2-14x+10 so that it becomes exactly divisible by 2x-3. Find g(x).
Answer» A polynomial g(x) of degree zero is added to the polynomial 2x^3 + 5x^2-14x+10 so that it becomes exactly divisible by 2x-3. Find g(x).

Discussion

16.	The direction cosines of the line joining points (4, 3, –5) and (–2, 1, –8) are ______________.
Answer» The direction cosines of the line joining points (4, 3, –5) and (–2, 1, –8) are ______________.

Discussion

17.	if modulis a vector +b vector =modulus a vector -b vector then angle between a vector and b vector is equal t
Answer» if modulis a vector +b vector =modulus a vector -b vector then angle between a vector and b vector is equal t

Discussion

18.	Solve each of the following systems of equations by the method of cross-multiplication :mx-ny=m2+n2x+y=2m
Answer» Solve each of the following systems of equations by the method of cross-multiplication : $m x - n y = m^{2} + n^{2} x + y = 2 m$

Discussion

19.	If two numbers in the ratio 10:4 and when 3 is added to the numbers ratio becomes 3:1. Find the numbers.
Answer» If two numbers in the ratio 10:4 and when 3 is added to the numbers ratio becomes 3:1. Find the numbers.

Discussion

20.	For an AP of 14 terms, find the option which gives the value equal to a4+a11.
Answer» For an AP of 14 terms, find the option which gives the value equal to $a_{4} + a_{11}$ .

Discussion

21.	On December 31, 2010, the cash book of Mittal Bros showed an overdraft of Rs. 6,920. From the following particulars, prepare a Bank Reconciliation Statement and ascertain the balance as per pass book. (i) Debited by the bank for Rs. 200 on account of Interest on overdraft and Rs. 50 on account of charges for collecting bills. (ii) Cheques were drawn but not encashed before December 31, 2010, for Rs. 4,000. (iii) The bank has collected interest and has credited Rs. 600 in passbook. (iv) A bill receivable for Rs. 700 previously discounted with the bank had been dishonoured and debited in the passbook. (v) Cheques paid into the bank but not collected and credited before December 31, 2010, amounted Rs. 6,000.
Answer» On December 31, 2010, the cash book of Mittal Bros showed an overdraft of Rs. 6,920. From the following particulars, prepare a Bank Reconciliation Statement and ascertain the balance as per pass book. (i) Debited by the bank for Rs. 200 on account of Interest on overdraft and Rs. 50 on account of charges for collecting bills. (ii) Cheques were drawn but not encashed before December 31, 2010, for Rs. 4,000. (iii) The bank has collected interest and has credited Rs. 600 in passbook. (iv) A bill receivable for Rs. 700 previously discounted with the bank had been dishonoured and debited in the passbook. (v) Cheques paid into the bank but not collected and credited before December 31, 2010, amounted Rs. 6,000.

21.

On December 31, 2010, the cash book of Mittal Bros showed an overdraft of Rs. 6,920. From the following particulars, prepare a Bank Reconciliation Statement and ascertain the balance as per pass book. (i) Debited by the bank for Rs. 200 on account of Interest on overdraft and Rs. 50 on account of charges for collecting bills. (ii) Cheques were drawn but not encashed before December 31, 2010, for Rs. 4,000. (iii) The bank has collected interest and has credited Rs. 600 in passbook. (iv) A bill receivable for Rs. 700 previously discounted with the bank had been dishonoured and debited in the passbook. (v) Cheques paid into the bank but not collected and credited before December 31, 2010, amounted Rs. 6,000.

Answer»

On December 31, 2010, the cash book of Mittal Bros showed an overdraft of Rs. 6,920. From the following particulars, prepare a Bank Reconciliation Statement and ascertain the balance as per pass book.

(i) Debited by the bank for Rs. 200 on account of Interest on overdraft and Rs. 50 on account of charges for collecting bills.

(ii) Cheques were drawn but not encashed before December 31, 2010, for Rs. 4,000.

(iii) The bank has collected interest and has credited Rs. 600 in passbook.

(iv) A bill receivable for Rs. 700 previously discounted with the bank had been dishonoured and debited in the passbook.

(v) Cheques paid into the bank but not collected and credited before December 31, 2010, amounted Rs. 6,000.

Discussion

22.	A copper wire, 3mm in diameter, is wound about a cylinder whose length is 12 cm and diameter 10 cm, so as to cover the curved surface of the cylinder. Find the length of the mass of the wire, assuming the density of copper to be 8.88 g/cm3.
Answer» A copper wire, 3mm in diameter, is wound about a cylinder whose length is 12 cm and diameter 10 cm, so as to cover the curved surface of the cylinder. Find the length of the mass of the wire, assuming the density of copper to be 8.88 g/ $c m^{3}$ .

Discussion

23.	If the area of the triangle formed by the points(x,2x),(−2,6) and(3,1) is 5 square units , then x(a)23(b) 35(c)3(d) 5
Answer» If the area of the triangle formed by the points $(x, 2 x), (- 2, 6)$ and $(3, 1)$ is $5$ square units , then $x$ (a) $23$ (b) $35$ (c) $3$ (d) $5$

Discussion

24.	Solve the following systems of equations:6x+y=7x-y+312x+y=13x-y'where x + y ≠ 0 and x − y ≠ 0
Answer» Solve the following systems of equations: $\frac{6}{x + y} = \frac{7}{x - y} + 3 \frac{1}{2 (x + y)} = \frac{1}{3 (x - y)'}$ where x + y ≠ 0 and x − y ≠ 0

Discussion

25.	Question 8 (i)In right triangle ABC, right angled at C, M is the mid-point of hypotenuse AB. C is joined to M and produced to a point D such that DM = CM. Point D is joined to point B (see the given figure). Show that:ΔAMC≅ΔBMD
Answer» Question 8 (i) In right triangle ABC, right angled at C, M is the mid-point of hypotenuse AB. C is joined to M and produced to a point D such that DM = CM. Point D is joined to point B (see the given figure). Show that: $Δ A M C ≅ Δ B M D$

Discussion

26.	Find the HCF of the smallest prime number and the smallest composite number.
Answer» Find the HCF of the smallest prime number and the smallest composite number.

Discussion

27.	Draw a right triangle in which sides (other than hypotenuse) are of lengths 4 cm and 3 cm. Then, construct another triangle whose sides are 53 times the corresponding sides of the given triangle. [CBSE 2011]
Answer» Draw a right triangle in which sides (other than hypotenuse) are of lengths 4 cm and 3 cm. Then, construct another triangle whose sides are $\frac{5}{3}$ times the corresponding sides of the given triangle. [CBSE 2011]

Discussion

28.	A line segment AB is divided in the ratio 4:9 by a point C.Find the length AC (in cm) if AB=26 cm.8
Answer» A line segment AB is divided in the ratio 4:9 by a point C. Find the length AC (in cm) if AB=26 cm. 8

28.

A line segment AB is divided in the ratio 4:9 by a point C.Find the length AC (in cm) if AB=26 cm.8

Answer»

A line segment AB is divided in the ratio 4:9 by a point C.

Find the length AC (in cm) if AB=26 cm.

8

Discussion

29.	2. Integrate=sin(log x)
Answer» 2. Integrate=sin(log x)

Discussion

30.	If m ∝ n and when m = 154, n = 7. Find the value of m, when n = 14
Answer» If m ∝ n and when m = 154, n = 7. Find the value of m, when n = 14

Discussion

31.	A and B are partners in a business sharing profits and losses in the ratio of 1/3rd and 2/3rd. On 1st April, 2019, their capitals were ₹ 8,000 and ₹ 10,000 respectively. On that date, they admit C in partnership and give him 1/4th share in the future profits. C brings ₹ 8,000 as his capital and ₹ 6,000 as goodwill. The amount of goodwill is withdrawn by the old partners in cash. Draft the journal entries and show the Capital Accounts of all the Partners. Calculate proportion in which partners would share profits and losses in future.
Answer» A and B are partners in a business sharing profits and losses in the ratio of 1/3rd and 2/3rd. On 1st April, 2019, their capitals were ₹ 8,000 and ₹ 10,000 respectively. On that date, they admit C in partnership and give him 1/4th share in the future profits. C brings ₹ 8,000 as his capital and ₹ 6,000 as goodwill. The amount of goodwill is withdrawn by the old partners in cash. Draft the journal entries and show the Capital Accounts of all the Partners. Calculate proportion in which partners would share profits and losses in future.

Discussion

32.	If 3sinθ+4cosθ=5, then the value of tanθ is _____.
Answer» If $3 s i n θ + 4 c o s θ = 5$ , then the value of $t a n θ$ is _____.

Discussion

33.	If the angle of elevation of a tower from a distance of 100 m from its foot is 60∘, then the height of the tower is
Answer» If the angle of elevation of a tower from a distance of 100 m from its foot is $60^{\circ}$ , then the height of the tower is

Discussion

34.	The perimeter of a triangle is 30 cm and the circumference of its incircle is 88 cm. The area of the triangle is(a) 70 cm2(b) 140 cm2(c) 210 cm2(d) 420 cm2
Answer» The perimeter of a triangle is 30 cm and the circumference of its incircle is 88 cm. The area of the triangle is (a) 70 cm² (b) 140 cm² (c) 210 cm² (d) 420 cm²

Discussion

35.	Find zeroes of the polynomial x2−2.
Answer» Find zeroes of the polynomial $x^{2} - 2$ .

Discussion

36.	The radius of a circular garden is 100 m. There is a road 10 m wide, running all around it. Find the area of the road and the cost of levellingit at Rs 20 per m2. [Use π = 3.14] [CBSE 2011]
Answer» The radius of a circular garden is 100 m. There is a road 10 m wide, running all around it. Find the area of the road and the cost of levelling it at Rs 20 per m². [Use π = 3.14] [CBSE 2011]

Discussion

37.	The lengths of the sides of a right angled triangle are all given in natural numbers. If two of these numbers are odd and they differ by 50, then the least possible value for the third side is A)61 B)60 C)51 D)50
Answer» The lengths of the sides of a right angled triangle are all given in natural numbers. If two of these numbers are odd and they differ by 50, then the least possible value for the third side is A)61 B)60 C)51 D)50

37.

The lengths of the sides of a right angled triangle are all given in natural numbers. If two of these numbers are odd and they differ by 50, then the least possible value for the third side is A)61 B)60 C)51 D)50

Answer»

The lengths of the sides of a right angled triangle are all given in natural numbers. If two of these numbers are odd and they differ by 50, then the least possible value for the third side is

A)61

B)60

C)51

D)50

Discussion

38.	The surface of water in a swimming pool, when it is full of water, is rectangular with length and breadth 36 m and 10.5 m respectively. The depth of water increases uniformly from 1 m at one end to 1.75 m at the other end. The water in pool is emptied by a cylindrical pipe of radius 7 cm at the rate of 5km/h. The time ( in hours) to empty water in pool is
Answer» The surface of water in a swimming pool, when it is full of water, is rectangular with length and breadth 36 m and 10.5 m respectively. The depth of water increases uniformly from 1 m at one end to 1.75 m at the other end. The water in pool is emptied by a cylindrical pipe of radius 7 cm at the rate of 5km/h. The time ( in hours) to empty water in pool is

Discussion

39.	Amita has 12 marbles and Reeta has 8 marbles. Reeta says that she has x/y times the marbles that Amita has, where x and y are co-prime numbers. Then x + y = ___
Answer» Amita has 12 marbles and Reeta has 8 marbles. Reeta says that she has x/y times the marbles that Amita has, where x and y are co-prime numbers. Then x + y = ___

39.

Amita has 12 marbles and Reeta has 8 marbles. Reeta says that she has x/y times the marbles that Amita has, where x and y are co-prime numbers. Then x + y = ___

Answer»

Amita has 12 marbles and Reeta has 8 marbles. Reeta says that she has x/y times the marbles that Amita has, where x and y are co-prime numbers.

Then x + y =

___

Discussion

40.	In the given figure, AB and CD are two chords of a circle, intersecting each other at a point E.Prove that ∠AEC = 12(angle subtended by arc CXA at the centre + angle subtended by arc DYB at the centre).
Answer» In the given figure, AB and CD are two chords of a circle, intersecting each other at a point E. Prove that ∠AEC = $\frac{1}{2}$ (angle subtended by arc CXA at the centre + angle subtended by arc DYB at the centre).

Discussion

41.

Surya does not keep a systematic record of his transactions. He is able to give you the following information regarding his assets and liabilities: 31st March 2017 (₹) 31st March, 2018 (₹) Creditors for goods 21,000 19,000 Creditors for expenses 1,500 1,800 Bills Payable 8,700 11,500 Sundry Debtors 35,000 34,000 Stock (At cost) 28,000 25,000 Furniture and Fittings 10,000 12,000 Cash 5,100 Following additional information is also avialable for the year ended 31st March, 2018: ₹ Bills Payable Issued 20,800 Cash Sales 15,000 Payment to Sundry Creditors 31,000 Expenses paid 6,600 Drawings 8,000 Bad Debts during the year were ₹900. As regards sale, Surya tells you that he always sells goods at Cost plus 25%. Furniture and Fittings are to be depreciated at 10% of the value in the beginning of the year.Prepare Surya's Trading and Profit and Loss Account for the year ended 31st March, 2018 and his Balance Sheet on that date.

Answer» Surya does not keep a systematic record of his transactions. He is able to give you the following information regarding his assets and liabilities:

	31st March 2017 (₹)	31st March, 2018 (₹)
Creditors for goods	21,000	19,000
Creditors for expenses	1,500	1,800
Bills Payable	8,700	11,500
Sundry Debtors	35,000	34,000
Stock (At cost)	28,000	25,000
Furniture and Fittings	10,000	12,000
Cash	5,100

Following additional information is also avialable for the year ended 31st March, 2018:

	₹
Bills Payable Issued	20,800
Cash Sales	15,000
Payment to Sundry Creditors	31,000
Expenses paid	6,600
Drawings	8,000

Bad Debts during the year were ₹900. As regards sale, Surya tells you that he always sells goods at Cost plus 25%. Furniture and Fittings are to be depreciated at 10% of the value in the beginning of the year.

Prepare Surya's Trading and Profit and Loss Account for the year ended 31st March, 2018 and his Balance Sheet on that date.

Discussion

42.	In the given figure, OABC is a square of side 7 cm. If COPB is a quadrant of a circle with centre C find the area of the shaded region.
Answer» In the given figure, OABC is a square of side 7 cm. If COPB is a quadrant of a circle with centre C find the area of the shaded region.

Discussion

43.	Find the value of CD?
Answer» Find the value of CD?

43.

Find the value of CD?

Answer»

Find the value of CD?

Discussion

44.	Question 1 (d) Find the HCF of the following numbers: 27, 63
Answer» Question 1 (d) Find the HCF of the following numbers: 27, 63

44.

Question 1 (d) Find the HCF of the following numbers: 27, 63

Answer»

Question 1 (d)

Find the HCF of the following numbers:
27, 63

Discussion

45.	In the given figure, AOBC is the quadrant of the circle of radius 8 cm. If P and Q are the mid-points of AO and OB respectively, then the ratio of area of APQB and area of minor segment ACB is
Answer» In the given figure, $A O B C$ is the quadrant of the circle of radius $8 cm$ . If $P$ and $Q$ are the mid-points of $A O$ and $O B$ respectively, then the ratio of area of $A P Q B$ and area of minor segment $A C B$ is

Discussion

46.	For the following distribution: Below: 10 20 30 40 50 60Number of students: 3 12 27 57 75 80the modal class is (a) 10-20 (b) 20-30 (c) 30-40 (d) 50-60
Answer» For the following distribution: Below: 10 20 30 40 50 60 Number of students: 3 12 27 57 75 80 the modal class is (a) 10-20 (b) 20-30 (c) 30-40 (d) 50-60

Discussion

47.	Question 8 Find the solution of the linear equation x + 2y = 8 which represent a point on: (i) x-axis (ii) y-axis
Answer» Question 8 Find the solution of the linear equation x + 2y = 8 which represent a point on: (i) x-axis (ii) y-axis

Discussion

48.	Solve each of the following quadratic equations:x-1x-2+x-3x-4=313, x≠2, 4 [CBSE 2010]
Answer» Solve each of the following quadratic equations: $\frac{x - 1}{x - 2} + \frac{x - 3}{x - 4} = 3 \frac{1}{3}, x \neq 2, 4$ [CBSE 2010]

Discussion

49.	If the sum of the zeros of the quadratic polynomial f(t) = kt2 + 2t + 3k is equal to their product, find the value of k.
Answer» If the sum of the zeros of the quadratic polynomial f(t) = kt² + 2t + 3k is equal to their product, find the value of k.

Discussion

50.	A data has 25 observations arranged in a descending order. Which observation represents the median? [CBSE 2014]
Answer» A data has 25 observations arranged in a descending order. Which observation represents the median? [CBSE 2014]

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Which is the side opposite to the angle θ?

The area of triangle whose vertices are the incentre, centroid and circumcentre of a triangle with sides 14,50,48 is

Question 1 (v) Write211 in decimal form and say what kind of decimal expansion it has.

The construction of triangle ΔA'C'B similar to triangle ΔACB is shown in the figure below. Then

is the cubic polynomial whose zeroes are 2, - 3 and 4.

The sum of all two digit odd numbers is:

In a right angle triangle ΔABC, a perpendicular BD is drawn on to the largest side from the vertex B. Which of the following does NOT give the ratios of the areas of ΔABD and ΔBCD ?

Solve each of the following quadratic equations: (i) 1x+1+2x+2=5x+4,x≠−1,−2,−4 (ii) 1x+1+35x+1=5x+4,x≠−115,−4

Question 1 Find the surface area of a sphere of radius: (i) 10.5 cm (ii) 5.6 cm (iii) 14 cm [Assume π=227]

Kumar and Kavya together have 45 marbles. Both of them lost 5 marbles each, and the product of the number of marbles they now have is 124. Representing the problem mathematically gives the quadratic equation _____.

Question 5Two identical cubes each of volume 64 cm3 are joined together end to end. What is the surface area of the resulting cuboid?

Show graphically that each one of the following systems of equations has infinitely many solutions:2x + 3y = 64x + 6y = 12

Write ‘True’ or ‘False’ and justify your answer in each of the following :(i) The length of tangents from an external point P on a circle is always greater than the radius of the circle.(ii) The length of tangents from an external point P on a circle with centre O is always less than OP.

A polynomial g(x) of degree zero is added to the polynomial 2x^3 + 5x^2-14x+10 so that it becomes exactly divisible by 2x-3. Find g(x).

The direction cosines of the line joining points (4, 3, –5) and (–2, 1, –8) are ______________.

if modulis a vector +b vector =modulus a vector -b vector then angle between a vector and b vector is equal t

Solve each of the following systems of equations by the method of cross-multiplication :mx-ny=m2+n2x+y=2m

If two numbers in the ratio 10:4 and when 3 is added to the numbers ratio becomes 3:1. Find the numbers.

For an AP of 14 terms, find the option which gives the value equal to a4+a11.

A copper wire, 3mm in diameter, is wound about a cylinder whose length is 12 cm and diameter 10 cm, so as to cover the curved surface of the cylinder. Find the length of the mass of the wire, assuming the density of copper to be 8.88 g/cm3.

If the area of the triangle formed by the points(x,2x),(−2,6) and(3,1) is 5 square units , then x(a)23(b) 35(c)3(d) 5

Solve the following systems of equations:6x+y=7x-y+312x+y=13x-y'where x + y ≠ 0 and x − y ≠ 0

Question 8 (i)In right triangle ABC, right angled at C, M is the mid-point of hypotenuse AB. C is joined to M and produced to a point D such that DM = CM. Point D is joined to point B (see the given figure). Show that:ΔAMC≅ΔBMD

Find the HCF of the smallest prime number and the smallest composite number.

Draw a right triangle in which sides (other than hypotenuse) are of lengths 4 cm and 3 cm. Then, construct another triangle whose sides are 53 times the corresponding sides of the given triangle. [CBSE 2011]

A line segment AB is divided in the ratio 4:9 by a point C.Find the length AC (in cm) if AB=26 cm.8

2. Integrate=sin(log x)

If m ∝ n and when m = 154, n = 7. Find the value of m, when n = 14

If 3sinθ+4cosθ=5, then the value of tanθ is _____.

If the angle of elevation of a tower from a distance of 100 m from its foot is 60∘, then the height of the tower is

The perimeter of a triangle is 30 cm and the circumference of its incircle is 88 cm. The area of the triangle is(a) 70 cm2(b) 140 cm2(c) 210 cm2(d) 420 cm2

Find zeroes of the polynomial x2−2.

The radius of a circular garden is 100 m. There is a road 10 m wide, running all around it. Find the area of the road and the cost of levellingit at Rs 20 per m2. [Use π = 3.14] [CBSE 2011]

The lengths of the sides of a right angled triangle are all given in natural numbers. If two of these numbers are odd and they differ by 50, then the least possible value for the third side is A)61 B)60 C)51 D)50

Amita has 12 marbles and Reeta has 8 marbles. Reeta says that she has x/y times the marbles that Amita has, where x and y are co-prime numbers. Then x + y = ___

In the given figure, AB and CD are two chords of a circle, intersecting each other at a point E.Prove that ∠AEC = 12(angle subtended by arc CXA at the centre + angle subtended by arc DYB at the centre).

In the given figure, OABC is a square of side 7 cm. If COPB is a quadrant of a circle with centre C find the area of the shaded region.

Find the value of CD?

Question 1 (d) Find the HCF of the following numbers: 27, 63

In the given figure, AOBC is the quadrant of the circle of radius 8 cm. If P and Q are the mid-points of AO and OB respectively, then the ratio of area of APQB and area of minor segment ACB is

For the following distribution: Below: 10 20 30 40 50 60Number of students: 3 12 27 57 75 80the modal class is (a) 10-20 (b) 20-30 (c) 30-40 (d) 50-60

Question 8 Find the solution of the linear equation x + 2y = 8 which represent a point on: (i) x-axis (ii) y-axis

Solve each of the following quadratic equations:x-1x-2+x-3x-4=313, x≠2, 4 [CBSE 2010]

If the sum of the zeros of the quadratic polynomial f(t) = kt2 + 2t + 3k is equal to their product, find the value of k.

A data has 25 observations arranged in a descending order. Which observation represents the median? [CBSE 2014]