32581 + Interview Questions in Mathematics

1.	If the zeroes of the quadratic polynomial ax2+bx+c, c ≠ 0 are equal, then (a) c and a have opposite signs (b) c and b have opposite signs(c) c and a have the same sign (d) c and b have the same sign
Answer» If the zeroes of the quadratic polynomial $a x^{2} + b x + c$ , $c \neq 0$ are equal, then (a) c and a have opposite signs (b) c and b have opposite signs (c) c and a have the same sign (d) c and b have the same sign

Discussion

2.	32. The locus of the centre of the circle which bisect the circumference of the circle x2+y2=4 and x2+y2-2x+6y+1=0.explain details
Answer» 32. The locus of the centre of the circle which bisect the circumference of the circle x2+y2=4 and x2+y2-2x+6y+1=0.explain details

Discussion

3.	If in two triangles DEF and PQR, ∠D = ∠Q and ∠R = ∠E, then DEQR=DFPQ = _________.
Answer» If in two triangles DEF and PQR, ∠D = ∠Q and ∠R = ∠E, then $\frac{D E}{Q R} = \frac{D F}{P Q}$ = _________.

Discussion

4.	In the given figure, PT is a tangent drawn from an external point T to the circle with centre O and PQ is the diameter of the circle. Point Q and T are joined by a line which is intersecting the circle at R. If∠POR=78∘, then find the value of ∠PTR.
Answer» $In the given figure, PT is a tangent drawn from an external point T to the circle with centre O and PQ is the diameter of the circle. Point Q and T are joined by a line which is intersecting the circle at R. If ∠ P O R = 78^{\circ}, then find the value of ∠ P T R .$

Discussion

5.	If α and β are the zeros of the polynomial f(x)=6x2+x−2, find the value of (αβ+βα).
Answer» If $α$ and $β$ are the zeros of the polynomial $f (x) = 6 x^{2} + x - 2$ , find the value of $(\frac{α}{β} + \frac{β}{α}) .$

Discussion

6.	If the value of Sin A=1√2, then find out the value of tan A−cot A.0
Answer» If the value of $S i n A = \frac{1}{\sqrt{2}}$ , then find out the value of $t a n A - c o t A$ . 0

Discussion

7.	There are 40 students in a class, out of them 15 are boys. The mean of marks obtained by boys is 33 and that for girls is 35. Find out the mean of all students in the class.
Answer» There are 40 students in a class, out of them 15 are boys. The mean of marks obtained by boys is 33 and that for girls is 35. Find out the mean of all students in the class.

Discussion

8.	In a circle of radius, 4.5 cm , draw two radii such that the angle between them is 60°. Draw two tangents at the end of the radii.
Answer» In a circle of radius, 4.5 cm , draw two radii such that the angle between them is 60°. Draw two tangents at the end of the radii.

Discussion

9.	Draw two concentric circles of radii 3 cm and 5 cm. Construct a tangent to smaller circle from a point on the larger circle. Also measure its length.
Answer» Draw two concentric circles of radii 3 cm and 5 cm. Construct a tangent to smaller circle from a point on the larger circle. Also measure its length.

Discussion

10.	If 5a = 3125, then the value of 5(a - 3) is:
Answer» If 5^a = 3125, then the value of 5^{(a - 3)} is:

Discussion

11.	If −1,−1,α,β are roots of x4+3x2+bx+c=0, then (1+α)(1+β) is equal to
Answer» If $- 1, - 1, α, β$ are roots of $x^{4} + 3 x^{2} + b x + c = 0,$ then $(1 + α) (1 + β)$ is equal to

Discussion

12.	Shriya and Vidya solved a quadratic equation. In solving it, Shriya made a mistake in the constant term and obtained the roots as 5, – 3 while Vidya made a mistake in the coefficient of x and obtained the roots as 1, –3. The correct roots of the equation are
Answer» Shriya and Vidya solved a quadratic equation. In solving it, Shriya made a mistake in the constant term and obtained the roots as 5, – 3 while Vidya made a mistake in the coefficient of x and obtained the roots as 1, –3. The correct roots of the equation are

Discussion

13.	Find the roots of each of the following equations, if they exist, by applying the quadratic formula:2x2+53x+6=0
Answer» Find the roots of each of the following equations, if they exist, by applying the quadratic formula: $2 x^{2} + 5 \sqrt{3} x + 6 = 0$

Discussion

14.	A pen stand made of wood is in the shape of a cuboid with four conical depressions to hold pens. The dimensions of the cuboid are 15 cm × 10 cm × 3.5 cm. The radius of each of the depressions is 0.5 cm and the depth is 1.4 cm. Find the volume of wood in the entire stand.
Answer» A pen stand made of wood is in the shape of a cuboid with four conical depressions to hold pens. The dimensions of the cuboid are 15 cm × 10 cm × 3.5 cm. The radius of each of the depressions is 0.5 cm and the depth is 1.4 cm. Find the volume of wood in the entire stand.

14.

A pen stand made of wood is in the shape of a cuboid with four conical depressions to hold pens. The dimensions of the cuboid are 15 cm × 10 cm × 3.5 cm. The radius of each of the depressions is 0.5 cm and the depth is 1.4 cm. Find the volume of wood in the entire stand.

Answer»

A pen stand made of wood is in the shape of a cuboid with four conical depressions to hold pens. The dimensions of the cuboid are 15 cm × 10 cm × 3.5 cm. The radius of each of the depressions is 0.5 cm and the depth is 1.4 cm. Find the volume of wood in the entire stand.

Discussion

15.	In fig. (a) What is AE + EC? (b) What is AC – EC? (c) What is BD – BE? (d) What is BD – DE? [4 MARKS]
Answer» In fig. (a) What is AE + EC? (b) What is AC – EC? (c) What is BD – BE? (d) What is BD – DE? [4 MARKS]

15.

In fig. (a) What is AE + EC? (b) What is AC – EC? (c) What is BD – BE? (d) What is BD – DE? [4 MARKS]

Answer»

In fig.

(a) What is AE + EC?

(b) What is AC – EC?

(c) What is BD – BE?

(d) What is BD – DE?

[4 MARKS]

Discussion

16.	1. The side AB of parallelogram ABCD is produced to any point P. A line through A and parallel to CP meets CB produced at Q and then parallelogram PBQR is completed. Show that ar(ABCD)= ar(PBQR).
Answer» 1. The side AB of parallelogram ABCD is produced to any point P. A line through A and parallel to CP meets CB produced at Q and then parallelogram PBQR is completed. Show that ar(ABCD)= ar(PBQR).

Discussion

17.	The radius of the circular base of a cylinder is 14 cm and height is 10 cm. Calculate the curved surface area of the cylinder.
Answer» The radius of the circular base of a cylinder is 14 cm and height is 10 cm. Calculate the curved surface area of the cylinder.

17.

The radius of the circular base of a cylinder is 14 cm and height is 10 cm. Calculate the curved surface area of the cylinder.

Answer»

The radius of the circular base of a cylinder is 14 cm and height is 10 cm. Calculate the curved surface area of the cylinder.

Discussion

18.	If tan theta= 2-root3, then prove that tan^3 + cot^3-2 = 50
Answer» If tan theta= 2-root3, then prove that tan^3 + cot^3-2 = 50

Discussion

19.	Mr. Tiwari invested Rs 29,040 in 15% Rs 100 shares quoted at a premium of 20% . Calculate: (i) the number of shares bought by Mr. Tiwari. (ii) Mr. Tiwari's income from the investment. (iii) the percentage return on his investment.
Answer» Mr. Tiwari invested Rs 29,040 in 15% Rs 100 shares quoted at a premium of 20% . Calculate: (i) the number of shares bought by Mr. Tiwari. (ii) Mr. Tiwari's income from the investment. (iii) the percentage return on his investment.

19.

Mr. Tiwari invested Rs 29,040 in 15% Rs 100 shares quoted at a premium of 20% . Calculate: (i) the number of shares bought by Mr. Tiwari. (ii) Mr. Tiwari's income from the investment. (iii) the percentage return on his investment.

Answer»

Mr. Tiwari invested Rs 29,040 in 15% Rs 100 shares quoted at a premium of 20% . Calculate:

(i) the number of shares bought by Mr. Tiwari.

(ii) Mr. Tiwari's income from the investment.

(iii) the percentage return on his investment.

Discussion

20.	Show that a-b2, a2+b2 and a+b2 are in AP.
Answer» Show that ${(a - b)}^{2}, (a^{2} + b^{2})$ and ${(a + b)}^{2}$ are in AP.

Discussion

21.	The ages of the two sisters are 11 years and 14 years. In how many years time will the product of their ages be 304?
Answer» The ages of the two sisters are 11 years and 14 years. In how many years time will the product of their ages be 304?

Discussion

22.

Pass entries in the books of Mukerjee & Sons. assuming all transactions have taken place within the state of Uttar Pradesh. Assume CGST 9% and SGST 9%. 2018 March 1 Purchased goods for ₹ 5,00,000 from Mehta Bros. March 10 Sold goods for ₹ 8,00,000 to Munjal & Co. March 15 Paid for advertisement ₹ 40,000 by cheque. March 18 Purchased furniture for office use ₹ 50,000 and payment made by cheque. March 25 Paid for printing and stationery ₹ 8,000. March 31 Payment made of balance amount of GST.

Answer» Pass entries in the books of Mukerjee & Sons. assuming all transactions have taken place within the state of Uttar Pradesh. Assume CGST 9% and SGST 9%.

2018
March 1	Purchased goods for ₹ 5,00,000 from Mehta Bros.
March 10	Sold goods for ₹ 8,00,000 to Munjal & Co.
March 15	Paid for advertisement ₹ 40,000 by cheque.
March 18	Purchased furniture for office use ₹ 50,000 and payment made by cheque.
March 25	Paid for printing and stationery ₹ 8,000.
March 31	Payment made of balance amount of GST.

Discussion

23.	The shaded portion is cut out from the circle, and then the remaining portion is folded to make a cone. Now, if the bottom of the cone is covered with paper to form the base, what will be the ratio of the area of original circle to the total surface area of the cone made?
Answer» The shaded portion is cut out from the circle, and then the remaining portion is folded to make a cone. Now, if the bottom of the cone is covered with paper to form the base, what will be the ratio of the area of original circle to the total surface area of the cone made?

Discussion

24.	The sum of first five multiples of 3 is:(a) 45(b) 65(c) 75(d) 90
Answer» The sum of first five multiples of 3 is: (a) 45 (b) 65 (c) 75 (d) 90

Discussion

25.	The horizontal distance between two trees of different heights is 60 m. The angle of depression of the top of the first tree when seen from the top of the second tree is 45°. If the height of the second tree is 80 m, find the height of the first tree.
Answer» The horizontal distance between two trees of different heights is 60 m. The angle of depression of the top of the first tree when seen from the top of the second tree is 45°. If the height of the second tree is 80 m, find the height of the first tree.

Discussion

26.	For what value of k, is the polynomial f(x) = 3x4 – 9x3 + x2 + 15x + k completely divisible by 3x2 – 5?
Answer» For what value of k, is the polynomial f(x) = 3x⁴ – 9x³ + x² + 15x + k completely divisible by 3x² – 5?

Discussion

27.	Solve the following equation by using the method of completing the square: 2x2−5x+2=0
Answer» Solve the following equation by using the method of completing the square: $\frac{2}{x^{2}} - \frac{5}{x} + 2 = 0$

Discussion

28.	In ΔABC,D and E are the midpoints of AB and AC respectively. Find the ratio of the areas of ΔADE and ΔABC.
Answer» In $Δ A B C, D$ and E are the midpoints of AB and AC respectively. Find the ratio of the areas of $Δ A D E a n d Δ A B C$ .

28.

In ΔABC,D and E are the midpoints of AB and AC respectively. Find the ratio of the areas of ΔADE and ΔABC.

Answer»

In $Δ A B C, D$ and E are the midpoints of AB and AC respectively. Find the ratio of the areas of $Δ A D E a n d Δ A B C$ .

Discussion

29.	What is the volume of a square pyramid of base edge 10 centimetres and slant height 15 centimetres?
Answer» What is the volume of a square pyramid of base edge 10 centimetres and slant height 15 centimetres?

Discussion

30.	Question 1 (vii)Find the square roots of each of the following numbers by Division method:7921
Answer» Question 1 (vii) Find the square roots of each of the following numbers by Division method: 7921

30.

Question 1 (vii)Find the square roots of each of the following numbers by Division method:7921

Answer»

Question 1 (vii)

Find the square roots of each of the following numbers by Division method:

7921

Discussion

31.	IF ONE ZERO OF THE QUARDATIC POLYNOMIAL KX^2+2X+K^2+2 IS 3, THEN FIND THE VALUE OF K.
Answer» IF ONE ZERO OF THE QUARDATIC POLYNOMIAL KX^2+2X+K^2+2 IS 3, THEN FIND THE VALUE OF K.

Discussion

32.	Question 12If 7 times the 7th term of an AP is equal to 11 times its 11th term, then its 18th term will beA) 7B) 11C) 18D) 0
Answer» Question 12 If 7 times the $7^{t h}$ term of an AP is equal to 11 times its $11^{t h}$ term, then its $18^{t h}$ term will be A) 7 B) 11 C) 18 D) 0

Discussion

33.	A cylindrical bucket, 32 cm high and with radius of base 18 cm, is filled with sand. This bucket is emptied out on the ground and a conical heap of sand is formed. If the height of the conical heap is 24 cm, find the radius and slant height of the heap.
Answer» A cylindrical bucket, 32 cm high and with radius of base 18 cm, is filled with sand. This bucket is emptied out on the ground and a conical heap of sand is formed. If the height of the conical heap is 24 cm, find the radius and slant height of the heap.

Discussion

34.	Question 8Find the area of the sector of a circle of radius 5 cm, if the corresponding arc length is 3.5 cm.
Answer» Question 8 Find the area of the sector of a circle of radius 5 cm, if the corresponding arc length is 3.5 cm.

Discussion

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

Discussion

36.	If AB and CD are two equal chords of a circle with centre O such that ∠AOB=80∘, then find ∠COD.
Answer» If AB and CD are two equal chords of a circle with centre O such that $∠ A O B = 80^{\circ}$ , then find $∠ C O D$ .

Discussion

37.	There is a tent in a conical shape. The slant height of the tent is 14 m. If the curved surface area of the tent is 308 m2 , then what is the base area of the tent? (Take π=227)
Answer» There is a tent in a conical shape. The slant height of the tent is 14 m. If the curved surface area of the tent is 308 m², then what is the base area of the tent? (Take $π = \frac{22}{7}$ )

37.

There is a tent in a conical shape. The slant height of the tent is 14 m. If the curved surface area of the tent is 308 m2 , then what is the base area of the tent? (Take π=227)

Answer»

There is a tent in a conical shape. The slant height of the tent is 14 m. If the curved surface area of the tent is 308 m², then what is the base area of the tent? (Take $π = \frac{22}{7}$ )

Discussion

38.	The relationship between Mean, Median and Mode is
Answer» The relationship between Mean, Median and Mode is

Discussion

39.

Yogesh and Naresh are partners sharing profits in the ratio of 3 : 2. They admit Ramesh for 1/3rd share on 1st April, 2019 and also decide to share future profits equally. Balance Sheet of the firm as at 31st March, 2019 was as follows: Liabilities Amount (₹) Assets Amount (₹) Capital A/cs: Land 4,00,000 Yogesh 5,00,000 Building 4,00,000 Naresh 5,00,000 10,00,000 Furniture 50,000 Current A/cs: Computers 1,00,000 Yogesh 1,10,000 Stock 1,50,000 Naresh 90,000 2,00,000 Sundry Debtors 2,10,000 Employees' Provident Fund 25,000 Less: Provision for Doubtful Debts 10,000 2,00,000 Workmen Compensation Reserve 1,00,000 Cash 10,000 Sundry Creditors 75,000 Bank 70,000 Expenses Payable 10,000 Advertisement Suspense 30,000 14,10,000 14,10,000 They admitted Ramesh on the following terms:(a) He will bring ₹ 5,00,000 as his capital.(b) His share of goodwill is valued at ₹ 1,00,000 but he is unable to bring cash for his share of goodwill. It is agreed to debit the amount to his Current Account.(c) Value of Land and Building is to be appreciated by ₹ 40,000 each.(d) Value of Furniture to be reduced to ₹ 40,000.(e) Provision for Doubtful Debts to be increased to 10%.(f) A liability for damages of ₹ 10,000 is to be created.Pass the Journal entries on admission of Ramesh and prepare Revaluation Account.

Answer» Yogesh and Naresh are partners sharing profits in the ratio of 3 : 2. They admit Ramesh for 1/3rd share on 1st April, 2019 and also decide to share future profits equally. Balance Sheet of the firm as at 31st March, 2019 was as follows:

Liabilities		Amount (₹)	Assets		Amount (₹)
Capital A/cs:			Land		4,00,000
Yogesh	5,00,000		Building		4,00,000
Naresh	5,00,000	10,00,000	Furniture		50,000
Current A/cs:			Computers		1,00,000
Yogesh	1,10,000		Stock		1,50,000
Naresh	90,000	2,00,000	Sundry Debtors	2,10,000
Employees' Provident Fund		25,000	Less: Provision for Doubtful Debts	10,000	2,00,000
Workmen Compensation Reserve		1,00,000	Cash		10,000
Sundry Creditors		75,000	Bank		70,000
Expenses Payable		10,000	Advertisement Suspense		30,000
		14,10,000			14,10,000

They admitted Ramesh on the following terms:

(a) He will bring ₹ 5,00,000 as his capital.

(b) His share of goodwill is valued at ₹ 1,00,000 but he is unable to bring cash for his share of goodwill. It is agreed to debit the amount to his Current Account.

(c) Value of Land and Building is to be appreciated by ₹ 40,000 each.

(d) Value of Furniture to be reduced to ₹ 40,000.

(e) Provision for Doubtful Debts to be increased to 10%.

(f) A liability for damages of ₹ 10,000 is to be created.

Pass the Journal entries on admission of Ramesh and prepare Revaluation Account.

Discussion

40.	In the figure of ∆PQR, ∠P=θ° and ∠R=ϕ°. Findi x+1cotϕii x3+x2tanθiii cosθ
Answer» In the figure of $∆ PQR, ∠ P = θ ° and ∠ R = ϕ °$ . Find $(i) (\sqrt{x + 1}) \cot ϕ (ii) (\sqrt{x^{3} + x^{2}}) \tan θ (iii) \cos θ$

Discussion

41.	The value of tan 1° tan 2° tan 3° ...... tan 89° is(a) 1(b) −1(c) 0(d) None of these
Answer» The value of tan 1° tan 2° tan 3° ...... tan 89° is (a) 1 (b) −1 (c) 0 (d) None of these

Discussion

42.	From the choices given below, choose the equation whose graphs are given in Fig. 4.6 and Fig. 4.7.For Fig.4.6 For Fig.4.7(i)y=x (i)y=−x+2(ii)x+y=0 (ii)y=x−2
Answer» From the choices given below, choose the equation whose graphs are given in Fig. $4.6$ and Fig. $4.7$ . $F o r F i g . 4. 6$ $F o r F i g . 4.7$ $(i) y = x$ $(i) y = - x + 2$ $(i i) x + y = 0$ $(i i) y = x - 2$

Discussion

43.	66. Twelve men can make 24 articles in 6 days .How many articles can 3 men make in 3 days.
Answer» 66. Twelve men can make 24 articles in 6 days .How many articles can 3 men make in 3 days.

Discussion

44.	The work done by (x - 2) men in (4x + 1) days and the work done by (4x + 1) men in (2x - 3) days are in the ratio 3 : 8. Find the value of x.
Answer» The work done by (x - 2) men in (4x + 1) days and the work done by (4x + 1) men in (2x - 3) days are in the ratio 3 : 8. Find the value of x.

Discussion

45.	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

46.	Solve each of the following systems of equations by the method of cross-multiplication: 2ax+3by=a+2b 3ax+2by=2a+b
Answer» Solve each of the following systems of equations by the method of cross-multiplication: $2 a x + 3 b y = a + 2 b$ $3 a x + 2 b y = 2 a + b$

46.

Solve each of the following systems of equations by the method of cross-multiplication: 2ax+3by=a+2b 3ax+2by=2a+b

Answer»

Solve each of the following systems of equations by the method of cross-multiplication:

$2 a x + 3 b y = a + 2 b$

$3 a x + 2 b y = 2 a + b$

Discussion

47.	A card is drawn from a well shuffled deck of 52 cards. What is the probability of getting a spade?
Answer» A card is drawn from a well shuffled deck of 52 cards. What is the probability of getting a spade?

Discussion

48.	The following table gives the number of branches and number of plants in the garden of a school. No. of branches (x) : 2 3 4 5 6 No. of plants (f) : 49 43 57 38 13 Calculate the average number of branches per plant.
Answer» The following table gives the number of branches and number of plants in the garden of a school. No. of branches (x) : 2 3 4 5 6 No. of plants (f) : 49 43 57 38 13 Calculate the average number of branches per plant.

Discussion

49.	Question 3If tan2A=cot(A−18∘), where 2A is an acute angle, find the value of A.
Answer» Question 3 If $t a n 2 A = c o t (A - 18^{\circ})$ , where 2A is an acute angle, find the value of A.

Discussion

50.	If the probability of occurence of an event is p then the probability of non-happening of this event is [CBSE 2013C](a) (p − 1)(b) (1 − p)(c) p(d) 1-1p
Answer» If the probability of occurence of an event is p then the probability of non-happening of this event is [CBSE 2013C] (a) (p − 1) (b) (1 − p) (c) p (d) $(1 - \frac{1}{p})$

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

If the zeroes of the quadratic polynomial ax2+bx+c, c ≠ 0 are equal, then (a) c and a have opposite signs (b) c and b have opposite signs(c) c and a have the same sign (d) c and b have the same sign

32. The locus of the centre of the circle which bisect the circumference of the circle x2+y2=4 and x2+y2-2x+6y+1=0.explain details

If in two triangles DEF and PQR, ∠D = ∠Q and ∠R = ∠E, then DEQR=DFPQ = _________.

In the given figure, PT is a tangent drawn from an external point T to the circle with centre O and PQ is the diameter of the circle. Point Q and T are joined by a line which is intersecting the circle at R. If∠POR=78∘, then find the value of ∠PTR.

If α and β are the zeros of the polynomial f(x)=6x2+x−2, find the value of (αβ+βα).

If the value of Sin A=1√2, then find out the value of tan A−cot A.0

There are 40 students in a class, out of them 15 are boys. The mean of marks obtained by boys is 33 and that for girls is 35. Find out the mean of all students in the class.

In a circle of radius, 4.5 cm , draw two radii such that the angle between them is 60°. Draw two tangents at the end of the radii.

Draw two concentric circles of radii 3 cm and 5 cm. Construct a tangent to smaller circle from a point on the larger circle. Also measure its length.

If 5a = 3125, then the value of 5(a - 3) is:

If −1,−1,α,β are roots of x4+3x2+bx+c=0, then (1+α)(1+β) is equal to

Shriya and Vidya solved a quadratic equation. In solving it, Shriya made a mistake in the constant term and obtained the roots as 5, – 3 while Vidya made a mistake in the coefficient of x and obtained the roots as 1, –3. The correct roots of the equation are

Find the roots of each of the following equations, if they exist, by applying the quadratic formula:2x2+53x+6=0

A pen stand made of wood is in the shape of a cuboid with four conical depressions to hold pens. The dimensions of the cuboid are 15 cm × 10 cm × 3.5 cm. The radius of each of the depressions is 0.5 cm and the depth is 1.4 cm. Find the volume of wood in the entire stand.

In fig. (a) What is AE + EC? (b) What is AC – EC? (c) What is BD – BE? (d) What is BD – DE? [4 MARKS]

1. The side AB of parallelogram ABCD is produced to any point P. A line through A and parallel to CP meets CB produced at Q and then parallelogram PBQR is completed. Show that ar(ABCD)= ar(PBQR).

The radius of the circular base of a cylinder is 14 cm and height is 10 cm. Calculate the curved surface area of the cylinder.

If tan theta= 2-root3, then prove that tan^3 + cot^3-2 = 50

Mr. Tiwari invested Rs 29,040 in 15% Rs 100 shares quoted at a premium of 20% . Calculate: (i) the number of shares bought by Mr. Tiwari. (ii) Mr. Tiwari's income from the investment. (iii) the percentage return on his investment.

Show that a-b2, a2+b2 and a+b2 are in AP.

The ages of the two sisters are 11 years and 14 years. In how many years time will the product of their ages be 304?

The shaded portion is cut out from the circle, and then the remaining portion is folded to make a cone. Now, if the bottom of the cone is covered with paper to form the base, what will be the ratio of the area of original circle to the total surface area of the cone made?

The sum of first five multiples of 3 is:(a) 45(b) 65(c) 75(d) 90

The horizontal distance between two trees of different heights is 60 m. The angle of depression of the top of the first tree when seen from the top of the second tree is 45°. If the height of the second tree is 80 m, find the height of the first tree.

For what value of k, is the polynomial f(x) = 3x4 – 9x3 + x2 + 15x + k completely divisible by 3x2 – 5?

Solve the following equation by using the method of completing the square: 2x2−5x+2=0

In ΔABC,D and E are the midpoints of AB and AC respectively. Find the ratio of the areas of ΔADE and ΔABC.

What is the volume of a square pyramid of base edge 10 centimetres and slant height 15 centimetres?

Question 1 (vii)Find the square roots of each of the following numbers by Division method:7921

IF ONE ZERO OF THE QUARDATIC POLYNOMIAL KX^2+2X+K^2+2 IS 3, THEN FIND THE VALUE OF K.

Question 12If 7 times the 7th term of an AP is equal to 11 times its 11th term, then its 18th term will beA) 7B) 11C) 18D) 0

A cylindrical bucket, 32 cm high and with radius of base 18 cm, is filled with sand. This bucket is emptied out on the ground and a conical heap of sand is formed. If the height of the conical heap is 24 cm, find the radius and slant height of the heap.

Question 8Find the area of the sector of a circle of radius 5 cm, if the corresponding arc length is 3.5 cm.

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

If AB and CD are two equal chords of a circle with centre O such that ∠AOB=80∘, then find ∠COD.

There is a tent in a conical shape. The slant height of the tent is 14 m. If the curved surface area of the tent is 308 m2 , then what is the base area of the tent? (Take π=227)

The relationship between Mean, Median and Mode is

In the figure of ∆PQR, ∠P=θ° and ∠R=ϕ°. Findi x+1cotϕii x3+x2tanθiii cosθ

The value of tan 1° tan 2° tan 3° ...... tan 89° is(a) 1(b) −1(c) 0(d) None of these

From the choices given below, choose the equation whose graphs are given in Fig. 4.6 and Fig. 4.7.For Fig.4.6 For Fig.4.7(i)y=x (i)y=−x+2(ii)x+y=0 (ii)y=x−2

66. Twelve men can make 24 articles in 6 days .How many articles can 3 men make in 3 days.

The work done by (x - 2) men in (4x + 1) days and the work done by (4x + 1) men in (2x - 3) days are in the ratio 3 : 8. Find the value of x.

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

Solve each of the following systems of equations by the method of cross-multiplication: 2ax+3by=a+2b 3ax+2by=2a+b

A card is drawn from a well shuffled deck of 52 cards. What is the probability of getting a spade?

The following table gives the number of branches and number of plants in the garden of a school. No. of branches (x) : 2 3 4 5 6 No. of plants (f) : 49 43 57 38 13 Calculate the average number of branches per plant.

Question 3If tan2A=cot(A−18∘), where 2A is an acute angle, find the value of A.

If the probability of occurence of an event is p then the probability of non-happening of this event is [CBSE 2013C](a) (p − 1)(b) (1 − p)(c) p(d) 1-1p