32581 + Interview Questions in Mathematics

1.	Solve the following systems of equations:x + y = 5xy3x + 2y = 13xy,x ≠ 0, y ≠ 0
Answer» Solve the following systems of equations: x + y = 5xy 3x + 2y = 13xy, x ≠ 0, y ≠ 0

Discussion

2.	(sec A – cos A) (cot A + tan A) = sec A tan A
Answer» (sec A – cos A) (cot A + tan A) = sec A tan A

Discussion

3.	If x ∝ 1/y then :
Answer» If x ∝ 1/y then :

Discussion

4.	Which term fo the AP 121, 117, 113, .. is its first negative term?
Answer» Which term fo the AP 121, 117, 113, .. is its first negative term?

Discussion

5.	Question 90 Solve the following: Two equal sides of a triangle are each 4 m less than three times the third side. Find the dimensions of the triangle, if its perimeter is 55m.
Answer» Question 90 Solve the following: Two equal sides of a triangle are each 4 m less than three times the third side. Find the dimensions of the triangle, if its perimeter is 55m.

5.

Question 90 Solve the following: Two equal sides of a triangle are each 4 m less than three times the third side. Find the dimensions of the triangle, if its perimeter is 55m.

Answer»

Question 90

Solve the following:

Two equal sides of a triangle are each 4 m less than three times the third side. Find the dimensions of the triangle, if its perimeter is 55m.

Discussion

6.	2 tangents are drawn from a point P to a circle shown . If PA = 8 cm, what is the value of PB
Answer» 2 tangents are drawn from a point P to a circle shown . If PA = 8 cm, what is the value of PB

6.

2 tangents are drawn from a point P to a circle shown . If PA = 8 cm, what is the value of PB

Answer»

2 tangents are drawn from a point P to a circle shown . If PA = 8 cm, what is the value of PB

Discussion

7.	Find the lengths of the medians of a triangle whose vertices are A(–1, 1), B(5, –3) and C(3, 5).
Answer» Find the lengths of the medians of a triangle whose vertices are A(–1, 1), B(5, –3) and C(3, 5).

Discussion

8.	If a semicircle with 'AB' as diameter and having a radius of 5 cm is drawn as shown in below figure then the coordinates of B is___.
Answer» If a semicircle with 'AB' as diameter and having a radius of 5 cm is drawn as shown in below figure then the coordinates of B is___.

8.

If a semicircle with 'AB' as diameter and having a radius of 5 cm is drawn as shown in below figure then the coordinates of B is___.

Answer»

If a semicircle with 'AB' as diameter and having a radius of 5 cm is drawn as shown in below figure then the coordinates of B is___.

Discussion

9.	Solve the following system of equations graphically and find the vertices and area of the triangle formed by these lines and the y-axis.2x-5y+4=0 2x+y-8=0
Answer» Solve the following system of equations graphically and find the vertices and area of the triangle formed by these lines and the y-axis. $2 x - 5 y + 4 = 0 2 x + y - 8 = 0$

Discussion

10.	If 40 metres of a cloth costs Rs. 2000, then how many metres of cloth can be bought for Rs. 100
Answer» If 40 metres of a cloth costs Rs. 2000, then how many metres of cloth can be bought for Rs. 100

Discussion

11.	Solve the following: (a) If the point (a,0) lies on the line x - y = 2, then find the value of a. (b) Find the point of intersection of y = 6x - 9 with the X axis. [3 MARKS]
Answer» Solve the following: (a) If the point (a,0) lies on the line x - y = 2, then find the value of a. (b) Find the point of intersection of y = 6x - 9 with the X axis. [3 MARKS]

Discussion

12.

Record following transactions in the Purchases Return Book of Kamla Stores for June 2017: 2018 June 6 Returned goods to Ramesh Brothers, Delhi purchased for ₹ 5,000 plus CGST and SGST 6% each June 8 Returned goods to Sohan Brothers, Meerut purchased for ₹ 10,000 plus IGST 12% June 17 Returned goods to Mahesh Brothers of ₹ 2,000 plus CGST and SGST 6% each

Answer» Record following transactions in the Purchases Return Book of Kamla Stores for June 2017:

2018
June 6	Returned goods to Ramesh Brothers, Delhi purchased for ₹ 5,000 plus CGST and SGST 6% each
June 8	Returned goods to Sohan Brothers, Meerut purchased for ₹ 10,000 plus IGST 12%
June 17	Returned goods to Mahesh Brothers of ₹ 2,000 plus CGST and SGST 6% each

Discussion

13.	A solid is in the shape of a frustum of a cone, The diameters of the two circular ends are 60 cm and 36 cm and the height is 9 cm. Find the area of its whole surface and the volume.
Answer» A solid is in the shape of a frustum of a cone, The diameters of the two circular ends are 60 cm and 36 cm and the height is 9 cm. Find the area of its whole surface and the volume.

Discussion

14.	Gopi buys a fish from a shop for his aquarium. The shopkeeper takes out one fish at random from a tank containing 5 male fishes and 8 female fishes (see figure). What is the probability that the fish taken out is a male fish?
Answer» Gopi buys a fish from a shop for his aquarium. The shopkeeper takes out one fish at random from a tank containing 5 male fishes and 8 female fishes (see figure). What is the probability that the fish taken out is a male fish?

Discussion

15.	If sec 4A = cosec (A – 20°), where 4A is an acute angle, find the value of A.
Answer» If sec 4A = cosec (A – 20°), where 4A is an acute angle, find the value of A.

Discussion

16.	For the following A.Ps, write the first term and the common difference.(i) 3, 1, - 1, - 3 …(ii) -5, - 1, 3, 7 …
Answer» For the following A.Ps, write the first term and the common difference. (i) 3, 1, - 1, - 3 … (ii) -5, - 1, 3, 7 …

Discussion

17.	In ∆ABC, ray BD bisects ∠ABC and ray CE bisects ∠ACB. If seg AB ≅ seg AC then prove that ED \|\| BC.
Answer» In ∆ABC, ray BD bisects ∠ABC and ray CE bisects ∠ACB. If seg AB ≅ seg AC then prove that ED \|\| BC.

Discussion

18.	In each of the figures given below, an altitude is drawn to the hypotenuse by a right-angled triangle. The length of different line-segment are marked in each figure. Determine x, y, z in each case.(i)(ii)
Answer» In each of the figures given below, an altitude is drawn to the hypotenuse by a right-angled triangle. The length of different line-segment are marked in each figure. Determine x, y, z in each case. (i) (ii)

Discussion

19.	PQ is a tangent to a circle with centre O at the point P. If △OPQ is an isosceles triangle, then ∠OQP is equal to [CBSE 2014](a) 30∘(b) 45∘(c) 60∘(d) 90∘
Answer» PQ is a tangent to a circle with centre O at the point P. If △OPQ is an isosceles triangle, then ∠OQP is equal to [CBSE 2014] (a) 30^∘ (b) 45^∘ (c) 60^∘ (d) 90^∘

Discussion

20.	Define power set. What is the cardinality of the power set of X if the cardinality of X is 5?
Answer» Define power set. What is the cardinality of the power set of X if the cardinality of X is 5?

Discussion

21.	The horizontal distance between two poles is 15 m. The angle of depression of the top of first pole as seen from the top of second pole is 30∘. If the height of the second pole is 24 m, find the height of the first pole. [Use√3=1.732]
Answer» The horizontal distance between two poles is 15 m. The angle of depression of the top of first pole as seen from the top of second pole is $30^{\circ}$ . If the height of the second pole is 24 m, find the height of the first pole. $[U s e \sqrt{3} = 1.732]$

Discussion

22.	A is elder to B by 2 years. A’s father F is twice as old as A and B is twice as old as his sister S. If the ages of the father and sister differ by 40 years, find the age of A.
Answer» A is elder to B by 2 years. A’s father F is twice as old as A and B is twice as old as his sister S. If the ages of the father and sister differ by 40 years, find the age of A.

Discussion

23.	In the given figure, ∠ABC = 90° and BD ⊥ AC. If BD = 8 cm and AD = 4 cm, find CD.
Answer» In the given figure, ∠ABC = 90° and BD ⊥ AC. If BD = 8 cm and AD = 4 cm, find CD.

Discussion

24.	Find the sum of n terms of the series 4-1n+4-2n+4-3n+..........
Answer» Find the sum of n terms of the series $(4 - \frac{1}{n}) + (4 - \frac{2}{n}) + (4 - \frac{3}{n}) + . . . . . . . . . .$

Discussion

25.	An arithmetic progression 5,12,19.....has 50 terms.Find its last term.Hence find the sum of its last 15 terms.
Answer» An arithmetic progression 5,12,19.....has 50 terms.Find its last term.Hence find the sum of its last 15 terms.

Discussion

26.	Question 1 From a point Q, the length of the tangent to a circle is 24 cm and the distance of Q from the centre is 25 cm. The radius of the circle is (A) 7 cm (B) 12 cm (C) 15 cm (D) 24.5 cm
Answer» Question 1 From a point Q, the length of the tangent to a circle is 24 cm and the distance of Q from the centre is 25 cm. The radius of the circle is (A) 7 cm (B) 12 cm (C) 15 cm (D) 24.5 cm

Discussion

27.	In triangle ABC angle A is greater than B .if the measures of angles A and B satisfy the equation 4cos^3x -3cosx=k ,k belongs to -1,1 in closed interval . Excluding zero.then the measure of angle C is Ais less than 2pie/3.A) pie/6B)pie/3C)pie/2
Answer» In triangle ABC angle A is greater than B .if the measures of angles A and B satisfy the equation 4cos^3x -3cosx=k ,k belongs to -1,1 in closed interval . Excluding zero.then the measure of angle C is Ais less than 2pie/3. A) pie/6 B)pie/3 C)pie/2

Discussion

28.	The points (–3, 2) and (2, –3) lie in __________ and __________ quadrants respectively.
Answer» The points (–3, 2) and (2, –3) lie in __________ and __________ quadrants respectively.

Discussion

29.	Two poles of height 9 in and 14 m stand on a plane ground. If the distanee their feet is 12 m, find the distance between their tops.
Answer» Two poles of height 9 in and 14 m stand on a plane ground. If the distanee their feet is 12 m, find the distance between their tops.

Discussion

30.	The height of a cone increases by 2%, it's semi vertical angle remaining the same. What is the approximate percentage increase (1).In total surface area, (2). in the volume.
Answer» The height of a cone increases by 2%, it's semi vertical angle remaining the same. What is the approximate percentage increase (1).In total surface area, (2). in the volume.

Discussion

31.	In the given figure, Δ ABC and Δ AMP are right angled at B and M respectively. Given AC = 10 cm, AP = 15 cm and PM = 12 cm. (i) Prove that : (i) Δ ABC ~ Δ AMP (ii) Find : AB and BC.
Answer» In the given figure, $Δ$ ABC and $Δ$ AMP are right angled at B and M respectively. Given AC = 10 cm, AP = 15 cm and PM = 12 cm. (i) Prove that : (i) $Δ$ ABC ~ $Δ$ AMP (ii) Find : AB and BC.

31.

In the given figure, Δ ABC and Δ AMP are right angled at B and M respectively. Given AC = 10 cm, AP = 15 cm and PM = 12 cm. (i) Prove that : (i) Δ ABC ~ Δ AMP (ii) Find : AB and BC.

Answer»

In the given figure, $Δ$ ABC and $Δ$ AMP are right angled at B and M respectively. Given AC = 10 cm, AP = 15 cm and PM = 12 cm. (i) Prove that : (i) $Δ$ ABC ~ $Δ$ AMP
(ii) Find : AB and BC.

Discussion

32.	The diameter of the base of a cone is 42 cm and its volume is 12936 cm3. Its height is (a) 28 cm (b) 21 cm (c) 35 cm (d) 14 cm
Answer» The diameter of the base of a cone is 42 cm and its volume is 12936 $c m^{3}$ . Its height is (a) 28 cm (b) 21 cm (c) 35 cm (d) 14 cm

32.

The diameter of the base of a cone is 42 cm and its volume is 12936 cm3. Its height is (a) 28 cm (b) 21 cm (c) 35 cm (d) 14 cm

Answer»

The diameter of the base of a cone is 42 cm and its volume is 12936 $c m^{3}$ . Its height is

(a) 28 cm (b) 21 cm (c) 35 cm (d) 14 cm

Discussion

33.	Two numbers 'a' and 'b' are selected successively without replacement in that order from the integers 1 to 10. The probability that ab is an integer, is(a) 1745(b) 15(c) 1790(d) 845
Answer» Two numbers 'a' and 'b' are selected successively without replacement in that order from the integers 1 to 10. The probability that $\frac{a}{b}$ is an integer, is (a) $\frac{17}{45}$ (b) $\frac{1}{5}$ (c) $\frac{17}{90}$ (d) $\frac{8}{45}$

Discussion

34.	An electrician has to repair an electric falut on a pole of height 4 metres, He needs to reach a point 1 metre below the top of pole to undertake the repair work. What should be the length of the ladder that the should use, which when inclined at an angle of 60∘ to the horizontal would enable him to reach the required position ? [Use √3=1.732.]
Answer» An electrician has to repair an electric falut on a pole of height 4 metres, He needs to reach a point 1 metre below the top of pole to undertake the repair work. What should be the length of the ladder that the should use, which when inclined at an angle of $60^{\circ}$ to the horizontal would enable him to reach the required position ? [Use $\sqrt{3} = 1.732.$ ]

Discussion

35.	There are 300 shelves in a gym. Each shelf has 2 lockers. The gym just opened today. Ram and Arjun are its first customers. It is given that Ram gets allotted one locker in the 235th shelf. What is the probability that Arjun also gets allotted a locker in the 235th shelf?
Answer» There are 300 shelves in a gym. Each shelf has 2 lockers. The gym just opened today. Ram and Arjun are its first customers. It is given that Ram gets allotted one locker in the $235^{t h}$ shelf. What is the probability that Arjun also gets allotted a locker in the $235^{t h}$ shelf?

Discussion

36.	If sinθ=34, show that cosec2θ-cot2θsec2θ-1=73.
Answer» If $\sin θ = \frac{3}{4}$ , show that $\sqrt{\frac{{cosec}^{2} θ - \cot^{2} θ}{\sec^{2} θ - 1}} = \frac{\sqrt{7}}{3}$ .

Discussion

37.	Solve the following systems of equations:3x-1y=-92x+3y=5
Answer» Solve the following systems of equations: $\frac{3}{x} - \frac{1}{y} = - 9 \frac{2}{x} + \frac{3}{y} = 5$

Discussion

38.	Solve each of the following equations by using the method of completing the square:3x2+10x+73=0
Answer» Solve each of the following equations by using the method of completing the square: $\sqrt{3} x^{2} + 10 x + 7 \sqrt{3} = 0$

Discussion

39.	Finding the square root of the polynomial 4x4+8x3+8x2+4x+1.
Answer» Finding the square root of the polynomial $4 x^{4} + 8 x^{3} + 8 x^{2} + 4 x + 1.$

Discussion

40.	Using ruler and compasses only: i) Construct a ΔABC in which BC = 6cm, ∠ABC = 120∘ and AB = 3.5 cm. ii) In the above figure draw a circle with BC as diameter. Find a point P on the circumference of the circle that is equidistant from AB and BC. Measure the ∠BCP.
Answer» Using ruler and compasses only: i) Construct a $Δ$ ABC in which BC = 6cm, $∠$ ABC = 120 $^{\circ}$ and AB = 3.5 cm. ii) In the above figure draw a circle with BC as diameter. Find a point P on the circumference of the circle that is equidistant from AB and BC. Measure the $∠$ BCP.

40.

Using ruler and compasses only: i) Construct a ΔABC in which BC = 6cm, ∠ABC = 120∘ and AB = 3.5 cm. ii) In the above figure draw a circle with BC as diameter. Find a point P on the circumference of the circle that is equidistant from AB and BC. Measure the ∠BCP.

Answer»

Using ruler and compasses only:

i) Construct a $Δ$ ABC in which BC = 6cm, $∠$ ABC = 120 $^{\circ}$ and AB = 3.5 cm.

ii) In the above figure draw a circle with BC as diameter. Find a point P on the circumference of the circle that is equidistant from AB and BC. Measure the $∠$ BCP.

Discussion

41.

A and B are partners in a firm. The net profit of the firm is divided as follows: 1/2 to A, 1/3 to B and 1/6 carried to a Reserve. They admit C as a partner on 1st April, 2019 on which date, the Balance Sheet of the firm was: Liabilities ₹ Assets ₹ Capital A/cs: Building 50,000 A 50,000 Plant and Machinery 30,000 B 40,000 90,000 Stock 18,000 Reserve 10,000 Debtors 22,000 Creditors 20,000 Bank 5,000 Outstanding Expenses 5,000 1,25,000 1,25,000 Following are the required adjustments on admission of C:(a) C brings in ₹ 25,000 towards his capital.(b) C also brings in ₹ 5,000 for 1/5th share of goodwill.(c) Stock is undervalued by 10%.(d) Creditors include a liability of ₹ 4,000, which has been decided by the court at ₹ 3,200.(e) In regard to the Debtors, the following Debts proved Bad or Doubtful−₹ 2,000 due from X−bad to the full extent;₹ 4,000 due from Y−insolvent, estate expected to pay only 50%.You are required to prepare Revaluation Account, Partners' Capital Accounts and Balance Sheet of the new firm.

Answer» A and B are partners in a firm. The net profit of the firm is divided as follows: 1/2 to A, 1/3 to B and 1/6 carried to a Reserve. They admit C as a partner on 1st April, 2019 on which date, the Balance Sheet of the firm was:


Liabilities		₹	Assets	₹
Capital A/cs:			Building	50,000
A	50,000		Plant and Machinery	30,000
B	40,000	90,000	Stock	18,000
Reserve		10,000	Debtors	22,000
Creditors		20,000	Bank	5,000
Outstanding Expenses		5,000

		1,25,000		1,25,000

Following are the required adjustments on admission of C:

(a) C brings in ₹ 25,000 towards his capital.

(b) C also brings in ₹ 5,000 for 1/5th share of goodwill.

(c) Stock is undervalued by 10%.

(d) Creditors include a liability of ₹ 4,000, which has been decided by the court at ₹ 3,200.

(e) In regard to the Debtors, the following Debts proved Bad or Doubtful−

₹ 2,000 due from X−bad to the full extent;

₹ 4,000 due from Y−insolvent, estate expected to pay only 50%.

You are required to prepare Revaluation Account, Partners' Capital Accounts and Balance Sheet of the new firm.

Discussion

42.	A box contains slips numbered 1, 2, 3, 4. Another box contains slips numbered 1, 2, 3. If one slip is taken from each, what is the probability of getting a sum which is a multiple of three?
Answer» A box contains slips numbered 1, 2, 3, 4. Another box contains slips numbered 1, 2, 3. If one slip is taken from each, what is the probability of getting a sum which is a multiple of three?

Discussion

43.	Find the value of k, if (2k,k) lies on the line represented by an equation y=10−2x.
Answer» Find the value of $k$ , if $(2 k, k)$ lies on the line represented by an equation $y = 10 - 2 x$ .

Discussion

44.	The coordinates of the point of trisection of the line segment joining the points A(4, 8) and B(-2, 4) are
Answer» The coordinates of the point of trisection of the line segment joining the points A(4, 8) and B(-2, 4) are

44.

The coordinates of the point of trisection of the line segment joining the points A(4, 8) and B(-2, 4) are

Answer»

The coordinates of the point of trisection of the line segment joining the points A(4, 8) and B(-2, 4) are

Discussion

45.	Write the degree of the polynomial x cube + y square + 1
Answer» Write the degree of the polynomial x cube + y square + 1

Discussion

46.	Given that x and y are in inverse proportion, and y1, y2 are values of y corresponding to the values x1,x2 of x respectively. Which of the following is correct?
Answer» Given that x and y are in inverse proportion, and $y_{1}$ , $y_{2}$ are values of y corresponding to the values $x_{1}, x_{2}$ of x respectively. Which of the following is correct?

Discussion

47.	129.Given that root 2 is a zero of the cubic polynomial six x cube + root 2 x square - 10x - 4 root 2, find its other two zeros
Answer» 129.Given that root 2 is a zero of the cubic polynomial six x cube + root 2 x square - 10x - 4 root 2, find its other two zeros

Discussion

48.	Question 9 If Q (0, 1) is equidistant from P (5, - 3) and R (x, 6), find the values of x. Also find the distance QR and PR.
Answer» Question 9 If Q (0, 1) is equidistant from P (5, - 3) and R (x, 6), find the values of x. Also find the distance QR and PR.

Discussion

49.	An aeroplane when flying at a height of 3000 metres from the ground passes vertically above another aeroplane at an instant when the angles of elevation of the two planes from the same point on the ground are 60∘ and 45∘ respectively. Find the vertical distance between the aeroplanes at that instant. [Take √3=1.73] [3 MARKS]
Answer» An aeroplane when flying at a height of 3000 metres from the ground passes vertically above another aeroplane at an instant when the angles of elevation of the two planes from the same point on the ground are $60^{\circ}$ and $45^{\circ}$ respectively. Find the vertical distance between the aeroplanes at that instant. [Take $\sqrt{3} = 1.73$ ] [3 MARKS]

Discussion

50.	Which of the following should be the LAST sentence after rearrangement?
Answer» Which of the following should be the LAST sentence after rearrangement?

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Solve the following systems of equations:x + y = 5xy3x + 2y = 13xy,x ≠ 0, y ≠ 0

(sec A – cos A) (cot A + tan A) = sec A tan A

If x ∝ 1/y then :

Which term fo the AP 121, 117, 113, .. is its first negative term?

Question 90 Solve the following: Two equal sides of a triangle are each 4 m less than three times the third side. Find the dimensions of the triangle, if its perimeter is 55m.

2 tangents are drawn from a point P to a circle shown . If PA = 8 cm, what is the value of PB

Find the lengths of the medians of a triangle whose vertices are A(–1, 1), B(5, –3) and C(3, 5).

If a semicircle with 'AB' as diameter and having a radius of 5 cm is drawn as shown in below figure then the coordinates of B is___.

Solve the following system of equations graphically and find the vertices and area of the triangle formed by these lines and the y-axis.2x-5y+4=0 2x+y-8=0

If 40 metres of a cloth costs Rs. 2000, then how many metres of cloth can be bought for Rs. 100

Solve the following: (a) If the point (a,0) lies on the line x - y = 2, then find the value of a. (b) Find the point of intersection of y = 6x - 9 with the X axis. [3 MARKS]

A solid is in the shape of a frustum of a cone, The diameters of the two circular ends are 60 cm and 36 cm and the height is 9 cm. Find the area of its whole surface and the volume.

Gopi buys a fish from a shop for his aquarium. The shopkeeper takes out one fish at random from a tank containing 5 male fishes and 8 female fishes (see figure). What is the probability that the fish taken out is a male fish?

If sec 4A = cosec (A – 20°), where 4A is an acute angle, find the value of A.

For the following A.Ps, write the first term and the common difference.(i) 3, 1, - 1, - 3 …(ii) -5, - 1, 3, 7 …

In ∆ABC, ray BD bisects ∠ABC and ray CE bisects ∠ACB. If seg AB ≅ seg AC then prove that ED || BC.

In each of the figures given below, an altitude is drawn to the hypotenuse by a right-angled triangle. The length of different line-segment are marked in each figure. Determine x, y, z in each case.(i)(ii)

PQ is a tangent to a circle with centre O at the point P. If △OPQ is an isosceles triangle, then ∠OQP is equal to [CBSE 2014](a) 30∘(b) 45∘(c) 60∘(d) 90∘

Define power set. What is the cardinality of the power set of X if the cardinality of X is 5?

The horizontal distance between two poles is 15 m. The angle of depression of the top of first pole as seen from the top of second pole is 30∘. If the height of the second pole is 24 m, find the height of the first pole. [Use√3=1.732]

A is elder to B by 2 years. A’s father F is twice as old as A and B is twice as old as his sister S. If the ages of the father and sister differ by 40 years, find the age of A.

In the given figure, ∠ABC = 90° and BD ⊥ AC. If BD = 8 cm and AD = 4 cm, find CD.

Find the sum of n terms of the series 4-1n+4-2n+4-3n+..........

An arithmetic progression 5,12,19.....has 50 terms.Find its last term.Hence find the sum of its last 15 terms.

Question 1 From a point Q, the length of the tangent to a circle is 24 cm and the distance of Q from the centre is 25 cm. The radius of the circle is (A) 7 cm (B) 12 cm (C) 15 cm (D) 24.5 cm

In triangle ABC angle A is greater than B .if the measures of angles A and B satisfy the equation 4cos^3x -3cosx=k ,k belongs to -1,1 in closed interval . Excluding zero.then the measure of angle C is Ais less than 2pie/3.A) pie/6B)pie/3C)pie/2

The points (–3, 2) and (2, –3) lie in __________ and __________ quadrants respectively.

Two poles of height 9 in and 14 m stand on a plane ground. If the distanee their feet is 12 m, find the distance between their tops.

The height of a cone increases by 2%, it's semi vertical angle remaining the same. What is the approximate percentage increase (1).In total surface area, (2). in the volume.

In the given figure, Δ ABC and Δ AMP are right angled at B and M respectively. Given AC = 10 cm, AP = 15 cm and PM = 12 cm. (i) Prove that : (i) Δ ABC ~ Δ AMP (ii) Find : AB and BC.

The diameter of the base of a cone is 42 cm and its volume is 12936 cm3. Its height is (a) 28 cm (b) 21 cm (c) 35 cm (d) 14 cm

Two numbers 'a' and 'b' are selected successively without replacement in that order from the integers 1 to 10. The probability that ab is an integer, is(a) 1745(b) 15(c) 1790(d) 845

There are 300 shelves in a gym. Each shelf has 2 lockers. The gym just opened today. Ram and Arjun are its first customers. It is given that Ram gets allotted one locker in the 235th shelf. What is the probability that Arjun also gets allotted a locker in the 235th shelf?

If sinθ=34, show that cosec2θ-cot2θsec2θ-1=73.

Solve the following systems of equations:3x-1y=-92x+3y=5

Solve each of the following equations by using the method of completing the square:3x2+10x+73=0

Finding the square root of the polynomial 4x4+8x3+8x2+4x+1.

Using ruler and compasses only: i) Construct a ΔABC in which BC = 6cm, ∠ABC = 120∘ and AB = 3.5 cm. ii) In the above figure draw a circle with BC as diameter. Find a point P on the circumference of the circle that is equidistant from AB and BC. Measure the ∠BCP.

A box contains slips numbered 1, 2, 3, 4. Another box contains slips numbered 1, 2, 3. If one slip is taken from each, what is the probability of getting a sum which is a multiple of three?

Find the value of k, if (2k,k) lies on the line represented by an equation y=10−2x.

The coordinates of the point of trisection of the line segment joining the points A(4, 8) and B(-2, 4) are

Write the degree of the polynomial x cube + y square + 1

Given that x and y are in inverse proportion, and y1, y2 are values of y corresponding to the values x1,x2 of x respectively. Which of the following is correct?

129.Given that root 2 is a zero of the cubic polynomial six x cube + root 2 x square - 10x - 4 root 2, find its other two zeros

Question 9 If Q (0, 1) is equidistant from P (5, - 3) and R (x, 6), find the values of x. Also find the distance QR and PR.

Which of the following should be the LAST sentence after rearrangement?

The points (–3, 2) and (2, –3) lie in and quadrants respectively.