32581 + Interview Questions in Mathematics

1.	Two towers A and B are standing at some distance apart. From the top of tower A, the angle of depression of the foot of tower B is found to be 30∘. From the top of tower B, the angle of depression of the foot of tower A is found to be 60∘. If the height of tower B is ‘h’ m then the height of tower A in terms of ‘h’ is _____ m
Answer» Two towers A and B are standing at some distance apart. From the top of tower A, the angle of depression of the foot of tower B is found to be $30^{\circ}$ . From the top of tower B, the angle of depression of the foot of tower A is found to be $60^{\circ}$ . If the height of tower B is ‘h’ m then the height of tower A in terms of ‘h’ is _____ m

Discussion

2.	In the given figure, P is the centre of the circle.Prove that : ∠XPZ = 2(∠XZY + ∠YXZ)
Answer» In the given figure, P is the centre of the circle. Prove that : ∠XPZ = 2(∠XZY + ∠YXZ)

Discussion

3.	(13 * ) If by + czb2 + c2= cz +ax c2 + a2= ax + bya2 + b2 then prove that xa= yb= zc .
Answer» (13 * ) If $\frac{b y + c z}{b^{2} + c^{2}} = \frac{c z + a x}{c^{2} + a^{2}} = \frac{a x + b y}{a^{2} + b^{2}}$ then prove that $\frac{x}{a} = \frac{y}{b} = \frac{z}{c}$ .

Discussion

4.	The 4 term of an AP is zero, then prove that 25 term of the AP is three times it's 11 term
Answer» The 4 term of an AP is zero, then prove that 25 term of the AP is three times it's 11 term

Discussion

5.	Write the value of cot2θ-1sin2θ.
Answer» Write the value of $(\cot^{2} θ - \frac{1}{\sin^{2} θ})$ .

Discussion

6.

Pass the Opening Entry from the following Balance Sheet as at 31st March, 2019 of Vikas: Liabilities ₹ Assets ₹ Capital A/c: Land and Building 1,50,000 Opening Balance 5,05,115 Plant and Machinery 2,50,750 Add: Profit for the year 1,20,115 Chandra & Sons 71,270 6,25,230 Closing Stock 56,250 Less: Drawings 60,000 5,65,230 Cash in Hand 15,700 Salary Payable 15,000 Cash at Bank 75,250 Magic Trades 27,220 Input CGST 5,000 Babbar & Co. 11,770 Output SGST 5,000 6,24,220 6,24,220

Answer» Pass the Opening Entry from the following Balance Sheet as at 31st March, 2019 of Vikas:


Liabilities		₹	Assets	₹
Capital A/c:			Land and Building	1,50,000
Opening Balance	5,05,115		Plant and Machinery	2,50,750
Add: Profit for the year	1,20,115		Chandra & Sons	71,270
	6,25,230		Closing Stock	56,250
Less: Drawings	60,000	5,65,230	Cash in Hand	15,700
Salary Payable		15,000	Cash at Bank	75,250
Magic Trades		27,220	Input CGST	5,000
Babbar & Co.		11,770
Output SGST		5,000

		6,24,220		6,24,220

Discussion

7.	Two similar triangles have areas 392 sq. cm and 200 sq. cm respectively, find the ratio of any pair of corresponding sides.
Answer» Two similar triangles have areas 392 sq. cm and 200 sq. cm respectively, find the ratio of any pair of corresponding sides.

Discussion

8.	If 15:1x=1x:11.25, then the value of x is
Answer» If $\frac{1}{5}$ : $\frac{1}{x}$ = $\frac{1}{x}$ : $\frac{1}{1.25}$ , then the value of $x$ is

Discussion

9.	Represent the following situations in the form of quadratic equations.(i) The area of a rectangular plot is 528 m2. The length of the plot (in metres) is one more than twice its breadth. We need to find the length and breadth of the plot.(ii) The product of two consecutive positive integers is 306. We need to find the integers.(iii) Rohan’s mother is 26 years older than him. The product of their ages (in years) 3 years from now will be 360. We would like to find Rohan’s present age.(iv) A train travels a distance of 480 km at a uniform speed. If the speed had been 8 km/h less, then it would have taken 3 hours more to cover the same distance. We need to find the speed of the train.
Answer» Represent the following situations in the form of quadratic equations. (i) The area of a rectangular plot is 528 m². The length of the plot (in metres) is one more than twice its breadth. We need to find the length and breadth of the plot. (ii) The product of two consecutive positive integers is 306. We need to find the integers. (iii) Rohan’s mother is 26 years older than him. The product of their ages (in years) 3 years from now will be 360. We would like to find Rohan’s present age. (iv) A train travels a distance of 480 km at a uniform speed. If the speed had been 8 km/h less, then it would have taken 3 hours more to cover the same distance. We need to find the speed of the train.

9.

Represent the following situations in the form of quadratic equations.(i) The area of a rectangular plot is 528 m2. The length of the plot (in metres) is one more than twice its breadth. We need to find the length and breadth of the plot.(ii) The product of two consecutive positive integers is 306. We need to find the integers.(iii) Rohan’s mother is 26 years older than him. The product of their ages (in years) 3 years from now will be 360. We would like to find Rohan’s present age.(iv) A train travels a distance of 480 km at a uniform speed. If the speed had been 8 km/h less, then it would have taken 3 hours more to cover the same distance. We need to find the speed of the train.

Answer»

Represent the following situations in the form of quadratic equations.

(i) The area of a rectangular plot is 528 m². The length of the plot (in metres) is one more than twice its breadth. We need to find the length and breadth of the plot.

(ii) The product of two consecutive positive integers is 306. We need to find the integers.

(iii) Rohan’s mother is 26 years older than him. The product of their ages (in years) 3 years from now will be 360. We would like to find Rohan’s present age.

(iv) A train travels a distance of 480 km at a uniform speed. If the speed had been 8 km/h less, then it would have taken 3 hours more to cover the same distance. We need to find the speed of the train.

Discussion

10.	Solve for x and y: 2x+3y=0,3x+4y=5.
Answer» Solve for x and y: $2 x + 3 y = 0, 3 x + 4 y = 5.$

10.

Solve for x and y: 2x+3y=0,3x+4y=5.

Answer»

Solve for x and y:

$2 x + 3 y = 0, 3 x + 4 y = 5.$

Discussion

11.	Amir Enterprise purchased chocolate sauce bottles and paid GST of Rs 3800. He sold those bottles to Akbari Bros. and collected GST of Rs 4100. Mayank Food Corner purchased these bottles from Akabari Bros and paid GST of Rs 4500. Find the amount of GST payable at every stage of trading and hence find payable CGST and SGST.
Answer» Amir Enterprise purchased chocolate sauce bottles and paid GST of Rs 3800. He sold those bottles to Akbari Bros. and collected GST of Rs 4100. Mayank Food Corner purchased these bottles from Akabari Bros and paid GST of Rs 4500. Find the amount of GST payable at every stage of trading and hence find payable CGST and SGST.

Discussion

12.	Find the roots of each of the following equations, if they exist, by applying the quadratic formula:3x2-22x-23=0 [CBSE 2015]
Answer» Find the roots of each of the following equations, if they exist, by applying the quadratic formula: $\sqrt{3} x^{2} - 2 \sqrt{2} x - 2 \sqrt{3} = 0$ [CBSE 2015]

Discussion

13.	In Fig. 1, PQ and PR are tangents to the circle with centre O such that ∠QPR = 50°,(a) 25°(b) 30°(c) 40°(d) 50°
Answer» In Fig. 1, PQ and PR are tangents to the circle with centre O such that ∠QPR = 50°, (a) 25° (b) 30° (c) 40° (d) 50°

Discussion

14.	Without using trigonometric tables, evaluate the following:sec 37°cosec 53°+2 cot 15° cot 25° cot 45° cot 75° cot 65°-3sin2 18°+sin2 72°
Answer» Without using trigonometric tables, evaluate the following: $\frac{\sec 37 °}{cosec 53 °} + 2 \cot 15 ° \cot 25 ° \cot 45 ° \cot 75 ° \cot 65 ° - 3 (\sin^{2} 18 ° + \sin^{2} 72 °)$

Discussion

15.	Find two natural numbers, the sum of whose squares is 25 times their sum and also equal to 50 times their difference.
Answer» Find two natural numbers, the sum of whose squares is 25 times their sum and also equal to 50 times their difference.

Discussion

16.	x+y≤9,y is greater than x and x≥ o.solve the inequalit
Answer» x+y≤9,y is greater than x and x≥ o.solve the inequalit

Discussion

17.	general solution of †an5θ=cot2θ
Answer» general solution of †an5θ=cot2θ

Discussion

18.	∑fx = 5x + 2, ∑f = 12. If the mean of the distribution is 6, then the value of x is less than
Answer» $\sum$ fx = 5x + 2, $\sum$ f = 12. If the mean of the distribution is 6, then the value of x is less than

Discussion

19.	The length and breadth of a rectangle are 10 centimetres and 4 centimetres. It is made larger, increasing the length and breadth by the same amount. Find algebraic expressions to compute the perimeters and areas of such enlarged rectangles in terms of the increase in the lengths of sides.
Answer» The length and breadth of a rectangle are 10 centimetres and 4 centimetres. It is made larger, increasing the length and breadth by the same amount. Find algebraic expressions to compute the perimeters and areas of such enlarged rectangles in terms of the increase in the lengths of sides.

19.

The length and breadth of a rectangle are 10 centimetres and 4 centimetres. It is made larger, increasing the length and breadth by the same amount. Find algebraic expressions to compute the perimeters and areas of such enlarged rectangles in terms of the increase in the lengths of sides.

Answer»

The length and breadth of a rectangle are 10 centimetres and 4 centimetres. It is made larger, increasing the length and breadth by the same amount.

Find algebraic expressions to compute the perimeters and areas of such enlarged rectangles in terms of the increase in the lengths of sides.

Discussion

20.	Find the sum of first 8 multiples of 3.
Answer» Find the sum of first 8 multiples of 3.

Discussion

21.	Find the values of a and b for which the following system of equations has infinitely many solutions: (i) (2a - 1) x - 3y = 5 3x + (b - 2) y = 3 (ii) 2x - (2a + 5) y = 5 (2b + 1) x - 9y = 15 (iii) (a - 1) x + 3y = 2 6x + (1 - 2b) y = 6 (iv) 3x + 4y = 12 (a + b) x + 2 (a - b) y = 5a - 1 (v) 2x + 3y = 7 (a - b) x + (a + b) y = 3a + b - 2 (vi) 2x + 3y - 7 = 0 (a - 1) x + (a + 1) y = (3a - 1) (vii) 2x + 3y = 7 (a - 1) x + (a + 2) y = 3a (viii) x + 2y = 1 (a - b) x + (a + b) y = a + b - 2 (ix) 2x + 3y = 7 2ax + ay = 28 - by
Answer» Find the values of a and b for which the following system of equations has infinitely many solutions: (i) (2a - 1) x - 3y = 5 3x + (b - 2) y = 3 (ii) 2x - (2a + 5) y = 5 (2b + 1) x - 9y = 15 (iii) (a - 1) x + 3y = 2 6x + (1 - 2b) y = 6 (iv) 3x + 4y = 12 (a + b) x + 2 (a - b) y = 5a - 1 (v) 2x + 3y = 7 (a - b) x + (a + b) y = 3a + b - 2 (vi) 2x + 3y - 7 = 0 (a - 1) x + (a + 1) y = (3a - 1) (vii) 2x + 3y = 7 (a - 1) x + (a + 2) y = 3a (viii) x + 2y = 1 (a - b) x + (a + b) y = a + b - 2 (ix) 2x + 3y = 7 2ax + ay = 28 - by

21.

Find the values of a and b for which the following system of equations has infinitely many solutions: (i) (2a - 1) x - 3y = 5 3x + (b - 2) y = 3 (ii) 2x - (2a + 5) y = 5 (2b + 1) x - 9y = 15 (iii) (a - 1) x + 3y = 2 6x + (1 - 2b) y = 6 (iv) 3x + 4y = 12 (a + b) x + 2 (a - b) y = 5a - 1 (v) 2x + 3y = 7 (a - b) x + (a + b) y = 3a + b - 2 (vi) 2x + 3y - 7 = 0 (a - 1) x + (a + 1) y = (3a - 1) (vii) 2x + 3y = 7 (a - 1) x + (a + 2) y = 3a (viii) x + 2y = 1 (a - b) x + (a + b) y = a + b - 2 (ix) 2x + 3y = 7 2ax + ay = 28 - by

Answer»

Find the values of a and b for which the following system of equations has infinitely many solutions:

(i) (2a - 1) x - 3y = 5

3x + (b - 2) y = 3

(ii) 2x - (2a + 5) y = 5

(2b + 1) x - 9y = 15

(iii) (a - 1) x + 3y = 2

6x + (1 - 2b) y = 6

(iv) 3x + 4y = 12

(a + b) x + 2 (a - b) y = 5a - 1

(v) 2x + 3y = 7

(a - b) x + (a + b) y = 3a + b - 2

(vi) 2x + 3y - 7 = 0

(a - 1) x + (a + 1) y = (3a - 1)

(vii) 2x + 3y = 7

(a - 1) x + (a + 2) y = 3a

(viii) x + 2y = 1

(a - b) x + (a + b) y = a + b - 2

(ix) 2x + 3y = 7

2ax + ay = 28 - by

Discussion

22.	A box contains 90 discs, numbered from 1 to 90. If one disc is drawn at random from the box, the probability that it bears prime number less than 23 is [CBSE 2013] (a) 790(b) 19(c) 415(d) 889
Answer» A box contains 90 discs, numbered from 1 to 90. If one disc is drawn at random from the box, the probability that it bears prime number less than 23 is [CBSE 2013] (a) $\frac{7}{90}$ (b) $\frac{1}{9}$ (c) $\frac{4}{15}$ (d) $\frac{8}{89}$

Discussion

23.	If tanθ = 1 them, find the values of sinθ+cosθsecθ+cosecθ .
Answer» If tanθ = 1 them, find the values of $\frac{sinθ + cosθ}{secθ + cosecθ}$ .

Discussion

24.	A triangle is drawn by joining a point on the semi-circle to the ends of the diameter. Two semi-circles are drawn with the other two sides as diameter. The sum of the areas of shaded part is ______
Answer» A triangle is drawn by joining a point on the semi-circle to the ends of the diameter. Two semi-circles are drawn with the other two sides as diameter. The sum of the areas of shaded part is ______

24.

A triangle is drawn by joining a point on the semi-circle to the ends of the diameter. Two semi-circles are drawn with the other two sides as diameter. The sum of the areas of shaded part is ______

Answer»

A triangle is drawn by joining a point on the semi-circle to the ends of the diameter. Two semi-circles are drawn with the other two sides as diameter.

The sum of the areas of shaded part is ______

Discussion

25.	Pooja and Ritu can do a piece of work in 1717 days. If one day work of Pooja be three fourth of one day work of Ritu; find in how many days each alone will do the work.
Answer» Pooja and Ritu can do a piece of work in $17 \frac{1}{7}$ days. If one day work of Pooja be three fourth of one day work of Ritu; find in how many days each alone will do the work.

Discussion

26.	Find the roots of the following quadratic equations by the factorization method. 2x2+53x−2=0
Answer» Find the roots of the following quadratic equations by the factorization method. $2 x^{2} + \frac{5}{3} x - 2 = 0$

Discussion

27.	A triangle is drawn by joining a point on the semi-circle to the ends of the diameter. Two semi-circles are drawn with the other two sides as diameter. Find the sum of the areas of shaded part.
Answer» A triangle is drawn by joining a point on the semi-circle to the ends of the diameter. Two semi-circles are drawn with the other two sides as diameter. Find the sum of the areas of shaded part.

27.

A triangle is drawn by joining a point on the semi-circle to the ends of the diameter. Two semi-circles are drawn with the other two sides as diameter. Find the sum of the areas of shaded part.

Answer»

A triangle is drawn by joining a point on the semi-circle to the ends of the diameter. Two semi-circles are drawn with the other two sides as diameter.

Find the sum of the areas of shaded part.

Discussion

28.	Question 6 The vertices of triangle ABC are A (4, 6), B (1, 5) and C (7, 2). A line is drawn to intersect sides AB and AC at D and E respectively, such that ADAB=AEAC=14. Calculate the area of triangle ADE and compare it with area of triangle ABC.
Answer» Question 6 The vertices of triangle ABC are A (4, 6), B (1, 5) and C (7, 2). A line is drawn to intersect sides AB and AC at D and E respectively, such that $\frac{A D}{A B} = \frac{A E}{A C} = \frac{1}{4}$ . Calculate the area of triangle ADE and compare it with area of triangle ABC.

Discussion

29.	if the roots of the equation px^2-2px+r=0 and qx^2-2rootpr*x + q = 0 are simultaneously real, then prove that q^2=pr
Answer» if the roots of the equation px^2-2px+r=0 and qx^2-2rootpr*x + q = 0 are simultaneously real, then prove that q^2=pr

Discussion

30.	In ∆ABC (Fig. 4.59), if ∠1 = ∠2, prove that ABAC=BDDC.
Answer» In ∆ABC (Fig. 4.59), if ∠1 = ∠2, prove that $\frac{AB}{AC} = \frac{BD}{DC}$ .

Discussion

31.	Prove that (23-1) is an irrational number.
Answer» Prove that ( $2 \sqrt{3} - 1$ ) is an irrational number.

Discussion

32.	If tanθ=512, find (1+cos θ)×(1−sinθ)(1+sinθ)×(1−cosθ).
Answer» If $t a n θ = \frac{5}{12}$ , find $\frac{(1 + c o s θ) \times (1 - s i n θ)}{(1 + s i n θ) \times (1 - c o s θ)}$ .

Discussion

33.	If the probability of winning a game is 0.3, what is the probability of loosing it ?
Answer» If the probability of winning a game is 0.3, what is the probability of loosing it ?

Discussion

34.	in square ABCD AC and BD meet at O the angle bisector of \angle CAB meets BD at F,meets BC at G .Find the ratio of OF toCG
Answer» in square ABCD AC and BD meet at O the angle bisector of \angle CAB meets BD at F,meets BC at G .Find the ratio of OF toCG

Discussion

35.	From which point shown below can we draw one tangent to the following circle?
Answer» From which point shown below can we draw one tangent to the following circle?

35.

From which point shown below can we draw one tangent to the following circle?

Answer»

From which point shown below can we draw one tangent to the following circle?

Discussion

36.	The line joining the points A (-3, -10) and B (-2, 6) is divided by the point P such that PBAB=15. Find the co-ordinates of P.
Answer» The line joining the points A (-3, -10) and B (-2, 6) is divided by the point P such that $\frac{P B}{A B} = \frac{1}{5}$ . Find the co-ordinates of P.

Discussion

37.	Find x intercept and y intercept of the equation 3y – 4x = 10. Hence find the coordinates of the midpoint of the line joining the intercepts.
Answer» Find x intercept and y intercept of the equation 3y – 4x = 10. Hence find the coordinates of the midpoint of the line joining the intercepts.

Discussion

38.	You are given a circle with radius ‘r’ and centre O. You are asked to draw a pair of tangents which are inclined at an angle of 60∘ with each other. Refer to the figure and select the option which would lead us to the required construction. 'd' is the distance OE.
Answer» You are given a circle with radius ‘r’ and centre O. You are asked to draw a pair of tangents which are inclined at an angle of $60^{\circ}$ with each other. Refer to the figure and select the option which would lead us to the required construction. 'd' is the distance OE.

Discussion

39.	A right triangle is formed by connecting the 3 coordinates A, B and C. Find the area of the ΔABC, if AB and BC are parallel to the coordinate axes as shown in the figure.
Answer» A right triangle is formed by connecting the 3 coordinates A, B and C. Find the area of the $Δ A B C$ , if AB and BC are parallel to the coordinate axes as shown in the figure.

Discussion

40.	If the sum of first 7 terms of an AP is 49 and that of 17 terms is 289, then find the common difference.2
Answer» If the sum of first 7 terms of an AP is 49 and that of 17 terms is 289, then find the common difference. 2

Discussion

41.	Question 3 (ii) Find the roots of the following equations: (ii) 1x+4−1x−7=1130,x≠−4,7
Answer» Question 3 (ii) Find the roots of the following equations: (ii) $\frac{1}{x + 4} - \frac{1}{x - 7} = \frac{11}{30}, x \neq - 4, 7$

Discussion

42.	Solve each of the following equations by using the method of completing the square:3x2-2x-1=0
Answer» Solve each of the following equations by using the method of completing the square: $3 x^{2} - 2 x - 1 = 0$

Discussion

43.	Which of the following can be the equation of the line drawn in the graph?
Answer» Which of the following can be the equation of the line drawn in the graph?

Discussion

44.	6. The distance of the chord of lenght 16cm from the centre of the circle of diameter 20 cm is A 3cm B 4cm C 6cm D 5cm
Answer» 6. The distance of the chord of lenght 16cm from the centre of the circle of diameter 20 cm is A 3cm B 4cm C 6cm D 5cm

Discussion

45.	In the following figure, PQ and PR are tangents to the circle, with centre O. If ∠QPR=60o, calculate : (i)∠QOR, (ii)∠OQR, (iii)∠QSR,
Answer» In the following figure, PQ and PR are tangents to the circle, with centre O. If $∠ Q P R = 60^{o}$ , calculate : (i) $∠ Q O R,$ (ii) $∠ O Q R,$ (iii) $∠ Q S R,$

45.

In the following figure, PQ and PR are tangents to the circle, with centre O. If ∠QPR=60o, calculate : (i)∠QOR, (ii)∠OQR, (iii)∠QSR,

Answer»

In the following figure, PQ and PR are tangents to the circle, with centre O. If $∠ Q P R = 60^{o}$ , calculate :

(i) $∠ Q O R,$
(ii) $∠ O Q R,$
(iii) $∠ Q S R,$

Discussion

46.	Write the coefficient of the polynomial p(z) = z5 − 2z2 + 4.
Answer» Write the coefficient of the polynomial p(z) = z⁵ − 2z² + 4.

Discussion

47.	She is aiming _______ winning a gold medal _______ the nest Olympic Games.
Answer» She is aiming _______ winning a gold medal _______ the nest Olympic Games.

Discussion

48.	Question 8 From a solid cylinder whose height is 2.4 cm and diameter 1.4 cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid to the nearest cm2.
Answer» Question 8 From a solid cylinder whose height is 2.4 cm and diameter 1.4 cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid to the nearest $c m^{2}$ .

Discussion

49.	A toy is in the form of a cone mounted on a hemisphere of radius 3.5 cm. The total height of the toy is 15.5 cm find the total surface area and volume of the toy.
Answer» A toy is in the form of a cone mounted on a hemisphere of radius 3.5 cm. The total height of the toy is 15.5 cm find the total surface area and volume of the toy.

Discussion

50.	The sum of the first n terms of an A.P. is 2235.The first term is 2 and the common difference is 5.What is n=?
Answer» The sum of the first n terms of an A.P. is 2235.The first term is 2 and the common difference is 5.What is n=?

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

In the given figure, P is the centre of the circle.Prove that : ∠XPZ = 2(∠XZY + ∠YXZ)

(13 * ) If by + czb2 + c2= cz +ax c2 + a2= ax + bya2 + b2 then prove that xa= yb= zc .

The 4 term of an AP is zero, then prove that 25 term of the AP is three times it's 11 term

Write the value of cot2θ-1sin2θ.

Two similar triangles have areas 392 sq. cm and 200 sq. cm respectively, find the ratio of any pair of corresponding sides.

If 15:1x=1x:11.25, then the value of x is

Solve for x and y: 2x+3y=0,3x+4y=5.

Find the roots of each of the following equations, if they exist, by applying the quadratic formula:3x2-22x-23=0 [CBSE 2015]

In Fig. 1, PQ and PR are tangents to the circle with centre O such that ∠QPR = 50°,(a) 25°(b) 30°(c) 40°(d) 50°

Without using trigonometric tables, evaluate the following:sec 37°cosec 53°+2 cot 15° cot 25° cot 45° cot 75° cot 65°-3sin2 18°+sin2 72°

Find two natural numbers, the sum of whose squares is 25 times their sum and also equal to 50 times their difference.

x+y≤9,y is greater than x and x≥ o.solve the inequalit

general solution of †an5θ=cot2θ

∑fx = 5x + 2, ∑f = 12. If the mean of the distribution is 6, then the value of x is less than

The length and breadth of a rectangle are 10 centimetres and 4 centimetres. It is made larger, increasing the length and breadth by the same amount. Find algebraic expressions to compute the perimeters and areas of such enlarged rectangles in terms of the increase in the lengths of sides.

Find the sum of first 8 multiples of 3.

A box contains 90 discs, numbered from 1 to 90. If one disc is drawn at random from the box, the probability that it bears prime number less than 23 is [CBSE 2013] (a) 790(b) 19(c) 415(d) 889

If tanθ = 1 them, find the values of sinθ+cosθsecθ+cosecθ .

A triangle is drawn by joining a point on the semi-circle to the ends of the diameter. Two semi-circles are drawn with the other two sides as diameter. The sum of the areas of shaded part is ______

Pooja and Ritu can do a piece of work in 1717 days. If one day work of Pooja be three fourth of one day work of Ritu; find in how many days each alone will do the work.

Find the roots of the following quadratic equations by the factorization method. 2x2+53x−2=0

A triangle is drawn by joining a point on the semi-circle to the ends of the diameter. Two semi-circles are drawn with the other two sides as diameter. Find the sum of the areas of shaded part.

Question 6 The vertices of triangle ABC are A (4, 6), B (1, 5) and C (7, 2). A line is drawn to intersect sides AB and AC at D and E respectively, such that ADAB=AEAC=14. Calculate the area of triangle ADE and compare it with area of triangle ABC.

if the roots of the equation px^2-2px+r=0 and qx^2-2rootpr*x + q = 0 are simultaneously real, then prove that q^2=pr

In ∆ABC (Fig. 4.59), if ∠1 = ∠2, prove that ABAC=BDDC.

Prove that (23-1) is an irrational number.

If tanθ=512, find (1+cos θ)×(1−sinθ)(1+sinθ)×(1−cosθ).

If the probability of winning a game is 0.3, what is the probability of loosing it ?

in square ABCD AC and BD meet at O the angle bisector of \angle CAB meets BD at F,meets BC at G .Find the ratio of OF toCG

From which point shown below can we draw one tangent to the following circle?

The line joining the points A (-3, -10) and B (-2, 6) is divided by the point P such that PBAB=15. Find the co-ordinates of P.

Find x intercept and y intercept of the equation 3y – 4x = 10. Hence find the coordinates of the midpoint of the line joining the intercepts.

You are given a circle with radius ‘r’ and centre O. You are asked to draw a pair of tangents which are inclined at an angle of 60∘ with each other. Refer to the figure and select the option which would lead us to the required construction. 'd' is the distance OE.

A right triangle is formed by connecting the 3 coordinates A, B and C. Find the area of the ΔABC, if AB and BC are parallel to the coordinate axes as shown in the figure.

If the sum of first 7 terms of an AP is 49 and that of 17 terms is 289, then find the common difference.2

Question 3 (ii) Find the roots of the following equations: (ii) 1x+4−1x−7=1130,x≠−4,7

Solve each of the following equations by using the method of completing the square:3x2-2x-1=0

Which of the following can be the equation of the line drawn in the graph?

6. The distance of the chord of lenght 16cm from the centre of the circle of diameter 20 cm is A 3cm B 4cm C 6cm D 5cm

In the following figure, PQ and PR are tangents to the circle, with centre O. If ∠QPR=60o, calculate : (i)∠QOR, (ii)∠OQR, (iii)∠QSR,

Write the coefficient of the polynomial p(z) = z5 − 2z2 + 4.

She is aiming _______ winning a gold medal _______ the nest Olympic Games.

Question 8 From a solid cylinder whose height is 2.4 cm and diameter 1.4 cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid to the nearest cm2.

A toy is in the form of a cone mounted on a hemisphere of radius 3.5 cm. The total height of the toy is 15.5 cm find the total surface area and volume of the toy.

The sum of the first n terms of an A.P. is 2235.The first term is 2 and the common difference is 5.What is n=?

She is aiming _ winning a gold medal _ the nest Olympic Games.