32581 + Interview Questions in Mathematics Page 164 InterviewSolution

8151.	In the given figure, ∠ABC=∠AED=90°,AB=12cm,AC=15cmandDE=3cm.Find the area of△ABCand△AED.
Answer» $I n t h e g i v e n f i g u r e, ∠ A B C = ∠ A E D = 90 °, A B = 12 c m, A C = 15 c m a n d D E = 3 c m . F i n d t h e a r e a o f △ A B C a n d △ A E D .$

Discussion

8152.	Mia goes for shopping to buy a dress which costs ₹ 1809. The rate of sales tax is 8%. She tells the shopkeeper to reduce the price to such an extent that she has to pay ₹ 1809, inclusive of sales tax. Find the reduction needed in the price of the dress.
Answer» Mia goes for shopping to buy a dress which costs ₹ 1809. The rate of sales tax is $8 %$ . She tells the shopkeeper to reduce the price to such an extent that she has to pay ₹ 1809, inclusive of sales tax. Find the reduction needed in the price of the dress.

Discussion

8153.	Show that 42 is an irrational number.
Answer» Show that 4 $\sqrt{2}$ is an irrational number.

Discussion

8154.	Express 0.2545454..........as a fraction in simplest form.
Answer» Express 0.2545454..........as a fraction in simplest form.

Discussion

8155.	In the following figure, DE \|\| AC and DF \|\| AE. Prove that
Answer» In the following figure, DE \|\| AC and DF \|\| AE. Prove that

8155.

In the following figure, DE || AC and DF || AE. Prove that

Answer»

In the following figure, DE || AC and DF || AE. Prove that

Discussion

8156.	41. The mean of 5 numbers is 18 if one no is excluded their mean is 16 find the excluded no
Answer» 41. The mean of 5 numbers is 18 if one no is excluded their mean is 16 find the excluded no

Discussion

8157.	A hollow sphere of internal and external diameters 4 cm and 8 cm respectively is melted into a cone of base diameter 8 cm. The height of the cone is(a) 12 cm(b) 14 cm(c) 15 cm(d) 18 cm
Answer» A hollow sphere of internal and external diameters 4 cm and 8 cm respectively is melted into a cone of base diameter 8 cm. The height of the cone is (a) 12 cm (b) 14 cm (c) 15 cm (d) 18 cm

Discussion

8158.	42. A bucket of height 8 cm and made up of copper sheet is in the form of frustum of a right circular cone with radii of it Lower and upper end are as 3cm and 9 cm calculate ---- height , volume and area of copper sheet to make bucket all of frustum
Answer» 42. A bucket of height 8 cm and made up of copper sheet is in the form of frustum of a right circular cone with radii of it Lower and upper end are as 3cm and 9 cm calculate ---- height , volume and area of copper sheet to make bucket all of frustum

Discussion

8159.	Which of the following polynomials below is identical to the polynomial (x2−1)(x2−4)?
Answer» Which of the following polynomials below is identical to the polynomial $(x^{2} - 1) (x^{2} - 4)$ ?

Discussion

8160.	In the given figure, two tangents RQ and RP are drawn from an external point R to the circle with centre O. If ∠ PRQ = 120o, then prove that OR = PR + RQ.
Answer» In the given figure, two tangents RQ and RP are drawn from an external point R to the circle with centre O. If $∠$ PRQ = $120^{o}$ , then prove that OR = PR + RQ.

Discussion

8161.	The hypotenuse of a right triangle is 25 cm. The difference between the lengths of the other two sides of the triangle is 5 cm. Find the lengths of these sides.
Answer» The hypotenuse of a right triangle is 25 cm. The difference between the lengths of the other two sides of the triangle is 5 cm. Find the lengths of these sides.

Discussion

8162.	ABCD is a parallelogram with diagonal AC. If a line XY is drawn such that it cuts the side AD at point Z and XY \|\| AB, thenBXXC can be equal to:
Answer» $ABCD is a parallelogram with diagonal AC. If a line XY is drawn such that it cuts the side AD at point Z and XY \|\| AB, then \frac{B X}{X C} can be equal to:$

Discussion

8163.	Fill In The Blanks A collection of two or more possible outcomes (elementary events) of a trial is called a ________ event.
Answer» Fill In The Blanks A collection of two or more possible outcomes (elementary events) of a trial is called a ________ event.

Discussion

8164.	If an arithmetic sequence has a common difference 10 and its 6th term is 52, then find its 15th term.
Answer» If an arithmetic sequence has a common difference 10 and its $6^{t h}$ term is 52, then find its $15^{t h}$ term.

Discussion

8165.

Prince Limited issued a prospectus inviting applications for 20,000 equity shares of ₹10 each at a premium of ₹ 3 per share payable as follows: With application — ₹2, On allotment (including premium) — ₹5, On first call — ₹3, On second call — ₹3. Applications were received for 30,000 shares and allotment was made on pro rata basis. Money overpaid on application s was adjusted to the amount due on allotment. Mr Mohit whom 400 shares were allotted , failed to pay the allotment money and the first call , and his shares were forfeited after the first call . Mr Joly, whom 600 shares were allotted , failed to pay for the two calls and hence, his shares were forfeited .Of the shares forfeited, 800 shares were reissued to Supriya as fully paid for ₹ 9 per share , the whole of Mr Mohit's shares being included.

Answer» Prince Limited issued a prospectus inviting applications for 20,000 equity shares of ₹10 each at a premium of ₹ 3 per share payable as follows:

With application	$—$	₹2,
On allotment (including premium)	$—$	₹5,
On first call	$—$	₹3,
On second call	$—$	₹3.

Applications were received for 30,000 shares and allotment was made on pro rata basis. Money overpaid on application s was adjusted to the amount due on allotment.

Mr Mohit whom 400 shares were allotted , failed to pay the allotment money and the first call , and his shares were forfeited after the first call . Mr Joly, whom 600 shares were allotted , failed to pay for the two calls and hence, his shares were forfeited .

Of the shares forfeited, 800 shares were reissued to Supriya as fully paid for ₹ 9 per share , the whole of Mr Mohit's shares being included.

Discussion

8166.	A metallic cone having base radius 2.1 cm and height 8.4 cm is melted and moulded into a sphere. The radius of the sphere is (a) 2.1 cm (b) 1.05 cm (c) 1.5 cm (d) 2 cm
Answer» A metallic cone having base radius 2.1 cm and height 8.4 cm is melted and moulded into a sphere. The radius of the sphere is (a) 2.1 cm (b) 1.05 cm (c) 1.5 cm (d) 2 cm

8166.

A metallic cone having base radius 2.1 cm and height 8.4 cm is melted and moulded into a sphere. The radius of the sphere is (a) 2.1 cm (b) 1.05 cm (c) 1.5 cm (d) 2 cm

Answer»

A metallic cone having base radius 2.1 cm and height 8.4 cm is melted and moulded into a sphere. The radius of the sphere is

(a) 2.1 cm (b) 1.05 cm (c) 1.5 cm (d) 2 cm

Discussion

8167.	One of the steps involved in solving a quadratic equation x2+4x+a=9 using completing the square method is as given below: (x+b)2=5 Find a and b.
Answer» One of the steps involved in solving a quadratic equation $x^{2} + 4 x + a = 9$ using completing the square method is as given below: $(x + b)^{2} = 5$ Find $a$ and $b$ .

Discussion

8168.	The diagram represents two inequations A and B on real number lines : (i) Write down A and B in set builder notation. (ii) Represent A∩B and A∩B′ on two different number lines.
Answer» The diagram represents two inequations A and B on real number lines : (i) Write down A and B in set builder notation. (ii) Represent $A \cap B a n d A \cap B^{'}$ on two different number lines.

8168.

The diagram represents two inequations A and B on real number lines : (i) Write down A and B in set builder notation. (ii) Represent A∩B and A∩B′ on two different number lines.

Answer»

The diagram represents two inequations A and B on real number lines :

(i) Write down A and B in set builder notation.

(ii) Represent $A \cap B a n d A \cap B^{'}$ on two different number lines.

Discussion

8169.

VXN Ltd. invited applications for issuing 50,000 equity shares of ₹ 10 each at a premium of ₹ 8 per share . The amount was payable as follows: On Application — ₹ 4 per share (Including ₹ 2 premium); On Allotment — ₹ 6 per share (Including ₹ 3 premium); On First Call — ₹ 5 per share (Including ₹ 1 premium); and On Second and Final Call — Balance Amount The issue was fully subscribed . Gopal, a shareholder holding 200 shares, did not pay the allotment money and Madhav, a holder of 400 shares, paid his entire share money along with the allotment money. Gopal's shares were immediately forfeited after allotment . Afterwards, the first call was made. Krishna, a holder of 100 shares , failed to pay the first call money and Girdhar, a holder of 300 shares, paid the second call money also along with the first call . Krishna's shares were forfeited immediately after the first call. Second and final call was made afterwards and was duly received . All the forfeited shares were reissued at ₹ 9 per share fully paid-up.Pass necessary journal entries for the above transactions in the books of the company.

Answer» VXN Ltd. invited applications for issuing 50,000 equity shares of ₹ 10 each at a premium of ₹ 8 per share . The amount was payable as follows:

On Application	$—$	₹ 4 per share (Including ₹ 2 premium);
On Allotment	$—$	₹ 6 per share (Including ₹ 3 premium);
On First Call	$—$	₹ 5 per share (Including ₹ 1 premium); and
On Second and Final Call	$—$	Balance Amount

The issue was fully subscribed . Gopal, a shareholder holding 200 shares, did not pay the allotment money and Madhav, a holder of 400 shares, paid his entire share money along with the allotment money. Gopal's shares were immediately forfeited after allotment . Afterwards, the first call was made. Krishna, a holder of 100 shares , failed to pay the first call money and Girdhar, a holder of 300 shares, paid the second call money also along with the first call . Krishna's shares were forfeited immediately after the first call. Second and final call was made afterwards and was duly received . All the forfeited shares were reissued at ₹ 9 per share fully paid-up.

Pass necessary journal entries for the above transactions in the books of the company.

Discussion

8170.	14. In one side of a rhombus is "a" and one diagonal is "d1" then its area will be
Answer» 14. In one side of a rhombus is "a" and one diagonal is "d1" then its area will be

Discussion

8171.	The radii of two circular ends of frustum shape bucket are 14 cm and 7 cm. Height of the bucket is 30 cm. How many liters of water it can hold ?(1 litre = 1000 cm3 )
Answer» The radii of two circular ends of frustum shape bucket are 14 cm and 7 cm. Height of the bucket is 30 cm. How many liters of water it can hold ? (1 litre = 1000 cm³)

Discussion

8172.	A big iron boiler tank which is cylindrical in shape is open at the top. Its height is 10 m and radius is 7 m. It gets corroded at a rate of 3 m2/day. The number of days it will take to corrode completely is ____ . (use π=227)
Answer» A big iron boiler tank which is cylindrical in shape is open at the top. Its height is 10 $m$ and radius is 7 $m$ . It gets corroded at a rate of 3 $m^{2}$ /day. The number of days it will take to corrode completely is ____ . $(u s e π = \frac{22}{7})$

Discussion

8173.	Draw a circle with radius 3.4 cm. Draw a chord MN of length 5.7 cm in it. construct tangents at point M and N to the circle.
Answer» Draw a circle with radius 3.4 cm. Draw a chord MN of length 5.7 cm in it. construct tangents at point M and N to the circle.

Discussion

8174.	Determine the AP whose third term is 16 and the 7th term exceeds the 5th term by 12.
Answer» Determine the AP whose third term is 16 and the $7^{t h}$ term exceeds the $5^{t h}$ term by 12.

Discussion

8175.	In the given figure, O is the centre of the circle and TP is the tangent to the circle from an external point T. If ∠PBT = 30∘ , prove thatBA : AT = 2 : 1 [CBSE 2015]
Answer» In the given figure, O is the centre of the circle and TP is the tangent to the circle from an external point T. If ∠PBT = 30^∘ , prove that BA : AT = 2 : 1 [CBSE 2015]

Discussion

8176.	Find the zeroes of the polynomial 5√5 x2+30x+8√5.
Answer» Find the zeroes of the polynomial $5 \sqrt{5} x^{2} + 30 x + 8 \sqrt{5}$ .

Discussion

8177.	Draw a circle of radius 4.2 cm. Draw a pair of tangents to this circle inclined to each other at an angle of 45∘.
Answer» Draw a circle of radius 4.2 cm. Draw a pair of tangents to this circle inclined to each other at an angle of $45^{\circ}$ .

Discussion

8178.	Question 1 (a)Given here are some figures:Classify each of them on the basis of the following:(a) Simple curve
Answer» Question 1 (a) Given here are some figures: Classify each of them on the basis of the following: (a) Simple curve

Discussion

8179.	if the middle points of sides of a triangle abc is (2,4),(4,12),(8,20) respectively then find A,B,C
Answer» if the middle points of sides of a triangle abc is (2,4),(4,12),(8,20) respectively then find A,B,C

Discussion

8180.	Enter the value of remainder when 830 is divided by 8.6
Answer» Enter the value of remainder when 830 is divided by 8. 6

Discussion

8181.	The standard deviation (S.D) of the scores 1, 2, 3, 4, 5 is:
Answer» The standard deviation (S.D) of the scores 1, 2, 3, 4, 5 is:

Discussion

8182.	Find the equation of the straight line passing through origin and the point of intersection of the lines x + 2y = 7 and x - y = 4.
Answer» Find the equation of the straight line passing through origin and the point of intersection of the lines x + 2y = 7 and x - y = 4.

Discussion

8183.	Seven years ago, Varun's age was 5 times the square of swatis age. Three years hence swatis age will be two fifth of Varun's age. Find their present ages if Varun's present age is x and swatis present age is y.
Answer» Seven years ago, Varun's age was 5 times the square of swatis age. Three years hence swatis age will be two fifth of Varun's age. Find their present ages if Varun's present age is x and swatis present age is y.

Discussion

8184.	Prem and Manoj are partners in a firm sharing profits in the ratio of 3 : 2. The Partnership Deed provided that Prem was to be paid salary of ₹ 2,500 per month and Manoj was to ger a commission of ₹ 10,000 per year. Interest on capital was to be allowed 5% p.a. and interest on drawings was to be charged 6% p.a. Interest on Prem's drawings was ₹ 1,250 and on Manoj's drawings was ₹ 425. Interest on Capitals of the partners were ₹ 10,000 and ₹ 7,500 respectively. The firm earned a profit of ₹ 90,575 for the year ended 31st March, 2018.Prepare Profit and Loss Appropriation Account of the firm.
Answer» Prem and Manoj are partners in a firm sharing profits in the ratio of 3 : 2. The Partnership Deed provided that Prem was to be paid salary of ₹ 2,500 per month and Manoj was to ger a commission of ₹ 10,000 per year. Interest on capital was to be allowed 5% p.a. and interest on drawings was to be charged 6% p.a. Interest on Prem's drawings was ₹ 1,250 and on Manoj's drawings was ₹ 425. Interest on Capitals of the partners were ₹ 10,000 and ₹ 7,500 respectively. The firm earned a profit of ₹ 90,575 for the year ended 31st March, 2018. Prepare Profit and Loss Appropriation Account of the firm.

Discussion

8185.	Aarushi sold 100 lottery tickets in which 5 tickets carry prizes. If Priya purchased a ticket, what is the probability of Priya winning a prize?(a) 1920(b) 125(c) 120(d) 1720
Answer» Aarushi sold 100 lottery tickets in which 5 tickets carry prizes. If Priya purchased a ticket, what is the probability of Priya winning a prize? (a) $\frac{19}{20}$ (b) $\frac{1}{25}$ (c) $\frac{1}{20}$ (d) $\frac{17}{20}$

Discussion

8186.	Find:(i) the 20th term of the AP 9, 13, 17, 21, ... .(ii) the 35th term of the AP 20, 17, 14, 11, ... .(iii) the 18th term of the AP 2, 18, 50, 98, ... .(iv) the 9th term of the AP 34,54,74,94, ... .(v) the 15th term of the AP −40, −15, 10, 35, ... .
Answer» Find: (i) the 20th term of the AP 9, 13, 17, 21, ... . (ii) the 35th term of the AP 20, 17, 14, 11, ... . (iii) the 18th term of the AP $\sqrt{2}, \sqrt{18}, \sqrt{50}, \sqrt{98}$ , ... . (iv) the 9th term of the AP $\frac{3}{4}, \frac{5}{4}, \frac{7}{4}, \frac{9}{4}$ , ... . (v) the 15th term of the AP −40, −15, 10, 35, ... .

Discussion

8187.	What is the value of sin2 θ+11+tan2 θ?
Answer» What is the value of $\sin^{2} θ + \frac{1}{1 + \tan^{2} θ}$ ?

Discussion

8188.	John's age was the square of his son’s age six years ago. After nine years, John's age will be twice his son's age. (i) If six years ago son’s age =x years . The quadratic equation representing the situation is:[1 mark]
Answer» John's age was the square of his son’s age six years ago. After nine years, John's age will be twice his son's age. (i) If six years ago son’s age $= x$ years . The quadratic equation representing the situation is: [1 mark]

Discussion

8189.	The sum of first m terms of an A.P. is 4m2-m. If its nth terms is 107, find the value of n. Also, find the 21st term of this A.P.
Answer» The sum of first m terms of an A.P. is $4 m^{2}$ -m. If its nth terms is 107, find the value of n. Also, find the 21st term of this A.P.

Discussion

8190.	Construct triangles of the measures given below.In ∆ABC, l(AC) = 7.5 cm, m ∠ABC = 90° , l(BC) = 5.5 cm.
Answer» Construct triangles of the measures given below. In ∆ABC, l(AC) = 7.5 cm, m ∠ABC = 90^° , l(BC) = 5.5 cm.

Discussion

8191.	Divide a line segment of length 9 cm internally in the ratio 4 : 3. Also, give justification of the construction.
Answer» Divide a line segment of length 9 cm internally in the ratio 4 : 3. Also, give justification of the construction.

Discussion

8192.	In Figure 6, P and Q are the midpoints of the sides CA and CB respectively of ∆ABC right angled at C. Prove that 4(AQ2 + BP2) = 5 AB2.
Answer» In Figure 6, P and Q are the midpoints of the sides CA and CB respectively of ∆ABC right angled at C. Prove that 4(AQ² + BP²) = 5 AB².

Discussion

8193.	Solve the following pair of equations.7x−2yxy=58x+6yxy=15Here, x ≠ 0 and y ≠ 0.
Answer» Solve the following pair of equations. $\frac{7 x - 2 y}{x y} = 5$ $\frac{8 x + 6 y}{x y} = 15$ Here, x $\neq$ 0 and y $\neq$ 0.

8193.

Solve the following pair of equations.7x−2yxy=58x+6yxy=15Here, x ≠ 0 and y ≠ 0.

Answer»

Solve the following pair of equations.

$\frac{7 x - 2 y}{x y} = 5$

$\frac{8 x + 6 y}{x y} = 15$

Here, x $\neq$ 0 and y $\neq$ 0.

Discussion

8194.	Harmeet tosses two coins simultaneously. The probability of getting at least one head is
Answer» Harmeet tosses two coins simultaneously. The probability of getting at least one head is

Discussion

8195.	Raju wants to buy two books. Twice the prize of one of the book is ₹510 more than thrice the prize of the second book. Which of the following equation represent the given information?
Answer» Raju wants to buy two books. Twice the prize of one of the book is ₹510 more than thrice the prize of the second book. Which of the following equation represent the given information?

Discussion

8196.	Question 4A chord of a circle of radius 10 cm subtends a right angle at the centre. Find the area of the corresponding: (i) minor segment (ii) major sector. (Use π=3.14)
Answer» Question 4 A chord of a circle of radius 10 cm subtends a right angle at the centre. Find the area of the corresponding: (i) minor segment (ii) major sector. $(U s e π = 3.14)$

Discussion

8197.	A swimming academy has student members of various ages. Student distribution according to age is given below. What is the total number of student members in the academy? Student age interval Number of student 8−10710−121012−14914−161316−181118−202 ___
Answer» A swimming academy has student members of various ages. Student distribution according to age is given below. What is the total number of student members in the academy? $\begin{matrix} S t u d e n t a g e i n t e r v a l & N u m b e r o f s t u d e n t 8 - 10 & 7 10 - 12 & 10 12 - 14 & 9 14 - 16 & 13 16 - 18 & 11 18 - 20 & 2 \end{matrix}$ ___

8197.

A swimming academy has student members of various ages. Student distribution according to age is given below. What is the total number of student members in the academy? Student age interval Number of student 8−10710−121012−14914−161316−181118−202 ___

Answer»

A swimming academy has student members of various ages. Student distribution according to age is given below. What is the total number of student members in the academy?

$\begin{matrix} S t u d e n t a g e i n t e r v a l & N u m b e r o f s t u d e n t 8 - 10 & 7 10 - 12 & 10 12 - 14 & 9 14 - 16 & 13 16 - 18 & 11 18 - 20 & 2 \end{matrix}$

___

Discussion

8198.	Find the area of a circle whose circumference is 8π. [CBSE 2014]
Answer» Find the area of a circle whose circumference is 8π. [CBSE 2014]

Discussion

8199.	If sinθ+cosθ=2cosθ, show that cotθ=2+1.
Answer» If $(\sin θ + \cos θ) = \sqrt{2} \cos θ$ , show that $\cot θ = (\sqrt{2} + 1)$ .

Discussion

8200.	Two equal circles of radius r intersect such that each passes through the center of the other. The lenght of the common chord isA. sq root of rB. r × sq root of 2C. r × sq root of 3D. (r × sq root of 3) ÷ 2
Answer» Two equal circles of radius r intersect such that each passes through the center of the other. The lenght of the common chord is A. sq root of r B. r × sq root of 2 C. r × sq root of 3 D. (r × sq root of 3) ÷ 2

Discussion

Explore topic-wise InterviewSolutions in .

In the given figure, ∠ABC=∠AED=90°,AB=12cm,AC=15cmandDE=3cm.Find the area of△ABCand△AED.

Mia goes for shopping to buy a dress which costs ₹ 1809. The rate of sales tax is 8%. She tells the shopkeeper to reduce the price to such an extent that she has to pay ₹ 1809, inclusive of sales tax. Find the reduction needed in the price of the dress.

Show that 42 is an irrational number.

Express 0.2545454..........as a fraction in simplest form.

In the following figure, DE || AC and DF || AE. Prove that

41. The mean of 5 numbers is 18 if one no is excluded their mean is 16 find the excluded no

A hollow sphere of internal and external diameters 4 cm and 8 cm respectively is melted into a cone of base diameter 8 cm. The height of the cone is(a) 12 cm(b) 14 cm(c) 15 cm(d) 18 cm

42. A bucket of height 8 cm and made up of copper sheet is in the form of frustum of a right circular cone with radii of it Lower and upper end are as 3cm and 9 cm calculate ---- height , volume and area of copper sheet to make bucket all of frustum

Which of the following polynomials below is identical to the polynomial (x2−1)(x2−4)?

In the given figure, two tangents RQ and RP are drawn from an external point R to the circle with centre O. If ∠ PRQ = 120o, then prove that OR = PR + RQ.

The hypotenuse of a right triangle is 25 cm. The difference between the lengths of the other two sides of the triangle is 5 cm. Find the lengths of these sides.

ABCD is a parallelogram with diagonal AC. If a line XY is drawn such that it cuts the side AD at point Z and XY || AB, thenBXXC can be equal to:

Fill In The Blanks A collection of two or more possible outcomes (elementary events) of a trial is called a ________ event.

If an arithmetic sequence has a common difference 10 and its 6th term is 52, then find its 15th term.

A metallic cone having base radius 2.1 cm and height 8.4 cm is melted and moulded into a sphere. The radius of the sphere is (a) 2.1 cm (b) 1.05 cm (c) 1.5 cm (d) 2 cm

One of the steps involved in solving a quadratic equation x2+4x+a=9 using completing the square method is as given below: (x+b)2=5 Find a and b.

The diagram represents two inequations A and B on real number lines : (i) Write down A and B in set builder notation. (ii) Represent A∩B and A∩B′ on two different number lines.

14. In one side of a rhombus is "a" and one diagonal is "d1" then its area will be

The radii of two circular ends of frustum shape bucket are 14 cm and 7 cm. Height of the bucket is 30 cm. How many liters of water it can hold ?(1 litre = 1000 cm3 )

A big iron boiler tank which is cylindrical in shape is open at the top. Its height is 10 m and radius is 7 m. It gets corroded at a rate of 3 m2/day. The number of days it will take to corrode completely is ____ . (use π=227)

Draw a circle with radius 3.4 cm. Draw a chord MN of length 5.7 cm in it. construct tangents at point M and N to the circle.

Determine the AP whose third term is 16 and the 7th term exceeds the 5th term by 12.

In the given figure, O is the centre of the circle and TP is the tangent to the circle from an external point T. If ∠PBT = 30∘ , prove thatBA : AT = 2 : 1 [CBSE 2015]

Find the zeroes of the polynomial 5√5 x2+30x+8√5.

Draw a circle of radius 4.2 cm. Draw a pair of tangents to this circle inclined to each other at an angle of 45∘.

Question 1 (a)Given here are some figures:Classify each of them on the basis of the following:(a) Simple curve

if the middle points of sides of a triangle abc is (2,4),(4,12),(8,20) respectively then find A,B,C

Enter the value of remainder when 830 is divided by 8.6

The standard deviation (S.D) of the scores 1, 2, 3, 4, 5 is:

Find the equation of the straight line passing through origin and the point of intersection of the lines x + 2y = 7 and x - y = 4.

Seven years ago, Varun's age was 5 times the square of swatis age. Three years hence swatis age will be two fifth of Varun's age. Find their present ages if Varun's present age is x and swatis present age is y.

Aarushi sold 100 lottery tickets in which 5 tickets carry prizes. If Priya purchased a ticket, what is the probability of Priya winning a prize?(a) 1920(b) 125(c) 120(d) 1720

Find:(i) the 20th term of the AP 9, 13, 17, 21, ... .(ii) the 35th term of the AP 20, 17, 14, 11, ... .(iii) the 18th term of the AP 2, 18, 50, 98, ... .(iv) the 9th term of the AP 34,54,74,94, ... .(v) the 15th term of the AP −40, −15, 10, 35, ... .

What is the value of sin2 θ+11+tan2 θ?

John's age was the square of his son’s age six years ago. After nine years, John's age will be twice his son's age. (i) If six years ago son’s age =x years . The quadratic equation representing the situation is:[1 mark]

The sum of first m terms of an A.P. is 4m2-m. If its nth terms is 107, find the value of n. Also, find the 21st term of this A.P.

Construct triangles of the measures given below.In ∆ABC, l(AC) = 7.5 cm, m ∠ABC = 90° , l(BC) = 5.5 cm.

Divide a line segment of length 9 cm internally in the ratio 4 : 3. Also, give justification of the construction.

In Figure 6, P and Q are the midpoints of the sides CA and CB respectively of ∆ABC right angled at C. Prove that 4(AQ2 + BP2) = 5 AB2.

Solve the following pair of equations.7x−2yxy=58x+6yxy=15Here, x ≠ 0 and y ≠ 0.

Harmeet tosses two coins simultaneously. The probability of getting at least one head is

Raju wants to buy two books. Twice the prize of one of the book is ₹510 more than thrice the prize of the second book. Which of the following equation represent the given information?

Question 4A chord of a circle of radius 10 cm subtends a right angle at the centre. Find the area of the corresponding: (i) minor segment (ii) major sector. (Use π=3.14)

A swimming academy has student members of various ages. Student distribution according to age is given below. What is the total number of student members in the academy? Student age interval Number of student 8−10710−121012−14914−161316−181118−202 ___

Find the area of a circle whose circumference is 8π. [CBSE 2014]

If sinθ+cosθ=2cosθ, show that cotθ=2+1.

Two equal circles of radius r intersect such that each passes through the center of the other. The lenght of the common chord isA. sq root of rB. r × sq root of 2C. r × sq root of 3D. (r × sq root of 3) ÷ 2