Class X : HOTS Question Answers: Math Unit - 6 ii ( Heights & Distance)

Heights & Distance

If the angle of elevation of cloud from a point ‘h’ meters above a lake is QUOTE and the angle of depression of its reflection in the lake is QUOTE , prove that the height of the cloud is QUOTE .

From an aero plane vertically above a straight horizontal road, the angles of depression of two consecutive milestones on opposite sides of the aero plane are observed to be α and β. Show that the height of the aero plane above the road is QUOTE .

Two stations due south of a tower, which leans towards north are at distances ‘a’ and ‘b’ from its foot. If α and β be the elevations of the top of the tower from the situation, prove that its inclination ‘θ’ to the horizontal given by QUOTE

The angle of elevation of the top of a tower from a point on the same level as the foot of the tower is α. On advancing ‘p’ meters towards the foot of the tower, the angle of elevation becomes β. show that the height ‘h’ of the tower is given by h= QUOTE

A boy standing on a horizontal plane finds a bird flying at a distance of 100m from him at an elevation of 300. A girl standing on the roof of 20 meter high building finds the angle of elevation of the same bird to be 450. Both the boy and the girl are on opposite sides of the bird. Find the distance of the bird from the girl

From a window x meters high above the ground in a street, the angles of elevation and depression of the top and the foot of the other house on the

Class X : HOTS Question Answers: Math Unit - 7 (CO-ORDINATE GEOMETRY)

CO-ORDINATE GEOMETRY

Find the points on the y axis whose distances from the points (6, 7) and (4,-3) are in the ratio 1:2

Determine the ratio in which the line 2x + y -4 = 0 divide the line segment joining the points A (2,-2) and B (3, 7).Also find the coordinates of the point of division

Find the third vertex of a triangle if its two vertices are (-1, 4) and (5, 2) and mid point of one side is (0, 3).

If the vertices of a triangle are (1, k), (4, -3), (-9, 7) and its area is 15 sq units, find the value (s) of k..    

The centre of a circle is (2x – 1, 3x + 1).Find x if the circle passes through (-3,-1) and the length of the diameter is 20 units

If A & B are (-2,-2) and (2,-4) respectively, find the co ordinates of P such that    AP = AB and P lies on the line segment AB.

Show that the points (3, 0), (4, 5), (-1, 4) and (-2, -1) taken in order are the vertices of a rhombus. Also find the area of the rhombus.

If A, B and P are the points (-4, 3), (0, -2) and (ab) respectively and P is equidistant from A and B, show that 8a - 10b + 21= 0

If two vertices of an equilateral triangle are (0, 0) and (3, 0), find the third vertex

Find the centre of a circle passing through the points (6, -6), (3, -7) and (3, 3).Also find the radius.. .     

Class X : HOTS Question Answers: Math Unit - 10 (CONSTRUCTIONS)

CONSTRUCTIONS

1. Draw a line segment AB of length 4.4cm. Taking A as centre, draw a circle of radius 2cm and taking B as centre, draw another circle of radius 2.2cm. Construct tangents to each circle from the centre of the other circle.

2. Draw a pair of tangents to a circle of radius 2cm that are inclined to each other at an angle of 900.

3. Construct a tangent to a circle of radius 2cm from a point on the concentric circle of radius 2.6cm and measure its length. Also, verify the measurements by actual calculations. (length of tangent =2.1cm)

Class X : HOTS Question Answers: Math Unit - 3 (CIRCLES)

CIRCLES

A circle touches the sides of a quadrilateral ABCD at P, Q, R and S respectively. Show that the angles subtended at the centre by a pair of opposite sides are supplementary

In figure, XP and XQ are tangents from X to the circle with centre O. R is a point on the circle. Prove that XA+AR=XB+BR

A circle touches the side BC of a triangle ABC at P and touches AB and AC when produced at Q and R respectively as shown in

Prove that the parallelogram circumscribing a circle is rhombus

Two tangents PA and PB are drawn to the circle with center O, such that ÐAPB=120o.  Prove that OP=2AP

Class X : HOTS Question Answers: Math Unit - 5 (Arithmetic Progression)

ARITHMETIC PROGRESSIONS

1. The fourth term of an AP is 0. Prove that its 25th term is triple its 11th term

2. Find the 20th term from the end of the AP 3, 8, 13……..253

3. If the pth, qth & rth term of an AP is x, y and z respectively,
   show that x(q-r) + y(r-p) + z(p-q) = 0

4. Find the sum of first 40 positive integers divisible by 6 also find the sum of first 20 positive integers divisible by 5 or 6.

5. A man arranges to pay a debt of Rs.3600 in 40 monthly installments which are in a AP. When 30 installments are paid he dies leaving one third of the debt unpaid. Find the value of the first instalment

6. Find the sum of all 3 digit numbers which leave remainder 3 when divided by 5.

7. Find the value of x if 2x + 1, x2 + x +1, 3x2 - 3x +3 are consecutive terms of an AP

8. Raghav buys a shop for Rs.1,20,000.He pays half the balance of the amount in cash and agrees to pay the balance in 12 annual installments of Rs.5000 each. If the rate of interest is 12% and he pays with the installment the interest due for the unpaid amount. Find the total cost of the shop.

9. Prove that am + n + am - n =2am

10. If the roots of the equation (b-c)x2 +(c-a) x +(a-b) = 0 are equal show that a, b, c are in AP.&

CBSE Class IX Information Technology Sample Paper for 2010

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CBSE Class IX Social Science Sample Paper for 2010

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CBSE Class IX Mathematics Sample Paper for 2010

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CBSE Class IX  Science Sample Paper for 2010

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CBSE Class IX English Sample Paper for 2010

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National Institute of Open Schooling (NIOS) | Class Xth Sample Paper - Business Studies

Senior Secondary Course (Paper)
Business Studies

Subject: Business Studies
Maximum Marks: 100
Class: X
Time: 3 hrs.

1. Weightage by Objectives

2. Weightage by types of Questions

3. Weightage by Contents

* 10 minutes for reading the Question Paper and revision of Answers.

Sample Question Paper
Business Studies
(Secondary Course)

Time: Three Hours
Max. Marks: 100

Answer all the questions.

1) Prevention and control of environmental pollution is a /an:
A. Economic objective of business.
B. Social objective of business.
C. National objective of business.
D. Human objective of business. 1

2) Which of the following is not a feature of business?
A. Exchange of goods and service.
B. Exchange on a regular basis.
C. Risk and uncertainties.
D. Work for others. 1

3) The maximum number of members in case of a private limited company is
A. Ten.
B. Twelve.
C. Fifty.
D. Not fixed. 1

4) Consumers Co-operative Societies are formed to
A. Provide housing facilities to the members.
B. Facilitate marketing of goods.
C. Protect the interest of the consumers.
D. Provide financial support to the members. 1

5) Post restante letters are generally retained in the post office for a period of :
A. 7 days.
B. 10 days.
C. 14 days.
D. 30 days. 1

6) Which of the following amount cannot be deposited in a public provident fund account?
A. Rs 500/-.
B. Rs. 600/-.
C. Rs. 700/-.
D. Rs. 750/-. 1

7) The shops which are owned by the same proprietor and located in different parts of the city or country are known as:
A. Departmental store.
B. Super bazar.
C. Multiple shops.
D. Mail order business. 1

8) Which of the following is not an advantage of mail order business?
A. It required less capital.
B. There is no risk of bad debts.
C. It is not suitable for illiterates.
D. Home delivery of goods is possible. 1

9) What happens if you affixed postal stamp of Rs. 7/- on an envelop instead of Rs. 5/- and dropped it in the letter-box?
A. The envelop will be retuned to the sender.
B. The envelop will be delivered to the receiver.
C. The postman will charge penalty from the receiver.
D. The postman will not charge any penalty from the receiver. 1

10) Why should business be socially responsible? Give any two reasons. 3

Preparations are in full swing for class x and xii cbse board exams 2010

Preparations are in full swing for the Central Board of Secondary Education (CBSE) examinations for Class X and XII in Ajmer region scheduled to be held from March 2. For the first time, the board will give grades in Class-X exams. The board has set up 450 examination centres in Rajasthan, Madhya Pradesh, Gujarat, Chhattisgarh where 1.79 lakh students will appear in both the examinations.

For the first time, the board has also introduced national common test for Class IX in all CBSE schools and question papers are sent to them in CDS. The Class IX exams will start from February 25.

Joint Entrance Examination is likely to become history from 2013

The joint entrance examination (JEE) for admission to the Indian Institutes of Technology (IITs) is likely to become history from 2013 as the central government Tuesday decided to work on a common entrance test for all government engineering colleges.

Explaining the situation, HRD ministry joint secretary S.C. Khuntia said: 'We will work for a common entrance test for every stream. One examination for all engineering institutions, which means IITs will also follow it.'

About AIEEE: Programme of Action (PoA), 1992 under the National Policy on Education (NPE), 1986 envisaged conduct of a common entrance examination on all India basis for admission to professional and technical programmes in the country. For admission to Engineering and Architecture/Planning programmes, Government of India vide Resolution dated 18th October 2001 has laid down a Three Exam Scheme (JEE and AIEEE at the National Level and the State Level Engineering Entrance Examinations (SLEEE) for State Level Institutions with an option to join AIEEE). This takes care of varying admission standards in these programmes and helps in maintenance of professional standards. This also solves problems of overlaps and reduces physical, mental and financial burden on students and their parents due to multiplicity of entrance examinations.

The particulars of all the candidates applied for AIEEE 2010 have been displayed on Board’s websites www.aieee.nic.in and www.cbse.nic.in.

The candidates are advised to verify their particulars on the above websites. In case, there is any variation in the particulars, the same may be intimated to the Board’s office on the proforma available on the website through any of the following mode latest by 05.03.2010.

CBSE Class XI Maths Sample Paper for 2010

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CBSE Class XI English Sample Paper for 2010

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CBSE Class XI Computer science Sample Paper for 2010

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CBSE Class XI Physics Sample Paper for 2010

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CBSE: Class XII Math Study Notes of Limits, Continuity, Differentiability

Contents:

• Synopsis
  • Limit of a function
  • In-determinant forms
  • Results in Limits
  • Standard Limits
  • L - Hospital's Rule
• Continuity
  • Continuity in an interval
  • Types of Discontinuity
• Differentiability
  • Logarithmic Differentiation  & Some "SOLVED OBJECTIVE QUESTIONS"

CBSE: Class XII Math Study Notes of Indefinite Integration (Theory)

Indefinite Integration

• Basic Concept:
  Let F(x) be a differentiable function of x such that [image]. Then F (x) is called the integral of f(x). Symbiotically, it is written as [image]
  f (x), the function to be integrated is called the integrand.
  F(x) is also called the anti-derivate (or primitive function) of f (x).
• Constant of Integration:
  As the differential coefficient of a constant is zero...[..]