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Define radian, Prove that 1^@<1^c....

Define radian, Prove that `1^@<1^c`.

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Let S be a set of containing more than two elements and a binary operaton @ on S be defined by a@b=a for all a,binS . Prove that @ is associative but not commutative on .

A binary operation ** on QQ the set of all rational numbers is defined as a**b=(1)/(2)ab for all a,binQQ . Prove that ** is commutative as well as associative on QQ .

An operation ** on ZZ , the set of integers, is defined as, a**b=a-b+ab for all a,binZZ . Prove that ** is a binary operation on ZZ which is neither commutative nor associative.

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UNITED BOOK HOUSE-RAMAKRISHNA MISSION VIDYALAYA, NARENDRAPUR-EXERCISE
  1. If x= (sqrt2+1)/(sqrt2-1) and x-y= 4sqrt2 then find the value of x^4+y...

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  2. Three variable x,y,z such that y+z-x is a constant and if (z+x-y)(x+y-...

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  3. If (ad-bc)/(a-b-c+d) = (ac-bd)/(a-b+c-d) then show that each ratio = (...

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  4. If a+c = 2b and 2/c= 1/b+1/d then prove that a:b = c:d.

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  5. Prove that opposite angles of a cyclic quadrilateral are supplementary

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  6. State and prove Pythagoras theorem.

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  7. In triangleABC, angleB is an acute angle and AD botBC. Prove that AC^2...

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  8. AC is a diamter of a circle with centre O, If triangleABC is cyclic an...

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  9. Construct a right angled triangled whose hypotenuse is 10cm and aother...

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  10. Find geometrically, the value f 2sqrt5.

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  11. Define radian, Prove that 1^@<1^c.

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  12. If 5 cos theta+ 12 sin theta = 13 show that tan theta = 12/5.

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  13. Find the value of (cos^2pi/16+ cos^2 (3pi)/16+cos^2(5pi)/16+cos^2(7pi)...

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  14. A passenger in an aeroplane flying over a straight road observed two c...

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  15. As seen from the deck of a ship the angle of elevations of the top and...

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  16. The diameter of the base and height of a solid right circular cylinder...

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  17. The cloth required to make a right circular conical tent is 188 4/7 sq...

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  18. If the median of the following data is 32, find the values of x and b...

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  19. From the frequency distribution table give, below, draw a less than ty...

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  20. Find the mode from the following distribution table.

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