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Show that the sum of 4 + 12 + 20 + 28 + ...

Show that the sum of 4 + 12 + 20 + 28 + .... up to n the term is a square of even number

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Find the sum of 1 + 5 + 12 + 22 + 35 +….upto n term.

Show that the sum of n terms of the series {4+12+20+28+…} is the square of an even number.

A geometric progression of real number is such that the sum of its first four terms is equal to 30 and the sum of teh square of the first four terms is 340. then

Show that the sum of (m + n)^(th) and (m – n)^(th) terms of an A.P. is equal to twice the m^(th) term.

Find the least value of n for which the sum of the series 20 + 28 + 36 +… to n terms is greater than 1000.

Show that the ratio of the sum of first n terms of a G.P. to the sum of terms from (n + 1)^("th") " to " (2n)^("th") term is 1/r^n .

The common ratio of a series in G.P. is 3, the sum of the 1st and 3rd terms is equal to the sum of the squares of the 1st and 2nd terms, find the sum of n terms. If n = 6, show that the sum is 364.

The sum of first 21 terms of an A.P. is 28 and the sum of the 1st 28 terms is 21. Show that one term of the progression is zero and find the sum of the preceding terms.

If the sum of n terms of an A.P is cn (n-1) where c ne 0 then find the sum of the squares of these terms.

if the ratio of the sum of n terms of two A Ps is (3n + 5) : (5n - 9). Show that their 4th terms are equal.

UNITED BOOK HOUSE-MODEL QUESTION PAPERS-SET 11-EXERCISE
  1. show that ^nCr+^(n-1)C(r-1)+^(n-1)C(r-2)=^(n+1)Cr

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  2. Find the middle term of the expansion of (P^2-1/P)^9

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  3. Show that the sum of 4 + 12 + 20 + 28 + .... up to n the term is a squ...

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  4. If the distance from- origin to- the straight line 3x + 5y + a = 0 is3...

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  5. Find the co-ordinate of the image of (3, 2, -4) on xy plane.

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  6. If f(x)=x^5+x^3-2x+3,Prove that f'(1)+f'(-1)=4f(0).

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  7. Evaluate :lim(xrarroo)(1+2+3+...+n)/n^2

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  8. For any three sets A,B and C ,prove that A-(BcupC)=(A-B)cap(A-C).

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  9. For any two positive acute angles theta and phi if sin(theta+phi)=k s...

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  10. Solve :sqrt3sinx+cosx=2

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  11. Prove by mathematical induction. 1.1! + 2. 2! + 3. 3! + ... +n . n! = ...

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  12. If z = x + iy then l z - 8| + Iz + 8| = 20. represents a ellipse

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  13. If (1+x)^n=c0+c1x+c2x^2+....+cnx^n,then show that c0/1+c2/3+c4/5+...=2...

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  14. If the ath and bth term of an AP are 1/b and 1/a,then show that (ab)th...

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  15. In /\XYZthe co-ordinate of Y and Z are (-a, 0) and (a, 0), andangle XZ...

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  16. If the three straight lines ax + 2y + 1 = 0, 3y + bx + 1 = 0 and cx+ 4...

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  17. If the circles x^2+y^2+2ax+c^2=0and x^2+y^2+2by+c^2=0touch each other,...

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  18. Find the co-ordinate of a point equidistance from the points' (0, 0. 0...

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  19. Prove that lim(xrarr1)(x^2-sqrtx)/(sqrtx-1)=3

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  20. Prove that sqrt5 is irrational, (use the method of contradiction).

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