Frequent Algebra Questions

Q.1 In how many ways can clean & clouded (overcast) days occur in a week assuming that an entire day is either clean or clouded. Q.2 Four visitors A , B , C & D arrive at a town which has 5 hotels . In how many ways can they ...

If a, b, c are the sides of triangle ABC satisfying log(1+c/a) + log a – log b = log 2. Also a(1 – x2) + 2bx + c(1 + x2) = 0 has two equal roots. Find the value of sin A + sin B + sin C. ...

1) If the curves ax2 + 4xy + 2y2 + x + y + 5 = 0 and ax2 + 6xy + 5y2 + 2x + 3y + 8 = 0 intersect at four concyclic points, then the value of |a| is... 2) For 0 < x < pi/2 the solution of \sum_{m=1}^{6}{} cosec {x + (m - ...

If z1,z2 and z3,z4 are two pairs of conjugate complex numbers, prove that arg(z1/z4) + arg(z2/z3) = 0. ...

If m men and n women are to be seated in a row such that no two women seat together,then find the ways in this can be done. ...

12+14+24+58+164+........+n=????? The answer is 3n-n2+11n-1 Please someone show me the way to solve it. ...

The ratio of A.M. (arithmetic mean) and G.M. (geometric mean) of two positive number a and b is m:n. Prove that a:b = (m2 + m2 - n2 ):(m2 - m2 - n2 ...

The equation x + frac{2}{{1 - x}} = 1 + frac{2}{{1 - x}}, has a) No real root b) One real root c) Two equal roots d) Infinitely many roots ...

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Find the square root of ((0.75)^3/1-(0.75)) + (0.75 + (0.75)^2 + 1). My problem is that I am getting an answer 2.5 which is NOT one of the options provided. ...

\sqrt{x+\sqrt{x+\sqrt{x+}..}}=y \sqrt{y+\sqrt{y+\sqrt{y+}..}}=5 find √(x+y) ...

If x2-x+1=0 and the two roots of the equation are α and β;then find the value of α2013+β2013. ...

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if a x x x x b x x = f(x)-xf/(x). x x c x x x x d then f(x)=? ...

If a) x1 + x2 + ...................+x1007 =(2014)2 b) x1 /(x1 +1)=x2 /(x2 +3)=.....................=x1007 /(x1007 +2013) then x253 =? ...

Find the numebr of solutions of the equation- 8[x2 - x] + 4[x]=13+12[sinx],where [.]denotes the G.I.F. ...

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Please post a brief soln to the problem 1) The no. of right triangles with integer sides and inradius r=2013 2)Let a,b,c,d be non zero digits. If n is the no. of 4 digit no.s abcd such that ab+cd is even, then last digit of n ...

There are three coplanar parallel lines.If any p points are taken on each of the line,the maximum number of triangles with vertices at these points is a.3p2(p-1) b.3p2(p-1)+1 c.p2(4p-3) d.None of these ...

The solution of the equation {log _7}{log _5}(sqrt {{x^2} + 5 + x} ) = 0 a) x = 2 b) x = 3 c) x = 4 d) x = - 2 ...

The value of sqrt {(log _{0.5}^24)} is a) –2 b) sqrt {( - 4)} c) 2 d) None of these ...

If {log _{10}}2 = 0.30103,{log _{10}}3 = 0.47712, the number of digits in {3^{12}} imes {2^8} is a) 7 b) 8 c) 9 d) 10 ...

If one root of the equation ax2+bx+c=0 is the square of the other, then a(c-b)3=cX, where X is (a) a3+b3 (b) (a-b)3 (c) a3-b3 (d) N.O.T Please show the method .. ...

1 + 1+2/1! + 1+2+3/2! + 1+2+3+4/3! + ..... ∞ = (a) 0 (b) 1 (c) 7e/2 (d) 2e Brahmastra - Exponential and logarithmic series Q No.5 ...

Σ 1/1+xa-b+xa-c =? (A) 1 (B)-1 (C) 0 (D) N.O.T. ...

If the roots of the equation x2-bx/ax-c = m-1/m+1 are equal but opposite in sign, then the value of of m will be (a) a-b/a+b (b) b-a/a+b (c) a+b/a-b (d) a+b/b-a Brahmastra, Quadratic Equations Q No. 10. ...

For x ≥ 0, the smallest value of the function f(x) = 4x2+8x +13/ 6(x+1) is : ...

If S(n) = Σnk=1 4 k /4 k 4 + 1 then find the value of 221s(10)/10 lz show the ful sonn... ...