Recently Active Mathematics Questions

15. Equation of a line is given by y+2at=t(x-at2), t being the parameter. Find the locus of the point of intersection of the lines which are at right angles. 16.The ends A,B of a strait line line segment of a constant length ...

How do u prove any linear eqn in x,y,z represent a plane? The reason I ask this is bcoz I'm having a fundamental problem in the proof itself! ...

1) In a batch of 10 articles, 4 articles are defective. 6 articles are taken from the batch for inspection. If more than 2 articles in this batch are defective, the whole batch is rejected. Find the probability that the batch ...

The largest interval in which x12 - x9 + x4 - x + 1 > 0 is: A. [0,∞) B. (-∞,0] C. (-∞,∞) D. none of these ...

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There are n straight lines in a plane,no two of which is parallel,and no three pass through the same point.If their points of intersections are joined,find the number of fresh lines thus obtained. ...

Determine naturals x and y satisfying \frac{1}{x}+\frac{1}{y}=\frac{1}{14} .....It was done in goiit once! ...

GIVEN A f:n "g" continous for every x→R such that g(1)=5 & ∫10 g(t)dt =2; if o∫1 (x-t)2 g(t) d(t) . find f'''(1) -f''(1) ??? f:n is function abbrevation ...

if v1→=a*(b*c) ; v2→ =b*(c*a) ; & v3 → = c*(a*b) then : a) v1 +v2 + v3 is anull vector b)v1 ,v2 ,v3 can form side of a triangle c)v1 , v2 , v3 are coplanar d)v1 , v2 ,v3 are linearly dependent ...

A parabola is drawn touching the axis of x at the origin & having its vertex at a given distance k,from the axis. P.T the axis of the parabola of the parabola is a tangent to the parabola --- x2=-8k(y-2k) ...

1) If f(x) is continous for allx belonging to R and range of f(x) is (2, √26) and g(x) = [ f(x) / a ] is continous for all x belonging to R (where [.] denotes the greatest integral function). Then the least posiitve integra ...

The coordinates of the extremities of a rod are A(1,2) and B(3,4). S(0,0) is the source of light. The rod AB is parallel to the wall and is midway betwen the point source of light and the wall. CD is the shadow of AB on the w ...

5. Find the equation of the straight lines passing through (-2,-7) &having an intercept of length 3 between the straight lines 4x+3y=12, 4x+3y=3. 7. Two sides of a rhombous ABCD are parallel to the lines Y=x+2 & y=7x+3. If th ...

Problem 1) Let f(x) be a polynomial of degree one and f(x)be a function defined by f(x) = { g(x) ; for x ≤ 0 { and (1+x) / (2+x) 1/x ; for x >0 If f(x) is continous at x=0 and f(-1) = f ' (1), then g(x) is equals to :- ( ...

prove that the orthocentre of triangle ABC with A(x1,y1) , B(x2,y2) and C(x3,y3) is H( \sum{} x1tan A/ \sum{} tan A , \sum{} y1tan A/ \sum{} tan A) ...

C I R C L E S 1 ) A circle S = 0 is drawn with its centre at (-1.1) so as to touch the circle x2 + y2 - 4x + 6y -3 = 0 externally. Find the intercept made by the circle on the coord axes ? ...

Suppose a_1, a_2, a_3,...,a_n are n real numbers It is obvious that if the ai are all positive, then the numbers \sum a_i, \sum_{i<j} a_i a_j \sum_{i<j<k} a_ia_ja_k,..., \prod_{i=1}^n a_i will all be positive Prove t ...

If 1,α1,α2,...,αn-1 are nth roots of unity , then value of (1+α1(1+α2)...(1+αn-1) ...

If the eqn ax2+bx+c=0 (0 < a < b< c) has non real complex roots z1 and z2. Show that |z1| > 1 ; |z2| > 1. ...

A particle is projected at an angle 60degree with speed 17.32 from the point A.At the same time the wedge is made to move with speed 17.32 towards right .Then the time after which the particle will strike the wedge is ------- ...

Prove that \tan(\frac{3\pi}{11})+4\sin(\frac{2\pi}{11})=\sqrt{11} ...

(1) Find The Remainder when (32) (32)^(32) is divided by 7 (using no. Theory). ...

1. \int_{0}^{\pi /4}{ln(1+tant) dt} 2. \int (x.e^t^a^n^^^-^^^1^x)dx / (\sqrt{1+x^2}) ...

If n is an even integer and a,b,c are distinct numbers,then find the number of distinct terms in the expansion of (a+b+c)^n + (a+b-c)^n My approach>>>> It should b (n+1)+(n-1)+(n-3)+........+1 So ans should b ((n+ ...

If 7^103 is divided by 25,Then find the remainder? ...

Prove that no of ways in which n identical objects can be dived in r different groups is: n+r-1 C r-1 (I did'nt get the prove of this in any of the books.) ...

ABCD is square having its centre ai the origin. If A is(x,y), find the remaining vertices. By a suitable translation of axes or otherwise, find the vertices of the square two of whose opposite vertices are(4,5) and (-2,-3). ...

I am not a fan of these.. but these have been discussed a few times here.. once long back.. an year.. and once recently by eureka.. A couple of these for those who are interested... Try to integrate 1) \int_{0}^{\infty}\frac{ ...

Find the minimum odd value of a for this equation to hold true \int _{10}^{19}\frac {\sin x}{1+x^a}<\frac {1}{9} ...

Find the number of divisors of N=22335375 of the form 4n+2 Ans=95 ...