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Evaluate the following integrals:∫x2x4-x2-12dx

Consider a triangle having vertices A(–2,3),B(1,9) and C(3,8). If a line L passing through the circumcenter of triangle ABC, bisects line BC, and intersects y-axis at point (0.α2), then the value of real number α is

If x&gt;0,then the sum of the series e−x−e−2x+e−3x−..............∞ is

5. x2 + xy + y2-100

Evaluate: ∫π40(sin x+cos x3+sin 2x) dx.

Given that the inverse trigonometric functions take principal values only. Then, the number of real values of x which satisfy sin−1(3x5)+sin−1(4x5)=sin−1x is equal to :

The least value of a for which the equation 4sinx+11−sinx=a has atleast one solution in the interval (0,π2) is

Let f(x)=⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩1−sinπx1+cos2πx,x&lt;12p,x=12√2k+√2x−1−2√2x−1,x&gt;12If f is continuous at x=12, then the value of k+12p is

What is the distance between point B and point C ?

List the set of letters of the following words in Roster form.(i) INDIA(ii) PARALLELOGRAM(iii) MISSISSIPPI

If cosα+2cosβ+3cosγ=sinα+2sinβ+3sinγ=0, then

If f(x)+2f(1−x)=x2+1 ∀ xϵR then f(x) is

Findvalues of x, if(i) (ii)

Find the sum to nterms of each of the series in Exercises 1 to 7.

At what point of the parabola x^2=9y is the abscissa three times that of ordinate ?

If 3∫sec4x dx=f(x)+2tanx, then the value of f(π4) is equal to(Assume integration constant to be zero)

If A=[−32−10], then A satisfies the relation

6.3×8+6×11+9×14+…

A unit vector perpendicular to the plane of a=2^i−6^j−3^k,b=4^i+3^j−^k is

Evaluate the following limits: limx→π2(π2−x)tanx

7 gentlemen and 3 ladies are to be seated in a row. If the ladies insist on sitting together while two of the gentlemen refuse to take consecutive seats, then the number of ways in which they can be seated is

Product of roots of the equation √13−x2=x+5

The general solution of the differential equation dydx=x−y+1x+y+1 is (where c is constant of integration)

Points (–2, 4, 7), (3, –6, –8) and (1, –2, –2) are[AI CBSE 1982]

the position of a particle moving in a straight line along x - axis varies with time t as x=(12t-3t^2) m, where t is in seconds. The distance covered by particle in first 5 sec is

The value of ⎧⎪⎨⎪⎩limx→0(1+x)2x⎫⎪⎬⎪⎭ (where {x} denotes fractional part of x) is equal to

root 16 is rational or irrational number

7. The quadratic equation whose roots are the AM and HM of the roots of the equation x2+7x-1=0

16. If for the two vectors ,vector A and vector B ,the sum of vectors is perpendicular to their difference .the ratio of their magnitude is. a)1 b)2. c)3 d)4

Slope of normal to the curve y=x2−1x2 at (−1,0)​ is ​

40. The number of words with or without meaningthat can be formed from letters of word'BIKANER' so that each start with 'A' and endwith 'B' is(1) 124(2) 24(3) 72014) 120

The function f(x)= (x^2-1)|x^2-3x+2| + cos (|x|) is not differentiable at x=

Minimise Z= 3x + 5ysuchthat.

If a,b and c are the greatest values of 19Cp, 20Cq, 21Cr respectively, then:

what is the law of reciprocal constant and explain formula also.

In a workshop, there are five machines and the probability of any one of them to be out of service on a day is 14. If the probability that at most two machines will be out of service on the same day is (34)3k, then k is equal to :

y raise to the power 2/3 - 2y raise to the power 1/3 = 15how to solve this step by step

Solution of |x+1|+|2x+3|=5 is

15.Length of major axis 26, foci (+ 5, 0)

Let I be any interval disjoint from (−1, 1). Prove thatthe function f given by is strictly increasing on I.

If cos−1(cosx5)=x−10π5 holds good for some x∈R, then the number of integral values of x satisfying it is

An ellipse is rotated through a right angle in its own plane about its centre, which is fixed. If at a point tangents are drawn before and after rotation then locus of point of intersection of such tangents is

1. A couple has three children . The probability of having 2sons and a daughter , if the eldest child is a son is ?.

38. Let a=3-n, where n is a natural number.If 'p' is the least positive value of 'a',then the value of p+1÷p is what?

1(x2+1x)43 can be expanded by binomial theorem, if

Compute the indicated product. ⎡⎢⎣234345456⎤⎥⎦⎡⎢⎣1−35024305⎤⎥⎦

13.If sin-1 x = y, then(A) 0 y π(C) 0< y

r44,x>0x +4

15.cos'xelogsin

If x>0,then the sum of the series e−x−e−2x+e−3x−..............∞ is

Let f(x)=⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩1−sinπx1+cos2πx,x<12p,x=12√2k+√2x−1−2√2x−1,x>12If f is continuous at x=12, then the value of k+12p is

Slope of normal to the curve y=x2−1x2 at (−1,0) is