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Write down the equation of x-axis.

Let f(x)={:[(x^(2)","xge0),(-x^(2)","xlt0):}, then :

Figure shows a practical situation.The event is observed by four observer.List-II gives the value of acceleration and intial velocity of ball as observed by observer given in List-I . Match them correctly : -(g=10 m//s)^2

A plane passes through (1,-2,1) and is perpendicular to two planes 2x-2y+z=0 and x-y+2z=4. The distance of the plane form the point (1,2,2) is

Solve in R and represent the solution on the number line. 2x + 1 ge 0

Consider two positive integer a and b. Find the least possible value of the product ab if a^(b)b^(a)is divisible by 2000

During contraction and relaxation of striated muscle fibre the length of A band usually :-

x+y=2 and x-y=2 are tangents on a parabola at (1,1) and (4,2) respectivley. Which of the followings is/are correct.

If f(x) is a differentiable function wherever it is continuous and f'(c_(1))=f'(c_(2))=0, f''(c_(1)).f''(c_(2)) lt 0,f(c_(1))=5,f(c_(2))=0 and (c_(1) lt c_(2)) If f(x) is continuous in [c_(1),c_(2)] and f''(c_(1))-f''(c_(2)) gt 0, then minimum number of roots of f'(x)=0 in [c_(1)-1, c_(2)+1] is

Solvefollowingsystem usingmatrixx-y+2z =1, 2y -3z =1, 3x -2y +4z =2

If |veca|=1,|vecb|=2 and veca*vecb=1. Then the angle between veca and vecb is :

Show that, int_(0)^((pi)/(4))(sinx+cosx)/(cos^(2)x+sin^(4)x)dx

For any two vectors bara" and "barb show that |bara.barb|le|bara||barb| (Caucy- Schwartz inequality).

Prove that : Find the 8^("th")" term of "(1-(5x)/(2))^(-3//5)

If the normal at one end of the latusrectumof the parabola y^(2)=16x meets the X-axis at the point P, then the length of the chord passing through P and perpendicular to the normal is

If the area of the triangle with vertices (2,-6),(5,4) and (K,4) is 35 sq. units, then find the values of K, using determinants.

If the sum of n terms of an A.P. is n P +(1)/(2) n (n - 1) Q ,where P and Q are constants,then the common difference is

int_(0)^(pi//2)(cos^(3)x)/(sinx+cosx)dx=

Differentiate w.r.t x the function cos (a cos x + b sin x), for some constant a and b

Let A be a square matrix of order 2x2 thenabs[KA] is equal to

Evaluate int_(0)^(pi/2)(sin^(4)x)/(sin^(4)x+cos^(4)x)dx

Which of the following will not give any colout to flame?

Evaluate the following integrals inte^(x)((x+2))/((x+3)^(2))dx

(1-costheta+isintheta)/(1+costheta-isintheta)

Evaluate the definite integrals int_(4)^(5)e^(x)dx

For what value of x, the matrix [(5-x,x+1),(2,4)] are singular.

If x, y, z are in A.P then e^(-x),e^(-y)and e^(-z) are

The radius of the smallest circle, which passes through the points of intersection of the circles : x^2+y^2+2x-3=0 and x^2+y^2 +3x-y=0 is :

The value of sqrt(8 + 2 sqrt(8 + 2 sqrt(8 + 2 sqrt(8 + . . . . ))))is

Evaluate:int _0^((pi)/(2))(sin ^(2) x .cos ^(2) x )/((sin ^(3) x+ cos ^(3) x)^(2)) dx

Find the shortest distance between the lines whose vector equations are vecr=(1-t)hati+(t-2)hatj+(3-2t)hatk and vecr=(s+1)hati+(2s-1)hatj-(2s+1)hatk.

Two of the three values of (-1)^(1//3) are cos(pi//3)+isin(pi//3),cos(5pi//3)+isin(5pi//3).The third value is

How many +ve integers can be formed using 0,1,2 which are less than 10^n where n is +ve integer

A circular ring of radius 3 cm is suspended horizontally from a point 4 cm vertically above the centre by 4 strings attached at equal intervals to its cirumference . If the angle between two consecutive strings be theta,then cos 0-

Integrate the functions sqrt(sin2x)cos2x

Leta,b,c,d beanyfourrealnumbers, thena^n +b^n= c^n+d^nholdsfor anynaturalnumber n, if

Integrate the functions (sin^(-1)sqrtx-cos^(-1)sqrtx)/(sin^(-1)sqrtx+cos^(-1)sqrtx),xin[0,1]

If f(x) is a differentiable function wherever it is continuous and f'(c_(1))=f'(c_(2))=0, f''(c_(1)).f''(c_(2)) lt 0,f(c_(1))=5,f(c_(2))=0 and (c_(1) lt c_(2)) If f(x) is continuous in [c_(1), c_(2)] and f''(c_(1))-f''(c_(2)) gt0, then minimum number of roots of f(x)=0 in [c_(2)-1, c_(2)+1] is

If f(x) is a differentiable function wherever it is continuous and f'(c_(1))=f'(c_(2))=0, f''(c_(1)).f''(c_(2)) lt 0,f(c_(1))=5,f(c_(2))=0 and (c_(1) lt c_(2)) If f(x) is continuous in [c_(1),c_(2)] and f''(c_(1))-f''(c_(2)) lt 0, then minimum number of roots of f'(x)=0 in c_(1)-1, c_(2)+1] is

Which one of the following vectors is a magnitude 6 and perpendicular to both a=2hati+2hatj+hatk and b=hati-2hatj+2hatk?

Find dy/dx if x^y = c

If tanh^(-1)x =alog((1+x)/(1-x)), |x|lt 1 ,then is a equal to

If n is a product of k distinct primes what is the total number of factors of n ?

f: N rarr N , f(n) = (n+5)^(2) , n in N , then the function f is ............

The set of value of x for which the inequality [x]^(2)-5[x]+6 le 0 (where [.] denote the greatest integral function) hold good if

Integrate the functions xsec^(2)x

intxsinxdx

The total number of ways in which 5 balls of different colours can be distributed among 3 persons so that each person gets at least one ball is