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MODERN PUBLICATION-MOCK TEST-1-EXERCISE
- Evaluate : int1/(x(logx)^m)dx, m>0
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- Solve : dy/dx= sqrt(9-y^2)
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- Find the angle between the vectors veca=hati-hatj+hatk and hatb=hati+h...
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- Construct a 3xx4 matrix, whose elements are given by: aij = 1/2|-3i +...
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- If A(ij) is the co-factor of the element a(ij) of the determinant |[2,...
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- If x sin (a+y) + sin a cos (a+y) = 0, then prove that : dy/dx = (sin^...
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- Prove that the function f given by f(x) = x^2-x+1 is neither strictly ...
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- Find the approximate change in the volume V of a cube of side x metres...
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- Evaluate int(pi//6)^(pi//3) ((1)/(1+sqrttanx dx
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- Solve the following differential equations x dy + ( y - x^3) dx =0
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- Find the value of 'lambda' such that the vectors : 3hati+lambda hatj+5...
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- tan^-1 frac{1}{5} + tan^-1 frac{1}{7} + tan^-1 frac {1}{3} + tan^-1 fr...
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- Prove that : tan^-1((cosx)/(1+sinx)) = pi/4 - x/2, x in (-pi/2,pi/2)
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- Show that if A = [[cos theta, sin theta],[-sin theta, cos theta]], th...
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- Using the properties of determinant, show that :|[a^2+1,ab,ac],[ab,b^2...
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- The funtion f(x) is defined as follows: f(x) = {:{(x^2+ax+b,0lex<2),...
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- Evalute : int(5x+3)/sqrt(x^2+4x+10)dx
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- By using the properties of definite integrals, evaluate the integral: ...
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- Solve: dy/dx+(2x)/(x^2+1)y=1/(x^2+1)^2, y(0)=0.
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- Find the shortest distance between the lines: vecr=6hati+2hatj+2hatk+l...
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