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If 2hati-hatj+3hatk,3hati+2hatj+hatk,hat...

If `2hati-hatj+3hatk,3hati+2hatj+hatk,hati+mhatj+4hatk` are coplanar, find the value of m.

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If vectors veca =hati +2hatj -hatk, vecb = 2hati -hatj +hatk and vecc = lamdahati +hatj +2hatk are coplanar, then find the value of (lamda -4) .

If veca=2hati+3hatj-hatk, vecb= -hati+2hatj-4hatk, vec c =hati+hatj+hatk , then find the value of (veca xx vecb)*(veca xx vec c) .

Show that the points whose position vectors 4hati + 5hatj + hatk, -hatj -hatk, 3hati + 9hatj + 4hatk and -4hati + 4hatj + 4hatk are coplanar.

Show that the lines vecr=(-2hati-4hatj-6hatk)+t(hati+4hatj+7hatk) vecr=(hati+3hatj+5hatk)+s(3hati+5hatj+7hatk) are coplanar. Find the equation of such plane in non parametric form and in cartesian form.

veca=hati-hatj+hatk, vecb=2hati+hatj-hatk, vec c=lambda hati-hatj+lambda hatk are coplanar then lambda is :

Prove that the points 2hati+3hatj+4hatk,3hati+4hatj+2hatk,4hati+2hatj+3hatk from an equilateral triangle.

Determine whether the lines vecr=(hati-hatj)+t(hati-hatj+3hatk) and vecr=(2hati+hatj-hatk)+s(hati+2hatj-hatk) are parallel. Find the shortest distance between them.

SURA PUBLICATION-MODAL QUESTION PAPER-PART - II
  1. If adj A = [[-1,2,2],[1,1,2],[2,2,1]], find A^(-1).

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  2. Simplify : ("sin"pi/6+i"cos"pi/6)^(08).

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  3. Form a polynomial equation with integer coefficients with sqrt((sqrt2)...

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  4. Find the value of tan^(-1)("tan"(3pi)/5).

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  5. Condition for y = mx + c to be a tangent to the circle x^(2) + y^(2...

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  6. If 2hati-hatj+3hatk,3hati+2hatj+hatk,hati+mhatj+4hatk are coplanar, fi...

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  7. Show that ( 2 + i sqrt(3))^(10) - (2 - i sqrt(3))^(10)is purely imag...

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  8. Determine the number of positive and negative roots of the equation x^...

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  9. Find the value of cot^(-1)(sin^(-1)""(3)/(5)+sin^(-1)""(4)/(5))

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  10. If the system of linear equation x + 2ay + az = 0, x + 3by + bz = 0, x...

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  11. Simplify : i^(59)+1/i^(59).

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  12. If alpha, beta and gamma are the roots of the cubic equation x^3 + 2x^...

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  13. Find the principal value of "cosec"^(-1) (-1)

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  14. Find the equation of the parabola if the curve is opened upward, verte...

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  15. If 2hati-hatj+3hatk,3hati+2hatj+hatk,hati+mhatj+4hatk are coplanar, fi...

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  16. Determine whether the pair of straight lines vecr=(2hati+6hatj+3hatk)+...

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  17. Using Rolle's theorem find the point on the curve y=x^(2)+1,-2lexle2 w...

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  18. Find differential dy for y=((1-2x)^(3))/(3-4x).

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  19. Evaluate : int((-pi)/2)^(pi/2)xcosxdx.

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  20. Write the Maclaurin series expansion of e^(-x).

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