Maths | KA Board | Grade 12 | 2014
Q. If A=[1234], find |2A|.
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Q. Write the domain of f(x)=cos1x.
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Q. If y=xx, find dydx.
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Q. Verify Rolle's theorem for the function y=x2+2. xϵ|2, 2|.
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Q. Write the simplest form of tan1(1cosx1+cosx)0<x<π..
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Q. Evaluate sin[π3sin1(12)].
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Q. Evaluate (sinx+cosx)dx.
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Q. Find the equation of line joining (1, 2) and (3, 6) using determinants.
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Q. Find the equation of the plane with intercept 4 on Z-axis and parallel to XY plane.
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Q. A relation R on A = {1, 2, 3} defined by R = { (1, 1) (1, 2) (3, 3) } is not symmetric. Why?
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Q. Define a scalar matrix.
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Q. Find the approximate change in the volume V of a cube of side x meters caused by increasing the side by 2%.
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Q. Find the direction cosines of the vector ^i+2^j+3^k.
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Q. Evaluate sin2x1+cosxdx.
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Q. If y=log(sinx), find dydx.
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Q. Find the probability distribution of number of heads in two tosses of a coin.
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Q. Find the area of a parallelogram whose adjacent sides are given by the vectors a=3^i+^j+4^k and b=^i^j+^k.
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Q. Find the angle between the pair of lines
r=3^i+2^j4^k+λ(^i+2^j+2^k) and
r=5^i2^j+μ(3^i+2^j+6^k)
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Q. If a is a unit vector such that (xa)(x+a)=8, find |x|.
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Q. Verify whether the operation defined on ϱ by ab=ab2 is associative or not.
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Q. Define feasible region.
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Q. Find the order and degree of the differential equation
xyd2ydx2+x(dydx)2ydydx=0.
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Q. By using elementary transformation find the inverse of the matrix A=[1221].
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Q. Prove that 3cos1x=cos1(4x33x), xϵ[12, 1].
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Q. Find the general solution of the differential equation
extanydx+(1ex)sec2y dy=0.
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Q. If P(A)=45 and P(B/A)=25, find P(AB).
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Q. Find dydx if x=a(cosθ+θsinθ). and y=a(sinθθcosθ).
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Q. Evaluate : e11xdx.
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Q. If y+siny=cosx, find dydx.
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Q. Find g o f and f o g if f:RR and g:RR are given by f(x)=cosx and g(x)=3x2. Show that g o f f o g.
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