Maths | AP Board | Grade 12 | 2015
Q. Prove that C0+2.C1+4.C2+8.C3+......+2n.Cn=3n.
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Q. Prove that 4nC2n2nCn=1.3.5......(4n1){1.3.5......(2n1)}2
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Q. The probability that a person chosen at random is left handed (in hand writing) is 0.1. What is the probability that in a group of 10 people, there is one who is left handed?
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Q. Solve the differential equation: (xy2+x)dx+(yx2+y)dy=0
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Q. Evaluate : π20|1x|dx
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Q. If the length of the tangent from (5, 4) to the circle x2+y2+2ky=0 is 1, then find k
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Q. For what values of x is the expression 15+4x3x2 negative?
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Q. If A, B, C are three events, then show that P(ABC)=P(A)+P(B)+P(C)P(AB)P(BC)P(CA)+P(ABC)
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Q. Form the differential equation corresponding to y=Acos3x+B sin3x, where A and B are parameters.
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Q. Find : ex(1+xlogx)xdx
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Q. If (2, 0), (0, 1), (4, 5) and (0, C) are concyclics then find C
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Q. Define rectangular hyperbola and find its eccentricity
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Q. Find : π20dx4+5cosxdx
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Q. If A, B, C are angles of a triangle such that x=cisA, y=cisB, z=cisC, then find the value of xyz=
1. i
2. 1
3. i
4. 1
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Q. Find the value a if 2x2+ay23x+2y1=0 represent a circle and also find its radius.
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Q. Find : sin(tan1x)1+x2dx, x ϵ R
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Q. If the letters of the word MASTER are permuted in all possible ways and the words thus formed are arranged in dictionary order, then find the rank of the word MASTER.
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Q. Resolve the fraction 2x2+3x+4(x1)(x2+2) into partial fractions.
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Q. Find the number of 4 letter words that can be formed using the letters of the word PISTON, in which at least one letter is repeated.
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Q. Find the transformed equation whose roots are the negatives of the roots of x4+5x3+11x+3=0.
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Q. If 10×nC2=3×(n+1)C3, find n.
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Q. Find the equation of the common chord of the circles:
(xa)2+(yb)2=c2, (xb)2+(ya)2=c2, (ab)
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Q. Find the variance for an ungrouped data 5, 12, 3, 18, 6, 8, 2, 10.
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Q. Write the conjugate of complex number 5i7+i
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Q. Find the co-ordinates of the points on the parabola y2=2x whose focal distance is 52
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Q. Express 1i in modulus-amplitude form.
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Q. If x+y=3 is the equation of the chord AB of the circle x2+y22x+4y8=0, find the equation of the circle having AB as diameter.
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Q. Find the value of k if 4x+y+k=0 is a tangent to the ellipse x2+3y2=3
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Q. Find the equations of the tangents to the hyperbola 3x24y2=12, which are:
(i) Parallel and (ii) Perpendicular to the line
y=x7
AP Board
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Q. Find the equation of tangent and normal to the ellipse 9x2+16y2=144
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