a)Unit 1Expand (1+x)ˣ by Maclaurin's Theorem.
a)Unit 1
Expand (1+x)ˣ by Maclaurin's Theorem.
b)Unit 1Find the Maximum value of u=sin x sin y sin(x+y).
b)Unit 1
Find the Maximum value of u=sin x sin y sin(x+y).
Previous Year Question Paper
BT-102 (GS) – Mathematics-I
June 2024•COMMON•SEMESTER-1
June 2024
Max Marks: 70
Duration: 3 Hours
Instructions:
• Attempt any five questions.
• All questions carry equal marks.
a)Unit 2Find the volume of the solid generated by the revolution of the Cardioid r=a(1+cosθ) about the initial line.
a)Unit 2
Find the volume of the solid generated by the revolution of the Cardioid r=a(1+cosθ) about the initial line.
b)Unit 2Prove that ∫₀^∞ cos(x²)dx = ½√(π/2).
b)Unit 2
Prove that ∫₀^∞ cos(x²)dx = ½√(π/2).
a)Unit 3Show that Sequence (xₙ) where |x|<1 converge to 0.
a)Unit 3
Show that Sequence (xₙ) where |x|<1 converge to 0.
b)Unit 3Find the Fourier Series for the function f(x)=x sin x, (-π<x<π).
b)Unit 3
Find the Fourier Series for the function f(x)=x sin x, (-π<x<π).
a)Unit 5Show that the following equations are consistent and solve them: x-y+2z=4, 3x+y+4z=6, x+y+z=1.
a)Unit 5
Show that the following equations are consistent and solve them: x-y+2z=4, 3x+y+4z=6, x+y+z=1.
b)Unit 4If w₁ and w₂ be two subspace of V(F) then Show that w₁ ∩ w₂ also subspace of V(F).
b)Unit 4
If w₁ and w₂ be two subspace of V(F) then Show that w₁ ∩ w₂ also subspace of V(F).
a)Unit 5Find the Characteristic equation of the matrix and hence find the Eigen values and Eigen vectors.
a)Unit 5
Find the Characteristic equation of the matrix and hence find the Eigen values and Eigen vectors.
b)Unit 5Show that the following matrix A is Diagonalizable.
b)Unit 5
Show that the following matrix A is Diagonalizable.
a)Unit 1Find the Maximum and Minimum value of u=a²x²+b²y²+c²z², where x²+y²+z²=1 and lx+my+nz=0.
a)Unit 1
Find the Maximum and Minimum value of u=a²x²+b²y²+c²z², where x²+y²+z²=1 and lx+my+nz=0.
b)Unit 3Find the Fourier Series for the function f(x)=x+x², (-π<x<π).
b)Unit 3
Find the Fourier Series for the function f(x)=x+x², (-π<x<π).
a)Unit 2Show that the surfaces area of the solid generated by revolution of the loop of the curve x=t², y=t-t³/3 about the x axis is 3π.
a)Unit 2
Show that the surfaces area of the solid generated by revolution of the loop of the curve x=t², y=t-t³/3 about the x axis is 3π.
b)Unit 5Investigate for what values of λ and μ the simultaneous equations have solutions.
b)Unit 5
Investigate for what values of λ and μ the simultaneous equations have solutions.
a)Unit 1Expand log x in power (x-1) by Taylor's theorem and hence find the value log 1.1.
a)Unit 1
Expand log x in power (x-1) by Taylor's theorem and hence find the value log 1.1.
b)Unit 2Evaluate ∬ xy dx dy where the region of integration is x+y<1 in the positive quadrant.
b)Unit 2
Evaluate ∬ xy dx dy where the region of integration is x+y<1 in the positive quadrant.