31st March for July session, 30th September for January session
BCS-012 Solved Assignment
Q1: For what value of ‘ kk ‘ the points (-k+1,2k),(k,2-2k)(-k+1,2 k),(k, 2-2 k) and (-4-k,6-2k)(-4-k, 6-2 k) are collinear.
Q2: Solve the following system of equations by using Matrix Inverse Method.
Q4: How many terms of the sequence sqrt3,3,3sqrt3,dots\sqrt{3}, 3,3 \sqrt{3}, \ldots must be taken to get the sum 39+13sqrt339+13 \sqrt{3} ?
Q5: If y=ae^(mx)+be^(-mx)y=a e^{m x}+b e^{-m x}, Prove that d^(2)y//dx^(2)=m^(2)yd^2 y / d x^2=m^2 y
Q6: Integrate function f(x)=x//[(x+1)(2x-1)]f(x)=x /[(x+1)(2 x-1)] w.r.t xx
Q7: If 1, w,w^(2)w, w^2 are Cube Roots of unity show that (1+w)^(2)-(1+w)^(3)+w^(2)=0(1+w)^2-(1+w)^3+w^2=0.
Q8: If alpha,beta\alpha, \beta are roots of equation 2x^(2)-3x-5=02 x^2-3 x-5=0, them find a Quadratic equation whose roots are alpha^(2),beta^(2)\alpha^2, \beta^2
Q9: Solve the inequality (3)/(5)(x-2) <= (5)/(3)(2-x)\frac{3}{5}(x-2) \leq \frac{5}{3}(2-x) and graph the solution set.
Q10: If a positive number exceeds its positive square root by 12 , then find the number.
Q11: Find the area bounded by the curves x^(2)=y\mathrm{x}^2=\mathrm{y} and y=xy=x. Q12: Find the inverse of the matrix A=([1,6,4],[2,4,-1],[-1,2,5])A=\left(\begin{array}{ccc}1 & 6 & 4 \\ 2 & 4 & -1 \\ -1 & 2 & 5\end{array}\right), if it exists,
Q13: If mm times the m^(“th “)m^{\text {th }} term of an A.P. is nn times its n^(“th “)n^{\text {th }} term, show that (m+n)^(“th “)(m+n)^{\text {th }} term of the A.P. is zero.
Q14: Show that
i) lim_(n rarr0)(|x|)/(x)\lim _{n \rightarrow 0} \frac{|x|}{x} does not exist
ii) f(x)=|x|\mathrm{f}(x)=|x| is continuous at x=0x=0.
Q15: Suriti wants to Invest at most 12000 in saving certificates and National Saving Bonds. She has to invest at least 2000 in Saving certificates and at least 4000 in National Saving Bonds. If Rate of
Interest on saving certificates is 8%8 \% per annum and rate of interest on national saving bond is 10%10 \% per annum. How much money should she invest to earn maximum yearly income? Find also the maximum yearly income.
Q16: A spherical balloon is being Inflated at the rate of 900cm^(3)//sec900 \mathrm{~cm}^3 / \mathrm{sec}. How fast is the Radius of the balloon Increasing when the Radius is 15 cm .
Expert Answer
BCS-012 Solved Assignment
Question:-01
For what value of ‘ kk ‘ the points (-k+1,2k),(k,2-2k)(-k+1,2 k),(k, 2-2 k) and (-4-k,6-2k)(-4-k, 6-2 k) are collinear.
Answer:
To determine the value of kk such that the points (-k+1,2k)(-k+1, 2k), (k,2-2k)(k, 2 – 2k), and (-4-k,6-2k)(-4 – k, 6 – 2k) are collinear, we need to use the condition that the area of the triangle formed by three collinear points is zero.
The formula for the area of a triangle formed by three points (x_(1),y_(1))(x_1, y_1), (x_(2),y_(2))(x_2, y_2), and (x_(3),y_(3))(x_3, y_3) is:
For the given points (-k+1,2k)(-k + 1, 2k), (k,2-2k)(k, 2 – 2k), and (-4-k,6-2k)(-4 – k, 6 – 2k), we can substitute their coordinates into this formula and set the area equal to zero.