a. 7/2 b. 3/2 c. 5/2 d. 1/2 Solution: Answer: (a) \(\begin{array}{l}\lim_{n\to \infty }\frac{1}{n}\sum_{r=0}^{n-1}f(\frac{5r}{n})\end{array} \) = ∫01 f(5x) = ∫01(5x+1)... View Article
a. 2 b. 1 c. 3 d. 4 Solution: Answer: (b) Mean = 10 (7+10+11+15+a+b)/6 = 10 a + b... View Article
a. -2 b. 2 c. -4 d. 4 Solution: Answer: (b) log(x+1) (2x+5)(x+1) + log(2x+5) (x+1)2 = 4 1+ log(x+1)... View Article
Solution: Answer: (3) \(\begin{array}{l}\lim_{x\to 0}\frac{\alpha x(1+x+\frac{x^{2}}{2!}+\frac{x^{3}}{3!}+…)-\beta (x-\frac{x^{2}}{2}+\frac{x^{3}}{3}+…)+\gamma x^{2}(1-x+\frac{x^{2}}{2!}-\frac{x^{3}}{3!}+…)}{x^{3}}=10\end{array} \) ⇒ α – β = 0 ⇒ α = β ⇒... View Article
a. -2 b. 1 c. 0 d. -1 Solution: Answer: (c) I = ∫-π/2π/2([x] – [sinx ])dx Using the property... View Article
Answer: (1/8)(π-1) x (dy/dx). tan (y/x) = y tan (y/x) + x (dy/dx) tan(y/x) = (y/x) tan(y/x) + 1 Let... View Article
a. 60 b. 45 c. 40 d. 90 Solution: Answer: (a) (ab + bc + ca)6 = \(\begin{array}{l}\sum_{p+q+r=6}^{}\frac{6!}{p!q!r!}(ab)^{p}(bc)^{q}(ca)^{r}\end{array} \) =... View Article
a. 20/27 b. −20/27 c. 88/27 d. -88/27 Solution: Answer: (d) \(\begin{array}{l}f(x)=\begin{vmatrix} 1 & -x &2x+1 \\ -x& 1 &... View Article
a. 9 + ln 2 b. 10 + ln 2 c. 10 d. 9 Solution: Answer: (b) Let a =... View Article
Answer: 1/2 x2+ 2(a+4)x – (5a – 64)>0 D<0 Therefore 4(a+4)2 + 4(5a – 64) < 0 ⇒ a2 +... View Article
a. (x-8)/3 b. (x+8)/3 c. (x-3)/8 d. (x+3)/8 Solution: Answer: (b) f-1 (g-1(x) ) = x-2 ⇒ f(x-2) = g-1... View Article
a. π/4 b. -π/4 c. 3π/4 d. -3π/4 Solution: Answer: = (1-2i)/(1+3i) = -½ – ½ i arg( -½ –... View Article
a. point of local maxima b. point of local minima c. point of inflection d. None of these Solution: Answer:... View Article
Answer: 34 Focus of parabola is (−16,0) So, −16m + c=0 ⇒c = 16m …(i) Now slope form of tangent... View Article
a. 6+8√3 b. 3+4√3 c. 3+8√3 d. 6+4√3 Solution: Answer: (a) cos B = ⅗ ⇒ sinB = 4/5, R... View Article
a. 50⋅324 b. 51⋅324 c. 52⋅324 d. 104⋅324 Solution: Answer: (c) x2 + 31/2 = – 31/4x ⇒ x4 +... View Article
a. √(A2 + B2√(2AB)) b. √(A2 + B2 – √(2AB)) c. √(A2 + B2 – √2 AB) d. √(A2 +... View Article
Answer: 25/2 Equation of tangent at A yy1 = x+x1 ⇒2y = x+2 Tangent at A intersects the x-axis at... View Article
Answer: ≡ p → q ~(p∧~q) ∨ (q∨~p) ≡ (~p∨q) ∨ (q∨~p) ≡ ~p∨q ≡ p → q