GTU Engineering 1st Year MCQ | Calculus-2110014 Winter 2015 Sem-1

Calculus (2110014)
Winter 2015 Sem-1

MCQ(s) of Calculus (2110014) - Winter 2015 Sem-1

- Q. 1 $T h e v a l u e o f \lim_{n \to \infty} {(1 + \frac{1}{n})}^{n} i s$
- (A) $1$
  
  (B) $- 1$
- (C) $e$
  
  (D) $\frac{1}{e}$
- Answer
  
  (C) $e$
- Q. 2 $T h e v a l u e o f \lim_{x \to 0} x^{x} i s$
- (A) $1$
  
  (B) $- 1$
- (C) $e$
  
  (D) $\frac{1}{e}$
- Answer
  
  (A) $1$
- Q. 3 $M a c l a u r i n ’ s s e r i e s o f e^{- x} i s$
- (A) $\sum_{n = 0}^{\infty} \frac{x^{n}}{n!}$
  
  (B) $\sum_{n = 0}^{\infty} \frac{{(- 1)}^{n} x^{n}}{n!}$
- (C) $\sum_{n = 1}^{\infty} \frac{x^{n}}{n!}$
  
  (D) $\sum_{n = 1}^{\infty} \frac{{(- 1)}^{n} x^{n}}{n!}$
- Answer
  
  (B) $\sum_{n = 0}^{\infty} \frac{{(- 1)}^{n} x^{n}}{n!}$
- Q. 4 $I f f (x, y, z, w) = 3 \frac{\cos (x w) \sin y^{5}}{e^{y} + (1 + y^{2}) / x y w} + 5 x z w, t h e n \frac{\partial f}{\partial z} a t (1, 2, 3, 4) i s$
- (A) 20
  
  (B) 200
- (C) 0
  
  (D) 1
- Answer
  
  (A) 20
- Q. 5 $M i n i m u m v a l u e o f f (x, y) = x^{2} y^{2} i s$
- (A) 1
  
  (B) 2
- (C) 4
  
  (D) 0
- Answer
  
  (D) 0
- Q. 6 $T h e s u m o f t h e s e r i e s \sum_{n = 1}^{\infty} \frac{1}{2^{n}} i s$
- (A) 0
  
  (B) $\frac{3}{4}$
- (C) 1
  
  (D) 2
- Answer
  
  (C) 1
- Q. 7 $V a l u e o f t h e \lim_{(x, y) \to (0, 0)} \frac{x^{2} - x y}{\sqrt{x} - \sqrt{y}} i s$
- (A) 1
  
  (B) 0
- (C) -1
  
  (D) Limit does not exist
- Answer
  
  (B) 0
- Q. 8 $T h e v a l u e o f \iint 3 y d x d y o v e r t h e t r i a n g l e w i t h v e r t i c e s (- 1, 1), (0, 0), a n d (1, 1) i s$
- (A) 0
  
  (B) 1
- (C) 2
  
  (D) 3
- Answer
  
  (A) 0
- Q. 9 $T h e s e r i e s \sum_{n = 1}^{\infty} \frac{(- 1)^{n}}{n} i s$
- (A) Divergent
  
  (B) Absolutely convergent
- (C) Conditionally convergent
  
  (D) Nothing can be said
- Answer
  
  (C) Conditionally convergent
- Q. 10 $I f J = \frac{\partial (x, y)}{\partial (r, θ)} a n d J * = \frac{\partial (r, θ)}{\partial (x, y)}, t h e n t h e v a l u e o f J J * i s$
- (A) 0
  
  (B) 1
- (C) -1
  
  (D) Always J=J*
- Answer
  
  (B) 1
- Q. 11 What does the polar equation r=a,a>0 represent?
- (A) Line
  
  (B) Rectangle
- (C) Circle
  
  (D) Parabola
- Answer
  
  (C) Circle
- Q. 12 $T h e c u r v e x^{3} + y^{3} = 3 a x y i s s y m m e t r i c a b o u t$
- (A) X-axis
  
  (B) Y-axis
- (C) Origin
  
  (D) The line y=x
- Answer
  
  (D) The line y=x
- Q. 13 $T h e v a l u e o f \int_{1}^{\infty} \frac{1}{x^{2}} d x i s$
- (A) 1
  
  (B) 0
- (C) -1
  
  (D) Does not exist
- Answer
  
  (A) 1
- Q. 14 $I f f (x, y) = \frac{x}{y} + \sin (\frac{y}{x}) e^{\frac{y}{x}}, t h e n t h e v a l u e o f x \frac{\partial f}{\partial x} + y \frac{\partial f}{\partial y} i s$
- (A) 1
  
  (B) 0
- (C) -1
  
  (D) f
- Answer
  
  (B) 0