Limits, Continuity & Derivatives · NDA previous year questions

509 questions asked across 18 exam years, newest first

Year-wise papers Topic-wise questions

Practise this topic

2011 24 questions

Q102011 · 21 Aug 2011
The function $y = f (x) = m x + c$ has
1. A.maximum point but no minimum point
2. B.minimum point but no maximum point
3. C.both maximum and minimum points
4. D.neither maximum point nor minimum point
Show answer
Answer: D
Q162011 · 21 Aug 2011
At an extreme point of a function $f (x)$ , the tangent to the curve is
1. A.parallel to the x-axis
2. B.perpendicular to the x-axis
3. C.inclined at an angle $4 5^{\circ}$ to the x-axis
4. D.inclined at an angle $6 0^{\circ}$ to the x-axis
Show answer
Answer: A
Q172011 · 21 Aug 2011
If $y = (1 + x^{\frac{1}{4}}) (1 + x^{\frac{1}{2}}) (1 - x^{\frac{1}{4}})$ , then what is $\frac{d y}{d x}$ equal to?
1. A.1
2. B. $- 1$
3. C. $x$
4. D. $x^{\frac{1}{2}}$
Show answer
Answer: B
Q312011 · 21 Aug 2011
The point in the interval $(0, 2 π)$ where $f (x) = e^{x} sin x$ has maximum slope is
1. A. $\frac{π}{4}$
2. B. $\frac{π}{2}$
3. C. $π$
4. D. $\frac{3 π}{2}$
Show answer
Answer: B
Q322011 · 21 Aug 2011
If $tan θ = m$ , where $m$ is a non-square natural number $m$ , then $sec 2 θ$ is
1. A.a negative number
2. B.a transcendental number
3. C.an irrational number
4. D.a rational number
Show answer
Answer: A, D
Q782011 · 21 Aug 2011
What is the maximum value of $3 cos x + 4 sin x + 5$ ?
1. A.5
2. B.7
3. C.10
4. D.12
Show answer
Answer: C
Q792011 · 21 Aug 2011
If $sin θ = cos^{2} θ$ , then what is $cos^{2} θ (1 + cos^{2} θ)$ equal to?
1. A.1
2. B.0
3. C. $cos^{2} θ$
4. D. $2 sin θ$
Show answer
Answer: A
Q822011 · 21 Aug 2011
If the rate of change in volume of spherical soap bubble is uniform, then the rate of change of surface area varies as
1. A.square of radius
2. B.square root of radius
3. C.inversely proportional to radius
4. D.cube of the radius
Show answer
Answer: C
Q832011 · 21 Aug 2011
What is $\frac{s i n x}{1 + c o s x} + \frac{1 + c o s x}{s i n x}$ equal to?
1. A. $2 tan x$
2. B. $2 cosec x$
3. C. $2 cos x$
4. D. $2 sin x$
Show answer
Answer: B
Q852011 · 21 Aug 2011
If $f (x) = x ln x$ , then $f (x)$ attains minimum value at which one of the following points?
1. A. $x = e^{- 2}$
2. B. $x = e$
3. C. $x = e^{- 1}$
4. D. $x = 2 e^{- 1}$
Show answer
Answer: C
Q962011 · 21 Aug 2011
If the roots of the equation $x^{2} - 4 x - lo g_{3} N = 0$ are real, then what is the minimum value of N?
1. A. $1/256$
2. B. $1/27$
3. C. $1/64$
4. D. $1/81$
Show answer
Answer: D
Q1112011 · 21 Aug 2011
1. A.1995
2. B.1996
3. C.1997
4. D.1998
Show answer
Answer: C
Q1122011 · 21 Aug 2011
1. A.1995
2. B.1996
3. C.1997
4. D.1998
Show answer
Answer: A
Q1132011 · 21 Aug 2011
1. A. $\frac{80}{3} %$
2. B. $\frac{100}{3} %$
3. C. $35%$
4. D. $40%$
Show answer
Answer: A
Q1142011 · 21 Aug 2011
NOTE: STUDY THE PIE CHART GIVEN BELOW AND ANSWER THE NEXT 04 (FOUR) QUESTIONS THAT FOLLOW: The following pie chart gives the distribution of funds in a five year plan under the major heads of development expenditures: Agriculture (A), Industry (B), Education (C), Employment (D) and Miscellaneous (E). The total allocation is 36,000 (in crores of rupees). Which head is allocated maximum funds?
1. A.Agriculture
2. B.Industry
3. C.Employment
4. D.Miscellaneous
Show answer
Answer: C
Q1152011 · 21 Aug 2011
NOTE: STUDY THE PIE CHART GIVEN BELOW AND ANSWER THE NEXT 04 (FOUR) QUESTIONS THAT FOLLOW: The following pie chart gives the distribution of funds in a five year plan under the major heads of development expenditures: Agriculture (A), Industry (B), Education (C), Employment (D) and Miscellaneous (E). The total allocation is 36,000 (in crores of rupees). How much money (in crores) is allocated to Education?
1. A.3000
2. B.6000
3. C.9000
4. D.10800
Show answer
Answer: A
Q1162011 · 21 Aug 2011
NOTE: STUDY THE PIE CHART GIVEN BELOW AND ANSWER THE NEXT 04 (FOUR) QUESTIONS THAT FOLLOW: The following pie chart gives the distribution of funds in a five year plan under the major heads of development expenditures: Agriculture (A), Industry (B), Education (C), Employment (D) and Miscellaneous (E). The total allocation is 36,000 (in crores of rupees). How much money (in crores) is allocated to both Agriculture and Employment?
1. A.20000
2. B.21000
3. C.24000
4. D.27000
Show answer
Answer: B
Q1172011 · 21 Aug 2011
NOTE: STUDY THE PIE CHART GIVEN BELOW AND ANSWER THE NEXT 04 (FOUR) QUESTIONS THAT FOLLOW: The following pie chart gives the distribution of funds in a five year plan under the major heads of development expenditures: Agriculture (A), Industry (B), Education (C), Employment (D) and Miscellaneous (E). The total allocation is 36,000 (in crores of rupees). How much excess money (in crores) is allocated to Miscellaneous over Education?
1. A.3600
2. B.4200
3. C.4500
4. D.4800
Show answer
Answer: C
Q322011 · 17 Apr 2011
Consider the following statements in respect of the function $f (x) = x^{3} - 1, x \in [- 1, 1]$ 1. $f (x)$ is increasing in $[- 1, 1]$ 2. $f (x)$ has no root in $(- 1, 1)$ Which of the statements given above is/are correct?
1. A.1 only
2. B.2 only
3. C.Both 1 and 2
4. D.Neither 1 nor 2
Show answer
Answer: C
Q332011 · 17 Apr 2011
The largest value of $2 x^{3} - 3 x^{2} - 12 x + 5$ for $- 2 \leq x \leq 2$ occurs when
1. A. $x = - 2$
2. B. $x = - 1$
3. C. $x = 2$
4. D. $x = 0$
Show answer
Answer: B
Q342011 · 17 Apr 2011
What is $\int_{0}^{π} \frac{d x}{1 + 2 s i n ^{2} x}$ equal to?
1. A. $π$
2. B. $\frac{π}{3}$
3. C. $\frac{π}{3}$
4. D. $\frac{2 π}{3}$
Show answer
Answer: C
Q572011 · 17 Apr 2011
Which one of the following is correct in respect of the function $f (x) = ∣ x ∣ + x^{2}$ ?
1. A. $f (x)$ is not continuous at $x = 0$
2. B. $f (x)$ is differentiable at $x = 0$
3. C. $f (x)$ is continuous but not differentiable at $x = 0$
4. D.None of the above
Show answer
Answer: C
Q602011 · 17 Apr 2011
The function $f (x) = k sin x + \frac{1}{3} sin 3 x$ has maximum value at $x = \frac{π}{3}$ . What is the value of $k$ ?
1. A.3
2. B. $\frac{1}{3}$
3. C.2
4. D. $\frac{1}{2}$
Show answer
Answer: C
Q672011 · 17 Apr 2011
What is the value of $k$ for which the following function $f (x)$ is continuous for all $x$ ? $f (x) = ⎩ ⎨ ⎧ \frac{x ^{3} - 3 x + 2}{( x - 1 ) ^{2}} k for x \neq = 1 for x = 1$
1. A.3
2. B.2
3. C.1
4. D. $- 1$
Show answer
Answer: A