Available Questions 450 found Page 15 of 23
Standalone Questions
#811
Mathematics
Differential Equations
MCQ_SINGLE
APPLY
2023
KNOWLEDGE
1 Marks
The general solution of the differential equation $x dy-(1+x^{2})dx=dx$ is:
(A) $y=2x+\frac{x^{3}}{3}+C$
(B) $y=2\log x+\frac{x^{3}}{3}+C$
(C) $y=\frac{x^{2}}{2}+C$
(D) $y=2\log x+\frac{x^{2}}{2}+C$
Key: D
Sol:
Sol:
$y=2\log x+\frac{x^{2}}{2}+C$
#810
Mathematics
Differential Equations
MCQ_SINGLE
UNDERSTAND
2023
KNOWLEDGE
1 Marks
The sum of the order and the degree of the differential equation \frac{d^{2}y}{dx^{2}}+(\frac{dy}{dx})^{3}=sin\~y is:
(A) 5
(B) 2
(C) 3
(D) 4
Key:
Sol:
Sol:
#809
Mathematics
Differential Equations
MCQ_SINGLE
APPLY
2023
KNOWLEDGE
1 Marks
The sum of the order and the degree of the differential equation d/dx((dy/dx)³) is
(A) 2
(B) 3
(C) 5
(D) 0
Key:
Sol:
Sol:
#808
Mathematics
Integrals
MCQ_SINGLE
APPLY
2023
KNOWLEDGE
1 Marks
$\int\frac{2\cos 2x-1}{1+2\sin x}dx$ is equal to:
(A) $x-2\cos x+C$
(B) $x+2\cos x+C$
(C) $-x-2\cos x+C$
(D) $-x+2\cos x+C$
Key:
Sol:
Sol:
#807
Mathematics
Integrals
MCQ_SINGLE
APPLY
2023
KNOWLEDGE
1 Marks
$\int 2^{x+2}dx$ is equal to :
(A) $2^{x+2}+C$
(B) $2^{x+2}\log 2+C$
(C) $\frac{2^{x+2}}{\log 2}+C$
(D) $2\cdot\frac{2^{x}}{\log 2}+C$
Key: C
Sol:
Sol:
Let $u = x+2$, then $du = dx$.$$\int 2^u \, du = \frac{2^u}{\log 2} + C$$Substitute $u$ back:$$= \frac{2^{x+2}}{\log 2} + C$$
#806
Mathematics
Integrals
MCQ_SINGLE
APPLY
2023
KNOWLEDGE
1 Marks
9. If $\int_{0}^{a}3x^{2}dx=8$, then the value of 'a' is :
(A) 2
(B) 4
(C) 8
(D) 10
Key:
Sol:
Sol:
#805
Mathematics
Integrals
MCQ_SINGLE
APPLY
2023
KNOWLEDGE
1 Marks
8. $\int e^{5\log x}dx$ is equal to :
(A) $\frac{x^{5}}{5}+C$
(B) $\frac{x^{6}}{6}+C$
(C) $5x^{4}+C$
(D) $6x^{5}+C$
Key:
Sol:
Sol:
#804
Mathematics
Integrals
MCQ_SINGLE
APPLY
2023
KNOWLEDGE
1 Marks
\int_{0}^{\frac{\pi}{6}}sec^{2}(x-\frac{\pi}{6})dx is equal to :
(A) \frac{1}{\sqrt{3}}
(B) -\frac{1}{\sqrt{3}}
(C) \sqrt{3}
(D) -\sqrt{3}
Key:
Sol:
Sol:
#803
Mathematics
Integrals
MCQ_SINGLE
UNDERSTAND
2023
KNOWLEDGE
1 Marks
If \frac{d}{dx}(f(x))=log\~x, then f(x) equals :
(A) -\frac{1}{x}+C
(B) x(log\~x-1)+C
(C) x(log\~x+x)+C
(D) \frac{1}{x}+C
Key:
Sol:
Sol:
#801
Mathematics
Integrals
MCQ_SINGLE
APPLY
2023
KNOWLEDGE
1 Marks
∫ [sec x / (sec x - tan x)] dx equals
(A) sec x - tan x + c
(B) sec x + tan x + c
(C) tan x - sec x + c
(D) -(sec x + tan x) + c
Key:
Sol:
Sol:
#799
Mathematics
Applications of Derivatives
MCQ_SINGLE
APPLY
2023
KNOWLEDGE
1 Marks
The interval in which the function f(x)=2x³+9x²+12x-1 is decreasing, is
(A) (-1, ∞)
(B) (-2,-1)
(C) (-∞, -2)
(D) [-1, 1]
Key: B
Sol:
Sol:
#798
Mathematics
Continuity and Differentiability
MCQ_SINGLE
APPLY
2023
KNOWLEDGE
1 Marks
If $y=\frac{\cos x-\sin x}{\cos x+\sin x}$ then $\frac{dy}{dx}$ is:
(A) $-\sec^{2}(\frac{\pi}{4}-x)$
(B) $\sec^{2}(\frac{\pi}{4}-\pi)$
(C) $\log|\sec(\frac{\pi}{4}-x)|$
(D) $-\log|\sec(\frac{\pi}{4}-x)|$
Key:
Sol:
Sol:
#797
Mathematics
Continuity and Differentiability
MCQ_SINGLE
UNDERSTAND
2023
KNOWLEDGE
1 Marks
The value of k for which function $f(x)=\begin{cases}x^{2},&x\ge0\\ kx,&x<0\end{cases}$ is differentiable at $x=0$ is:
(A) 1
(B) 2
(C) any real number
(D) 0
Key:
Sol:
Sol:
#796
Mathematics
Continuity and Differentiability
MCQ_SINGLE
APPLY
2023
KNOWLEDGE
1 Marks
7. If $y=\sin^{2}(x^{3})$, then $\frac{dy}{dx}$ is equal to :
(A) $2\sin x^{3}\cos x^{3}$
(B) $3x^{3}\sin x^{3}\cos x^{3}$
(C) $6x^{2}\sin x^{3}\cos x^{3}$
(D) $2x^{2}\sin^{2}(x^{3})$
Key: C
Sol:
Sol:
#795
Mathematics
Continuity and Differentiability
MCQ_SINGLE
UNDERSTAND
2023
KNOWLEDGE
1 Marks
6. The function $f(x)=|x|$ is
(A) continuous and differentiable everywhere.
(B) continuous and differentiable nowhere.
(C) continuous everywhere, but differentiable everywhere except at $x=0$.
(D) continuous everywhere, but differentiable nowhere.
Key:
Sol:
Sol:
#794
Mathematics
Continuity and Differentiability
MCQ_SINGLE
APPLY
2023
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
The value of k for which$ f(x)=\begin{cases}3x+5,&x\ge2\\ kx^{2},&x<2\end{cases}$ is a continuous function, is :
(A) $-\frac{11}{4}$
(B) $\frac{4}{11}$
(C) 11
(D) $\frac{11}{4}$
Key:
Sol:
Sol:
#793
Mathematics
Continuity and Differentiability
MCQ_SINGLE
APPLY
2023
KNOWLEDGE
1 Marks
If x=A cos 4t + B sin 4t, then d²x/dt² is equal to
(A) x
(B) -x
(C) 16x
(D) -16x
Key:
Sol:
Sol:
#792
Mathematics
Continuity and Differentiability
MCQ_SINGLE
UNDERSTAND
2023
KNOWLEDGE
1 Marks
The function f(x)=[x], where [x] denotes the greatest integer less than or equal to x, is continuous at
(A) x=1
(B) x=1.5
(C) x=-2
(D) x=4
Key: B
Sol:
Sol:
#791
Mathematics
Continuity and Differentiability
MCQ_SINGLE
UNDERSTAND
2023
KNOWLEDGE
1 Marks
The derivative of x²ⁿ w.r.t. x is
(A) x²ⁿ⁻¹
(B) 2x²ⁿ log x
(C) 2x²ⁿ(1+log x)
(D) 2x²ⁿ(1-log x)
Key:
Sol:
Sol:
#790
Mathematics
Inverse Trigonometric Functions
MCQ_SINGLE
APPLY
2023
KNOWLEDGE
1 Marks
sin[ π/3 + sin⁻¹(1/2) ] is equal to
(A) 1
(B) 1/2
(C) 1/3
(D) 1/4
Key:
Sol:
Sol: