Available Questions 601 found Page 20 of 31
Standalone Questions
#820
Mathematics
Vector Algebra
MCQ_SINGLE
APPLY
2023
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
If $\vec{a}+\vec{b}=\hat{i}$ and $\vec{a}=2\hat{i}-2\hat{j}+2\hat{k}$, then |$\vec{b}$| equals:
(A) \sqrt{14}
(B) 3
(C) \sqrt{12}
(D) \sqrt{17}
Key:
Sol:
Sol:
#819
Mathematics
Vector Algebra
MCQ_SINGLE
UNDERSTAND
2023
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
The value of $(\hat{i}\times\hat{j})\cdot \hat{j}+(\hat{j}\times\hat{i}) \hat{k}:$
(A) 2
(B) 0
(C) 1
(D) -1
Key:
Sol:
Sol:
#818
Mathematics
Vector Algebra
MCQ_SINGLE
APPLY
2023
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
The value of p for which the vectors $2\hat{i}+p\hat{j}+\hat{k}$ and $-4\hat{i}-6\hat{j}+26\hat{k}$ are perpendicular to each other, is:
(A) 3
(B) -3
(C) $-\frac{17}{3}$
(D) $\frac{17}{3}$
Key:
Sol:
Sol:
#817
Mathematics
Vector Algebra
MCQ_SINGLE
REMEMBER
2023
KNOWLEDGE
1 Marks
The magnitude of the vector 6î - 2î + 3ê is
(A) 1
(B) 5
(C) 7
(D) 12
Key:
Sol:
Sol:
#816
Mathematics
Vector Algebra
MCQ_SINGLE
REMEMBER
2023
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
Two vectors $\vec{a} = a_1\hat{i} + a_2\hat{j} + a_3\hat{k}$ and $\vec{b} = b_1\hat{i} + b_2\hat{j} + b_3\hat{k}$ are collinear if
(A) a₁b₁ + a₂b₂ + a₃b₃ = 0
(B) a₁/b₁ = a₂/b₂ = a₃/b₃
(C) a₁=b₁, a₂=b₂, a₃=b₃
(D) a₁+a₂+a₃ = b₁+b₂+b₃
Key:
Sol:
Sol:
#815
Mathematics
Differential Equations
MCQ_SINGLE
APPLY
2023
KNOWLEDGE
1 Marks
What is the product of the order and degree of the differential equation $\frac{d^{2}y}{dx^{2}}\sin y+(\frac{dy}{dx})^{3}\cos y=\sqrt{y}$ ?
(A) 3
(B) 2
(C) 6
(D) not defined
Key:
Sol:
Sol:
#814
Mathematics
Differential Equations
MCQ_SINGLE
UNDERSTAND
2023
KNOWLEDGE
1 Marks
The solution of the differential equation $\frac{dx}{x}+\frac{dy}{y}=0$ is:
(A) $\frac{1}{x}+\frac{1}{y}=C$
(B) $\log x-\log y=C$
(C) $xy=C$
(D) $x+y=C$
Key:
Sol:
Sol:
#813
Mathematics
Differential Equations
MCQ_SINGLE
APPLY
2023
KNOWLEDGE
1 Marks
11. The order and degree (if defined) of the differential equation, $(\frac{d^{2}y}{dx^{2}})^{2}+(\frac{dy}{dx})^{2}=x\sin(\frac{dy}{dx})$ respectively are :
(A) 2, 2
(B) 1, 3
(C) 2, 3
(D) 2, degree not defined
Key:
Sol:
Sol:
#812
Mathematics
Differential Equations
MCQ_SINGLE
APPLY
2023
KNOWLEDGE
1 Marks
The integrating factor for solving the differential equation $x\frac{dy}{dx}-y=2x^{2}$ is:
(A) $e^{-y}$
(B) $e^{-x}$
(C) $x$
(D) $\frac{1}{x}$
Key: D
Sol:
Sol:
#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:
#802
Mathematics
Integrals
MCQ_SINGLE
APPLY
2023
Competency
1 Marks
∫ from -1 to 1 [|x-2| / (x-2)] dx, x≠2 is equal to
(A) 1
(B) -1
(C) 2
(D) -2
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: