Available Questions Page 14 of 14
Standalone Questions
#572
Mathematics
Relations and Functions
MCQ_SINGLE
APPLY
2024
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
Let \(R_{+}\) denote the set of all non-negative real numbers. Then the function \(f:R_{+}\rightarrow R_{+}\) defined as \(f(x)=x^{2}+1\) is :
(A) one-one but not onto
(B) onto but not one-one
(C) both one-one and onto
(D) neither one-one nor onto
Key:
Sol:
Sol:
#571
Mathematics
Relations and Functions
MCQ_SINGLE
APPLY
2024
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
A function \(f:\mathbb{R}\rightarrow\mathbb{R}\) defined as \(f(x)=x^{2}-4x+5\) is:
(A) injective but not surjective.
(B) surjective but not injective.
(C) both injective and surjective.
(D) neither injective nor surjective.
Key: D
Sol:
Sol:
#570
Mathematics
Vector Algebra
MCQ_SINGLE
APPLY
2025
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
If vector \(\vec{a} = 3\hat{i} + 2\hat{j} - \hat{k}\) and vector \(\vec{b} = \hat{i} - \hat{j} + \hat{k}\), then which of the following is correct ?
(A) \(\vec{a} \parallel \vec{b}\)
(B) \(\vec{a} \perp \vec{b}\)
(C) \(|\vec{b}| > |\vec{a}|\)
(D) \(|\vec{a}| = |\vec{b}|\)
Key: B
Sol:
Sol:
**Correct Option if MCQ:** B
**Reasoning:**
* Calculate the dot product: \(\vec{a} \cdot \vec{b} = (3)(1) + (2)(-1) + (-1)(1) = 3 - 2 - 1 = 0\).
* Since the dot product is zero, the vectors are perpendicular.
* \(\vec{a} \perp \vec{b}\)
#568
Mathematics
Vector Algebra
MCQ_SINGLE
APPLY
2025
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
The projection vector of vector \(\vec{a}\) on vector \(\vec{b}\) is
(A) \((\frac{\vec{a}\cdot\vec{b}}{|\vec{b}|^{2}})\vec{b}\)
(B) \(\frac{\vec{a}\cdot\vec{b}}{|\vec{b}|}\)
(C) \(\frac{\vec{a}\cdot\vec{b}}{|\vec{a}|}\)
(D) \((\frac{\vec{a}\cdot\vec{b}}{|\vec{a}|^{2}})\vec{b}\)
Key: A
Sol:
Sol:
\((\frac{\vec{a}\cdot\vec{b}}{|\vec{b}|^{2}})\vec{b}\)
#567
Mathematics
Vector Algebra
MCQ_SINGLE
APPLY
2025
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
Let \(\vec{p}\) and \(\vec{q}\) be two unit vectors and \(\alpha\) be the angle between them. Then \((\vec{p}+\vec{q})\) will be a unit vector for what value of \(\alpha\)?
(A) \(\frac{\pi}{4}\)
(B) \(\frac{\pi}{3}\)
(C) \(\frac{\pi}{2}\)
(D) \(\frac{2\pi}{3}\)
Key: D
Sol:
Sol:
\(\frac{2\pi}{3}\)
#565
Mathematics
Vector Algebra
MCQ_SINGLE
APPLY
2025
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
Let \(\vec{a}\) be a position vector whose tip is the point \((2,-3)\). If \(\vec{AB}=\vec{a}\), where coordinates of A are \((-4, 5)\), then the coordinates of B are:
(A) \((-2,-2)\)
(B) \((2,-2)\)
(C) \((-2,2)\)
(D) \((2, 2)\)
Key:
Sol:
Sol:
#563
Mathematics
Vector Algebra
MCQ_SINGLE
APPLY
2025
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
Let \(|\vec{a}|=5\) and \(-2\le\lambda\le1\). Then, the range of \(|\lambda\vec{a}|\) is:
(A) [5, 10]
(B) [-2, 5]
(C) [2, 1]
(D) [-10, 5]
Key:
Sol:
Sol:
#561
Mathematics
Vector Algebra
MCQ_SINGLE
APPLY
2025
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
If \(|\vec{a}+\vec{b}|=|\vec{a}-\vec{b}|\) for any two vectors, then vectors \(\vec{a}\) and \(\vec{b}\) are:
(A) orthogonal vectors
(B) parallel to each other
(C) unit vectors
(D) collinear vectors
Key:
Sol:
Sol:
#560
Mathematics
Vector Algebra
MCQ_SINGLE
APPLY
2024
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
Let \(\theta\) be the angle between two unit vectors \(\hat{a}\) and \(\hat{b}\) such that \(\sin\theta=\frac{3}{5}\). Then, \(\hat{a} \cdot \hat{b}\) is equal to:
(A) \(\pm\frac{3}{5}\)
(B) \(\pm\frac{3}{4}\)
(C) \(\pm\frac{4}{5}\)
(D) \(\pm\frac{4}{3}\)
Key:
Sol:
Sol:
#559
Mathematics
Vector Algebra
MCQ_SINGLE
UNDERSTAND
2024
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
The vector with terminal point \(A(2,-3,5)\) and initial point \(B(3, 4, 7)\) is:
(A) \(\hat{i}-\hat{j}+2\hat{k}\)
(B) \(\hat{i}+\hat{j}+2\hat{k}\)
(C) \(-\hat{i}-\hat{j}-2\hat{k}\)
(D) \(-\hat{i}+\hat{j}-2\hat{k}\)
Key:
Sol:
Sol:
#558
Mathematics
Vector Algebra
MCQ_SINGLE
APPLY
2024
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
For any two vectors \(\vec{a}\) and \(\vec{b}\), which of the following statements is always true?
(A) \(\vec{a}.\vec{b}\ge
(B) \vec{a}
(C)
(D) \vec{b}
Key:
Sol:
Sol:
#557
Mathematics
Vector Algebra
MCQ_SINGLE
APPLY
2024
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
The unit vector perpendicular to both vectors \(\hat{i}+\hat{k}\) and \(\hat{i}-\hat{k}\) is:
(A) \(2\hat{j}\)
(B) \(\hat{j}\)
(C) \(\frac{\hat{i}-\hat{k}}{\sqrt{2}}\)
(D) \(\frac{\hat{i}+\hat{k}}{\sqrt{2}}\)
Key:
Sol:
Sol:
#556
Mathematics
Vector Algebra
MCQ_SINGLE
APPLY
2024
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
If \(\vec{a}=2\hat{i}-\hat{j}+\hat{k}\) and \(\vec{b}=\hat{i}+\hat{j}-\hat{k}\), then \(\vec{a}\) and \(\vec{b}\):
(A) collinear vectors which are not parallel
(B) parallel vectors
(C) perpendicular vectors
(D) unit vectors
Key: C
Sol:
Sol:
#555
Mathematics
Vector Algebra
MCQ_SINGLE
APPLY
2024
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
If \(|\vec{a}|= 2\) and \(-3\le k\le2\), then \(|\vec{k}\vec{a}|\in\):
(A) [-6, 4]
(B) [0, 4]
(C) [4, 6]
(D) [0, 6]
Key:
Sol:
Sol:
#554
Mathematics
Vector Algebra
MCQ_SINGLE
APPLY
2024
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
If \(\vec{a}\) and \(\vec{b}\) are two vectors such that \(|\vec{a}|=1,|\vec{b}|=2~and\vec{a}\cdot\vec{b}=\sqrt{3}\) then the angle between \(2\vec{a}\) and \(-\vec{b}\) is:
(A) \(\frac{\pi}{6}\)
(B) \(\frac{\pi}{3}\)
(C) \(\frac{5\pi}{6}\)
(D) \(\frac{11\pi}{6}\)
Key:
Sol:
Sol: