Available Questions 255 found Page 13 of 13
Standalone Questions
#589
Mathematics
Inverse Trigonometric Functions
MCQ_SINGLE
APPLY
2025
AISSCE(Board Exam)
Competency
1 Marks
The Graph of a trigonomertic finction is as shown. Which of the following will represent graphs of its inverse?(A) A
(B) B
(C) C
(D) D
Key: C
Sol:
Sol:
#584
Mathematics
Inverse Trigonometric Functions
MCQ_SINGLE
APPLY
2025
AISSCE(Board Exam)
Competency
1 Marks
If \(\tan^{-1}(x^{2}-y^{2})=a\), where 'a' is a constant, then \(\frac{dy}{dx}\) is:
(A) \(\frac{x}{y}\)
(B) \(-\frac{x}{y}\)
(C) \(\frac{a}{x}\)
(D) \(\frac{a}{y}\)
Key: A
Sol:
Sol:
#569
Mathematics
Vector Algebra
MCQ_SINGLE
APPLY
2025
AISSCE(Board Exam)
Competency
1 Marks
If \(\vec{a} + \vec{b} + \vec{c} = \vec{0}\), \(|\vec{a}| = \sqrt{37}\), \(|\vec{b}| = 3\) and \(|\vec{c}| = 4\), then the angle between \(\vec{b}\) and \(\vec{c}\) is
(A) \(\dfrac{\pi}{6}\)
(B) \(\dfrac{\pi}{4}\)
(C) \(\dfrac{\pi}{3}\)
(D) \(\dfrac{\pi}{2}\)
Key: C
Sol:
Sol:
#566
Mathematics
Vector Algebra
MCQ_SINGLE
APPLY
2025
AISSCE(Board Exam)
Competency
1 Marks
If the sides AB and AC of \(\triangle ABC\) are represented by vectors \(\hat{j}+\hat{k}\) and \(3\hat{i}-\hat{j}+4\hat{k}\) respectively, then the length of the median through A on BC is:
(A) \(2\sqrt{2}\) units
(B) \(\sqrt{18}\) units
(C) \(\frac{\sqrt{34}}{2}\) units
(D) \(\frac{\sqrt{48}}{2}\) units
Key: C
Sol:
Sol:
The position vector of the midpoint \(D\) is the average of the position vectors of \(B\) and \(C\) relative to \(A\):\[\vec{AD} = \frac{\vec{AB} + \vec{AC}}{2}\]
\[\vec{AD} = \frac{3}{2}\hat{i} + \frac{5}{2}\hat{k}\]
The length of the median is the magnitude of the vector \(\vec{AD}\), denoted as \(|\vec{AD}|\):\[|\vec{AD}| = \sqrt{\left(\frac{3}{2}\right)^2 + \left(0\right)^2 + \left(\frac{5}{2}\right)^2}\]
\[|\vec{AD}| = \frac{\sqrt{34}}{2}\]
#564
Mathematics
Vector Algebra
MCQ_SINGLE
APPLY
2025
AISSCE(Board Exam)
Competency
1 Marks
The respective values of \(|\vec{a}|\) and \(|\vec{b}|\), if given \((\vec{a}-\vec{b})\cdot(\vec{a}+\vec{b})=512\) and \(|\vec{a}|=3|\vec{b}|\), are:
(A) 48 and 16
(B) 3 and 1
(C) 24 and 8
(D) 6 and 2
Key:
Sol:
Sol:
#562
Mathematics
Vector Algebra
MCQ_SINGLE
APPLY
2025
AISSCE(Board Exam)
Competency
1 Marks
A student tries to tie ropes, parallel to each other from one end of the wall to the other. If one rope is along the vector \(3\hat{i}+15\hat{j}+6\hat{k}\) and the other is along the vector \(2\hat{i}+10\hat{j}+\lambda\hat{k}\), then the value of \(\lambda\) is :
(A) 6
(B) 1
(C) \(\frac{1}{4}\)
(D) 4
Key:
Sol:
Sol:
#553
Mathematics
Vector Algebra
MCQ_SINGLE
APPLY
2024
AISSCE(Board Exam)
Competency
1 Marks
The vectors \(\vec{a}=2\hat{i}-\hat{j}+\hat{k}\), \(\vec{b}=\hat{i}-3\hat{j}-5\hat{k}\) and \(\vec{c}=-3\hat{i}+4\hat{j}+4\hat{k}\) represents the sides of
(A) an equilateral triangle
(B) an obtuse-angled triangle
(C) an isosceles triangle
(D) a right-angled triangle
Key:
Sol:
Sol:
#552
Mathematics
Vector Algebra
MCQ_SINGLE
APPLY
2024
AISSCE(Board Exam)
Competency
1 Marks
Let \(\vec{a}\) be any vector such that \(|\vec{a}|=a\) The value of \(|\vec{a}\times\hat{i}|^{2}+|\vec{a}\times\hat{j}|^{2}+|\vec{a}\times\hat{k}|^{2}\) is:
(A) \(a^{2}\)
(B) \(2a^{2}\)
(C) \(3a^{2}\)
(D) 0
Key:
Sol:
Sol:
#551
Mathematics
Vector Algebra
MCQ_SINGLE
APPLY
2024
AISSCE(Board Exam)
Competency
1 Marks
The position vectors of points P and Q are \(\vec{p}\) and \(\vec{q}\) respectively. The point R divides line segment PQ in the ratio 3:1 and S is the mid-point of line segment PR. The position vector of S is:
(A) \(\frac{\vec{p}+3\vec{q}}{4}\)
(B) \(\frac{\vec{p}+3\vec{q}}{8}\)
(C) \(\frac{5\vec{p}+3\vec{q}}{4}\)
(D) \(\frac{5\vec{p}+3\vec{q}}{8}\)
Key:
Sol:
Sol: