Jamia Millia Islamia 2016 Previous Year Questions (PYQs) – Page 5 of 10
A Place for Latest Exam wise Questions, Videos, Previous Year Papers,
Study Stuff for MCA Examinations
Study Stuff for MCA Examinations
Showing 100 questions
The points $A(12,8)$, $B(-2,6)$ and $C(6,0)$ are the vertices of …
1
2
3
4
Solution
$AB^{2}=14^{2}+2^{2}=200,\ BC^{2}=(-8)^{2}+6^{2}=100,\ CA^{2}=(-6)^{2}+(-8)^{2}=100$.
Since $BC=CA$ the triangle is isosceles, and $BC^{2}+CA^{2}=AB^{2}$ ⇒ right-angled at $C$.
If the point $P(x,y)$ is equidistant from $A(a+b,\,b-a)$ and $B(a-b,\,a+b)$, then …
1
2
3
4
Solution
Set distances equal and square:
$(x-a-b)^{2}+(y-b+a)^{2}=(x-a+b)^{2}+(y-a-b)^{2}$.
Simplify ⇒ $-4b(x-a)+4a(y-b)=0 \Rightarrow bx=ay$.
The number of lines that are parallel to $2x+6y+7=0$ and have an intercept of length $10$ between the coordinate axes is …
1
2
3
4
Solution
Parallel lines: $2x+6y+c=0$.
Intercept points: $( -\tfrac{c}{2},0)$ and $(0,-\tfrac{c}{6})$.
Distance between them $=\sqrt{\left(\tfrac{c}{2}\right)^{2}+\left(\tfrac{c}{6}\right)^{2}}
=|c|\,\dfrac{\sqrt{10}}{6}$.
Set equal to $10$ ⇒ $|c|=6\sqrt{10}$ ⇒ two values $c=\pm6\sqrt{10}$.
The four lines $ax\pm by\pm c=0$ enclose a …
1
2
3
4
Solution
They form two pairs of parallel lines with slopes $\pm \dfrac{a}{b}$ (not necessarily perpendicular).
Under unequal scaling they form a rectangle (a square only if $a=b$).
The area bounded by the lines $y=|x|-1$ and $y=-|x|+1$ is …… square unit.
1
2
3
4
Solution
Vertices are $(0,1)$, $(1,0)$, $(0,-1)$, $(-1,0)$ — a rhombus with diagonals $2$ and $2$.
Area $=\dfrac{d_{1}d_{2}}{2}=\dfrac{2\times2}{2}=2$.
The number of vectors of unit length perpendicular to vectors $\vec{a} = \hat{i} + \hat{j}$ and $\vec{b} = \hat{k} + \hat{j}$ is …
1
2
3
4
Solution
$\vec{a} = \hat{i} + \hat{j}$ and $\vec{b} = \hat{k} + \hat{j}$.
The vector perpendicular to both is $\vec{a} \times \vec{b}$.
$\vec{a} \times \vec{b} =
\begin{vmatrix}
\hat{i} & \hat{j} & \hat{k} \\
1 & 1 & 0 \\
0 & 1 & 1
\end{vmatrix}
= \hat{i}(1 - 0) - \hat{j}(1 - 0) + \hat{k}(1 - 0) = \hat{i} - \hat{j} + \hat{k}$.
Two unit vectors along $\pm(\hat{i} - \hat{j} + \hat{k})$ are possible.
The angle between vectors $\vec{a} \times \vec{b}$ and $\vec{b} \times \vec{a}$ is …
1
2
3
4
Solution
$\vec{b} \times \vec{a} = -(\vec{a} \times \vec{b})$.
Hence, angle between them is $180^{\circ}$.
Two dice are thrown. The probability that the sum of the numbers on two dice is 7 is …
1
2
3
4
Solution
Total outcomes = $6 \times 6 = 36$.
Favorable outcomes for sum = 7 are $(1,6),(2,5),(3,4),(4,3),(5,2),(6,1)$ → 6 outcomes.
Probability $= \dfrac{6}{36} = \dfrac{1}{6}$.
A single letter is selected at random from the word “JAMIA”. The probability that it is a vowel is …
1
2
3
4
Solution
Letters in “JAMIA” = J, A, M, I, A → total 5 letters.
Vowels = A, I, A → 3 vowels.
Probability $= \dfrac{3}{5}$.
One die and a coin are tossed simultaneously. The probability of getting 6 on die and head on coin is …
1
2
3
4
Solution
Probability of 6 on die $= \dfrac{1}{6}$,
Probability of head on coin $= \dfrac{1}{2}$.
Required probability $= \dfrac{1}{6} \times \dfrac{1}{2} = \dfrac{1}{12}$.
Jamia Millia Islamia
Online Test Series, Information About Examination,
Syllabus, Notification
and More.
View More
Jamia Millia Islamia
Online Test Series, Information About Examination,
Syllabus, Notification
and More.
View More
Ask Your Question or Put Your Review.
