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Basic Mathematics

127 Questions Start Allen Test
All Exams Allen Objective Errorless
Q1 Allen 1. TRIGONOMETRY MCQ
As $\theta$ increases from $0^{\circ}$ to $90^{\circ}$ , the value of $\sin \theta : -$
A.
Increases
B.
Decreases
C.
Remains constant
D.
First decreases then increases.
Q2 Allen 1. TRIGONOMETRY MCQ
If $\sin \theta = \frac{\sqrt{2}}{\sqrt{3}}$ and $\theta$ lies in the first quadrant, the value of $\tan \theta$ is:
A.
$\sqrt{2}$
B.
$\frac{1}{\sqrt{2}}$
C.
$\frac{\sqrt{3}}{\sqrt{2}}$
D.
$\frac{1}{2}$
Q3 Allen 1. TRIGONOMETRY MCQ
Find $\theta$ for which $\sin \theta = \cos \theta$ , if $180^{\circ} < \theta < 360^{\circ}$
A.
$135^{\circ}$
B.
$315^{\circ}$
C.
$225^{\circ}$
D.
$150^{\circ}$
Q4 Allen 1. TRIGONOMETRY MCQ
If $\sin\theta_{1} + \sin\theta_{2} + \sin\theta_{3} = 3$ then value of $\cos\theta_{1} + \cos\theta_{2} + \cos\theta_{3}$ is :-
A.
3
B.
0
C.
-3
D.
1
Q5 Allen 1. TRIGONOMETRY MCQ
The greatest value of the function $7 \sin\theta - 24 \cos\theta$ is
A.
12
B.
13
C.
25
D.
17
Q6 Allen 1. TRIGONOMETRY MCQ
The length of hypotenuse of a right angle triangle exceeds the length of its base by 2 cm and exceeds twice the length of altitude by 1 cm. Find length of each side of the triangle.
A.
6, 8, 10
B.
7, 24, 25
C.
8, 15, 17
D.
7, 40, 41
Q7 Allen 2. CALCULUS MCQ
If $x = at^4$ and $y = bt^3$ . Find $\frac{dy}{dx}$
A.
$\frac{4a}{3bt}$
B.
$\frac{3b}{4at}$
C.
$\frac{3a}{4bt}$
D.
$\frac{4b}{3at}$
Q8 Allen 2. CALCULUS MCQ
A metallic disc is being heated. Its area at any time t is given by $A = 5t^{2} + 4t + 8$ . Calculate rate of increase in area at t = 3s.
A.
$30 \, m^{2}/s$
B.
$34 \, m^{2}/s$
C.
$28 \, m^{2}/s$
D.
$20 \, m^{2}/s$
Q9 Allen 2. CALCULUS MCQ
The side of a square is increasing at the rate of 0.1 cm/s. The rate of increase of perimeter w.r.t. time is :
A.
0.2 cm/s
B.
0.4 cm/s
C.
0.6 cm/s
D.
0.8 cm/s
Q10 Allen 2. CALCULUS MCQ
A particle moves along the straight line $3y = x + 5$ . Which coordinate changes at a faster rate?
A.
x-coordinate
B.
y-coordinate
C.
Both x and y coordinates
D.
Data insufficient.
Q11 Allen 2. CALCULUS MCQ
The slope of graph as shown in figure at points 1, 2 and 3 is $m_1$ , $m_2$ and $m_3$ respectively then
A.
$\mathrm{m}_1 > \mathrm{m}_2 > \mathrm{m}_3$
B.
$\mathrm{m}_1 < \mathrm{m}_2 < \mathrm{m}_3$
C.
$\mathrm{m}_1 = \mathrm{m}_2 = \mathrm{m}_3$
D.
$\mathrm{m}_1 = \mathrm{m}_3 > \mathrm{m}_2$
Q12 Allen 2. CALCULUS MCQ
Magnitude of slope of the shown graph.
A.
First increases then decreases
B.
First decreases then increases
C.
Increases
D.
Decreases
Q13 Allen 2. CALCULUS MCQ
Calculate the area enclosed under the curve $f(x) = x^2$ between the limits $x = 2$ and $x = 3$
A.
5
B.
$\frac{19}{3}$
C.
$\frac{17}{3}$
D.
8
Q14 Allen 2. CALCULUS MCQ
Find the value of $\int_{0}^{4}|(1-x)|.dx$
A.
zero
B.
1
C.
4
D.
5
Q15 Allen 3. GEOMETRY & GRAPHS MCQ
The equation of a curve is given as $y = x^{2} + 2 - 3x$ . The curve intersects the y-axis at
A.
(1, 0)
B.
(2, 0)
C.
(0, 2)
D.
No where
Q16 Allen 3. GEOMETRY & GRAPHS MCQ
Two particles A and B are moving in XY-plane. Their positions vary with time t according to relation: $x_{A}(t)=3t,\quad x_{B}(t)=6$ $y_{A}(t)=t,\quad y_{B}(t)=2+3t^{2}$ Distance between two particles at t=2 is:
A.
12
B.
13
C.
5
D.
$\sqrt{12}$
Q17 Allen 3. GEOMETRY & GRAPHS MCQ
The distance between points $(a + b, b + c)$ and $(a - b, c - b)$ is :-
A.
$2\sqrt{a^{2} + b^{2}}$
B.
$2\sqrt{b^{2} + c^{2}}$
C.
$2\sqrt{2}b$
D.
$\sqrt{a^{2} - c^{2}}$
Q18 Allen 3. GEOMETRY & GRAPHS MCQ
A dog is at point A(0, 3, 4)m and cat is at B(5,3,-8)m The dog is free to move but cat is fixed. The minimum distance travelled by dog to catch the cat is :-
A.
25m
B.
12m
C.
13m
D.
20m
Q19 Allen 3. GEOMETRY & GRAPHS MCQ
A particular straight line passes through origin and a point whose abscissa is equal to ordinate. The equation of such straight line is:
A.
y = x
B.
y = 2x
C.
y = -4x
D.
y = - $\frac{x}{4}$
Q20 Allen 3. GEOMETRY & GRAPHS MCQ
If $y = x^{2} + 2x - 3$ , then y-x graph is :-
A.
B.
C.
D.
Q21 Allen 3. GEOMETRY & GRAPHS MCQ
If y = |x - 1|, then y - x graph is :-
A.
B.
C.
D.
Q22 Allen 3. GEOMETRY & GRAPHS MCQ
Frequency f of a simple pendulum depends on its length $\ell$ and acceleration g due to gravity according to the following equation $f = \frac{1}{2\pi}\sqrt{\frac{g}{\ell}}$ . Graph between which of the following quantities is a parabola?
A.
f on the ordinate and $1 / \ell$ on the abscissa
B.
f on the ordinate and $\sqrt{\ell}$ on the abscissa
C.
$f^2$ on the ordinate and $\ell$ on the abscissa
D.
$f^2$ on the ordinate and $1 / \ell$ on the abscissa
Q23 Allen 4. ALGEBRA MCQ
The sum of the series $1 + \frac{1}{3} + \frac{1}{9} + \frac{1}{27} + \cdots\cdots\infty$ is :-
A.
$\frac{8}{7}$
B.
$\frac{6}{5}$
C.
$\frac{2}{3}$
D.
$\frac{3}{2}$
Q24 Allen 4. ALGEBRA MCQ
In the given figure, each box represents a function machine. A function machine illustrates what it does with the input. image.png Which of the following statements is correct?
A.
$z = (2x + 3)^{2}$
B.
$z = 2(x + 3)$
C.
$z = \sqrt{2x + 3}$
D.
$z = \sqrt{2(x + 3)}$
Q25 Allen 5. DEFINITION & TYPES OF VECTOR MCQ
Which of the following statements is false:
A.
Mass, speed and energy are scalars
B.
Momentum, force and torque are vectors
C.
Distance is a vector while displacement is a scalar
D.
A scalar has only magnitude whereas as a vector has both magnitude and direction