Basic Mathematics
127 Questions
Start Allen Test
Q1
Allen
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
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
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
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
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
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
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
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
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
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
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
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
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
CALCULUS
MCQ
Find the value of $\int_{0}^{4}|(1-x)|.dx$
A.
zero
B.
1
C.
4
D.
5
Q15
Allen
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
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
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
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
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
GEOMETRY & GRAPHS
MCQ
If $y = x^{2} + 2x - 3$ , then y-x graph is :-
A.
B.
C.
D.
Q21
Allen
GEOMETRY & GRAPHS
MCQ
If y = |x - 1|, then y - x graph is :-
A.
B.
C.
D.
Q22
Allen
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
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
ALGEBRA
MCQ
In the given figure, each box represents a function machine. A function machine illustrates what it does with the input.
Which of the following statements is correct?
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
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