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Published on: 26/05/2021
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Questions + Answers key
Take MCQ Mathematics Test
1.
Find the derivative of the following functions.
sin(x+a)
2.
Find the derivative of 2x4 + x
3.
Find the point on Y-axis which is at a distance \(\sqrt { 10 } \) from the point (1,2,3)
4.
Find the distance from the origin to (6,6,7).
5.
L is the foot of the perpendicular drawn from a point P(6,7,8) on the XY-plane.What are the coordinates of point L?
6.
Name the octant in which the point lies (-3,-1,6)
7.
Name the octant in which the point lies (4,-2,3)
8.
Find the distance between the following pair of lines.
3x + 4y = 9 and 6x + 8y = 15
9.
Find the equation of the line passing through the point (5, 2) and perpendicular to the line joining the points (2, 3) and (3, - 1).
10.
A straight line moves so that the sum of the reciprocals of its intercepts made on axes is constant. Show that the line passes through a fixed point.
11.
Find the equation of a line, which passes through the point (2, 3) and makes an angle of 30\(^{o}\) with the positive direction of X - axis.
12.
For specifying a straight line, how many geometrical parameters should be known?
13.
If the Sum of n terms of an AP is given by sn = 3n+ 2n2, then find the common difference of the AP.
14.
Find the value of 1+i2+i4+i6+....+i20.
15.
Which of the following are correct?
(i) sin10>sin1
(ii) sin10
(iv) \(sin{ 1 }^{ 0 }=\frac { \pi }{ 180 } sin1\)
16.
If \(sin\theta +cosec\theta =2\), then find the value of \({ sin }^{ 2 }\theta +{ cosec }^{ 2 }\theta .\)
17.
Find the value of tan 3A - tan 2A - tan A.
18.
If \(tan \alpha =\frac { m }{ m+1 } \) and \(tan \beta =\frac { 1 }{ 2m+1 } ,\) then find the value of \(\alpha +\beta \)
19.
Find the value of \(sin \left( { 45 }^{ o }+\theta \right) -cos\left( { 45 }^{ o }-\theta \right) .\)
20.
If n(A) = m and n(B) = n, then find the total number of non-empty relations that can be defined from A to B.
21.
Let U={1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, A={1, 2, 3}, B={2, 4, 6, 7} and C={2, 3, 4, 8}, then find (B \(\cup\) C)', (A \(\cup\) B)'
22.
Write down the contrapositive of the following statements.
If x and y are negative integers, then xy is positive.
23.
Write down the contrapositive of the following statements.
If n is a natural number, then n is an integer.
24.
Rewrite the following statements in the form of conditional statement.
The square of a prime number is not prime.
25.
Rewrite the following statements in the form of conditional statement.
The unit digit of an integer is 0 or 5, if it is divisible by 5.
1.
sin(x+a)=sin x cos a+cos x sina
Ans. cos(x+a)
2.
8x3+1
3.
\(\sqrt{(1-0)^2+(2-y)^2+(3-0)^2}=\sqrt{10}\)
\(\Rightarrow(y-2)^2=0 \Rightarrow y=2\)
Ans. (0,2,0)
4.
Origin = (0,0,0)
5.
(6,7,0)
6.
Third octant
7.
Fourth octant
8.
Given the equations can be rewritten as
3x + 4y - 9 = 0 and 3x + 4y - 15/2 = 0
Since, the slope of these lines are same and hence they are [parallel to each other].
Therefore, the distance between them is given by
\(d=\left|\frac{9-\frac{15}{2}}{\sqrt{3^2+4^2}}\right|
\)
Ans. \(\frac{3}{10}\) unit
9.
Slope of line joining (2, 3) and (3, - 1) is \(m_1 = \frac{-1-3}{3-2} = -4\)
Slope of the line perpendicular to it is \(m_2 = \frac{-1}{-4} = \frac{1}{4}\)
x - 4y + 3 = 0
10.
Given that, \(\frac{1}{a}+\frac{1}{b}=\)constant \(=\frac{1}{k}\) (say)
\(\because \frac{1}{a}+\frac{1}{b}=\frac{1}{k} \Rightarrow \frac{k}{a}+\frac{k}{b}=1\)
So, (k, k) lies on \(\frac{x}{a}+\frac{y}{b}=1\)
11.
m = tan30o = 1/√3
12.
For (i) y = mx + c, number of parameters = 2
(ii) \(\frac{x}{a} + \frac{y}{b} = 1\) , number of parameters = 2
(iii) y - y1 = m(x - x1), number of parameters = 2
(iv) xcosα + ysinα=p , parameter = 2
Ans. Two parameter should be known.
13.
4
14.
\(1+i^2+i^4+\ldots+i^{20}=\frac{1\left(\left(i^2\right)^{11}-1\right)}{\left(i^2\right)-1}=\frac{1(-1-1)}{-1-1}=1\)
15.
(ii) sinl° < sin1
16.
(sinθ+cosecθ)2=4⇒sin2θ+cosec2θ+2=4
⇒sin2θ+cosec2θ=2
17.
tan 3A = tan (2A + A)
\(\Rightarrow \tan 3 A=\frac{\tan 2 A+\tan A}{1-\tan 2 A \tan A}\)
18.
\(\tan (\alpha+\beta)=\frac{\tan \alpha+\tan \beta}{1-\tan \alpha \tan \beta} \)
\( =\frac{\frac{m}{m+1}+\frac{1}{2 m+1}}{1-\frac{m}{m+1} \times \frac{1}{2 m+1}} \)
\( \Rightarrow \tan (\alpha+\beta)=1 \therefore \alpha+\beta=\frac{\pi}{4}\)
19.
\(\sin \left(45^{\circ}+\theta\right)-\cos \left(45^{\circ}-\theta\right)\)
\(=\left(\sin 45^{\circ} \cos \theta+\cos 45^{\circ} \sin \theta\right)-\left(\cos 45^{\circ} \cos \theta+\sin 45^{\circ} \sin \theta\right) =0\)
20.
2mn−1
21.
(B ∪ C)' = {1, 5, 9, 10} and (A ∪ B)' ={5, 8, 9, 10}
22.
( )
If xy is non-positive integer, then either x or y is non-negative integer.
23.
( )
If n is not an integer, then it is not a natural number.
24.
( )
If the number is prime, then its square is not prime.
25.
( )
If an integer is divisible by 5, then its unit digit's are 0 or 5.
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