Bihar Board 12th Maths Objective Important Questions Part 1

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Bihar Board 12th Maths Objective Important Questions Part 1

Question 1.
Law ab + = b + a is called.
(a) closure law
(b) Associative law
(c) commutative law
(d) distributive law
Answer:
(c) commutative law

Bihar Board 12th Maths Objective Important Questions Part 1

Question 2.
Principal value of sin-1\(\frac{1}{\sqrt{2}}\) =
(a) \(\frac{\pi}{4}\)
(b) \(\frac{3 \pi}{4}\)
(c) \(\frac{5 \pi}{4}\)
(d) None of these
Answer:
(a) \(\frac{\pi}{4}\)

Question 3.
If y = e3logex then find \(\frac{d y}{d x}\) is equal to:
(a) 3x2
(b) 2log x
(c) \(\frac{3 y}{x}\)
(d) 3xy
Answer:
(a) 3s2

Question 4.
sin-1x + cos-1x =
(a) \(\frac{\pi}{4}\)
(b) π
(c) 0
(d) \(\frac{\pi}{4}\)
Answer:
(d) \(\frac{\pi}{4}\)

Bihar Board 12th Maths Objective Important Questions Part 1

Question 5
If A is skew symmetric matrix of oder 2 then det (A) is of the form :
(a) a2
(b) a2 – 1
(c) a2 + 1
(d) None of these
Answer:
(a) a2

Question 6.
If A = \(\left[\begin{array}{rr}
3 & 4 \\
1 & -2
\end{array}\right]\) then, |A| =
(a) 0
(b) 10
(c) -10
(d) -2
Answer:
(c) -10

Question 7.
If A = \(\left[\begin{array}{lll}
1 & 0 & 0 \\
0 & 1 & 0 \\
0 & 0 & 1
\end{array}\right]\) then A2 =
Bihar Board 12th Maths Objective Important Questions Part 1 1
Answer:
(d)

Question 8.
\(\left|\begin{array}{lll}
4 & 0 & 0 \\
0 & 3 & 0 \\
0 & 0 & 2
\end{array}\right|\) =
(a) 0
(b) 12
(c) 24
(d) 9
Answer:
(c) 24

Bihar Board 12th Maths Objective Important Questions Part 1

Question 9.
\(\left|\begin{array}{ccc}
x & y & z \\
x^{2} & y^{2} & z^{2} \\
-x & -y & -z
\end{array}\right|=\)
(a) x3 + y3 + z3
(b) x2 + y2 + z2
(c) x + y + z
(d) 0
Answer:
(d) 0

Question 10.
\(\frac{d}{d x}\left(\sin ^{3} x\right)=\)
(a) \(\frac{\sin ^{3} x}{3}\)
(b) 3sin2x cos x
(c) sin 2x
(d) cos2 x
Answer:
(b) 3sin2x cos x

Question 11.
\(\frac{d}{d x}\) =
(a) 2e2x
(b) e2x
(c) \(\frac{e^{3 x}}{3}\)
(d) 3e3x
Answer:
(a) 2e2x

Question 12.
\(\frac{d}{d x}\) (5 – cos x) =
(a) 5+sinx
(b) sinx
(c) 5 – sin x
(d) cosx
Answer:
(b) sinx

Bihar Board 12th Maths Objective Important Questions Part 1

Question 13.
\(\frac{d}{d x}\) (sin(logx)] =
(a) \(\frac{1}{x}\) cos (logx)
(b) cosx(logx)
(c) xcosx (logx)
(d) \(\frac{\sin (\log x)}{x}\)
Answer:
(a) \(\frac{1}{x}\) cos (logx)

Question 14.
\(\frac{d}{d x}\) [sec2x – tan2 x] =
(a) 1
(b) 0
(c) 2sec2x
(d) 2tan2x
Answer:
(b) 0

Question 15.
\(\frac{d}{d x}\) (l2 + m2 + n2) =
(a) 0
(b) 1
(c) 2
(d) 3
Answer:
(a) 0

Bihar Board 12th Maths Objective Important Questions Part 1

Question 16.
\(\frac{d}{d x}(\sqrt{\tan x})=\)
Bihar Board 12th Maths Objective Important Questions Part 1 2
Answer:
(c)

Question 17.
\(\mathbf{5} \overrightarrow{\boldsymbol{i}} \times \mathbf{2} \overrightarrow{\boldsymbol{j}}=\)
(a) 10 \(\vec{i}\)
(b) 10 \(\vec{j}\)
(c) 10 \(\vec{k}\)
(d) 0
Answer:
(c) 10 \(\vec{k}\)

Question 18.
\(\frac{d}{d x}(\vec{i} \times \vec{i})=\)
(a) 0
(b) 1
(c) 2\(\vec{i}\)
(d) 2\(\vec{j}\)
Answer:
(a) 0

Question 19.
\(\int_{a}^{b} e^{k x} d x=\)
Bihar Board 12th Maths Objective Important Questions Part 1 3
Answer:
(c)

Question 20.
∫tan2
(a) \(\frac{\tan ^{3} x}{e}+k\)
(b) 2tan xsec2x + k
(c) tan x – x + k
(d) 3tan3x + k
Answer:
(c) tan x – x + k

Question 21.
sin-1\(\frac{4}{5}\) + sin-1\(\frac{5}{13}\) =
If A be a matrix then, (A’)’ equals .
(a) sin-1 \(\frac{63}{65}\)
(b) sin-1 \(\frac{16}{65}\)
(e) sin-1 \(\frac{3}{65}\)
(d) 0
Answer:
(a) sin-1 \(\frac{63}{65}\)

Bihar Board 12th Maths Objective Important Questions Part 1

Question 22.
sin-1 \(\frac{3}{5}\) – sin-1\(\frac{16}{65}\)
(a) cos-1\(\frac{12}{13}\)
(b) cos-1\(\frac{5}{13}\)
(c) cos-1\(\frac{1}{2}\)
(d) 0
Answer:
(a) cos-1\(\frac{12}{13}\)

Question 23.
A = \(\left[\begin{array}{ll}
3 & -2 \\
4 & -2
\end{array}\right]\) ⇒ A2 =
Bihar Board 12th Maths Objective Important Questions Part 1 4
Answer:
(c)

Question 24.
If A be a matrix then, (A’)’ equals
(a) A’
(b) A
(c) A-1
(d) none of these
Answer:
(b) A

Question 25.
If A and B are matrices, compatible for addition then, (A + B)’ equal
(a) A + B
(b) A’ + B
(c) A + B’
(d) A’ + B’
Answer:
(d) A’ + B’

Question 26.
If A and B art- matrices compatible for multiplication then (AB)’ is equal to
(a) A’B’
(b) A’B
(c) B’A
(d) B’A’
Answer:
(d) B’A’

Question 27.
If A be a singular matrix then |Aj-=
(a) 1
(b) -1
(c) 0
(d) none of these
Answer:
(c) 0

Bihar Board 12th Maths Objective Important Questions Part 1

Question 28.
For a symmetric matrix A, |A| is equal to
(a) 0
(b) 1
(c) 2A
(d) none of these
Answer:
(c) 2A

Question 29.
For a skew symmetric matrix A, A + A’ is equal to
(a) 0
(b) 1
(c) 2A
(d) none of these
Answer:
(d) none of these

Question 30.
tan-1 x + tan-1 y is equal to
Bihar Board 12th Maths Objective Important Questions Part 1 5
Answer:
(c)

Question 31.
sin-1 + cos-1x =
(a) 0
(b) 1
(c) \(\frac{\pi}{2}\)
(d) π
Answer:
(c) \(\frac{\pi}{2}\)

Question 32.
sec-1 + cosec-1x =
(a) 0
(b) 1
(c) \(\frac{\pi}{2}\)
(d) π
Answer:
(c) \(\frac{\pi}{2}\)

Question 33.
tan-1 + cot-1x =
(a) 0
(b) 1
(c) 2π
(d) \(\frac{\pi}{2}\)
Answer:
(d) \(\frac{\pi}{2}\)

Question 34.
2tan-1x =
Bihar Board 12th Maths Objective Important Questions Part 1 6
Answer:
(b)

Bihar Board 12th Maths Objective Important Questions Part 1

Question 35.
\(\frac{d}{d x}\) (sin x) =
(a) cos x
(b) sin x
(c) tan x
(d) -cos x
Answer:
(a) cos x

Question 36.
\(\frac{d}{d x}\)(tanx) = dx
(a) sec x
(b) sec x cot x
(c) sec2x
(d) cot x
Answer:
(c) sec2x

Question 37.
\(\frac{d}{d x}\)(sin2x) =
(a) \(\frac{\sin ^{3} x}{3}\)
(b) cos2x
(c) sin2x
(d) -cox2x
Answer:
(c) sin2x

Question 38.
\(\frac{d^{2}}{d x^{2}}\)(x2) =
(a) 2x
(b) \(\frac{x^{3}}{3}\)
(c) 2
(d) 1
Answer:
(c) 2

Bihar Board 12th Maths Objective Important Questions Part 1

Question 39.
\(\frac{d^{3}}{d x^{3}}\)(x2) =
(a) \(\frac{x^{3}}{3}\)
(b) 2x
(c) 2
(d) 0
Answer:
(d) 0

Question 40.
\(\frac{d}{d x}\) (cotx) =
(a) cosec2x
(b) -cosec2x
(c) cot x cosec x
(d) cot x
Answer:
(b) -cosec2x

Question 41.
यदि  \(\vec{r}=x \vec{i}+y \vec{j}+z \vec{k}\) तो \(\vec{r}=x \vec{i}+y \vec{j}+z \vec{k}\) =
(a) x2 + y2 + z2
(b) \(\sqrt{x^{2}+y^{2}+z^{2}}\)
(c) x + y + z
(d) \(\frac{x^{2}+y^{2}+z^{2}}{z}\)
Answer:
(b) \(\sqrt{x^{2}+y^{2}+z^{2}}\)

Question 42.
\(\vec{a} \cdot \vec{b}=\)
(a) ab cos θ
(c) ab tan θ
(b) ab sin θ
(d) ab sec θ
Ans.
(a) ab cos θ

Bihar Board 12th Maths Objective Important Questions Part 1

Question 43.
\(\vec{a} \times \vec{b}=\)
(a) ab cosθ
(b) ab sinθ
(c) \(a b \sin \theta \hat{n}\)
(d) \(a b \cos \theta \hat{n}\)
Ans.
(d) \(a b \cos \theta \hat{n}\)

Question 44.
\(\vec{i} \times \vec{j}=\)
(a) 1
(b) 0
(c) \(\vec{j}\)
(d) \(\vec{k}\)
Answer:
(d) \(\vec{k}\)

Question 45.
\(\vec{k} \times \vec{k}=\)
(a) 0
(b) 1
(c) \(\overrightarrow{0}\)
(d) \(\overrightarrow{z}\)
Answer:

Question 46.
\(\vec{i} \times \vec{j}=\)
(a) \(\overrightarrow{k}\)
(b) 0
(c) 1
(d) \(\overrightarrow{z}\)
Answer:
(b) 0

Bihar Board 12th Maths Important Questions