# 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
(c) commutative law

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
(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
(a) 3s2

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

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
(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
(c) -10

Question 7.
If A = $$\left[\begin{array}{lll} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array}\right]$$ then A2 =

(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
(c) 24

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
(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
(b) 3sin2x cos x

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

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

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

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

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

Question 16.
$$\frac{d}{d x}(\sqrt{\tan x})=$$

(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
(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$$\vec{j}$$
(a) 0

Question 19.
$$\int_{a}^{b} e^{k x} d x=$$

(c)

Question 20.
∫tan2
(a) $$\frac{\tan ^{3} x}{e}+k$$
(b) 2tan xsec2x + k
(c) tan x – x + k
(d) 3tan3x + k
(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
(a) sin-1 $$\frac{63}{65}$$

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
(a) cos-1$$\frac{12}{13}$$

Question 23.
A = $$\left[\begin{array}{ll} 3 & -2 \\ 4 & -2 \end{array}\right]$$ ⇒ A2 =

(c)

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

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

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

Question 30.
tan-1 x + tan-1 y is equal to

(c)

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

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

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

Question 34.
2tan-1x =

(b)

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

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

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

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

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

Question 40.
$$\frac{d}{d x}$$ (cotx) =
(a) cosec2x
(b) -cosec2x
(c) cot x cosec x
(d) cot x
(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) $$\frac{x^{2}+y^{2}+z^{2}}{z}$$
(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

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) $$\vec{k}$$
(d) $$\vec{k}$$

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