# MATHEMATICS  ( New Syllabus )-2022PART-B

$~1.~$ Choose the correct answer from the given alternatives ( Alternatives are to be noted ) : $~~1 \times 10=10$

$~(i)~~$ An unbiased coin is tossed for $~3~$ times. Then the probability of getting only one head is

$~(a)~\frac 12~~~(b)~\frac 58~~~(c)~\frac 34~~~(d)~\frac 38$

OR

A coin is tossed $~10~$ times . The probability of getting head $~6~$ times is :

$~(a)~{}^{10}C_5 ~\cdot \frac{1}{2^{10}}~~~(b)~~{}^{10}C_3 ~\cdot \frac{1}{2^{10}}~~~\\(c)~{}^{10}C_4 ~\cdot \frac{1}{2^{10}}~~~(d)~{}^{10}C_8 ~\cdot \frac{1}{2^{10}}$

$~(ii)~~A=(1,0,2)~~$ and $~~B=(0,1,1)~,~$ then direction cosines of the line $~AB~$ are

$~(a)~~1,-1,1~~~(b)~~\frac{1}{\sqrt 3},-\frac{1}{\sqrt 3}, \frac{1}{\sqrt 3}~\\~(c)~~-\frac{1}{\sqrt 3}, \frac{1}{\sqrt 3},\frac{1}{\sqrt 3}~~(d)~~\frac{1}{\sqrt 2},-\frac{1}{\sqrt 2},\frac{1}{\sqrt 2}$
OR

$~\vec{a}=\hat{i}+3\hat{j}-\hat{k}~,~$ and $~\vec{b}=2\hat{i}+6\hat{j}+ \lambda \hat{k}~.$ If $~\vec{a}~$ and $~\vec{b}~$ vectors are parallel, then the value of $~\lambda~$ is :

$~(a)~3~~(b)~-6~~(c)~-3~~(d)~-2.$

$~(iii)~~f(x)=\log(3x+1)~,~$ then the value of $~f''(1)~$ is

$~(a)~~\frac{9}{16}~~~(b)~-\frac{9}{16}~~~(c)~\frac 94~~~(d)~-\frac 94$

OR

If $~f(x)=\frac{\sin x}{x}~(x \neq 0)~$ is continuous at $~x=0~,~$ then the value of $~f(0)~$ will be

$~(a)~~0~~~(b)~1~~~(c)~\pi~~~(d)~\frac{\pi}{2}.$

#$~(iv)~~A=\begin{pmatrix} a \\6 \end{pmatrix}~$ and $~~B=\begin{pmatrix} 3 \\b \end{pmatrix}~~$ and $~~A=B~,~$ then $~(a,b)~$ is equal to $~~(a)~(3,6)~~~(b)~(6,3)~~~(c)~(6,6)~~~(d)~(3,3).$

OR

#$~a+b+c=0~,~$ then the value of $~\begin{vmatrix} a&b & c \\ b & c & a \\ c & a & b \\ \end{vmatrix}~$ is $~(a)~1~~~(b)~a~~~(c)~0~~~(d)~-1.$

$~(v)~~$ The domain in which the functions $~~f(x)=3x^2-2x~~$ and $~~g(x)=3(3x-2)~~$ will be equal to

$~(a)~~\{1,\frac 23\}~~~(b)~\{1,3\}~~~(c)~\{\frac 23,3\}~~~(d)~\{\frac 23,0\}.$

OR

Let $~A=\{1,2,3\}~~$ and $~R~$ be a relation defined on $~A~,~$ such that $~~R=\{(1,1),(1,2),(2,1)\}~;~$ then the relation $~R~$ will be

$~(a)~$ Reflexive $~~(b)~$ Symmetric $~~(c)~$ Transitive $~~~(d)~$ none of these.

$~(vi)~~P(B)=\frac{9}{13}~,P(A \cap B)=\frac{4}{13},~$ then value of $~P(A/B)~$ is

$~(a)~\frac 29~~(b)~\frac{4}{13}~~(c)~\frac{9}{13}~~(d)~\frac 49$

$~(vii)~~$ The equation of the plane with intercepts $~2,3,4~$ units on the $~x~$-axis, $~~y-$axis and $~~z-$axis respectively is

$~~(a)~~6x+4y+3z=12\\~~(b)~4x+3y+6z=12\\~~(c)~~3x+6y+4z=12\\~~(d)~6x+2y+3z=12$

$~(viii)~~$ The value of the function $~f(x)=4x-x^2-3~$ will be maximum when

$~(a)~~x=3~~~(b)~~x=2~~~(c)~~x=-2~~~(d)~~x=-3.$

$~(ix)~$ The degree of the differential equation $~~\frac{d^3y}{dx^3}+y=\sqrt{1+\frac{dy}{dx}}~$ is

$~(a)~~1~~~(b)~~2~~~(c)~~3~~~(d)~~4$

OR

The value of  $~~\int{e^{a\log_ex}~dx}~$ will be $~~(a \neq -1)$

$~(a)~\frac 1a e^{a\log_ex}+c~~ ~(b)~\frac 1x+c~~ \\~(c)~ax^{a-1}+c~~ ~(d)~\frac{x^{a+1}}{a+1}+c$

$~(x)~$ The value of $~~\tan\left(\frac{\pi}{2}-\tan^{-1}\frac 13\right)~$ is equal to

$~~(a)~\frac 13~~~(b)~3~~~(c)~\frac 12~~~(d)~\frac 23.$

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HIGHER SECONDARY  MATHS COMPLETE SOLUTIONS  (2015-2019) [ WBCHSE ]

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