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Questions asked by vaishali.a
Questions
100
questions
0
answers selected
Prove that \[sin^{-1} \frac{8}{17} +sin^{-1} \frac{3}{5} =tan^{-1} \frac{77}{36}\]
cbse
class12
bookproblem
ch2
misc
q4
p51
medium
sec-b
math
asked
Nov 29, 2012
1
answer
Prove that \[cos^{-1} \frac {4}{5} +cos^{-1} \frac{12}{13}=cos^{-1} \frac{33}{65}\]
cbse
class12
bookproblem
ch2
misc
q5
p51
medium
sec-b
math
asked
Nov 29, 2012
1
answer
Prove that \[ cos^{-1} \frac {12}{13} +sin^{-1} \frac{3}{5}=sin^{-1} \frac{56}{65}\]
cbse
class12
bookproblem
ch2
misc
q6
p51
medium
sec-b
math
asked
Nov 29, 2012
1
answer
What does $\sin^{-1} \frac{5}{13}+\cos^{-1} \frac {3}{5}$ reduce to?
cbse
class12
ch2
q7
medium
additionalproblem
sec-b
math
asked
Nov 29, 2012
1
answer
Prove that \[tan^{-1} \frac{1}{5}+ tan^{-1} \frac{1}{7}+tan^{-1}\frac{1}{3}+tan^{-1} \frac{1}{8}= \frac{\pi}{4}\]
cbse
class12
bookproblem
ch2
misc
q8
p51
sec-c
medium
math
asked
Nov 29, 2012
1
answer
Prove that \[tan^{-1} \sqrt{x} = \frac{1}{2} cos^{-1} \;\; \bigg(\frac{1-x}{1+x}\bigg), x\in [0,1]\]
cbse
class12
bookproblem
ch2
misc
q9
p52
medium
sec-b
math
asked
Nov 29, 2012
1
answer
prove that \[tan^{-1} \left ( \frac {{\sqrt {1+x}}-{\sqrt {1-x}}}{{\sqrt {1+x}}+{\sqrt {1-x}}} \right ) = \frac {\pi}{4} -\frac{1}{2} cos^{-1}x,-\frac{1}{\sqrt2} \leq x \leq 1 \]
cbse
class12
bookproblem
ch2
misc
q11
p52
sec-b
medium
modelpaper
2012
q12
math
asked
Nov 29, 2012
1
answer
Prove that \[cot^{-1} \left ( \frac {{\sqrt {1+sinx}}+{\sqrt {1-sinx}}}{{\sqrt {1+sinx}}-{\sqrt {1-sinx}}} \right ) = \frac {x}{2} , x \in \left ( 0, \frac{\pi}{4} \right )\]
cbse
class12
bookproblem
ch2
misc
q10
p52
medium
sec-b
math
asked
Nov 29, 2012
1
answer
Prove that \[\frac{9 \pi}{8} - \frac{9}{4} sin ^{-1}\frac{1}{3}= \frac{9}{4} sin^{-1}\frac{2\sqrt 2}{3}\]
cbse
class12
bookproblem
ch2
misc
q12
p52
difficult
sec-b
math
asked
Nov 29, 2012
1
answer
Solve the following \[2tan^{-1} (cos x) = tan^{-1} (2\, cosec\, x) \]
cbse
class12
bookproblem
ch2
misc
q13
p52
medium
sec-b
math
asked
Nov 29, 2012
1
answer
Solve the following $tan^{-1} \frac{1-x}{1+x} =\frac{1}{2} tan^{-1} x,(x>0)$
cbse
class12
bookproblem
ch2
misc
q14
p52
sec-b
medium
math
asked
Nov 29, 2012
2
answers
Choose the correct answer $\sin (\tan^{-1}x), |x| <1 $ is equal to
cbse
class12
bookproblem
ch2
misc
q15
p52
sec-a
easy
math
asked
Nov 28, 2012
1
answer
Choose the correct answer. If \(\sin^{-1}(1-x) -2 \sin^{-1} x=\large\frac {\pi}{2}, \) then \(x\) is equal to
cbse
class12
bookproblem
ch2
misc
q16
p52
medium
sec-b
math
asked
Nov 28, 2012
1
answer
What is the value of: \[tan^{-1} \bigg( \frac {x}{y} \bigg) -tan^{-1} \frac {x-y}{x+y} \]
cbse
class12
bookproblem
ch2
misc
q17
p52
medium
sec-b
math
asked
Nov 28, 2012
1
answer
Solve the following $\tan^{-1} \sqrt{3} -sec^{-1} (-2)$:
cbse
class12
bookproblem
ch2
sec1
q14
p42
medium
sec-a
math
asked
Nov 28, 2012
2
answers
If $ \sin^{-1} x=y$ then:
cbse
class12
bookproblem
ch2
sec1
q13
p42
easy
sec-a
math
asked
Nov 28, 2012
1
answer
Find the value of the following:\[cos^{-1} \frac {1} {2} +2 sin^{-1}\frac {1} {2} \]
cbse
class12
bookproblem
ch2
sec1
q12
p42
medium
sec-b
math
asked
Nov 28, 2012
2
answers
Find the value of the following: \[ tan^{-1} (1) \;+ \; cos^{-1} \frac {-1} {2} + sin^{-1} \frac {-1} {2} \]
cbse
class12
bookproblem
ch2
sec1
q11
p42
easy
sec-b
math
asked
Nov 28, 2012
2
answers
Find the principal values of the following: <br> $ \mathrm{cosec}^{-1} (-\sqrt 2) $
cbse
class12
bookproblem
ch2
sec1
q10
p42
easy
sec-a
math
asked
Nov 28, 2012
2
answers
Find the principal value of the following: $cos^{-1} \bigg( -\frac {1} {\sqrt 2} \bigg) $
cbse
class12
bookproblem
ch2
sec1
q9
p42
sec-a
math
asked
Nov 28, 2012
2
answers
Find the principal values of the following : $\cot^{-1} (\sqrt 3) $
cbse
class12
bookproblem
ch2
sec1
q8
p42
sec-a
math
asked
Nov 28, 2012
2
answers
Find the principal values of the following: $sec^{-1} \bigg( \frac {2} {\sqrt 3} \bigg) $
cbse
class12
bookproblem
ch2
sec1
q7
p42
sec-a
math
asked
Nov 28, 2012
2
answers
Find the principal values of the following: $tan^{-1} (-1)$
cbse
class12
bookproblem
ch2
sec1
q6
p41
sec-a
math
asked
Nov 28, 2012
2
answers
Find the principal values of the following: $cos^{-1} \bigg(-\frac {1} {2} \bigg ) $
cbse
class12
bookproblem
ch2
sec1
q5
p41
easy
sec-a
math
asked
Nov 28, 2012
2
answers
Find the principal values of the following: <br>$ tan^{-1} (-\sqrt3)$
cbse
class12
bookproblem
ch2
sec1
q4
p41
easy
sec-a
math
asked
Nov 28, 2012
2
answers
Find the principal values of the following: $cosec^{-1} (2) $
cbse
class12
bookproblem
ch2
sec1
q3
p41
easy
sec-a
math
asked
Nov 28, 2012
1
answer
Find the principal values of the following: <br> $cos^{-1} \bigg(\large\frac { \sqrt 3} {2}\bigg)$
cbse
class12
bookproblem
ch2
sec1
q2
p41
easy
sec-a
math
asked
Nov 28, 2012
2
answers
Find the principal values of the following: <br> $ sin^{-1} \bigg( -\frac {1} {2}\bigg) $
cbse
class12
bookproblem
ch2
sec1
q1
p41
easy
sec-a
math
asked
Nov 28, 2012
2
answers
Number of binary operations on the set $\{a, b\}$ are
cbse
class12
bookproblem
ch1
misc
q19
p31
sec-a
math
asked
Nov 27, 2012
1
answer
Let \(f : R \to R\) be the Signum Function defined as \[ f(x) = \left \{ \begin {array} {1 1} 1, & \quad \text { x $>$ 0} \\ 0, & \quad \text { x $=$0} \\-1, & \quad \text { x $<$0} \\ \end {array} \right. \] and \(g:R \to R\) be the greatest Integer Function given by \(g(x)=[x]\) where \([x]\) is a greatest integer less thar or equal to \(x\) Then, does \(fog\) and \(gof\) coincide in \((0,1]\)?.
cbse
class12
bookproblem
ch1
misc
q18
p31
sec-b
math
asked
Nov 27, 2012
1
answer
Let $A = \{1, 2, 3\}$. Then number of equivalence relations containing $(1, 2)$ is
cbse
class12
bookproblem
ch1
misc
q17
p30
sec-a
math
asked
Nov 27, 2012
1
answer
Let $ A = \{1, 2, 3\}$. Then number of relations containing $(1, 2)\;$ and $\;(1, 3)$ which are reflexive and symmetric but not transitive is
cbse
class12
bookproblem
ch1
misc
q16
p30
sec-a
math
asked
Nov 27, 2012
1
answer
Let $A=\{\text{-1,0,1,2}\}$ and $B=\{\text{-4,-2,0,2}\} and $f,g: A $\rightarrow B$ be functions defined by $f(x)=x^2-x, \;x \in A$ and $g(x)=2 |x- \frac {1} {2} | -1,\; x \in A$. Are $f$ and $g$ equal?
cbse
class12
bookproblem
ch1
misc
q15
p30
sec-b
math
asked
Nov 26, 2012
1
answer
Define a binary operation \(\ast\) on the set \(\{0, 1, 2, 3, 4, 5\}\) as \[ a \ast b = \left\{ \begin{array} {1 1} a+b, & \quad \text{ if a$+$b $<$ 6} \\ a+b-6, & \quad \text{ if a+b $\geq$ 6} \\ \end{array} \right. \] Show that zero is the identity for this operation and each element $a\neq0$ of the set is invertible with $6-a$ being the inverse of $a$.
cbse
class12
bookproblem
ch1
misc
q14
p30
sec-b
medium
math
asked
Nov 22, 2012
1
answer
Given a non-empty set \( X,\) let \(\ast :\; P(X)\; \times\; P(X) \to P(X) \) be defined as \(A \ast B = \; ( A-B)\; \cup \; (B-A),\; \forall A, B \in \; P(X).\). Show that the empty set \(\emptyset \) is the identity for the operation $\ast$ and all the elemnets \(A\) of \( P(X) \) are invertible with \( A^{-1} \;= A\).
cbse
class12
bookproblem
ch1
misc
q13
p30
medium
sec-b
math
asked
Nov 22, 2012
1
answer
Consider the binary operation $\ast :\; R \times R \rightarrow R$ and $o :\; R \times R \rightarrow R$ defined as $a \ast b = | a \text{-b}|$ and \(\;a\;o\;b=a, \forall a,\;b \in R.\) Show that \(\ast\) is commutative but not associative, \(o\) is associative but not commutative. Further, show that \(\forall\; a,\; b,\; c \in R,\; a\; \ast\; (b\; o\; c) = (a \ast b) \;o\; (a \ast c)\). [If it is so, we say that the operation $\ast$ distributes over $o$]. Does $o$ distribute over? Justify your answer.
cbse
class12
bookproblem
ch1
misc
q12
p30
sec-b
medium
math
asked
Nov 22, 2012
1
answer
Find the number of all onto functions from the set $\{1, 2, 3, ... , n\}$ to itself.
cbse
class12
bookproblem
ch1
misc
q10
p30
sec-a
math
asked
Nov 22, 2012
1
answer
Given a non-empty set \(X\), consider the binary operation \(\ast : P(X) × P(X) \to P(X)\) given by \(A \ast B=A \cap B\; \forall A, \) \( B \;in\; P(X),\) where \(P(X)\) is the power set of \(X\). Show that \(X\) is the identity element for this operation and \(X\) is the only invertible element in \(P(X)\) with respect to the operation \(\ast\).
cbse
class12
bookproblem
ch1
misc
q9
p30
sec-a
math
asked
Nov 22, 2012
1
answer
Let $S=\{a,b,c\}\;$ and$ \;T = \{1,2,3\}$. Find the inverse of the following function \(F\) from \(S\) to \(T\), if it exists - \[\;\; F=\{(a,3), (b,2), (c,1)\}\]
cbse
class12
bookproblem
ch1
misc
q11
q11-1
p30
easy
sec-a
math
asked
Nov 22, 2012
1
answer
Given a non empty set $X$, consider $P(X)$ which is the set of all subsets of $X$. Define the relation $R$ in $P(X)$ as follows: For subsets $A,\; B$ in $ P(X),\; ARB$ if and only if $ A \subset B $ Is $R$ an equivalence relation on $P(X)$?
cbse
class12
bookproblem
ch1
misc
q8
p29
sec-a
math
asked
Nov 22, 2012
1
answer
Give examples of two functions \(f: N \to N\) and \(g: N \to N\) such that \(g\;o\;f \) is onto but \(f\) is not onto.
cbse
class12
bookproblem
ch1
misc
q7
p29
sec-a
math
asked
Nov 21, 2012
1
answer
Give examples of two functions \(f : N \to Z \) and \(g: Z \to Z\) such that \(g\;o\;f\) is injective but \(g\) is not injective.
cbse
class12
bookproblem
ch1
misc
q6
p29
sec-a
math
asked
Nov 21, 2012
1
answer
Show that the function \(f : R \to R\) given by \(f (x) = x^3\) is injective.
cbse
class12
bookproblem
ch1
misc
q5
p29
sec-a
easy
math
asked
Nov 21, 2012
1
answer
Show that the function f:R $\rightarrow \{ x \in$ R:-1$<$x$<$1 $\}$ defined by $f(x) = \frac {x} { 1+|\;x\;|}, x \in R$ is one-one and onto function.
cbse
class12
bookproblem
ch1
misc
q4
p29
sec-a
math
asked
Nov 21, 2012
1
answer
If $(f:R \to R)$ is defined by $f(x) = x^2$ - $3x+2$. Find $f(f(x))$:
cbse
class12
bookproblem
ch1
misc
q3
p29
sec-a
easy
math
asked
Nov 21, 2012
1
answer
Let \(f:W \to W\) be defined as $f(n)=n$ - $1$, if \(n\;is\;odd\;and\; f(n)=n+1,\;if\;n\;is\; even.\) Show that \(f\) is invertible. Find the inverse of \(f\). Here, \(W\) is the set of all whole numbers.
cbse
class12
bookproblem
ch1
misc
q2
p29
medium
sec-b
math
modelpaper-2014
q15
asked
Nov 21, 2012
1
answer
Let \(f:R \to R\) be defined as \(f(x)=10x+7.\)Find the function \(g:R \to R\) such that \(g\;o\;f = f\;o\;g = I_R.\)
cbse
class12
bookproblem
ch1
misc
q1
p29
sec-b
easy
modelpaper
2012
q11
math
asked
Nov 21, 2012
1
answer
Consider a binary operation $\ast$ on $N$ defined as $a \ast b = a^3 + b^3$. Choose the correct answer:
cbse
class12
bookproblem
ch1
sec4
q13
p26
easy
sec-a
math
asked
Nov 21, 2012
1
answer
Let $(A=N \times N \,and\, * )$ be the binary operation on $(A)$ defined by $( (a, b) * (c, d) = (a + c, b + d))$. Show that * is commutative and associative. Find the identity element for * on $( A )$, if any.
cbse
class12
bookproblem
ch1
sec4
q11
p25
sec-b
math
asked
Nov 21, 2012
1
answer
Find if the given operation has identity: $\;\; a \ast b = a^2 + b^2$
cbse
class12
bookproblem
ch1
sec4
p25
q10
q10-2
sec-a
math
asked
Nov 21, 2012
2
answers
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