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Recent questions tagged additionalproblem
Questions
Simplify $\tan^{-1}\big(\large \frac{\cos x}{1+\sin x}\big)$
cbse
class12
additionalproblem
kvquestionbank2012
ch2
q4
p5
medium
sec-b
math
asked
Jan 23, 2013
by
meena.p
1
answer
Solve for $x$: $\sin\bigg[\sin^{-1}\frac{1}{3}+\cos^{-1}x\bigg]=1$
cbse
class12
additionalproblem
kvquestionbank2012
ch2
q3
p5
easy
sec-a
math
asked
Jan 23, 2013
by
meena.p
1
answer
Find the value of $\tan^{-1}1+\tan^{-1}2+\tan^{-1}3.$
cbse
class12
additionalproblem
kvquestionbank2012
ch2
q2
p5
easy
sec-b
math
asked
Jan 23, 2013
by
meena.p
1
answer
Find the value of $\cos\bigg\{\cos^{-1}\bigg(\frac{-\sqrt {3}}{2}\bigg)+\frac{\pi}{6}\bigg\}$
cbse
class12
additionalproblem
kvquestionbank2012
ch2
q1
p5
easy
sec-a
math
asked
Jan 23, 2013
by
meena.p
1
answer
On the set N of natural numbers, define the operation * on N by m*n=gcd(m,n) for all m, n$ \varepsilon$ N. Show that * is commutative as well as associative.
cbse
class12
additionalproblem
kvquestionbank2012
ch1
q30
p4
math
sec-b
asked
Jan 23, 2013
by
meena.p
0
answers
Determine which of the following functions \[f:R \rightarrow R\;are\;(a)One-One\quad(b)Onto\]\[(i)f(x)=|x|+x\]\[(ii)f(x)=x-[x]\]
cbse
class12
additionalproblem
kvquestionbank2012
ch1
q29
p4
math
sec-a
asked
Jan 23, 2013
by
meena.p
0
answers
Let X = {1,2,3,4,5,6,7,8,9}. Let $ R_1\;andR_2$ be relations in x given by \[R_1=\{(x,y):x-y\;is\;divisible\;by\;3\}\;and\]\[R_2=\{(x,y)!\{x,y\} \varepsilon \{1,4,7\}or\{x,y\} \varepsilon \{2,5,8\}\]\[or \{x,y\} \varepsilon \{3,6,9\}\}.\; Show\; that \;R_1=R_2.\]
cbse
class12
additionalproblem
kvquestionbank2012
ch1
q28
p4
math
sec-b
asked
Jan 23, 2013
by
meena.p
0
answers
Prove that relation R defined on the set N of natural numbers by \[x\;R\;y \Leftrightarrow 2x^2-3xy+y^2=0\] is not symmetric but it is reflexive.
cbse
class12
additionalproblem
kvquestionbank2012
ch1
q27
p4
math
sec-b
asked
Jan 23, 2013
by
meena.p
1
answer
Show that the function $ f:N \rightarrow N$ given by $f(x) = x -(-1)^x\;for\;all\;x\; \varepsilon\;N $ is a bijection.
cbse
class12
additionalproblem
kvquestionbank2012
ch1
q26
p4
math
sec-b
asked
Jan 23, 2013
by
meena.p
0
answers
Define a binary operation $^*$ on the set A = {0,1,2,3,4,5} as \[a*b=\left \{ \begin{array} {1 1} a+b, & \quad \text{ if a+b<6} \\ a+b-6, & \quad { if a+b \geq 6} \end{array} \right.\]Show that zero is an identity element for this operation and each element a of the set is invertiable with 6-a being the inverse of a.
cbse
class12
additionalproblem
kvquestionbank2012
ch1
q25
p4
math
sec-b
asked
Jan 23, 2013
by
meena.p
0
answers
Let f and g be real valued functions, such that $(fog)(x)=\cos x^3\; and\;(gof)(x)=\cos^3x,$ find the functions f and g.
cbse
class12
additionalproblem
kvquestionbank2012
ch1
q24
p4
math
sec-b
asked
Jan 23, 2013
by
meena.p
0
answers
Let $f : A \rightarrow B$ be a given function. A relation R in the set A is given by $R = {(a,b) \varepsilon A \times A : f(a) = f(b)}.$ Check, if R is an equivalence relation.
cbse
class12
additionalproblem
kvquestionbank2012
ch1
q23
p4
math
sec-b
asked
Jan 23, 2013
by
meena.p
1
answer
Prove that the inverse of an equivalence relation is an equivalence relation.
cbse
class12
additionalproblem
kvquestionbank2012
ch1
q22
p4
math
sec-b
asked
Jan 23, 2013
by
meena.p
0
answers
Let N denote the set of all natural numbers and R be the relation on N x N defined by $ (a,b)R(c,d) \Leftrightarrow ad(b + c) = bc(a + d).$ Show that R is an equivalence relation on N x N.
cbse
class12
additionalproblem
kvquestionbank2012
ch1
q21
p4
math
sec-b
asked
Jan 23, 2013
by
meena.p
1
answer
Let a relation R on the set R of real numbers defined as $(x,y)\; \varepsilon\;R \Leftrightarrow x^24xy+3y^2\;=\;0.$Show that R is reflexive but neither symmetric nor transitive.
cbse
class12
additionalproblem
kvquestionbank2012
ch1
q20
p4
math
sec-b
asked
Jan 23, 2013
by
meena.p
0
answers
Let a relation R on the set R of real numbers be defined as $ (a,b) \varepsilon R \Leftrightarrow 1+ ab > 0 for\; all\; a, b\; \varepsilon\; R.$show that R is reflexive and symmetric but not transitive.
cbse
class12
additionalproblem
kvquestionbank2012
ch1
q19
p4
math
sec-b
asked
Jan 23, 2013
by
meena.p
0
answers
If the function $ f\;:\;R \rightarrow A $ given by $f(x)=\frac{x^2}{x^2+1}$is surjection, find the set A.
cbse
class12
additionalproblem
kvquestionbank2012
ch1
q18
p4
math
sec-b
asked
Jan 23, 2013
by
meena.p
0
answers
Show that the relation "congruence modulo 2" on the set Z (set of integers) is an equivalence relation. Also find the equivalence class of 1.
cbse
class12
additionalproblem
kvquestionbank2012
ch1
q17
p3
math
sec-b
asked
Jan 23, 2013
by
meena.p
0
answers
Let $f:R_+\rightarrow[-5,\infty) $ given by $f(x)=9x^2+6x-5.$ show that f is invertiable with $ f^{-1}(y)=\frac{\sqrt{y+6}-1}{3}.$
cbse
class12
additionalproblem
kvquestionbank2012
ch1
q16
p3
math
sec-b
asked
Jan 23, 2013
by
meena.p
1
answer
Show that the relation R on N x N defined by $(a,b)R(c,d)\;\Leftrightarrow \; a+d = b+c $is an equivalence relation.
cbse
class12
additionalproblem
kvquestionbank2012
ch1
q15
p3
math
sec-a
asked
Jan 23, 2013
by
meena.p
0
answers
If R is a relation on a set $A(A \neq \phi),$ prove that R is symmetric iff $R^{-1} = R$
cbse
class12
additionalproblem
kvquestionbank2012
ch1
q14
p3
math
sec-b
asked
Jan 23, 2013
by
meena.p
0
answers
If $f(x)=log \big(\frac{1+x}{1-x}\big)$ show that $f(x)+f(y)=f \big(\frac{x+y}{1+xy}\big)$
cbse
class12
additionalproblem
kvquestionbank2012
ch1
q13
p3
math
sec-b
asked
Jan 23, 2013
by
meena.p
0
answers
Let $ f(x)=\frac{\alpha x}{x+1},x\;\neq\;-1,$ find the value of $\alpha$ such that $f(f(x))=x$
cbse
class12
additionalproblem
kvquestionbank2012
ch1
q12
p3
math
sec-a
asked
Jan 23, 2013
by
meena.p
0
answers
Let f, g be two functions defined by \[f(x)=\frac{x}{x+1},g(x)=\frac{x}{1-x},\;then\;find\;(fog)^{-1}(x)\]
cbse
class12
additionalproblem
kvquestionbank2012
ch1
q11
p3
math
sec-b
asked
Jan 23, 2013
by
meena.p
0
answers
Show that $\frac{1}{\sin^3x}+\cot x+\frac{1}{x^5}+x^3 $ is an odd function.
cbse
class12
additionalproblem
kvquestionbank2012
ch1
q10
p3
math
sec-a
asked
Jan 23, 2013
by
meena.p
0
answers
If $f(x)=\frac{1+x}{1-x},$show that $f[f(\tan\theta)]= - cot\theta$
cbse
class12
additionalproblem
kvquestionbank2012
ch1
q9
p3
math
sec-b
asked
Jan 23, 2013
by
meena.p
0
answers
If $f(x)=\frac{5x+3}{4x-5}\big(x\neq\frac{5}{4}\big),$find g(x) such that $gof(x) = x$
cbse
class12
additionalproblem
kvquestionbank2012
ch1
q8
p3
math
sec-b
asked
Jan 23, 2013
by
meena.p
0
answers
Let $f :R \rightarrow R $ defined by $f(x) = (ax^2+b)^3$ find the function $g :R \rightarrow R $ such that $f(g(x)) = g(f(x))$
cbse
class12
additionalproblem
kvquestionbank2012
ch1
q7
p3
math
sec-b
asked
Jan 23, 2013
by
meena.p
0
answers
Let $ \int : {R\; \rightarrow \;R}$ be a function defined by $ f(x) = x^2-3x+4,$ for all $x \in R ,$ find the value of $f^{-1}(2)$.
cbse
class12
additionalproblem
kvquestionbank2012
ch1
q6
p3
math
sec-b
asked
Jan 23, 2013
by
meena.p
0
answers
Let A = {4,5,0}. Find the number of binary operations that can be defined on A.
cbse
class12
additionalproblem
kvquestionbank2012
ch1
q5
p3
math
sec-a
asked
Jan 22, 2013
by
meena.p
0
answers
Find the number of One-One functions from a finite set A to A, where n(A) = P
cbse
class12
additionalproblem
kvquestionbank2012
ch1
q4
math
sec-a
asked
Jan 22, 2013
by
meena.p
0
answers
Let * be a binary operation on the set of real numbers. If a * b = a+b-ab, 2 * ( 3 * x ) = -7, find the value of x.
cbse
class12
additionalproblem
kvquestionbank2012
ch1
q3
p3
math
sec-b
asked
Jan 22, 2013
by
meena.p
1
answer
If $f(x)=\sin^2x+\sin^2\big(x+\frac{\pi}{3}\big)+\cos x.cos\big(x+\frac{\pi}{3}\big)\;and\;g\big(\frac{5}{4}\big)=1$, then find the value of gof(x)=x.
cbse
class12
additionalproblem
kvquestionbank2012
ch1
q2
p3
math
sec-b
asked
Jan 22, 2013
by
meena.p
0
answers
If $f(x)=\frac{x-1}{x+1},(x \neq 1,-1),$ show that $fof^{-1}$ is an identity function.
cbse
class12
additionalproblem
kvquestionbank2012
ch1
q1
p3
math
sec-b
asked
Jan 22, 2013
by
meena.p
0
answers
If $y=y(x)$ satisfies $x\cos y + y\cos x = \pi$, then find $y''(0)$:
cbse
class12
ch5
math
differential-equations
additionalproblem
jeemain
difficult
sec-b
asked
Jan 3, 2013
by
sreemathi.v
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
by
vaishali.a
1
answer
Choose the correct answer. The planes: 2x – y + 4z = 5 and 5x – 2.5y + 10z = 6 are:
cbse
class12
additionalproblem
easy
sec-a
math
asked
Nov 2, 2012
by
balaji.thirumalai
1
answer
Let \( A\ =\ R–\ {3}\)andB=R-{1}.Considerthefunctionoff:A
additionalproblem
cbse
class12
sec-a
easy
math
asked
Nov 2, 2012
by
vaishali.a
0
answers
Let \[ F :R->R: f(x) =2x+1 \] and \[ g:R->R:g(x)=x^2 –2 \] find (I) gof (II) fog
cbse
class12
additionalproblem
ch1
sec-a
easy
math
asked
Nov 2, 2012
by
vaishali.a
0
answers
Show that function \( f\: N\ ->N\), given by \( f(x)\ =\ 2x\), is one – one.
cbse
class12
additionalproblem
ch1
sec-a
easy
math
asked
Nov 2, 2012
by
vaishali.a
0
answers
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