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\(7^{2 n}+16 n-1(n \in N)\) is divisible by

asked Dec 11, 2021 in Sets, relations and functions by kritika (90.1k points)

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3 answers

There are 7 greetings cards, each of a different colour and 7 envelopes of same 7 colours as that of the cards. The number of ways in which the cards can be put in envelopes, so that exactly 4 of the cards go into envelopes of respective colour is,

asked Dec 11, 2021 in Sets, relations and functions by kritika (90.1k points)

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A candidate is required to answer 6 out of 12 questions which are divided into two parts \(A\) and \(B\), each containing 6 questions and he/she is not permitted to attempt more than 4 questions from any part. In how many different ways can he/she make up his/her choice of 6 questions ?

asked Dec 11, 2021 in Sets, relations and functions by kritika (90.1k points)

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Let \(a, b, c\) be real numbers such that \(a+b+c<0\) and the quadratic equation \(a x^{2}+b x+c=0\) has imaginary roots. Then

asked Dec 11, 2021 in Sets, relations and functions by kritika (90.1k points)

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The general value of the real angle \(\theta\), which satisfies the equation, \((\cos \theta+i \sin \theta)(\cos 2 \theta+i \sin 2 \theta) \ldots \ldots .\) \((\cos n \theta+i \sin n \theta)=1\) is given by, (assuming \(k\) is an integer)

asked Dec 11, 2021 in Sets, relations and functions by kritika (90.1k points)

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3 answers

Let \(z\) be a complex number such that the principal value of argument, \(\arg z>0\). Then \(\arg z-\arg (-z)\) is

asked Dec 11, 2021 in Sets, relations and functions by kritika (90.1k points)

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If \(\log _{2} 6+\frac{1}{2 x}=\log _{2}\left(2^{\frac{1}{x}}+8\right)\), then the values of \(x\) are

asked Dec 11, 2021 in Sets, relations and functions by kritika (90.1k points)

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The three sides of a right-angled triangle are in G.P (geometric progression). If the two acute angles be \(\alpha\) and \(\beta\), then \(\tan \alpha\) and \(\tan \beta\) are

asked Dec 11, 2021 in Sets, relations and functions by kritika (90.1k points)

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1 answer

If the radius of a spherical balloon increases by \(0.1 \%\), then its volume increases approximately by

asked Dec 11, 2021 in Sets, relations and functions by kritika (90.1k points)

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2 answers

Let \(P(4,3)\) be a point on the hyperbola \(\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1 .\) If the normal at \(P\) intersects the \(X\)-axis at \((16,0)\), then the eccentricity of the hyperbola is

asked Dec 11, 2021 in Sets, relations and functions by kritika (90.1k points)

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General solution of \((x+y)^{2} \frac{d y}{d x}=a^{2}, a \neq 0\) is (c is an arbitrary constant)

asked Dec 11, 2021 in Sets, relations and functions by kritika (90.1k points)

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3 answers

The general solution of the differential equation \(\left(1+e^{\frac{x}{y}}\right) d x+\left(1-\frac{x}{y}\right) e^{\frac{x}{y}} d y=0\) is (c is an arbitrary constant)

asked Dec 11, 2021 in Sets, relations and functions by kritika (90.1k points)

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\(\lim _{n \rightarrow \infty} \frac{3}{n}\left\{1+\sqrt{\frac{n}{n+3}}+\sqrt{\frac{n}{n+6}}+\sqrt{\frac{n}{n+9}}+\ldots+\sqrt{\frac{n}{n+3(n-1)}}\right\}\)

asked Dec 11, 2021 in Sets, relations and functions by kritika (90.1k points)

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The value of the integeral \(\int_{-1}^{1}\left\{\frac{x^{2015}}{e^{|x|}\left(x^{2}+\cos x\right)}+\frac{1}{e^{|x|}}\right\} d x\) is equal to

asked Dec 11, 2021 in Sets, relations and functions by kritika (90.1k points)

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If \(\int 2^{2^{x}} \cdot 2^{x} d x=A \cdot 2^{2^{x}}+c\), then \(A=\)

asked Dec 11, 2021 in Sets, relations and functions by kritika (90.1k points)

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The value of \(\lim _{x \rightarrow 0} \frac{1}{x}\left[\int_{y}^{a} e^{\sin ^{2} t} d t-\int_{x+y}^{a} e^{\sin ^{2} t} d t\right]\) is equal to

asked Dec 11, 2021 in Sets, relations and functions by kritika (90.1k points)

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The value of the integration \(\int_{-\pi / 4}^{\pi / 4}\left(\lambda|\sin x|+\frac{\mu \sin x}{1+\cos x}+\gamma\right) d x\)

asked Dec 11, 2021 in Sets, relations and functions by kritika (90.1k points)

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\(y=\int \cos \left\{2 \tan ^{-1} \sqrt{\frac{1-x}{1+x}}\right\} d x\) is an equation of a family of

asked Dec 11, 2021 in Sets, relations and functions by kritika (90.1k points)

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If \(\int \cos x \log \left(\tan \frac{x}{2}\right) d x=\sin x \log \left(\tan \frac{x}{2}\right)+f(x)\) then \(f(x)\) is equal to, (assuming \(c\) is a arbitrary real constant)

asked Dec 11, 2021 in Sets, relations and functions by kritika (90.1k points)

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\(\lim _{x \rightarrow 0+}\left(x^{n} \ln x\right), n>0\)

asked Dec 11, 2021 in Sets, relations and functions by kritika (90.1k points)

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