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If the point of intersection of the lines \(2 a x+4 a y+c=0\) and \(7 b x+3 b y-d=0\) lies in the 4 th quadrant and is equidistant from the two axes, where \(a, b, c\) and \(d\) are non-zero numbers, then ad : bc equals to

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

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A variable line passes through the fixed point \((\alpha, \beta)\). The locus of the foot of the perpendicular from the origin on the line is,

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

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A straight line through the point \((3,-2)\) is inclined at an angle \(60^{\circ}\) to the line \(\sqrt{3} x+y=1\). If it intersects the \(x\)-axis, then its equation will be

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

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A variable line passes through a fixed point \(\left(x_{1}, y_{1}\right) \&\) meets the axes at \(A\) and \(B\). If the rectangle OAPB be completed, the locus of \(P\) is, ( \(O\) being the origin of the system of axes)

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

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The angles of a triangle are in the ratio \(2: 3: 7\) and the radius of the circumscribed circle is \(10 \mathrm{~cm}\). The length of the smallest side is

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

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If \(e^{\sin x}-e^{-\sin x}-4=0\), then the number of real values of \(x\) is

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

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If \(X\) is a random variable such that \(\sigma(X)=2.6\), then \(\sigma(1-4 X)\) is equal to,

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

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A problem in mathematics is given to 4 students whose chances of solving individually are \(\frac{1}{2}, \frac{1}{3}, \frac{1}{4}\) and \(\frac{1}{5}\). The probability that the problem will be solved at least by one student is

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

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Let the relation \(\rho\) be defined on \(R\) as \(a \rho b\) iff \(1+a b>0\). Then

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

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Let \(f: \mathbb{R} \rightarrow \mathbb{R}\) be defined by \(f(x)=x^{2}-\frac{x^{2}}{1+x^{2}}\) for all \(x \in \mathbb{R}\). Then

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

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Let \(P\) and \(T\) be the subsets of \(X-Y\) plane defined by \(P=\left\{(x, y): x>0, y>0\right.\) and \(\left.x^{2}+y^{2}=1\right\}\) \(T=\left\{(x, y): x>0, y>0\right.\) and \(\left.x^{8}+y^{8}<1\right\}\) Then \(\mathrm{P} \cap \mathrm{T}\) is

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

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Let \(A\) and \(B\) be two square matrices of order 3 and \(A B=O_{3}\), where \(O_{3}\) denotes the null matrix of order 3 . Then,

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

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If \(A=\left(\begin{array}{ccc}5 & 5 x & x \\ 0 & x & 5 x \\ 0 & 0 & 5\end{array}\right)\) and \(\left|A^{2}\right|=25\), then \(|x|\) is equal to

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

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If \(M\) is any square matrix of order 3 over \(\mathbb{R}\) and If \(M^{\prime}\) be the transpose of \(M\), then \(\operatorname{adj}\left(M^{\prime}\right)-(\operatorname{adj} M)^{\prime}\) is equal to

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

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Let \(A\) be a square matrix of order 3 whose all entries are 1 and let \(\mathrm{I}_{3}\) be the identity matrix of order 3 . Then the matrix \(A-3 I_{3}\) is

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

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The number of irrational terms in the expansion of \(\left(3^{\frac{1}{8}}+5^{\frac{1}{4}}\right)^{84}\) is

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

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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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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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