List of top Mathematics Questions asked in AP EAPCET

If \[ x^2+y^2-2x+2fy+c=0 \] intersects the two circles \[ x^2+y^2+2x-4y+1=0 \] and \[ x^2+y^2-4x-2y-11=0 \] orthogonally, then \[ f+c= \]

If the circle $x^2 + y^2 - 4x - 6y + \lambda = 0$ touches the x-axis, then the value of $\lambda$ is:

If a circle \(S\) passes through \((a, b)\) and cuts the circle \(x^2 + y^2 = 4\) orthogonally, then find the locus of the center of \(S\).

The sum of the squares of the lengths of the chords intercepted on \(x^2+y^2=16\) by the lines \(x+y=n, n \in \mathbb{N}\) is:

The line \( 5x-12y-4=0 \) cuts the circle \( x^{2}+y^{2}-2x+2y+c=0 \) at two points A, B. If \( AB=2\sqrt{3} \), then the length of the tangent drawn from the point (2, 1) to the given circle is

The sum of the slopes of the common tangents drawn to the circles \( x^{2}+y^{2}+4x-2y-11=0 \) and \( x^{2}+y^{2}-2x+6y+6=0 \) is

If a line makes angles $45^\circ$ and $60^\circ$ with the positive $x$ and $y$ axes respectively, then the acute angle it makes with the $z$-axis is:

The acute angle between the planes $2x - y + z = 6$ and $x + y + 2z = 3$ is:

The points (0, $\lambda$, 1), ($\mu$, 3, -1), ($\lambda$, 5, 0), ($\mu$, 6, $\mu$) taken in that order, form a square. If $\lambda$, $\mu$ are positive real numbers, then the length of its side is

\(A(-4,9,k)\), \(B(-1,k,k)\), \(C(0,7,10)\) form an isosceles right-angled triangle. If \(AB=BC\) and \(AC\) is an integer then the perimeter of \(\Delta ABC\) is

If \((K,3,5)\), \((2,-1,2)\) are direction ratios of two lines and the angle between them is \(45^\circ\), then a value of \(K\) is:

If N is the foot of the perpendicular drawn from the point \(P(5,-1,3)\) to the line passing through the points \(A(1,3,-5)\) and \(B(3,-1,5)\) then the ratio in which N divides AB is

If $\theta$ is the acute angle between a line $\frac{x-1}{1}=\frac{y-1}{-1}=\frac{z-1}{1}$ and a normal to the plane $2x+3y+4z=0$ then $\tan^{2}\theta+sec^{2}\theta=$

If l, m, n are the direction cosines of a normal drawn to the plane \(2x-3y+6z-7=0\) and d is the length of the perpendicular drawn from origin to this plane then \(7d|l+m+n|=\)

The ratio in which the $xy$-plane divides the line segment joining the points $(2, 4, 5)$ and $(3, 5, -4)$ is:

If the angle \(\theta\) between the line \[ \frac{x+1}{1}=\frac{y-1}{2}=\frac{z-2}{2} \] and the plane \[ 2x-y+\sqrt{\lambda}z+4=0 \] is such that \(\sin\theta=\frac13\), then the value of \(\lambda\) is:

Let $P$ and $Q$ are two sets such that \[ n(P)=27,\quad n(Q)=17,\quad n(P\cap Q)=5. \] If $x$ is the number of ways of selecting $7$ elements from $P$ such that all the elements of $P\cap Q$ are in each selection and $y$ is the number of ways of selecting $10$ elements from $Q$ such that no element of $P\cap Q$ is present in any selection, then $x+y+1=$

Let the numerical values of the coefficients of a polynomial belong to the set \( \{0, 1, 2, \dots, 9\} \). Then the number of reciprocal polynomials of third degree with the leading coefficient 1 that can be formed is:

The number of ways of arranging the letters of the word "EAPCET" is:

All the solutions \((n,r)\) of the equation \( \frac{{}^nC_r}{{}^{n+1}C_r} = \frac{1}{3} \) can be obtained from one of the following equations given in the options for \( k=1,2,3, \dots \):

If a and b are the greatest values of \( {}^{2n}C_{r} \) and \( {}^{(2n-1)}C_{r} \) respectively, then

If $^{n}C_{12} = ^{n}C_{8}$, then $^{n}C_{17} =$

In each of its move, a pawn in a chess board can move one step either horizontally or vertically to its adjacent cell from its current position. If a pawn is initially located at the South-West corner cell of the chess board, then the number of ways it can reach the North-East corner cell with minimum number of moves, is

All the letters of the word REMAIN are permuted in all possible ways and the words (with or without meaning) thus formed are arranged in the dictionary order. The rank of the word REMAIN, when counted from the rank of the word MARINE beginning with $1$ itself, is

If the number of permutations of $n$ different things taken all at a time is $5040$, then $n =$