JEE Mains Previous Year Questions (PYQ)

JEE Main 2023 10th April Morning Shift

Let the ellipse \( E:x^{2}+9y^{2}=9 \) intersect the positive \( x \)- and \( y \)-axes at the points \( A \) and \( B \) respectively. Let the major axis of \( E \) be a diameter of the circle \( C \). Let the line passing through \( A \) and \( B \) meet the circle \( C \) at the point \( P \). If the area of the triangle with vertices \( A \), \( P \) and the origin \( O \) is \( \dfrac{m}{n} \), where \( m \) and \( n \) are coprime, then \( m-n \) is equal to:

6.

The combined equation of the two lines \( ax+by+c=0 \) and \( a'x+b'y+c'=0 \) can be written as \( (ax+by+c)(a'x+b'y+c')=0 \). The equation of the angle bisectors of the lines represented by the equation \( 2x^{2}+xy-3y^{2}=0 \) is:

7.

Let the system of linear equations \( x+y+kz=2 \), \( 2x+3y-z=1 \), \( 3x+4y+2z=k \) have infinitely many solutions. Then the system
\( (k+1)x+(2k-1)y=7 \)
\( (2k+1)x+(k+5)y=10 \)
has:

8.

Let \( y=x+2 \), \( 4y=3x+6 \) and\( 3y=4x+1 \) be three tangent lines to the circle \( (x-h)^2+(y-k)^2=r^2 \). Then \( h+k \) is equal to:

9.

Let a common tangent to the curves \( y^{2}=4x \) and \( (x-4)^{2}+y^{2}=16 \) touch the curves at the points \( P \) and \( Q \). Then \( (PQ)^{2} \) is equal to ________.

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