Eamcet - Maths - Matrices Test

Test Instructions :

1. The Test is 1hr duration.
2. The Test Paper consists of 30 questions. The maximum marks are 30.
3. All the questions are multiple choice question type with three options for each question.
4. Out of the three options given for each question, only one option is the correct answer.
5. Each question is allotted 1 mark for each correct response.
6. 0.25 will be deducted for incorrect response of each question.
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If √2 and 3i are the two roots of a biquadratic equation with rational coefficients,then its equation is

  

  

  

  

If two circles(x-3) 2+(y-1)2=r2 and x2+y2-6x+4y+4=0 intersect in two distinct points then

  

  

  

  

The area of the triangle formed by the polar of (1,2) with respect to the circle 2x2+2y2-3x=0 and the coordinate axes (in square units) is

  

  

  

  

If the line 4x+3y+k=0 is a normal to the circle 2x2+2y2+7x+4y+8=0 then k=

  

  

  

  

In a throw with a pair of symmetrical dice the probability of obtaining a doublet is

  

  

  

  

The centre of the circumscribing the quadrilateral whose sides are 3x+y=22, x-3y=14 and 3x+ y=62 is

  

  

  

  

At a given instant the legs of a right angled triangle are 8 inch and 6 inch respectively. The first leg decreases1inch per minute and second increases at 2 inch per minute. The rate of increasing of the area after 2 minute is

  

  

  

  

Solution of (dy/dx)=(y+2)/(x-1) is

  

  

  

  

The angle made by the tangent to the circle x2+y2-8x+6y+20=0 at (3,-1) with the positive direction of the x-axis is

  

  

  

  

If the circles (x+a) 2+(y+b) 2=a2,(x+α) 2+(y+β) 2=β2 cut orthogonally then α2+b2=

  

  

  

  

If the circles x2+y2=4 and x2+y2-6x-8y+K=0 touch internally then K=

  

  

  

  

7 Coupons are numbered 1 to 7. Four are drawn one by one with replacement. The probability that the least number appearing on any selected coupon is greater then or equal to 5 is

  

  

  

  

If the latusrectum of a hyperbola subtends an angle 600 at the other focus then its e=

  

  

  

  

If a tangent to the circle x2+y2+4x-4y+4=0 makes equal intercepts on the coordinate axes then the equation of that tangent is

  

  

  

  

The solution of (dy/dx)=(1+y)/(1-x) is

  

  

  

  

A question paper contains 5 questions each having an alternative. The number of ways that a student can answer one or more questions is

  

  

  

  

The harmonic mean of the roots of the equation (5+√2)x2-(4+√5)x+8+2√5)=0 is

  

  

  

  

If the number of common tangents of the circles x2+y2+8x+6y+21=0, x2+y2+2y-15=0 are 2,then the point of their intersection is

  

  

  

  

If α, β are the roots of ax2+bx+c=0 then α3+ β3 =

  

  

  

  

x2 +4ax+3 =0 and 2x2+3ax-9 =0 have a common root, then a =

  

  

  

  

The equation to the conjugate hyperbola of xy+3x-4y+13=0 is

  

  

  

  

If the circles x2+y2+2ax+c=0 and x2+y2+2bx+c=0 touch eachother then 1/c=

  

  

  

  

The transformed equation of x3-(5/2)x2-(7/18)x+(1/108)=0 by removing fractional coefficients is

  

  

  

  

The angle between the normals at (1, 3),(-3,1) to the circle x2 + y2=10 is

  

  

  

  

If a tangent to the circle x2 + y2 + 4x - 4y+4=0 makes a equal intercepts on the coordinate axes then the equation of that tangent is

  

  

  

  

The chords of contact of the pair of tangents to the circle x2+y2=1 drawn from any point on the line 2x+y=4 pass through the point

  

  

  

  

The slopes of the lines passing through A(2, 0) and making an angle of 450 with the tangent at A to the circle x2 + y2 +4x-6y-12=0 is

  

  

  

  

Pole of the line x-2y+3=0 with respect to y2=4x is

  

  

  

  

The locus of the midpoint of the chord of the circle x2+y2=25 which subtends a right angle at (2,-3) is

  

  

  

  

The coefficient of x2y3z4 in the expansion of (ax-by+cz)9 is

  

  

  

  

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