Eamcet - Maths Test

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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 f(x)=√(1-√(1-x2)), then

  

  

  

  

If Cos (A-B) =  3/5 and tan A tan B  = 2 then which one of the following is true

  

  

  

  

.In ΔABC, if 2R+ r= r1, then the triangle isa

  

  

  

  

If the roots of the equation 4x3-12x2+11 x + k = 0 are in arithmetic progression, then k is equal to :

  

  

  

  

If (1,2),(4,3) are the limiting points of coaxal system,then the equation of the circle in its conjugate system having minimum area is

  

  

  

  

If y=x+1/(x+1/x+....∞) then dy/dx=

  

  

  

  

If the range of a random variable X is {0, 1, 2, 3, 4,........} with P(X = k) = (k+1)a / 3k for k ≥ 0 then a is equal to

  

  

  

  

If ak is the coefficient of xk in the expansion of  (1+x+x2)n for k = 0,1,2,..........2n then a1 + 2a2 +.....+2na2n  =

  

  

  

  

A person of height 180 cm starts from a lamp post of height 450 cm and walks at the constant rate of 4 km per hour. The rate at which his shadow increases is

  

  

  

  

The circumcentre of the triangle with vertices at A(5, 12),B(12, 5), c (2√(13 ) ,3√(13 )) is

  

  

  

  

If cos θ+ sin θ=a, then sin 2θ=

  

  

  

  

If g is the inverse of f and f1(x)=1/(1+xn),then g1(x) equals,

  

  

  

  

The circles x2+y2-4x+6y+8=0 and x2+y2-10x-6y+14=0,touch

  

  

  

  

If a=2i+3j+6k, b=3i-6j+2k, c=6i+2j-3k then axb=

  

  

  

  

If n positive integers are taken at random and multiplied together , the probability that the last digit of the product is 2,4,6 or 8 is

  

  

  

  

The equation of the circle cutting orthogonally circles x2+y2-4x+3y-1=0 and passing through the points (-2, 5), (0, 0) is

  

  

  

  

If the distance of two points P and Q on the parabola y2 = 4ax are 4 and 9 respectively,then 9  respectively,then the distance of the point of intersection of the tangents at P and Q fro the focus is

  

  

  

  

If (3+i) is a root of the equation x2 + ax+ b=0 then a =

  

  

  

  

If 3x-2y+4=0 and 2x+5y+k=0 are conjugate lines w.r to the ellipse 9x2+16y2=144 then the value of k is

  

  

  

  

The sum of divisors of 253453 is

  

  

  

  

2 cos 540. Sin 660=

  

  

  

  

∫ exloga , ex dx is equal to :

  

  

  

  

Assertion(A):x2+x+1 is greater than zero for all real x. Reason(R):when b2-4ac

  

  

  

  

If the inverse point of (1, -1) with respect to the circle x2+y2=1/4 is C then Cx+Cy=

  

  

  

  

(sin 3A+ sin A) sin A+ (cos 3A- cos A) cos A=

  

  

  

  

The number of non trivial solutions of the system x-y+z =0 ,x+2y-z=0  and 2x-y+3z=0  is

  

  

  

  

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

  

  

  

  

The sum of the first n terms of the series 12+2.22+32+2.42+52+2.62+…. Is n(n+1)2/2 when n is even. When n is odd the sum is

  

  

  

  

The system of circle x2+y2+2λx-5=0 is

  

  

  

  

If the coefficients of (2r+1)th term and (4r+5)th term in the expansion of (1+x)10 are equal then r=

  

  

  

  

If ax+by+c=0 is the equation of the common radical axis of the coaxial system (3x2+3y2-2x-2y-1)+λ(x2+y2-x-2y-3)=0 then ab+bc+ca=

  

  

  

  

The equation of the incircle of triangle formed by x=0,y=0 and (x/3)+(y/4)=1 is

  

  

  

  

The locus of the point of intersection of two tangents drawn to the circle x2+y2=a2 which make a constant angle α to each other is

  

  

  

  

If f(x,y,z)=√(yz)+ √(zx)+ √(xy) then xfx+yfy+zfz=

  

  

  

  

If n is a positive integer, then the coefficient of xn in the expansion of (1 + x)n/(1-x) is

  

  

  

  

All the values of x satisfying sin 2x+ sin 4x= 2 sin 3x are

  

  

  

  

If (1 + x)n = C0 + C1x + C2x2 + …. + CnXn, then C0 - C2 + C4 - C6 + … is equal to:

  

  

  

  

If two roots of x4-16x3+86x2-176x+105=0 are 1,7 then the roots are

  

  

  

  

If cot θ=8/15 and θ does not lie in the first quadrant, then cos(300+ θ) +sin(450- θ)+cos(1200+ θ)=

  

  

  

  

The locus of the point of intersection of the tangents at the ends of a chord of a circle x2+y2=a2 which touches the circle x2+y2-2ax=0 is

  

  

  

  

The point equidistant from the points (-, 0, 0),(1, 0, 0),(0, 2, 0) and (0, 0, 3) is:

  

  

  

  

d/dx{Tan-1√(1-sin x/1+sin x)}=

  

  

  

  

The parabola with directrix x + 2y - 1 = 0 and focus (1, 0) is

  

  

  

  

If x4-16x3+86x2-176x+105=0 then s1,s2,s3,s4 are

  

  

  

  

The perpendicular distance of radical axis determined by the circles x2 + y2 + 2x + 4y – 7 =0 and x2 + y2 – 6x + 2y – 5 =0 from the origin is:

  

  

  

  

4 Tan-1 1/5- Tan-1 1/239 =

  

  

  

  

The least value of (x-a) (x-b) occurs at x=

  

  

  

  

The radius of the sphere x2+y2+z2-2x+4y-6z+7=0 is

  

  

  

  

The circumcentre of the triangle formed by the points(1,2,3), (3,-1,5), (4,0,-3) is

  

  

  

  

The solution of dy/dx = y2 / (xy - x2) is

  

  

  

  

The angle between the line joining the points (1, -2), (3, 2) and the line x+2y-7=0 is

  

  

  

  

If the roots of the equation x2-5x+16=0 are α,β and the roots of the eqution x2+px+q=0 are α2+β2,αβ/2,then

  

  

  

  

1.22+2.32+3.4+….+n(n+1)2=

  

  

  

  

7/5(1+1/?102 +1.3/1.2.1/104 +1.3.5/1.2.3.1/106 +...........∞)

  

  

  

  

Statement I : If f:A→B, g:B→C are such that gof is an injection, then f is an injection. Statement II : If f:A→B, g:B→C are such that gof is an injection, then g is an injection. The correct statement is

  

  

  

  

The point P in the first quadrant of the ellipse x2/8+y2/18=1 so that the area of the triangle formed by the tangent at P and the coordinate axes is least

  

  

  

  

The equation of the auxiliary circle of x2/12+y2/18=1 is

  

  

  

  

The 4th term of (1-2x)-1 when x=1/3 is

  

  

  

  

The differential equation obtained by eliminating the arbitrary constants a and b from xy=aex + be-x is

  

  

  

  

If a, b, c form a geometric progression with common ratio r,then the sum of the ordinates of the Points of intersection of the line ax + by + c = 0 and the curve x + 2y2=0

  

  

  

  

If A(1, 1), B(√3+1, 2) and C(√3, √3+2) be three vertices of a square, then the diagonal through B is

  

  

  

  

(2 cos θ-1) (2 cos 2θ-1) (2 cos 4θ-1) (2 cos 8θ-1)=

  

  

  

  

The ratio in which ys-plane divides the line segment joining (-3, 4, - 2) and (2,1, 3)  is

  

  

  

  

A line l meets the circle x2 + y2 = 61 in A,B and P(-5,6) is such that PA = PB= 10.  Then the equation of l is :

  

  

  

  

The common chord of x2+y2-4x-4y=0 and x2+y2=16 substends at the origin an angle equal to

  

  

  

  

If sinA + sinB = l, cosA - cosB = m, then the value of cos(A - B) =

  

  

  

  

The The limiting points of the coaxal system x2+y2+2µy+9=0 are

  

  

  

  

If 2x-y+3=0, 4x+ky+3=0 are conjugate with respect to the ellipse 5x2+6y2-15=0 then k=

  

  

  

  

If 2x+3y+4=0is perpendicular bisector of the segment joining the points A (1, 2) and B (α, β) then the value of α+β is

  

  

  

  

If the circles x2+y2-4x+6y+8=0, x2+y2-10x-6y+14=0 touch each other , then the point of contact is

  

  

  

  

The equation of the normal to the curve y=3x2+4x-6 at (1, 1) is

  

  

  

  

Two cards are drawn at random from 10 cards numbered 1 to 10. The probability that their sum is odd, if the  two cards are drawn together is

  

  

  

  

A tangent to the circle x2+y2=4 meets the coordinate axes at P and Q. The locus of mindpoint of PQ is

  

  

  

  

The equation of the straight line perpendicular to the straight line 3* + 2y = 0 and passing through the point of intersection of the lines x + 3y - 1 = 0 and x - 2y + 4 = 0 is

  

  

  

  

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

  

  

  

  

tan 2A- sec Asin A=

  

  

  

  

3 horses A, B and C run a race. If the probability of A’s win is twice that of B and the probability of B’s win is thrice that of C then the probabilities of their winning are

  

  

  

  

If ax= by= cz = dw then the value of x[(1/y)+(1/z)+(1/w)]is

  

  

  

  

The radii of two circles are 2 units and 3 units.If the radical axis of the circles cuts one of the common tangents of the circles in P then ratio in which P divides the common tangent is

  

  

  

  

The equations of the diagonal of the square formed by the pairs of lines 12x2+7xy-12y2=0 and 12x2+7xy-12y2-x+7y=1 is

  

  

  

  

The angle A ofABC is found by measurement to be 630 an the area is calculated by the formula 1/2bc sin A. the percentage error in the calculated value of the area due to an error of 15 minutes in the measured value of A is

  

  

  

  

Three forces having magnitude 5, 4 and 3 act on a particle in the direction 2i-2j-k, i+2j+2k and -2i+2k respectively and the particle gets displacement rom the point A whose position vector is 6i-2j+3k to the point whose position vector is 9i+7j+5k. Then the work done by these forces is

  

  

  

  

The solution of (dy/dx)=ey-x is

  

  

  

  

A man throws a die until he gets a number bigger than 3. The probability that he gets a 5 in the last throw is

  

  

  

  

The length of the focal chord of the parbola y2 = 4ax which makes an angle θ with its axis is

  

  

  

  

The locus of the middle points of the chords of the circle x2+y2=8 which are at a distance of √2 units from the centre of circle is

  

  

  

  

Origin is the orthocentre  of the triangle formed by the points(5,-1), (-2,3) and (-4,-7) then its ninepoint centre is

  

  

  

  

Tan-1 3/2-Tan-11/5 =

  

  

  

  

6 sin 200- 8sin3200=

  

  

  

  

For a student the probability of getting a pass in one paper is75%and the probability of getting a pass in another paperis60%.The probability is 60% .The probability for the student to pass in one paper only is

  

  

  

  

If one end of the diameter of the circle x2+y2-6x+4y-12=0 is (7, -5),  then the other end of the diameter is

  

  

  

  

The longest distance from (-3, 2) to the circles x2+y2-2x+2y+1=0 is

  

  

  

  

If a= sin θ+ cos θ, b= sin3 θ+ cos3θ then

  

  

  

  

If α, β, γ are the angles made by a line with x, y, z axes in positive directions then the range of cos α cos β+ cos β cos γ+cos γ cos α is

  

  

  

  

The equation x2 - 3xy + λy2 + 3x - 5y + 2 = 0, where λ is a real number, represents a pair of straight lines. If θ is the angle between these lines then cosec2 = θ

  

  

  

  

A five digit number is formed by using the digits 0, 1,2,3,4 and 5 without repetetion.The probability that the number is divisible by 6 is

  

  

  

  

 If the rate of change in y=2x3+3x2-30x+7 is 6 times the rate of change in x, then x=

  

  

  

  

The centre of the circle whose centre is on the straight line 5x – 2y +1=0 and cuts the x-axis at two points whose abscissa are -5 and 3 is

  

  

  

  

If α,β,γ are roots of x3-2x2+3x-4=0,then Σα2β2

  

  

  

  

If 3x  /(x-a) (x-b)  =  2/(x-a)  +  1/(x-b)  then a:b =

  

  

  

  

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