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Straight Objective Type A 2 kg block initially at rest is dropped from a height of 0.4 m onto a spring whose force constant is 2000 N/m. The maximum compression in the spring is ...

Refer Prev Ques ...

Refer Prev Ques ...

Match for 20-23 A circle is given with centre O as x2+y2-6x+8y=0. A line x+y=4 cuts the circle is point P and Q. The tangents at P and Q meet at R Match the following 20) Area of triangle OPQ (A) 25/2 21) Area of tria ...

f(sinx)+g(sinx)= ...

fog(x)+gof(x)=Ï€/2 is true for x ...

Comprehension for 17-19 f(x)=sin-1x g(x)=cos-1x given cos1=0.54 and sin1=0.84 fof(x)+gog(x) exists for x in ...

solution matrix X is ...

5A-1= ...

Comprehension for 14-16 Given three equations x+2y+2z=0 2x+1y+2z=1 2x+2y+z=0 This can written in matrix form as AX=B i.e. \begin{bmatrix} 1 &2 &2 \\ 2 &1 &2 \\ 2 &2 &1 \end{bmatrix}\begin{bmatrix} x\\ y\\ z \e ...

The plane containing the lines L2 and the shortest line between L1 and L2 is ...

The shortest distance between the lines is ...

Comprehension for 21-23 Consider the lines L1: (x+1)/3=(y+2)/1=(z+1)/2 , L2: (x-2)/1=(y+2)/2=(z-3)/3 and the planes P1 and P2 containing the lines L1 and L2 respectively. Also P1 and P2 never intersect. Find t ...

The minimum area of the triangle OPQ is ...

The locus of the midpoint of PQ is ...

Comprehension for 18-20 Through the vertex O of the parabola y2=8x, chords OP and OQ are drawn at right angles to one another. PQ cuts axis of parabola at ...

A, B, C, D are also roots of the equation ...

A circle |Z|=1 cuts the curve in 4 points A, B, C and D. Find the area of the rectangle ABCD ...

Comprehension for 15-17 A curve is given as |Z+(2/3)√10|+|Z-(2/3)√10|=2√5 The eccentricity of the curve is ...

STATEMENT-I: The number of common tangents that can be drawn to the circle x2+y2=a2 and hyperbola x2-y2=a2 is two STATEMENT-II: y=mx±a√(m2-1) is a tangent to the hyperbola. For common tangent |a√(m2-1)|/√(m ...

STATEMENT-I: a,b,c are unit vectors, then maximum value of |a-b|2+|b-c|2+|c-a|2 is 9 STATEMENT-II: a.b+b.c+c.a≤(-3/2) ...

STATEMENT-I: For any three vectors a,b,c (bXc).[aX(bXc)]=0 STATEMENT-II: [aX(bXc)] lies in plane of b and c ...

Reasoning Type STATEMENT-I: From any point on the line 3x+4y-19=0, a tangent can be drawn to the circle x2+y2-4x+6y-12=0 STATEMENT-II: All points on the given line lies outside the circle ...

STATEMENT-I: The closest point on the curve y2-4x-2y+9=0 from the line 12x-4y-27=0 is (19/9,5/3) STATEMENT-II: The tangent at (19/9,5/3) has a slope same as the given line ...

A function f(x) is defined as f(x)=x2sin(1/x), x≠0 and f(0)=0 STATEMENT-I: f'(0)=0 STATEMENT-II: f'(x)=2xsin(1/x)-cos(1/x) ...

STATEMENT-I: If in a triangle acosA=bcosB, then triangle is always isosceles STATEMENT-II: sinAcosA=sinBcosB gives sin2A=sin2B ...

Reasoning Type STATEMENT-I: The equation 2sin2(x/4)cos2(x/2)=x2+1/x2 has one solution in 0≤x<2π STATEMENT-II: x2+1/x2≥2 ...

The value of x satisfying sin-1x+sin-1(1-x)=cos-1x are ...

A common tangent to x2+y2-4x+2y=0 and x2-5y2-4x-10y-126=0 is ...

y(2x3-y2)dx+x(y2-x3)dy=0 (1,1) lies on the curve Which of the following points lies on this curve? ...