Recently Active Disucss Test Question Questions

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? ...

Multiple Correct Answer follows Complex number satisfying the equations |(Z-16i)/(Z-8i)|=5/3 and |(Z-4)/(Z-8)|=1 ...

(3,-4) and (5,-2) are two consecutive vertices of a square in which (2,-2) is an interior point. The centre of the square is ...

a2+b2+c2=ca+ab√3 then the triangle is ...

The value of cot-1(-3)+cot-1(-2)= ...

The number of different matrices that can be with the numbers 1,2,3,4 each having four elements is ...

FInd lim(n→∞) 1/√(n2+n) + 1/√(n2+2n)+.....+ 1/√(n2+2n2) ...

Straight Objective Type \int_{0}^{1}{\frac{1-x^{2}}{1+x^{2}}.\frac{dx}{\sqrt{1+x^{4}}}} = ...

There are 8 seats in a row. Three persons take seats in random. The probability that the first seat is always occupied and no two persons are consecutive is ...

Let a,b,c be the unit vectors such that a+b+c=0. Then the area of the triangle formed by a,b and c is ...