A ray of light coming from the point (2, 2√3) is incident at an angle 300 on the line x =1 at the point A. The ray gets reflected on the line x = 1 and meets x-axis at the point B. Then, the line AB passes through the point: 1) (4,-√3)2) (3, -1/√3)3) (3,-√3)4) (4, -√3/2) Equation of line P’B passing through (0, 2√3)(y-y1) = m (x-x1)(y-2√3) = tan 1200 (x- 0)y-2√ 3 =... View Article
Let m and M be respectively the minimum and maximum values of … Let m and M be respectively the minimum and maximum values of R1 → R1-R2 R3→ R3-R2 ⇒ -1(sin2x) -1(1+cos2x +sin2x)⇒ -sin2x... View Article
The values of λ and μ for which the system of linear equations:x+y+z = 2, x+2y+3z = 5 and x+3y+λz = μ has infinitely many solutions are, respectively: 1) 6 and 82) 5 and 83) 5 and 74) 4 and 9x+y+z = 2x+2y+3z = 5x+3y+λz = μhas infinitely many solutionsΔ = R2 → R2-R1 R3... View Article
Two families with three members each and one family with four members are to be seated in a row. In how many ways can they be seated so that the same family members are not separated? 1) 2! 3! 4!2) (3!)3(4!)3) 3!(4!)34) (3!)2(4!)Total numbers in three families = 3+3+4 = 10So total arrangement = 10! Favourable cases=... View Article
Let a, b, c, d and p be any non zero distinct real numbers such that (a2+b2+c2)p2-2(ab+bc+cd)p +(b2 +c2+d2) = 0. Then: 1) a, c, p are in G.P.2) a, b, c, d are in G.P.3) a, b, c, d are in A.P.4) a, c, p are in A.P.(a2+b2+c2)p2-2(ab+bc+cd)p +(b2 +c2+d2) =... View Article
The shortest distance between the lines (x-1)/0 = (y+1)/-1 = z/1 and x+y+z+1 = 0, 2x-y+z+3 = 0 is: 1) 12) 1/√23) 1/√34) ½Plane through line of intersection isx+y+z+1+λ(2x-y+z+3) = 0It should be parallel to given... View Article
The area (in sq. units) of the region A = {(x, y): |x|+|y| ≤ 1, 2y2|x|} 1) 1/62) 5/63) 1/34) 7/6 Total area = = 4[(1/2)-(1/8)-(√2/3)(1/2)3/2]= 4×5/24= 5/6Answer: (2)... View Article
Let L1 be a tangent to the parabola y2 = 4(x+1) and L2 be a tangent to the parabola y2 = 8(x+2) such that L1 and L2 intersect at right angles. Then L1 and L2 meet on the straight line: 1) x+2y = 02) x+2 = 03) 2x+1 = 04) x+3 = 0Let t1 tangent of y2 = 4(x+1)L1 : t1y = (x+1)+t12 .......(i)and t2 tangent of y2 = 8(x+2)L2 : t2y =... View Article
The general solution of the differential equation √(1+x2+y2+x2y2)+xy(dy/dx) = 0(where C is a constant of integration) 1) 1+y2 = z2 2ydy = 2zdz ((t2-1+1)/(t2-1) )dt = -z+c1dt+(1/t2-1)dt = -z+ct+(1/2)ln((t-1)/(t+1)) = -z+c√(1+x2)+(1/2)ln(√(1+x2)-1/(√(1+x2 )+1) =... View Article
The negation of the Boolean expression p (~p∧q) is equivalent to: 1) p∧~q2) ~p~q3) ~pq4) ~p∧~qpV (~p∧q)(pV p) ∧ (pVq)t∧(pV q)pVq~(pV(~ p∧q)) = ~ (pVq)= (~ p)∧(~ q)Answer: (4)... View Article
The region represented by {z = x+iy ∈ C : z -Re(z) ≤1} is also given by the inequality: {z = x + iy ∈ C : z -Re(z) ≤ 1} 1) y2≤2(x+1/2)2) y2≤ x+(1/2)3) y2 2(x+1)4) y2 (x+1){z = x + iy ∈ C : z -Re(z) ≤ 1}|z| = √(x2+y2)Re(z) = xz- Re(z) ≤1⇒... View Article
Let M be any 3×3 matrix with entries from the set {0,1,2}. The maximum number of such matrices, for which the sum of diagonal elements of MTM is seven, is Answer: 540⇒ a2 + b2 + c2 + d2 + e2 + f2 + g2 + h2 + i2 = 7Case I∶ Seven (1’s) and two (0’s)9C2 = 36Case II∶ One (2) and three... View Article
If the least and the largest real values of α, for which the equation z + α|z-1| + 2 i = 0 (z∈C and i =√(-1)) has a solution, are p and q respectively; then 4(p2 + q2) is equal to Answer: 10x + iy + α√((x–1)2 +y2) + 2i=0⇒y + 2 = 0 and x + α√((x-1)2+y2)=0y = –2 & x2 = α2(x2... View Article
Let A = {n∈N∶ n is a 3-digit number}, B = {9k + 2∶ k∈N} and C = {9k + l∶ k∈N} for some l(0 < l < 9). If the sum of all the elements of the set A∩(B∪C) is 274×400, then l is equal to Answer: 53 digit number of the form 9K+2 are {101,109,⋯,992}⇒ Sum equal to (100/2)(1093) = S1= 54650Now 274 × 400 =S1+S2⇒274... View Article
Let three vectors a, b and c be such that c is coplanar with a and b, ac = 7 and … Let three vectors is _______Answer: 75... View Article
If [latex]\int_{-a}^{a}(\left | x \right |+\left | x-2 \right |)dx = 22[/latex] and [x] denotes the greatest integer ≤ x, then [latex]\int_{a}^{-a}(x+\left [ x \right ])dx[/latex] is equal to Answer: 3... View Article
[latex]\lim_{x \rightarrow \infty} tan[\sum_{r=1}^n tan^{-1}(\frac{1}{1+r+r^2})][/latex] is equal to Answer: 1 = tan (pi/4) = 1... View Article
If one of the diameters of the circle x2+y2 – 2x – 6y + 6 = 0 is a chord of another circle ‘C’ whose center is at (2,1), then its radius is Answer: 3distance between (1,3) and (2,1) is √5∴ (√5)2+(2)2= r2⇒r = 3... View Article
Let Bi (i = 1,2,3) be three independent events in a sample space. The probability that only B1 occur is… Let Bi (i = 1,2,3) be three independent events in a sample space. The probability that only B1 occur is α, only B2 occurs is β... View Article
Let P be an 3×3 matrix where alpha belongs to R. Suppose Q = [qij] is a matrix PQ = kl3.. Letwhere α∈R. Suppose Q = [qij ] is a matrix satisfying PQ = kI3 for some non-zero k∈R. If q23= - k/8 and |Q| = k2/2, then... View Article
