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The negation of the Boolean expression p (~p∧q) is equivalent to:

1) p∧~q 2) ~p~q 3) ~pq 4) ~p∧~q pV (~p∧q) (pV p) ∧ (pVq) t∧(pV q) pVq ~(pV(~ p∧q)) =... 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... 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 M^TM is seven, is

Answer: 540 ⇒ a2 + b2 + c2 + d2 + e2 + f2 + g2 + h2 + i2... 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: 10 x + iy + α√((x–1)2 +y2) + 2i=0 ⇒y + 2 = 0 and x + α√((x-1)2+y2)=0 y... 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: 5 3 digit number of the form 9K+2 are {101,109,⋯,992} ⇒ Sum equal to (100/2)(1093) = S1= 54650 Now... 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 \(\begin{array}{l}\vec{a}\end{array} \) ,\(\begin{array}{l}\vec{b}\end{array} \) and \(\begin{array}{l}\vec{c}\end{array} \) be such that \(\begin{array}{l}\vec{c}\end{array} \) is coplanar with \(\begin{array}{l}\vec{a}\end{array} \)... 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 \(\begin{array}{l}\int_{-a}^{a}(\left | x \right |+\left | x-2 \right |)dx = 22\end{array} \)

[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

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: 3 distance between (1,3) and (2,1) is √5 ∴ (√5)2+(2)2= r2 ⇒r = 3

Let B_i (i = 1,2,3) be three independent events in a sample space. The probability that only B₁occur is…

Let Bi (i = 1,2,3) be three independent events in a sample space. The probability that only B1 occur is... View Article

Let P be an 3×3 matrix where alpha belongs to R. Suppose Q = [q_ij] is a matrix PQ = kl₃..

Let where α∈R. Suppose Q = [qij ] is a matrix satisfying PQ = kI3 for some non-zero k∈R. If... View Article

The system of linear equations: 3x – 2y – kz = 10, 2x – 4y – 2z = 6 and x + 2y – z = 5m is inconsistent if :

a. k = 3, m = 4/5 b. k ≠ 3,m∈R c. k ≠ 3, m ≠ 4/5 d. k... View Article

If [latex]e^{(cos^{2}x + cos^{4}x + cos^{6}x + …..infty )log_{e}2}[/latex] satisfies the equation t² – 9t + 8 = 0, then the value of 2sin x/(sin x + √3cos x) 0< x<π/2 is:

a. 3/2 b. 2√3 c. 1/2 d. √3 Answer: (c) 0 < x < π/2 ⇒ cot⁡x = √3 ⇒(2... View Article

Let p and q be two positive number such that p + q = 2 and p⁴ + q⁴= 272. Then p and q are roots of the equation:

a. x2 – 2x + 2 = 0 b. x2 – 2x + 8 = 0 c. x2 – 2x... View Article

An ordinary dice is rolled for a certain number of times. If the probability of getting an odd number 2 times is equal to the probability of getting an even number 3 times, then the probability of getting an odd number for odd number of times is:

a. 3/16 b. 1/2 c. 5/16 d. 1/32 Answer: (b) P(odd no. twice) = P(even no. thrice) nC2 (1/2)n =... View Article

The value of – ¹⁵C₁ + 2. ¹⁵C₂ – 3.¹⁵C₃+ ….-15.¹⁵C₁ + ¹⁴C₁+ ¹⁴C₃ + ¹⁴C₅ + …¹⁴C₁₁ is

a. 214 b. 213 – 13 c. 216 – 1 d. 213 – 14 Answer: (d) = (14C1+ 14C3 +... View Article

If ∫(cos x -sin x)/√(8-sin 2x) dx = a sin^-1(sin x + cos x)/b + c where c is a constant of integration, then the ordered pair (a, b) is equal to:

a. (1, –3) b. (1, 3) c. (–1, 3) d. (3, 1) Answer: (b) Put sin x + cos x... View Article

The area (in sq.units) of the part of the circle x²+ y²= 36, which is outside the parabola y²= 9x, is:

a. 24π + 3√3 b. 12π + 3√3 c. 12π – 3√3 d. 24π – 3√3 Answer: (d) The curves... View Article

If the tangent to the curve y = x³ at the point P(t, t³) meets the curve again at Q, then the ordinate of the point which divides PQ internally in the ratio 1:2 is:

a. –2t3 b. –t3 c. 0 d. 2t3 Answer: (a) Equation of tangent at P(t, t3) (y – t3) =... View Article

The number of isomers possible for [Pt(en)(NO₂)₂] is:

1) 2 2) 3 3) 4 4) 1 Answer: (2) Three linkage isomers: [Pt(en)(NO2)2] [Pt(en)(ONO)2] [Pt(en)(NO2)(ONO)]

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