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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 = 4/5b. k ≠ 3,m∈Rc. k ≠ 3, m ≠ 4/5d. k = 3, m ≠ 4/5Answer: (d)⇒ 3(4 + 4) + 2(–2 + 2) -k(4 + 4) = 0⇒... 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. 3/2b. 2√3c. 1/2d. √3Answer: (c)0 < x < π/2 ⇒ cot⁡x = √3⇒(2 sin⁡x)/(sin⁡x+√3 cos⁡x )= 2/(1+√3... 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 = 0b. x2 - 2x + 8 = 0c. x2 - 2x + 136 = 0d. x2 - 2x + 16 = 0Answer: (d)(p2 + q2)2 – 2p2q2 = 272((p + q)2 - 2pq)2 - 2p2q2 =... 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. 3/16b. 1/2c. 5/16d. 1/32Answer: (b)P(odd no. twice) = P(even no. thrice)nC2 (1/2)n = nC3 (1/2)n⇒ n = 5Success is getting an odd number... View Article

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

a. 214b. 213 - 13c. 216 - 1d. 213 - 14Answer: (d)= (14C1+ 14C3 + 14C5 + ...14C11 + 14C13) - 14C13= 213 - 14∴ S1 + S2 = 213 - 14... 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 = t ⇒1 + sin 2x = t2(cos x -sin x ) dx = dt⇒I =... 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√3b. 12π + 3√3c. 12π - 3√3d. 24π - 3√3Answer: (d)The curves intersect at point (3, ±... 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. –2t3b. –t3c. 0d. 2t3Answer: (a)Equation of tangent at P(t, t3)(y - t3) = 3t2(x - t) ⋯(1)Now solve the above equation withy = x3... View Article

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Archives

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

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:

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:

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:

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

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:

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

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:

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

The pair in which both the species have the same magnetic moment (spin only) is:

For the equilibrium A ⇌ B the variation of the rate of the forward (a) and reverse (b) reaction with time is given by

[P] on treatment with Br₂ / FeBr₃ in CCl₄ produced a single isomer

For one mole of an ideal gas, which of these statements must be true

Among the statements (a)-(d), the correct ones are:

An organic compound (A)

Match the following

What are the functional groups present in the structure of maltose?

Identify the incorrect statement from the options below for the given cell:

AWS Full Form

The region in the electromagnetic spectrum where the Balmer series lines appear is:

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