For which of the following curves, the line x + √3y = 2√3 is the tangent at the point (3√3/2, 1/2)?
a. x2 + 9y2 = 9 b. 2x2 – 18y2 = 9 c. y2 = x/(6√3) d. x2 + y2... View Article
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For the system of linear equations:x − 2y = 1, x − y + kz = −2, ky + 4z = 6,k ∈ R
For the system of linear equations: x − 2y = 1, x − y + kz = −2, ky + 4z... View Article
The negation of the statement ~p∧(p∨q) is∶
a. ~p∧q b. p∧~q c. ~p∨q d. p∨∼q Answer: (d) Negation of ~p∧(p∨q) is ∼[~p∧(p∨q)] ≡ p∨ ∼(p∨q) ≡ p∨(∼p∧∼q)... View Article
If the curve y = ax2 + bx + c,x ∈ R passes through the point (1, 2) and the tangent line to this curve at origin is y = x, then the possible values of a, b, c are:
a. a = 1, b = 1, c = 0 b. a = -1, b = 1, c = 1... View Article
Let f: R → R be defined as
Let f: R → R be defined as Let A = {x ∈ R ∶ f is increasing}. Then A... View Article
The value of the integral, [latex]\int_{1}^{3}\left [ x^{2}-2x-2 \right ]dx[/latex] where [x] denotes the greatest integer less than or equal to x , is :
a. –4 b. –5 c. -√2 – √3 – 1 d. -√2 – √3 + 1 Answer: (c) \(\begin{array}{l}I =... View Article
Let a, b, c be in arithmetic progression. Let the centroid of the triangle with vertices (a, c), (2, b) and (a, b) be (10/3, 7/3). If α, β are the roots of the equation ax2 + bx + 1 = 0, then the value of α2 + β2 – αβ is:
a. 71/256 b. -69/256 c. 69/256 d. -71/256 Answer: (d) 2b = a + c (2a + 2)/3 = 10/3... View Article
The probability that two randomly selected subsets of the set {1, 2, 3, 4, 5} have exactly two elements in their intersection, is:
a. 65/27 b. 135/29 c. 65/28 d. 35/27 Answer: (b) Let A and B be two subsets. For each x∈{1,2,3,4,5}... View Article
A possible value of tan (¼ sin-1 √63/8) is:
a. 1/(2√2) b. 1/√7 c. √7 – 1 d. 2√2 – 1 Answer: (b) tan (¼ sin-1 √63/8) Let sin-1(√63/8)... View Article
Let f be a twice differentiable function defined on R such that f(0) = 1, f'(0) = 2 and f'(x) ≠ 0 for all x∈R. If |f(x) f'(x) f'(x) f”(x)| = 0, for all x∈R, then the value of f(1) lies in the interval:
a. (9, 12) b. (6, 9) c. (3, 6) d. (0, 3) Answer: (b) Given f(x) f”(x) – f'(x)2 =0... View Article
The lanthanoid that does NOT shows +4 oxidation state is
1) Dy 2) Ce 3) Tb 4) Eu Answer: 4 Fact Eu does not show +4 oxidation state. Hence option 4... View Article
Which of the following compounds shows geometrical isomerism?
2) 4-methylpent-2-ene 3) 2-methylpent-2-ene 4) 4-methylpent-1-ene 4-methylpent-2-ene shows geometrical isomerism.
The major product obtained from
The major product obtained from the following reactions is: Hence option 3 is the answer.
Consider the following reactions
Consider the following reactions A→ P1; B→ P2; C→ P3; D →P4, The order of the above reactions are a,b,c... View Article
The variation of equilibrium constant with temperature is given below
The variation of equilibrium constant with temperature is given below : Temperature Equilibrium Constant T1= 250C K1= 10 T2= 1000C... View Article
Arrange the following solutions in the decreasing order of pOH
(A) 0.01 M HCl (B) 0.01 M NaOH (C) 0.01 M CH3COONa (D) 0.01 M NaCl 1) (A) > (C)... View Article
Consider the following reactions A on ozonolyzis gives B + C
Consider the following reactions: ‘A’ is: Option 1 is the answer.
For the reaction [latex]Fe_{2}N(s)+frac{3}{2}H_{2}(g)rightleftharpoons 2Fe(s)+NH_{3}(g)[/latex]
1) Kc= Kp(RT)1/2 2) Kc= Kp(RT)-1/2 3) Kc= Kp(RT)3/2 4) Kc= Kp(RT) Answer: 1 \(\begin{array}{l}Fe_{2}N(s)+\frac{3}{2}H_{2}(g)\rightleftharpoons 2Fe(s)+NH_{3}(g)\end{array} \) Δng =1-3/2 =... View Article
The species that has a spin-only magnetic moment of 5.9 BM, is: (Td= tetrahedral)
1) [Ni(CN)4]2- (square planar) 2) Ni(CO)4(Td) 3) [MnBr4]2-(Td) 4) [NiCl4]2-(Td) Answer: 3 [MnBr4]2– Hence option 3 is the answer.
The INCORRECT statement is
The INCORRECT statement is: 1) Cast iron is used to manufacture wrought iron. 2) Brass is an alloy of copper... View Article
