Given below are two statements : Statement I: Due to increase in van der Waals forces, the order of boiling points is \text{CH}_3\text{CH}_2\text{CH}_2\text{I} > \text{CH}_3\text{C
Consider the following reaction. The major product (P) formed is:
Which statements are True? A. In Hoffmann bromamide degradation, 4 moles \text{NaOH} and 2 moles of \text{Br}_2 are consumed per mole o amide B. Hoffmann bromamide reaction is not
The incorrect statement from the following with res to carbohydrates is : (A) All monosaccharides are reducing sugars. (B) The monosaccharide units obtained from hydrolysis of olig
Which of the following amino acid will give vi coloured complex with neutral ferric chloride solution
Number of paramagnetic complexes among the following is _____ . [\text{MnBr}_4]^{2-}, [\text{NiCl}_4]^{2-}, [\text{Ni(CN)}_4]^{2-}, [\text{Ni(CO)}_4], [\text{CoF}_6]^{3-}, [\text{F
'x' is the product which is obtained from benzene by re-acting it with carbon monoxide and hydrogen chloride in the presence of cuprous chloride. 'y' is the major product obtained
Consider two radiations of wavelengths 1. \lambda_1 = 2000\text{ \AA} 2. \lambda_2 = 6000\text{ \AA}. The ratio of the energies of these two radiations \left(\frac{E_1}{E_2}\right)
Consider the reaction 2\text{H}_2\text{S}(g) + 3\text{O}_2(g) \rightleftharpoons 2\text{H}_2\text{O}(l) + 2\text{SO}_2(g) The magnitude of enthalpy change for the reactio \text{kJ}
Solid carbon, \text{CaO} and \text{CaCO}_3 are mixed and allowe attain equilibrium at \text{T K} . \text{CaCO}_3(s) \rightleftharpoons \text{CaO}(s) + \text{CO}_2(g) \quad K_{p_1}
Consider the relation R on the set \{-2, -1, 0, 1, 2\} defined by (a, b) \in R if and only if 1 + ab > 0. Then, among the statements: I. The number of elements in R is 17 II. R is
If a straight line drawn through the point of intersec of the lines 4x + 3y - 1 = 0 and 3x + 4y - 1 = 0, m the co-ordinate axes at the points P and Q , then the lo of the mid point
Let O be the vertex of the parabola y^2 = 4x and its ch OP and OQ are perpendicular to each other. If the locu the mid-point of the line segment PQ is a conic C , the length of its
Let \alpha = 3\sin^{-1}\left(\frac{6}{11}\right) and \beta = 3\cos^{-1}\left(\frac{4}{9}\right), where inv trigonometric functions take only the principal val Given below are two s
For the function f(x) = e^{\sin |x|} - |x|, x \in \mathbf{R}, consider following statements : Statement I : f is differenti for all x \in \mathbf{R}. Statement II: f is increasing
Let the foot of perpendicular from the point (\lambda, 2, 3) on the line \frac{x-4}{1} = \frac{y-9}{2} = \frac{z-5}{1} be the point (1, \mu, 2). Then the distance between the lines
The value of the integral \int_0^2 \frac{\sqrt{x(x^2+x+1)}}{(\sqrt{x}+1)(\sqrt{x^4+x^2+1})}\,dx is equal to:
Let y = y(x) be the solution of the differential equa x\sqrt{1-x^2}\,dy + (y\sqrt{1-x^2} - x\cos^{-1}x)\,dx = 0, (0, 1), \lim_{x\to 1^-} y(x) = 1. Then y\left(\frac{1}{2}\right) eq
Let f : (1, \infty) \to \mathbf{R} be a function defined as f(x) = Let f^{i+1}(x) = f(f^i(x)), i = 1, 2, \dots, 25, where f^1(x f(x). If g(x) + f^{26}(x) = 0, x \in (1, \infty), th
Let f(x) = \begin{cases} \frac{1}{3}, & x \le \pi/2 \\ \frac{b(1-\sin x)}{(\pi-2x)^2}, & x > \pi/2 \end{cases}. If f is continuou x = \pi/2, then the value of \int_0^{3b-6} |x^2 +
The number of values of z \in \mathbb{C}, satisfying the equations |z - (4 + 8i)| = \sqrt{10} and |z - (3 + 5i)| + |z - (5 + 11i)| = 4\sqrt{5}, is:
Let \frac{x^2}{f(a^2+7a+3)} + \frac{y^2}{f(3a+15)} = 1 represent an ellipse major axis along y-axis, where f is a strictly decrea positive function on \mathbf{R}. If the set of all
The sum of squares of all the real solutions of the equa- tion \log_{(x+1)}(2x^2 + 5x + 3) = 4 - \log_{(2x+3)}(x^2 + 2x + 1) is equal to _____ .
If \int_{\pi/6}^{\pi/4}\left(\cot\left(x-\frac{\pi}{3}\right)\cot\left(x+\frac{\pi}{3}\right)+1\right)dx = \alpha\log_e(\sqrt{3}-1), then 9\alpha^2 is equal to _____ .
Let a line L_1 pass through the origin and be perpendicular to the lines L_2 : \vec{r} = (3 + t)\hat{i} + (2t - 1)\hat{j} + (2t + 4)\hat{k}\text{and} L_3 : \vec{r} = (3 + 2s)\hat{i
Consider the circle C : x^2 + y^2 - 6x - 8y - 11 = 0. a variable chord AB of the circle C subtend a right a at the origin. If the locus of the foot of the perpendic drawn from the
Let f be a polynomial function such that \log_2(f(x)) = \left(\log_2\left(2 + \frac{2}{3} + \frac{2}{9} + \dots \infty\right)\right) \cdot \log_3\left(1 + \frac{f(x)}{f(1/x)}\right
If the system of linear equations: x + y + z = 6 x + 2y + 5z = 10 2x + 3y + \lambda z = \mu has infinitely many solutions, then the value of \lambda + \mu equals:
Let A = \begin{bmatrix} \alpha & 1 & 2 \\ 2 & 3 & 0 \\ 0 & 4 & 5 \end{bmatrix} and B = \begin{bmatrix} 1 & 0 & 0 \\ 0 & -5 & \alpha \\ 0 & 4\alpha & -2\alpha \end{bmatrix} + \opera
Let \alpha = 3 + 4 + 8 + 9 + 13 + 14 + \dots upto 40 terms. If (\tan \beta)^{\frac{\alpha}{1020}} is a root of the equation x^2 + x - 2 = 0, \beta \in (0, \frac{\pi}{2}), then \sin