Recent questions tagged past papers

The trans-alkenes are formed by the reduction of alkynes with ?

asked Dec 11, 2018 by pady_1

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An alkali is titrated against an acid with methyl orange as indictor, which of the following is a correct combination ?

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The increasing order of basicity of the following compounds is :

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Phenol reacts with methyl chloroformate in the presence at $NaOH$ to form product A. A reacts with $Br_4$ to form product B. A and B respectively

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Which of the following salts is the most basic in aqueous solution ?

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The total number of lone pair of electrons in $I^-_3$ ion is :

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Let the orthocenter and centroid of a triangle be A (-3, 5) and B (3, 3) respectively. If C is the circumcentre of this triangle, then the radius of the circle having line segement AC as diameter, is :

asked Dec 11, 2018 by pady_1

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Let A be the sum of the first 20 terms and B be sum of the first 40 terms of the series $1^2 + 2.2^2 + 3^2 + 2.4^2 + 5^2+2.6^2 + ...$ If $B - 2A = 100 \lambda$, then $\lambda$ is equal to :

asked Dec 11, 2018 by pady_1

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From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. The number of such arrangements is :

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PQR is a triangular park with PQ = PR = 200 m. A. T. V. tower stands at the mid-point of QR. If the angles of elevation of the top of the tower at P, Q and R are respectively $45^{\circ},\; 30^{\circ}$ and $30^{\circ}$, then the height of the tower (in m) is :

asked Dec 11, 2018 by pady_1

2 answers

The length of the projection of the line segment joining the points $(5, -1, 4)$ and $(4, -1, 3)$ on the plane, $x+y+z=7$ is

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Let $\overrightarrow{u}$ be a vector coplanar with the vectors $\overrightarrow{a} = 2 \hat{i} + 3 \hat{j} - \hat{k} $ and $\overrightarrow{b} = \hat{j} + \hat{k}$. If $\overrightarrow{u}$ is perpendicular to and $\overrightarrow{a}$ and $\overrightarrow{u} \overrightarrow{b} = 24$, then $| \overrightarrow{u}|^2$ is equal to :

asked Dec 11, 2018 by pady_1

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Let $y = y(x)$ be the solution of the differential equation $\sin x \frac{dy}{dx} + y \cos x = 4 x, \; x \subset (0, \pi)$. If $y (\frac{\pi}{2})=0$, then $y (\frac{\pi}{6})$ is equal to

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Let $S = \{ t \in R : f(x) = |x-\pi|. (e^{|x|} - 1) \sin |x|$ is not differentiable at $t\}$. Then the set $S$ is equal to :

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The integral $\begin{align} \int \frac{\sin^2 x \cos^2 x}{(\sin^5 x + \cos^3 x \sin^2 x + \sin^3 x \cos^2x + \cos^5x)^2} \end{align} \; dx$ is equal to: (where C is a constant of integration)

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If $\displaystyle\sum_{i=1}^{9} (x_i - 5) = 9$ and $ \displaystyle\sum_{i=1}^{9} (x_i - 5)^2 = 45$ then the standard deviation of the 9 items $x_1, \; x_2, .... x_9$ is :

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For each $t \in R$ let $[t]$ be the greatest integer less than or equal to $t$. Then $ \displaystyle\lim_{x \to 0^-} x$ $\begin{pmatrix} [\frac{1}{x} +[\frac{2}{x}] +....+[\frac{15}{x}] \end{pmatrix}$

asked Dec 11, 2018 by pady_1

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Let $g(x) = \cos x^2, \; f(x) = \sqrt{x}$ and $\alpha, \;\beta \;(\alpha < \beta)$ be the roots of the quadratic equation $18x^2-9 \pi x + x^2 = 0$. Then the area (in sq. units) bounded by the curve $y=(gof)(x) $ and the lines $x = \alpha,\; x = \beta$ and $y =0$, is

asked Dec 11, 2018 by pady_1

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The value of $\begin{align} \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \frac{\sin^2 x}{1+2^x} dx \end{align}$ is :

asked Dec 11, 2018 by pady_1

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A straight line through a fixed point $(2, 3)$ intersects the coordinate axes at distinct points P and Q. If O is the origin and the rectangle OPRQ is completed, then the locus of R is

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Let $a_1, a_2, a_3,.....,a_{49}$ be in A.P. such that $\displaystyle\sum_{k=0}^{12} a_{4k+1}=416$ and $a_9 + a_{43} =66$. If $a_1^2 + a_2^2....a_{17}^2=140\;m$ then $m$ is equal to :

asked Dec 11, 2018 by pady_1

1 answer

The sum of the co-effiicients of all odd degree terms in the expansion of $(x + \sqrt{x^3-1})^5 + (x-\sqrt{x^3 - 1})^5, (x>1)$ is :

asked Dec 11, 2018 by pady_1

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If $\begin{vmatrix} x-4 & 2x & 2x \\ 2x & x-4 & 2x \\ 2x & 2x & x-4 \end{vmatrix}= (A + Bx)(x-A)^2$ then the ordered pair (A, B) is equal to :

asked Dec 11, 2018 by pady_1

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Tangent and normal are drawn at $P(16, 16)$ on the parabola $y^2 =16x$, which intersect the axis of the parabola at A and B, respectively. If $C$ is the centre of the circle through the points $P, \;A$ and $B$ and $\angle CPB=\theta$, then a value of $\tan \theta$ is :

asked Dec 11, 2018 by pady_1

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The Boolean expression $\sim (p \lor q) \lor (\sim p \land q)$ is equivalent to :

asked Dec 11, 2018 by pady_1

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Two sets A and B are as under : $A =\{ (a,b) \in R \times R : |a-5|<1$ and $|b-5| <1\} $; $B= \{(a,b) \in R \times R$: $4(a-6)^2 + 9(b-5)^2 \leq 36 \}$. Then ;

asked Dec 11, 2018 by pady_1

1 answer

Let $f(x) = x^2 + \frac{1}{x^2} $ and $g(x) = x - \frac{1}{x},\; x \in R -\{-1, 0, 1\}$. If $h(x) = \frac{f(x)}{g(x)}$, then the local minimum value of $h(x)$ is :

asked Dec 11, 2018 by pady_1

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A bag contains 4 red and 6 black balls. A ball is drawn at random from the bag, its colour is observed and this ball along with two additional balls of the same colour are returned to the bag. If now a ball is drawn at random from the bag, then the probability that this drawn ball is red, is

asked Dec 11, 2018 by pady_1

2 answers

If sum of all the solutions of the equation $8 \cos x. (\cos (\frac{\pi}{6} + x) . \cos (\frac{\pi}{6} - x) - \frac{1}{2}) = 1$ in $[0, \pi]$ is $k \pi$, then $k$ is equal to :

asked Dec 11, 2018 by pady_1

1 answer

Let $S = \{x \in R : x \geq 0$ and $2|\sqrt{x} - 3| + \sqrt{x} (\sqrt{x} - 6) + 6 = 0\}$ Then $S$ :

asked Dec 11, 2018 by pady_1

1 answer

If the system of linear equations $x+ ky + 3z=0$ $3x + ky - 2z=0$ $2x + 4y - 3z =0 $ has a non-zero solution $(x, y, z)$, then $\frac{xz}{y^2}$ is equal to :

asked Dec 11, 2018 by pady_1

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If the curves $y^2 = 6x, \; 9x^2 + by^2=16$ intersect each other at right angles, then the value of $b$ is :

asked Dec 11, 2018 by pady_1

1 answer

Tangents are drawn to the hyperbola $4x^2 - y^2 = 36$ at the points P and Q. If these tangents intersect at the point $T(0,3)$ then the area (in sq. units) of $\Delta PTQ$ is :

asked Dec 11, 2018 by pady_1

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If $\alpha, \; \beta \in C$ are the distinct roots, of the equation $x^2 - x + 1 = 0$, then $\alpha^{101} + \beta^{107} $ is equal to :

asked Dec 11, 2018 by pady_1

1 answer

If $L_1$ is the line of intersection of the planes $2x- 2y+ 3z - 2 =0,\; x- y + z+1=0$ and $L_2$ is the line of intersection of the planes $x+2y -z-3=0, \; 3x - y + 2z - 1=0$, then the distance of the origin from the plane, containing the lines $L_1$ and $L_2$, is :

asked Dec 11, 2018 by pady_1

1 answer

If the tangent at (1, 7) to the curve $x^2 = y - 6$ touches the circle $x^2 + y^2 + 16x +12 y + c = 0$ then the value of $c$ is :

asked Dec 11, 2018 by pady_1

1 answer

A particle is moving with a uniform speed in a circular orbit of radius R in a central force inversely proportional to the $n^{th}$ power of $R$. If the period of rotation of the particle is T, then :

asked Dec 11, 2018 by pady_1

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Two moles of an ideal monoatomic gas occupies a volume $V$ at $27^{\circ}C$. The gas expands adiabatically to a volume $2V$. Calculate (a) the final temperature of the gas and (b) change in its internal energy.

asked Dec 11, 2018 by pady_1

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All the graph are intendent to represent the same motion. One of them does it incorrectly. Pick it up

asked Dec 11, 2018 by pady_1

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In an a.c circuit, the instantaneous e.m.f and current are given by $e = 100 \sin 30 t$ $i = 20 \sin (30 t - \frac{\pi}{4})$ In one cycle of a.c the average power consumed by the circuit and the wattless current are, respectively :

asked Dec 11, 2018 by pady_1

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On interchanging the resistances, the balance point of a meter bridge shifts to the left by 10 cm. The resistance of their series combination is $1\; K \Omega$. How much was the resistance on the left slot before interchanging the resistances ?

asked Dec 11, 2018 by pady_1

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The density of a material in the shape of a cube is determined by measuring three sides of the cube and its mass. If the relative errors in measuring the mass and length are respectively 1.5% and 1% the maximum error in determining the density is :

asked Dec 11, 2018 by pady_1

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The dipole moment of a circular loop carrying a current I, is m and the magnetic field at the centre of the loop is $B_t$. When the dipole moment is double by keeping the current constant, the magnetic field at the centre of loop is $B_z$. The ratio $\frac{B_1}{B_2}$ is:

asked Dec 11, 2018 by pady_1

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In a collinear collision, a particle with an initial speepd $v_0$ strikes a stationary particle of the same mass. If the final kinetic energy $50\%$ greater than the original kinetic energy, the magnitude of the relative velocity between the two particles, after collision, is :

asked Dec 11, 2018 by pady_1

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From a uniform circular disc of radius R and mass 9m, a small disc of radius $\frac{R}{3}$ is removed as shown in the figure. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through centre of disc is :

asked Dec 11, 2018 by pady_1

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A silver atom in a solid oscillates in simple harmonic motion in some direction with a frequency of $10^{12}/sec$. What is the force constant of the bonds connecting one atom with the other? (Mole wt. of silver = 108 and Avagadro number = $6.02 \times 10^{23} gm\; mole^{-1}$)

asked Dec 11, 2018 by pady_1

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The angular width of the central maximum in a single slit diffraction pattern is $60^{\circ}$. The width of the slit is $ 1\; \mu m$. The slit is illuminated by monochromatic plane waves. If another slit of same width is made near it, Young's fringes can be observed on a screen placed at a distance 50 cm from the slits. If the observed fringe width is 1 cm, what is slit separation distance? (i.e. distance between the centres of each slit.)

asked Dec 11, 2018 by pady_1

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The EM wave from air enters a medium. The electric fields are $E_1 = E_{01} \hat{x} \cos [ 2 \pi v (\frac{z}{c} - t)]$ in air and $E_2 = E_{02} \hat{x} \cos [k(2z - ct)]$ in medium, where the wave number $k$ and frequency $v$ refer to their values in air. The medium is non-magnetic. If $\in_{r_1}$ and $\in_{r_2}$ refer to relative permittivities of air and medium respectively, which of the following options is correct ?

asked Dec 11, 2018 by pady_1

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Three concentric metal shells A, B and C of respective radii a, b and c (a < b < c) have surface charge densities $+\sigma, \; -\sigma$ and $+\sigma$ respectively. The potential of shell B is :

asked Dec 11, 2018 by pady_1

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In a potentiometer experiment, it is found that no current passes through the galvanometer when the terminals of the cell are connected across 52 cm of the potentiometer wire. If the cell is shunted by resistance of $5 \Omega$, a balance is found when the cell is connected across 40 cm of the wire. Find the internal resistance of the cell.

asked Dec 11, 2018 by pady_1

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