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If the mean and variance of observations $x, y, 12, 14, 4, 10, 2$ is 8 and 16 respectively, where $x>y$, then the value of $3x-y$ is:

Ellipse E: $\frac{x^{2}}{36}+\frac{y^{2}}{16}=1$. A hyperbola is confocal with the ellipse and the eccentricity of the hyperbola is equal to 5. If the principal axis of the hyperbola is the x-axis, then the length of the latus rectum of the hyperbola is:

Consider the following reaction: $Ca+2HCl \rightarrow CaCl_2+H_2$. If 14g of calcium reacts with excess HCl, choose the incorrect option.

80 mL of an organic compound is mixed with 264 mL of $O_{2}$ and ignited. It gives 224 mL of gaseous mixture at NTP. After passing through KOH, 64 mL of gas remains. The organic compound is:

If the electric field of an EM wave is given by $60[\sin(3\times10^{14}t)+\sin(12\times10^{14}t)]$ at $x=0$ and it falls on a photosensitive material having work function $2.8 eV$, find the maximum kinetic energy (in eV) of the ejected electrons.

Find the moment of inertia of the system formed using two identical rods about the given axis of rotation as shown in the figure. Each rod has mass M and length L.

If $x^{2}+x+1=0$ then evaluate $(x+\frac{1}{x})^{4}+(x^{2}+\frac{1}{x^{2}})^{4}+...+(x^{25}+\frac{1}{x^{25}})^{4}$

Observe the following reaction sequence: $(P)\xrightarrow{NH_{3}, \Delta}(Q)\xrightarrow{Br_{2}/KOH}(R)$. Which of the following is the correct structure for P, Q and R? (Refer to image)

An air-filled capacitor of capacitance $C$ is filled with a dielectric $(k=3)$ of width $\frac{d}{3}$, where $d$ is the separation between the plates. The new capacitance is:

An $\alpha$-particle having kinetic energy $7.7 MeV$ is approaching a fixed gold nucleus (atomic number $Z=79$). Find the distance of closest approach. (Duplicate Question)

If O is the vertex of the parabola $x^{2}=4y$, Q is a point on the parabola. If C is the locus of a point which divides OQ in the ratio 2:3, then the equation of the chord of C which is bisected at the point (1,2) is:

An $\alpha$-particle having kinetic energy $7.7 MeV$ is approaching a fixed gold nucleus (atomic number $Z=79$). Find the distance of closest approach.

If $a_{1}, a_{2}, a_3,...$ are in increasing geometric progression such that $a_{1}+a_{3}+a_{5}=21$ and $a_{1}a_{3}a_{5}=64$, then $a_{1}+a_{2}+a_{3}$ is:

The locus of the point of intersection of tangents drawn to the circle $(x-2)^{2}+(y-3)^{2}=16$ which subtends an angle of $120^{\circ}$ is:

Benzene undergoes the following sequence of reactions (see figure). Find the percentage of nitrogen in compound (E).

Find the heat produced in the external circuit (AB) in one second (refer to circuit diagram).

Find dimensions of $\frac{A}{B}$ if $(P+\frac{A^{2}}{B})+\frac{1}{2}\rho V^{2}=$ constant, where $P\rightarrow$ pressure, $\rho\rightarrow$ density, $V$ speed.

If $y=y(x)$ and $(1+x^{2})dy+(1-\tan^{-1}x)dx=0$ and $y(0)=1$ then $y(1)$ is equal to:

An organic compound (A) undergoes the following reactions (see figure). Which of the following is compound (A)?

Correct order of acidic strength: (I) Phenol, (II) p-Cresol, (III) m-Nitrophenol, (IV) p-Nitrophenol