Class 11th

Let the area of the triangle with vertices A $\left(1,\alpha \right),B\left(\alpha ,0\right)C(0,\alpha )$ be 4 sq. units. If the points $\left(\alpha ,-\alpha \right),\left(-\alpha ,\alpha \right)and\left({\alpha }^2,\beta \right)$ are collinear, then $\beta$ is equal to

Let the maximum area of the triangle that can be inscribed in the ellipse $\frac{x^2}{a^2}+\frac{y^2}{4}=1,a>2,$ having one of its vertices at one end of the major axis of the ellipse and one of its sides parallel to the y-axis, be $6\sqrt[]{3}$ . Then the eccentricity of the ellipse is

A particle is moving in the xy-plane along a curve C passing through the point (3, 3). The tangent to the curve C at the point P meets the x-axis at Q. If the y-axis bisects the segment PQ, then C is a parabola with

Let x,y > 0. If x³y² = 2¹⁵, then the least value of 3x + 2y is

Let x * y = x² + y³ and (x * 1) * 1 = x * (1 * 1). Then a value of 2 $si{n}^{-1}\left(\frac{x^4+x^2-2}{x^4+x^2+2}\right)$  is.

In an experiment to verigy Newton's law of cooling, a graph is plotted between, the temperature difference $\left(\Delta T\right)$  of the water and surrounding and time as shown in figure. The initial temperature of water is taken as $80°C.$  The value of t₂ as mentioned in the graph will be _______.

A monoatomic gas performs a work of $\frac{Q}{4}$ where Q is the heat supplied to it. The molar heat capacity of the gas will be ________ R during this transformation. Where R is the gas constant.

Two travelling waves of equal amplitudes and frequencies move in opposite directions along a string. They interfere to produce a stationary wave whose equation is given by y = $\left(10cos\pi xsin\frac{2\pi t}{T}\right)cm$

The amplitude of the particle at x = $\frac{4}{3}$ cm will be _______cm.

A body is projected from the ground at an angle of $45°$  with horizontal. Its velocity after 2s is 20 ms^-1. The maximum height reached by the body during its motion is ______m. (use g = 10ms^-2)