Untitled Quiz

If (f(x) = \begin{cases} x - 2 & \text{if } 0 \le x \le 2\ -2 - x & \text{if} -2 \le x < 0 \end{cases}) and (h(x) = f(|x|) + |f(x)|), then (\int_{0}^{k} h(x) , dx) is equal to (k > 0)

There are three bags A, B, and C. Bag A contains 7 Black balls and 5 Red balls, Bag B contains 5 Red and 7 Black balls and Bag C contain 7 Red and 7 Black balls. A ball is drawn and found to be black, find probability that it is drawn from Bag A.

Find the number of rational numbers in the expansion of ((\frac{2}{5} + \frac{5}{3}) ^{15})

Find the value of (\int_{0}^{\frac{\pi}{2}} \frac{sin^2x}{1+sinxcosx}, dx)

If (x^2 - ax + b = 0) has roots 2, 6; and (a = \frac{2a + 1}{17}), (β = \frac{1}{2b-a}), find equation having roots a, β.

Find the value of (lim_{x \to 4} \frac{(5 + x)^{\frac{1}{3}} - (1 + 2x)^{\frac{1}{3}}}{(5 + x)^{\frac{1}{2}} - (1 + 2x)^{\frac{1}{2}}}).

AB, BC, CA are sides of triangle having 5, 6, 7 points respectively. How many triangles are possible using these points?

2, p and q are in G.P. in an A.P. 2 is the third term, p is the 7th term, and q is the 8th term. Find p and q.

If the domain of the function (sin(\frac{3x - 22}{2x - 19} ) * (\frac{x^2 - 3x - 10}{(x-3)(x-1)})) is ([a, β]), then (3a + 10β) is equal to

Find the nontrivial solution of the system of equations:(x + (2sin20)y + 2cos20 = 0)(x + (sinθ)y + cosθ = 0)(x + (cosθ)y - sinθ = 0)

Let (f(x) = x^5 + 2e^{\frac{x}{4}}) for all x ∈ R. Consider a function ((gof)(x) = x) for all x ∈ R. Then the value of (8g’(2)) is

Let (f(x) = \frac{2x^2 - 3x + 9}{2x^2 + 3x + 4}), if maximum value of (f(x)) is m and minimum value of (f(x)) is n then find (m + n)?

The function (f(x) = \begin{cases} \frac{1-cos2x}{x^2} & x < 0 \ \alpha & x = 0 \ \frac{\sqrt{1 - cosx}}{x} & x > 0\end{cases}) is continuous at (x = 0). Find (a^2 + β^2).

Let a and β be the sum and product of all the nonzero solutions of the equation ((z)^2 + z = 0, z∈ C), then (4(a^2 + β^2)) is equal to

A square is inscribed in the circle (x^2 + y^2 - 10x - 6y + 30 = 0). One side of this square is parallel to (y = x + 3). If ((x_i, y_i)) are the vertices of the square, then (∑(x_i + y_i)^2) is equal to:

If the differential equation satisfies (\frac{dy}{dx} - y = cosx) at (x = 0, y = 1). Find (y(\frac{\pi}{4})).

Let a, β, ∈ R. Let the mean and the variance of 6 observations −3, 4, 7, −6, a, β be 2 and 23 respectively. The mean deviation about the mean of these 6 observations is

A= 2i + 2j - k and b = i - k. c is an unit vector making angle 60° with a and 45° with b. Find c.

If the length of focal chord of (y^2 = 12x) is 15 and if the distance of the focal chord from origin is p, then (10p^2) is equal to

Find the shortest distance between the lines (\frac{x + 1}{-2} = \frac{y - 2}{2} = frac{z - 1}{1}) and (\frac{x - 5}{-3} = \frac{y - 2}{2} = \frac{z - 1}{1}) is (\frac{38k}{6\sqrt{5}}). Find k.

Y = y(x) is a solution of the differential equation ((x^2 + 2x^3 + 3x^2 + 2x + 2) dy - (2x^2 + 2x + 3) dx = 0). If (y(0) =\frac{\pi}{4}), find (y(-1)).

Curve (y = 1 + 3x - 2x^2) and y = 1 intersects at point ((\frac{1}{2}, 1)) then area enclosed between curve (y = 1 + 3x - 2x^2) and y = 1. Find the value of (l+m+n) if the area is ((\sqrt{5} +m) - nlog(1 + \sqrt{5})).

When a conducting platinum wire is placed in ice, its resistance is 8Ω and when placed in steam it is 10Ω. Find the resistance of wire at 400°C.

Fractional error in image distance (v) and object distance (u) are (\frac{Δv}{v}) and (\frac{Δu}{u}) then find the fractional error in focal length of the given spherical mirror.

Instantaneous current in a circuit is zero. In which of the options voltage will be maximum.

X and y coordinates of a body performing some motion is given as: (x = 3 + 4t)(y = 3t^2 + 4t) identify the trajectory of motion.

Choose the correct graph for kinetic energy vs r for an electron revolving around a infinite line of charge.

Pressure vs temperature graph is given for gas of different density. Compare p₁, p₂ and p₃?

Work done to expand the bubble of diameter 7 cm and surface tension 40 dyne/cm is 36960 erg. Find the radius of the expanded bubble?

De-Broglie wavelength of an electron moving from n = 4 to n = 3 of a hydrogen is b(π(a_0)); where (a_0) is Bohr radius of the hydrogen atom. Find the value of b.

An elastic string under tension of 3N has a length of 'a'. If length is 'b' then tension is 2N. Find tension when length is (3a- 2b).

An electron projected inside the solenoid along its axis which carries constant current, then its trajectory would be:

Current as a function of time is given as (i = 6 + √56sin(100t + \frac{π}{3})) A. Find rms value of current.

In Celsius the temperature of a body increases by 40 °C. The increasing temperature on Fahrenheit scale is:

Force on a particle varies linearly with time(t) (F ∝ t). Then select correct acceleration vs time graph.

A cubical arrangement of 12 resistors each having resistance R is shown. Find I shown in the given circuit.

Find R_eq?

Which of the following is the correct structure of L-Glucose

How many structural isomers are there in C₇H₁₆?

Which of the following has the maximum dipole moment?

Which of the following show only one oxidation state except it's elemental state?

Number of species having sp³ hybridised central atom NO₃⁻, BCl₃, ClO₂⁻, ClO₃⁻