List of practice Questions

A box contains 20 identical balls of which 10 are blue and 10 are green. The balls are drawn at random from the box one at a time with replacement. The probability that a blue ball is drawn 4th time on the 7th draw is
The number of common tangents to the circles \( x^2 + y^2 = 16 \) and \( x^2 + y^2 - 6x = 0 \) is
The value of \( \cos \left( \cos^{-1} \left( \frac{1}{3} \right) \right) \) is equal to
Consider the objective function \( Z = 40x + 50y \). The minimum number of constraints that are required to maximize \( Z \) are
In a culture the bacteria count is 1,00,000. The number is increased by 10% in 2 hours. In how many hours will the count reach 2,00,000 if the rate of growth of bacteria is proportional to the number present?
The value of \( \sin^{-1} \left( \frac{1}{\sqrt{5}} \right) + \cot^{-1}(3) \) is
If \( a = \cos 2\alpha + \sin 2\alpha, b = \cos 2\beta + \sin 2\beta, c = \cos 2\gamma + \sin 2\gamma \) and \( \cos 2\alpha + \cos 2\beta + \cos 2\gamma = 1 \), then \[ \sqrt{abc} = \text{?} \]
The mean of a binomial distribution is 25, then its standard deviation lies in the interval
If \( e^x = y + \sqrt{1 + y^2} \), then the value of \( y \) is
What is the area of a loop of the curve \( y = \sin 30^\circ \)?
Convert the hexadecimal numeral ABCD into binary numeral
The normal at the point \( (t_1, t_2) \) on the parabola, cuts the parabola again at the point whose parameter is
The distance moved by the particle in time \( t \) is given by \[ s = t^3 - 12t^2 + 6t + 8 \] At the instant, when its acceleration is zero, its velocity is
If \( |a| = 3, |b| = 2, |c| = 1 \) then the value of \[ |a \cdot b + b \cdot c + c \cdot c| \text{ is} \]
If \( A \) and \( B \) are matrices and \( AB = BA = A^{-1} \) then the value of \( (A + B)(A - B) \) is
The value of \( (1 + \omega)^3 \), where \( \omega = e^{i 2\pi/3} \) is
The moment about the point \( 2i + 3j + k \) of a force represented by \( i + j + k \) acting through the point \( 2i + 3j + k \) is
The equation of one of the common tangents to the parabola \( y^2 = 8x \) and \( x^2 = 4y - 4 \) is
The distance moved by the particle in time \( t \) is given by \[ s = t^3 - 12t^2 + 6t + 8 \] At the instant, when its acceleration is zero, its velocity is
The equation of one of the common tangents to the parabola \( y^2 = 8x \) and \( x^2 = 4y - 4 \) is
If the tangent to the function \( y = f(x) \) at \( (3, 4) \) makes an angle of \( \frac{3\pi}{4} \) with the positive direction of the x-axis in anticlockwise direction, then \( f'(3) \) is
The probability of India winning a test match against Australia is \( \frac{1}{2} \), assuming independence from match to match. The probability that in a match series India’s second win occurs at third test match is
The following data were obtained for a given reaction at 300 K. \[ \begin{array}{|c|c|} \hline \text{Reaction} & \text{Energy of activation (kJ mol}^{-1}\text{)} \\ \hline \text{(i) Uncatalysed} & 76 \\ \text{(ii) Catalysed} & 57 \\ \hline \end{array} \] The factor by which the rate of catalysed reaction is increased is
The foci of the ellipse \( \frac{x^2}{144} + \frac{y^2}{81} = 1 \) and the hyperbola \( \frac{x^2}{144} - \frac{y^2}{81} = 1 \) coincide then value of \( b^2 \) is
Which of the following reactions of xenon compounds is not feasible?