List of practice Questions

x	4	5	6	7	8	9
f	6	4	5	8	6	9
Total	10

If tan \(A = \frac{1}{\sqrt{3}}\) and tan \(B = \sqrt{3}\) then \(\cos A - \cos B - \sin A \cdot \sin B\) will be equal to

Distance between two lines \(3x + 4y - 9 = 0\) and \(3x + 4y + 10 = 0\) is

\(\sqrt{3}\) is

Value of 1 Radian is:

If \( A = \frac{x+1}{x-1} \) and \( B = \frac{x-1}{x+1} \), then \( A + B \) is:

If (1,5) is the midpoint of the segment of a line between the lines 5x −y −4 = 0 and 3x +4y −4=0,then the equation of the line will be:

A circle \( S \) passes through the points of intersection of the circles \( x^2 + y^2 - 2x - 3 = 0 \) and \( x^2 + y^2 - 2y = 0 \). If \( x + y + 1 = 0 \) is a tangent to the circle \( S \), then the equation of \( S \) is:

Let \( [P] \) denote the greatest integer \( \leq P \). If \( 0 \leq a \leq 2 \), then the number of integral values of \( a \) such that \( \lim_{x \to a} [x^2] - [x]^2 \) does not exist is:

Consider a circuit where a cell of emf \( E_0 \) and internal resistance \( r \) is connected across the terminal A and B as shown in the figure. The value of \( R \) for which the power generated in the circuit is maximum, is given by:

When two objects are moving along a straight line in the same direction, the distance between them increases by 6 m in one second. If the objects move with their constant speed towards each other, the distance decreases by 8 m in one second. Then the speed of the objects are:

For the curve \[ y = \alpha x^2 + \cos y + \beta, \] the value of \( \frac{dy}{dx} \) at \( (1,0) \) is 2. Then the value of \( \alpha \beta \) is equal to

The total energy of a gas mixture of one mole of oxygen and 3 moles of argon at a temperature \( T \) by neglecting vibrational modes is:

If three sources of sound of frequencies \( (n-1), n, (n+1) \) are vibrated together, the number of beats produced and heard per second respectively are:

The perimeter of two squares are 40 cm and 32 cm. The perimeter of a third square whose area is equal to the difference of the areas of the two squares is :

If the temperature of a gas is increased from \( 27^\circ C \) to \( 159^\circ C \), the increase in the rms speed of the gas molecules is:

A dealer sold three-fourth of his articles at a gain of 20% and the remaining at cost price. What is the gain earned by him in the whole transaction?

Mr. Jones gave 40% of the money he had to his wife. He also gave 20% of the remaining amount to each of his three sons. Half of the amount now left was spent on miscellaneous items and the remaining amount of 12,000 was deposited in the bank. What amount of money did Mr. Jones have initially?

The average of 25 results is 18. The average of the first twelve of them is 14 and that of the last twelve is 17. What is the thirteenth result?

If the length of a string is \(P\) when the tension in it is 6 N and its length is \(Q\) when the tension in it is 8 N, then the original length of the string is:

The pie chart provided below gives the distribution of land in a village under various food crops. Which combination of three crops contribute to 50% of the total area under the food crops ?