List of practice Questions

The angle between lines joining the origin to the point of intersection of the line \( \sqrt{3}x + y = 2 \) and the curve \( y^2 = x^3 \) is?

The equation of normal to the curve \( y = (1 + x) + \sin^{-1}(\sin x) \) at \( x = 0 \) is?

The value of from the Lagrange's mean value theorem for which \( f(x) = \sqrt{25 - x^2} \) in the interval \( [1,5] \) is?

Two lines \( x - y + 1 = 1 \) and \( x - 3y - k = 2 \) intersect at a point, if \( k \) is equal to?

The minimum value of \( \frac{x}{\log x} \) is?

The triangle formed by the tangent to the curve \( y = x^2 + x + 1 \) at the point \( (1, 3) \) and the coordinate axes lies in the first quadrant. If its area is 2, then the value of \( b \) is?

The statement \( p \rightarrow q \) is equivalent to?

If \( x + y = 2 \cos \theta + 5 \sin \theta \), then \( x^2 + y^2 \) is equal to?

The length of longer diagonal of the parallelogram constructed on \( 5a + 2b \) and \( a - 3b \), if it is given that \( |a| = 2\sqrt{2} \), \( |b| = 3 \), and the angle between \( a \) and \( b \) is \( \frac{\pi}{4} \), is?

If \( r = a \times b \times c + \beta \cdot a + \gamma \cdot b + [a \, b \, c] = 2 \), then \( a + \beta + \gamma \) is equal to?

If \( a \), \( b \), and \( c \) are three non-coplanar vectors and \( p, q, r \) are reciprocal vectors, then \( (p + q + r) \) is equal to?

If the integers \( m \) and \( n \) are chosen at random from 1 to 100, then the probability that a number of the form \( 7m + 7n \) is divisible by 5, equals to?

Let \( X \) denote the sum of the numbers obtained when two fair dice are rolled. The variance and standard deviation of \( X \) are?

A four digit number is formed by the digits 1, 2, 3, 4 with no repetition. The probability that the number is odd is?

The vertices of a triangle are \( A(0,4,1) \), \( B(2,-3,-1) \), and \( C(4,5,0) \), then the orthocenter of ABC is?

Which of the following isomerism is shown by ethyl acetoacetate?

The final product obtained in the reaction,

Among the following the strongest nucleophile is?

Which set has different class of compounds?

The solution of \( \frac{dy}{dx} = \frac{x^2 + y^2 + 1}{2xy} \), satisfying \( y(1) = 0 \), is given by?

If \( x \frac{dy}{dx} = x \cdot f(xy) \), then \( f(xy) \) is equal to?

The differential equation of the rectangular hyperbola, where axes are the asymptotes of the hyperbola, is?

If the elevation in boiling point of a solution of 10 g of solute (mol. wt. = 100) in 100 g of water is \( \Delta T_b \), the ebullioscopic constant of water is?

Which of the following compounds cannot be prepared singly by the Wurtz reaction?

Which of the following oxides is strongly basic?