The ionization constant of in water is 5.6 ×´ 10^-¹⁰ at 25^oC. The rate constant for the reaction of and OH^- to form NH₃ and H₂O at 25^oC is 3.4 × 10¹⁰ L mol^-¹ s^-¹. The rate constant for proton transfer from water to NH₃ is

For such questions, we should know the concept of subnormal and subtangent.

The length of the subtangent at any point on y = f(x) is 3/8 and the length of the subnormal is 24 then the ordinate of the point is

For such questions, we should know the formula to find subtangent and subnormal.

The length of the subtangent at any point on y = f(x) is 3/8 and the length of the subnormal is 24 then the ordinate of the point is

For such questions, we should know the formula to find subtangent and subnormal.

The length of the portion of the tangent at any point on the curve x^2/3 + y^2/3 = a^2/3 intercepted between the axis is

The equation of the tangent to the curve x² + 2y = 8 which is the perpendicular to x – 2y + 1 = 0 is

For such questions, we should know the formula to find the tangent and slope of lines and curves.

The equation of the tangent to the curve x² + 2y = 8 which is the perpendicular to x – 2y + 1 = 0 is

For such questions, we should know the formula to find the tangent and slope of lines and curves.

In an isosceles triangle the ends of the base are (2a, 0) and (0, a) and one side is parallel to x – axis. The third vertex is

If x + 2y + 3 = 0, x + 2y – 7 = 0 and 2x – y – 4 = 0 form the sides of square, the equation of the fourth side is

For such questions, we should know properties of square. We should know the formula to find distance between two parallel lines.

If x + 2y + 3 = 0, x + 2y – 7 = 0 and 2x – y – 4 = 0 form the sides of square, the equation of the fourth side is

For such questions, we should know properties of square. We should know the formula to find distance between two parallel lines.

The number of real values of k for which the lines x – 2y + 3 = 0, kx + 3y + 1 = 0 and 4x – ky + 2 = 0 are concurrent is

For such questions, we should know properties of concurrent lines.

The number of real values of k for which the lines x – 2y + 3 = 0, kx + 3y + 1 = 0 and 4x – ky + 2 = 0 are concurrent is

For such questions, we should know properties of concurrent lines.

The distance of the line 2x – 3y = 4 from the point (1, 1) in the direction of the line x + y = 1 is

The mid points of the sides of a triangle are (5, 0), (5, 12) and (0, 12). The orthocentre of this triangle is

The image of the point A (1, 2) by the line mirror y = x is the point B and the image of B by line mirror y = 0 is the point

If $y equals T a n to the power of negative 1 end exponent invisible function application open parentheses fraction numerator square root of 1 plus a to the power of 2 end exponent x to the power of 2 end exponent end root minus 1 over denominator a x end fraction close parentheses text then end text open parentheses 1 plus a to the power of 2 end exponent x to the power of 2 end exponent close parentheses y to the power of parallel to end exponent plus 2 a to the power of 2 end exponent x y to the power of ´ end exponent equals$

For such questions, we should know different trigonometric formulas. We should simplify the function first before finding derivatives.

If $y equals T a n to the power of negative 1 end exponent invisible function application open parentheses fraction numerator square root of 1 plus a to the power of 2 end exponent x to the power of 2 end exponent end root minus 1 over denominator a x end fraction close parentheses text then end text open parentheses 1 plus a to the power of 2 end exponent x to the power of 2 end exponent close parentheses y to the power of parallel to end exponent plus 2 a to the power of 2 end exponent x y to the power of ´ end exponent equals$

For such questions, we should know different trigonometric formulas. We should simplify the function first before finding derivatives.

If $y equals c o s to the power of negative 1 end exponent invisible function application open parentheses fraction numerator a to the power of 2 end exponent minus x to the power of 2 end exponent over denominator a to the power of 2 end exponent plus x to the power of 2 end exponent end fraction close parentheses plus s i n to the power of negative 1 end exponent invisible function application open parentheses fraction numerator 2 a x over denominator a to the power of 2 end exponent plus x to the power of 2 end exponent end fraction close parentheses text then end text fraction numerator d y over denominator d x end fraction equals$

For such questions, we should know the formulas of inverse functions.

If $y equals c o s to the power of negative 1 end exponent invisible function application open parentheses fraction numerator a to the power of 2 end exponent minus x to the power of 2 end exponent over denominator a to the power of 2 end exponent plus x to the power of 2 end exponent end fraction close parentheses plus s i n to the power of negative 1 end exponent invisible function application open parentheses fraction numerator 2 a x over denominator a to the power of 2 end exponent plus x to the power of 2 end exponent end fraction close parentheses text then end text fraction numerator d y over denominator d x end fraction equals$

For such questions, we should know the formulas of inverse functions.

If $y equals s i n invisible function application 2 x s i n invisible function application 3 x s i n invisible function application 4 x text then end text y to the power of parallel to end exponent equals$

For such questions, we should know different formulas.

If $y equals s i n invisible function application 2 x s i n invisible function application 3 x s i n invisible function application 4 x text then end text y to the power of parallel to end exponent equals$

For such questions, we should know different formulas.

$fraction numerator d over denominator d x end fraction open curly brackets Tan to the power of negative 1 end exponent invisible function application open parentheses fraction numerator square root of 1 plus x to the power of 2 end exponent end root minus 1 over denominator x end fraction close parentheses close curly brackets equals$

For such questions, we will use different formulas.

$fraction numerator d over denominator d x end fraction open curly brackets Tan to the power of negative 1 end exponent invisible function application open parentheses fraction numerator square root of 1 plus x to the power of 2 end exponent end root minus 1 over denominator x end fraction close parentheses close curly brackets equals$

For such questions, we will use different formulas.

The length of the perpendicular from the incentre of the triangle formed by the axes and the line $fraction numerator x over denominator 3 end fraction plus fraction numerator y over denominator 4 end fraction equals 1$ to the hypotenuse is