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

If $theta$ is the angle between two adjacent sides of a parallelogram and p, q are the distances between the parallel sides, then the area of the parallelogram

$fraction numerator d over denominator d x end fraction open parentheses fraction numerator a x plus b over denominator c x plus d end fraction close parentheses equals$

For such questions, we should know how to use u by v method.

$fraction numerator d over denominator d x end fraction open parentheses fraction numerator a x plus b over denominator c x plus d end fraction close parentheses equals$

For such questions, we should know how to use u by v method.

$fraction numerator d over denominator d x end fraction open parentheses e to the power of x to the power of 2 end exponent end exponent a to the power of x end exponent close parentheses equals$

For such questions, we should know u.v method.

$fraction numerator d over denominator d x end fraction open parentheses e to the power of x to the power of 2 end exponent end exponent a to the power of x end exponent close parentheses equals$

For such questions, we should know u.v method.

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

We should know different formulas to solve such questions.

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