MAH-MHT CET (PCM/PCB) entrance exam Question Bank Solutions for Mathematics

The equation 3x² + 10xy + 8y² = 0 represents ______ 

The contrapositive of (p ∧ r) → q is ______.

Let A and B be two events such that P(A) ≠ 1 and P(B) ≠ 0, then `"P"(bar"B"/bar"A")` = ______.

The difference between the slopes of lines represented by 6x² – 5.xy + y² = 0 is ______.

If f(x) = `(sin^2x)/(1 + cotx) + (cos^2x)/(1 + tan x)`, then `"f'"(pi/4)` is ______.

The equation of tangent to the curve `(x/"a")^"n" + (y/"b")^"n"` = 2 at the point (a, b) is ______.

The point of contact of the tangent lo the circle x² + y² = 5 at the point (1, –2) which touches the circle, x² + y² – 8x + 6y + 20 = 0 is ______.

If x = a cos³θ, y = a sin³θ, then `1 + (("d"y)/("d"x))^2` is ______.

The equation of the tangent to the curve x = 2 cos³ θ and y = 3 sin³ θ at the point θ = `pi/4` is ______.

The line passing through (– 2, 0) and (1, 3) makes an angle of ______ with X-axis.

If b², a², c² are in A.P., then `1/(a + b), 1/(b + c), 1/(c + a)` will be in ______

The contrapositive of (p v q) `implies` r is ______.

The gradient of the curve passing through (4, 0) is given by `"dy"/("d"x) - "y"/x + (5x)/((x + 2)(x - 3))` = 0 if the point (5, a) lies on the curve, then the value of a is ______.

The line which passes through the origin and intersect the two lines `(x - 1)/2 = (y + 3)/4 = (z - 5)/3, (x - 4)/2 = (y + 3)/3 = (z - 14)/4`, is ______.

A ray of light coming from the point (1, 2) is reflected at a point A on the x-axis and then passes through the point (5, 3). The co-ordinates of the point A is ______.

`int 1/(x^2 + 1)^2 dx` = ______.

If `int dx/sqrt(16 - 9x^2)` = A sin^–1 (Bx) + C then A + B = ______.

The contrapositive of the statement : "If the weather is fine then my friends will come and we go for a picnic."

If planes `vecr.(phati - hatj + 2hatk) + 3` = 0 and `vecr.(2hati - phatj - hatk) - 5` = 0 include angle `π/3` then the value of p is ______.

If `int 1/((x^2 + 4)(x^2 + 9))dx = A tan^-1  x/2 + B tan^-1(x/3) + C`, then A – B = ______.