MHT CET 2019 2nd May Morning Shift

The equation of normal to the curve $y=\log _\theta x$ at the point $P(1,0)$ is ............

A stone is dropped into a pond. Waves in the form of circles are generated and radius of outermost ripple increases at the rate of $5 \mathrm{~cm} / \mathrm{sec}$. Then area increased after 2 seconds is ............

If $f(x)=3 x^3-9 x^2-27 x+15$, then the maximum value of $f(x)$ is ...........

The area of the region bounded by the curve $y=2 x-x^2$ and the line $y=x$ is ........... units. square

The general solution of the differential equation of all circles having centre at $A(-1,2)$ is ........

The value of $\int_{-3}^3\left(a x^5+b x^3+c x+k\right) d x$, where $a, b, c, k$ are constants, depends only on

\(\int_0^4 \frac{1}{1+\sqrt{x}} d x=\ldots \ldots\)

The general solution of $x \frac{d y}{d x}=y-x \tan \left(\frac{y}{x}\right)$ is .............

The order of the differential equation of all circles whose radius is 4 , is ...........

Derivative of $\log _{e^2}(\log x)$ with respect to $x$ is

If $x=\sqrt{a^{\sin ^{-1} t}}, y=\sqrt{a^{\cos ^{-1} t}}$, then $\frac{d y}{d x}=\ldots .$.

If $f(x)=3 x-2$ and $g(x)=x^2$, then $(f \circ g)(x)=$

If the lengths of the transverse axis and the latusrectum of a hyperbola are 6 and $\frac{8}{3}$ respectively, then the equation of the hyperbola is ............

If $P\left(x_1, y_1\right)$ is a point on the hyperbola $x^2-y^2=a^2$, then $S P$. S'P $=$ .............

\(\int \frac{1}{\left(x^2+1\right)^2} d x=\ldots\)

\(\int \frac{\cos x+x \sin x}{x^2+x \cos x} d x=\) ...........

\(\int \frac{\sqrt{x^2-a^2}}{x} d x=\ldots \ldots\)

The value of $\tan ^{-1} \frac{1}{3}+\tan ^{-1} \frac{1}{5}+\tan ^{-1} \frac{1}{7}+\tan ^{-1} \frac{1}{8}$ is ...........

If $f(x)=\cos ^{-1}\left[\frac{1-(\log x)^2}{1+(\log x)^2}\right]$, then $f^{\prime}(e)=\ldots$

Which of the following function is not continuous at $x=0$ ?

If the function $f(x)=\frac{\log (1+a x)-\log (1-b x)}{x}$ $x \neq 0$ is continuous at $x=0$ then, $f(0)=\ldots \ldots$

The maximum value of $z=9 x+11 y$ subject to $3 x+2 y \leq 12,2 x+3 y \leq 12, x \geq 0, y \geq 0$ is $\ldots \ldots$.

The minimum value of $z=10 x+25 y$ subject to $0 \leq x \leq 3,0 \leq y \leq 3, x+y \geq 5$ is $\ldots$

The equivalent form of the statement $\sim(p \rightarrow \sim q)$ is $\ldots$

Which of the following is not equivalent to $p \rightarrow q$.

The statement pattern $(p \wedge q) \wedge[\sim r \vee(p \wedge q)] \vee(\sim p \wedge q)$ is equivalent to ...........

If $A=\left[\begin{array}{ll}x & 1 \\ 1 & 0\end{array}\right]$ and $A=A^{-1}$, then $x=\ldots \ldots$

If $A$ is non-singular matrix such that $(A-2 l)(A-4 I)=0$ then $A+8 A^{-1}=$ ..........

A random variable X has following probability distribution

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It is observed that $25 \%$ of the cases related to child labour reported to the police station are solved. If 6 new cases are reported, then the probability that atleast 5 of them will be solved is

A bag contains 6 white and 4 black balls. Two balls are drawn at random. The probability that they are of the same colour is ...........

If the c.d.f (cumulative distribution function) is given by $F(x)=\frac{x-25}{10}$, then $P(27 \leq x \leq 33)=\ldots \ldots$

In $\triangle A B C$; with usual notations, if $\cos A=\frac{\sin B}{\sin C}$ then the triangle is ............

For a GP, if $S_n=\frac{4^n-3^n}{3^n}$, then $t_2=$ ...........

For a GP, if $(m+n)^{\text {th }}$ term is $p$ and $(m-n)^{\mathrm{th}}$ term is $q$, then $m^{\text {th }}$ term is ......

If $A=\left(x \in R: x^2-5|x|+6=0\right\}$, then $n(A)=\ldots \ldots$

 The joint equation of pair of straight lines passing through origin and having slopes $(1+\sqrt{2})$ and $\left(\frac{1}{1+\sqrt{2}}\right)$ is .......

The joint equation of the lines passing through the origin and trisecting the first quadrant is

If $P(2,2), Q(-2,4)$ and $R(3,4)$ are the vertices of $\triangle P Q R$ then the equation of the median through vertex $R$ is ......

The equation of the plane passing through the point $(-1,2,1)$ and perpendicular to the line joining the points $(-3,1,2)$ and $(2,3,4)$ is

If $G(3,-5, r)$ is centroid of triangle $A B C$ where $A(7,-8,1), B(p, q, 5)$ and $C(q+1,5 p, 0)$ are vertices of a triangle then values of $p, q, r$ are respectively ......

The co-ordinates of the foot of perpendicular drawn from origin to the plane $2 x-y+5 z-3=0$ are $\ldots \ldots$

The angle between lines $\frac{x-2}{2}=\frac{y-3}{-2}=\frac{z-5}{1}$ and $\frac{x-2}{1}=\frac{y-3}{2}=\frac{z-5}{2}$ is ............

If the line passes through the points $P(6,-1,2), Q(8,-7,2 \lambda)$ and $R(5,2,4)$ then value of $\lambda$ is ...........

The number of solutions of $\sin ^2 \theta=\frac{1}{2}$ in $[0, \pi]$ is ..........

Which of the following equations has no solution?

The values of $x$ in $\left(0, \frac{\pi}{2}\right)$ satisfying the equation $\sin x \cos x=\frac{1}{4}$ are ..........

If $\theta=\frac{17 \pi}{3}$ then, $\tan \theta-\cot \theta=\ldots$

If $\mathbf{a}+\mathbf{b}, \mathbf{b}+\mathbf{c}$ anc $\mathbf{c}+\mathbf{a}$ are coterminous edges of a parallel opiped then its volume is ..........

If $\mathbf{p}, \mathbf{q}$ and $\mathbf{r}$ are non-zero, non-coplanar vectors