Consider the following propositions:

$p$: I take medicine

$q$: I can sleep

Then, the compound statement $\sim p \to \sim q$ means

1

The function $f(x)=\cos^2 x$ is strictly decreasing on

Topic: AMU MCA 2016

2

The maximum value of $\frac{\log x}{x}$ is

Topic: AMU MCA 2016

3

The sum of two numbers is $10$. Their product will be maximum when they are

Topic: AMU MCA 2016

4

$\int \sqrt{16 - 9x^2} , dx$ equals

Topic: AMU MCA 2016

5

The value of the integral $\int_{-2}^{0} \frac{dx}{\sqrt{12 - x^2 - 4x}}$ is

Topic: AMU MCA 2016

6

$\int \frac{x^3}{1 + x^4} , dx$ equals

Topic: AMU MCA 2016

7

The area bounded by the circle $x^2 + y^2 = 4$ and the line $x = y\sqrt{3}$ in the first quadrant (in sq units) is

Topic: AMU MCA 2016

8

The value of the integral $\int_{0}^{1} \frac{e^{5\log_e x} - e^{4\log_e x}}{e^{\log_e x^3} - e^{\log_e x^2}} , dx$ is

Topic: AMU MCA 2016

1

If $\left[\matrix{\alpha & \beta \cr \gamma & -\alpha}\right]$ is to be square root of the two rowed unit matrix, then …

Topic: AMU MCA 2016

2

If $A$ and $B$ are two square matrices such that $AB = A$ and $BA = B$, then

Topic: AMU MCA 2016

3

The only integral root of the equation $\left|\matrix{2 - y & 2 & 3 \cr 2 & 5 - y & 6 \cr 3 & 4 & 10 - y}\right| = 0$ …

Topic: AMU MCA 2016

4

The determinant $\left|\matrix{xp+y & x & y \cr yp+z & y & z \cr 0 & xp+y & yp+z}\right| = 0$ if

Topic: AMU MCA 2016

5

Out of $(2n+1)$ consecutively numbered tickets, three tickets are drawn at random. The probability that the numbers on …

Topic: AMU MCA 2016

6

A certain item is manufactured by machine $M_1$ and $M_2$. $M_1$ produces twice items as $M_2$. $4%$ from $M_1$ and $3%…

Topic: AMU MCA 2016

7

If $A$ and $B$ are independent events such that $P(B)=\frac{2}{7}$, $P(A \cup \overline{B})=0.8$, then $P(A)=$

Topic: AMU MCA 2016

8

If $A$ and $B$ are independent events such that $P(A^c \cap B)=\frac{2}{15}$ and $P(A \cap B^c)=\frac{1}{6}$, then $P(B…

Topic: AMU MCA 2016

9

The value of $\lambda$ so that the vectors $a = 2\hat{i} - \hat{j} + \hat{k}$, $b = \hat{i} + 2\hat{j} - 3\hat{k}$ and …

Topic: AMU MCA 2016

10

The differential equation of all parabolas whose axis of symmetry is parallel to $X$-axis is of order

Topic: AMU MCA 2016