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 $c = 3\hat{i} + \lambda \hat{j} + 5\hat{k}$ are coplanar is

1

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

2

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

3

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

4

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

Topic: AMU MCA 2016

5

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

6

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

7

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

Topic: AMU MCA 2016

8

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

9

Consider the following propositions:$p$: I take medicine$q$: I can sleepThen, the compound statement $\sim p \to \sim q…

Topic: AMU MCA 2016

10

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

Topic: AMU MCA 2016

1

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

Topic: AMU MCA 2016

2

If $p$ and $q$ are the order and degree of the differential equation $y \frac{dy}{dx} + x^3\left(\frac{d^2y}{dx^2}\rig…

Topic: AMU MCA 2016

3

The equation $x^2 + y^2 + 4x + 6y + 13 = 0$ represents

Topic: AMU MCA 2016

4

The two lines $ty = x + t^2$ and $y + tx = 2t + t^3$ intersect at the point lies on the curve whose equation is

Topic: AMU MCA 2016

5

The directrix of the parabola $4y^2 + 12x - 12y + 39 = 0$ is

Topic: AMU MCA 2016

6

A line perpendicular to the line segment joining the points $(1,0)$ and $(2,3)$ divides it in the ratio $1:n$. The equa…

Topic: AMU MCA 2016

7

If origin is the centroid of a $\triangle PQR$ with vertices $P(2a,2,6)$, $Q(-4,3b,-10)$ and $R(8,14,2c)$, then the val…

Topic: AMU MCA 2016

8

The angle between the lines with direction ratios $(4,-3,5)$ and $(3,4,5)$ is

Topic: AMU MCA 2016

9

Given that the points $P(3,2,-4)$, $Q(5,4,-6)$ and $R(9,8,-10)$ are collinear, the ratio in which $Q$ divides $PR$ exte…

Topic: AMU MCA 2016

10

The minimum value of $9^x + 9^{1-x}$, $x \in R$ is

Topic: AMU MCA 2016