MCA Entrance Previous Year Question Bank

Let $\vec{A}=2\hat{i}+\hat{j}-2\hat{k}$ and $\vec{B}=\hat{i}+\hat{j}$. If $\vec{C}$ is a vector such that $\vec{A}\cdot \vec{C}=|\vec{C}|,|\vec{C}-\vec{A}|=2\sqrt{2}$ and the angle between $\vec{A}\times \vec{B}$ and $\vec{C}$ is $30^{\circ }$, then $|(\vec{A}\times \vec{B})\times \vec{C}|$ is equal to:

The value of $\lambda$ such that the four points whose position vectors are $3\hat{i}-2\hat{j}+\lambda \hat{k}$, $6\hat{i}+3\hat{j}+\hat{k}$, $5\hat{i}+7\hat{j}+3\hat{k}$ and $2\hat{i}+2\hat{j}+6\hat{k}$ are coplanar is:

The value of \sin 12° \sin 48° \sin 54° is:

If $(1+\tan 1^{\circ })(1+\tan 2^{\circ })\dots (1+\tan 45^{\circ })=2^n$, then the value of $n$ is:

If $\cos \alpha +\cos \beta =a$, and $\sin \alpha +\sin \beta =b$ and $\theta$ is the arithmetic mean between $\alpha$ and $\beta$, then $\sin 2\theta +\cos 2\theta$ is equal to:

A letter is known to have come from either TATANAGAR or CALCUTTA. On the envelope, just two consecutive letters, TA, are visible. The probability that the letter has come from CALCUTTA is:

A six faced die is a biased one. It is thrice more likely to show an odd number than to show an even number. It is thrown twice. The probability that the sum of the numbers in the two throws is even is:

The value of $\lambda$ for which the volume of parallelopiped formed by the vectors $\hat{i}+\lambda \hat{j}+\hat{k}$, $\hat{j}+\lambda \hat{k}$ and $\lambda \hat{i}+\hat{k}$ is minimum is given by:

A bag contains 6 red and 4 green balls. A fair dice is rolled and a number of balls equal to that appearing on the dice is chosen from the urn at random. The probability that all the balls selected are red is:

A letter is taken at random from the letters of the word 'STATISTICS' and another letter is taken at random from the letters of the word 'ASSISTANT'. The probability that they are the same letters is: