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Topic: NIMCET 2012

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Topic: NIMCET 2012

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If $\mathbf{a},\; \mathbf{b},\; \mathbf{c}$ are unit vectors such that $\mathbf{a} + \mathbf{b} + \mathbf{c} = 0$, …

Topic: NIMCET 2012

4

Focus of the parabola $x^2 + y^2 - 2xy - 4(x + y - 1) = 0$ is:

Topic: NIMCET 2012

5

If the circles $ x^2 + y^2 + 2x + 2ky + 6 = 0$ and $x^2 + y^2 + 2ky + k = 0$ intersect orthogonally, then $k$ is:

Topic: NIMCET 2012

6

The equation of ellipse with major axis along the x–axis and passes through the point $(4,3)$ and $(-1,4)$.

Topic: NIMCET 2012

7

If $(4,-3)$ and $(-9,7)$ are two vertices of a triangle and $(1,4)$ is its centroid, find the area of the triangle.

Topic: NIMCET 2012

8

In a class of 100 students, 55 passed in Mathematics and 67 passed in Physics.The number of students who passed in Phys…

Topic: NIMCET 2012

9

Coefficients a, b, c of $ax^2 + bx + c = 0$ are chosen by tossing 3 fair coins. Head means 1, Tail means 2. Find the pr…

Topic: NIMCET 2012

10

The value of $\displaystyle \int_{0}^{\sin^2 x} \sin^{-1}\sqrt{t} dt + \int_{0}^{\cos^2 x} \cos^{-1}\sqrt{t} dt$ is:

Topic: NIMCET 2012

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Topic: NIMCET 2012

2

If $ \cos(\alpha+\beta)=\frac{4}{5}$ and  $\sin(\alpha-\beta)=\frac{5}{13},\quad 0<\alpha,\beta<\frac{\pi}{4…

Topic: NIMCET 2012

3

The number of words that can be formed by using the letters of the word 'MATHEMATICS' that start as well as end with T …

Topic: NIMCET 2012

4

If $A-B=\frac{\pi}{4}$, then $(1+\tan A)(1-\tan B)$ is equal to

Topic: NIMCET 2012

5

Let $P(E)$ denote the probability of event $E$. Given $P(A) = 1$, $P(B) = \frac{1}{2}$, the values of $P(A \mid B)$ a…

Topic: NIMCET 2012

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Topic: NIMCET 2012

7

Which of the following is correct?

Topic: NIMCET 2012

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Topic: NIMCET 2012

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Topic: NIMCET 2012

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Topic: NIMCET 2012