If $\vec{a}, \vec{b}$ are vector such that $|\vec{a}+\vec{b}|=\sqrt{29}$ and $\vec{a}\times (2\hat{i}+3\hat{j}+4\hat{k}) = (2\hat{i}+3\hat{j}+4\hat{k})\times \vec{b}$, then a possible value of $(\vec{a}+\vec{b})\cdot(-7\hat{i}+2\hat{j}+3\hat{k})$ is

1

Suppose a population $A$ has $100$ observations $101,102,\ldots,200$ and another population $B$ has $100$ observations …

Topic: NIMCET 2016

2

There are $4$ books on fairy tales, $5$ novels and $3$ plays. In how many ways can they be arranged in the order books …

Topic: NIMCET 2016

3

The number of points in $(-\infty,\infty)$, for which $x^2 - x\sin x - \cos x = 0$ is

Topic: NIMCET 2016

4

The vertex of the parabola whose focus is (-1,1) and directrix is 4x + 3y - 24 = 0 is

Topic: NIMCET 2016

5

Let $f(x) = x^2 - bx + c$, b is an odd positive integer. If f(x)=0 has two prime numbers as roots and b + c = 35, then …

Topic: NIMCET 2016

6

The system of equationsx + y + 2z = ax + z = b2x + y + 3z = chas a solution if

Topic: NIMCET 2016

7

If the sum of the slopes of the lines given by $x^2 - 2cxy - 7y^2 = 0$ is four times their product, then the value of $…

Topic: NIMCET 2016

8

Sum of the roots of the equation $4^x - 3(2^{x+3}) + 128 = 0$ is

Topic: NIMCET 2016

9

Let S={1,2,....,n}. The number of possible pairs of the form (A,B) with $A \subseteq B$ for subsets $A,B$ of $S$ is

Topic: NIMCET 2016

10

There are n equally spaced points 1,2,...,n marked on the circumference of a circle. If the point 15 is directly opposi…

Topic: NIMCET 2016

1

Let $x_1,x_2,\ldots,x_n$ be $n$ observations such that $\sum x_i^2 = 400$ and $\sum x_i = 80$. Then a possible value of…

Topic: NIMCET 2016

2

Area of the greatest rectangle that can be inscribed in the ellipse is

Topic: NIMCET 2016

3

. Two common tangents to the circles $x^2 + y^2 = 2a^2$ and parabola $y^2 = 8ax$ are

Topic: NIMCET 2016

4

If $a_1,a_2,\ldots,a_n$ are in A.P. and $a_1=0$ then the value of $\left(\dfrac{a_3}{a_2}+\dfrac{a_4}{a_3}+\cdots+\dfra…

Topic: NIMCET 2016

5

The value of $\cos 20^\circ + \cos 100^\circ + \cos 140^\circ$ is

Topic: NIMCET 2016

6

The permutations of ${a,b,c,d,e,f,g}$ are listed in lexicographic order. Which of the following permutations are just b…

Topic: NIMCET 2016

7

The foci of the ellipse $\dfrac{x^2}{16} + \dfrac{y^2}{b^2} = 1$ and the hyperbola $\dfrac{x^2}{144} - \dfrac{y^2}{81} …

Topic: NIMCET 2016

8

While cement is the basic raw material for producing cement tiles and cement paint which are used extensively in buildi…

Topic: NIMCET 2016

9

While cement is the basic raw material for producing cement tiles and cement paint which are used extensively in buildi…

Topic: NIMCET 2016

10

While cement is the basic raw material for producing cement tiles and cement paint which are used extensively in buildi…

Topic: NIMCET 2016