Two numbers $a$ and $b$ are chosen are random from a set of the first 30 natural numbers, then the probability that $a^2 - b^2$ is divisible by 3 is

1

If $\Delta=a^2-(b-c)^2$, where $\Delta$ is the are of the triangle ABC, then $tanA=$

Topic: NIMCET 2019

2

A particle P starts from the point z0=1+2i, where i=√−1 . It moves first horizontally awa…

Topic: NIMCET 2019

3

Let $f : \mathbb{R} \to \mathbb{R}$ be defined by $f(x)=\begin{cases} x \sin\left(\frac{1}{x}\right), & x>0,\\…

Topic: NIMCET 2019

4

For the two circles $x^2+y^2=16$ and $x^2+y^2-2y=0$, there is/are

Topic: NIMCET 2019

5

If $a, a, a_2, ., a_{2n-1},b$ are in AP, $a, b_1, b_2,...b_{2n-1}, b $are in GP and $a, c_1, c_2,... c_{2n-1}, b $ are …

Topic: NIMCET 2019

6

Let f(x) be a polynomial satisfying \(f(0) = 2\), \(f'(0) = 3\) and \(f''(x) = f(x)\). Then \(f(4)\) is equal to:

Topic: NIMCET 2019

7

If $x, y, z$ are distinct real numbers, then $$ \begin{vmatrix} x & x^{2} & 2 + x^{3} \\ y & y^{2} & 2 + y^{3} \\ z &…

Topic: NIMCET 2019

8

Let \(x_i, i = 1,2,\ldots n\) be n observations and \(w_i = p x_i + k\), \(i = 1,2,\ldots n\) where p and k are constan…

Topic: NIMCET 2019

9

A man takes a step forward with probability 0.4 and backward with probability 0.6. The probability that at the end of e…

Topic: NIMCET 2019

10

If \(a\) and \(b\) are the greatest values of \(^{2n}C_r\) and \(^{2n-1}C_r\) respectively, then:

Topic: NIMCET 2019

1

A train overtakes two persons who are walking in the same direction in which the train is going, at the rate of 2 kmph …

Topic: NIMCET 2019

2

Decide which of the give conclusions logically follow from from the given students(s) :Statements:All suns are moons.So…

Topic: NIMCET 2019

3

Ten points are marked on a straight line and eleven points are marked on another straight line. How many tria…

Topic: NIMCET 2019

4

The greatest number which on dividing 1657 and 2037 leaves remainders 6 and 5 respectively, is:

Topic: NIMCET 2019

5

If F is sitting between D and E, who is sitting to the left of K?

Topic: NIMCET 2019

6

If H is sitting between L and F, then he will be facing

Topic: NIMCET 2019

7

If G and E are facing C and H respectively, the neighbours of K are

Topic: NIMCET 2019

8

The integers 34041 and 32506, when divided by a 3 - digit integer n, leave the same remainder. What can be the value of…

Topic: NIMCET 2019

9

The number of solid spheres ,each of diameter 3 cm that could be moulded  to form a solid metal cylinder of height…

Topic: NIMCET 2019

10

1.All chickens are birds.2. Some chickens are hens.3. Female birds lay eggs.If the above three statements are facts, wh…

Topic: NIMCET 2019