If (1 + x – 2x²)⁶ = 1 + a₁x + a₂x² + ... + a₁₂x¹², then the value a₂ + a₄ + a₆ + ... + a₁₂

1

If a, b, c are in GP and log a - log 2b, log 2b - log 3c and log 3c - log a are in AP, then a, b, c are the lengths of …

Topic: NIMCET 2019

2

The solution set of the inequality  is

Topic: NIMCET 2019

3

Let S be the set $\{a\in Z^+:a\leq100\}$.If the equation $[tan^2 x]-tan x - a = 0$ has real roots (where [ . ] is the g…

Topic: NIMCET 2019

4

If \(\sum \limits_{i=1}^{n} x_i = 80\) and \(\sum \limits_{i=1}^{n} x_i^2 = 400\), then a possible value of n among the…

Topic: NIMCET 2019

5

If the mean deviation 1, 1+d, 1+2d, … , 1+100d from their mean is 255, then d is equal to

Topic: NIMCET 2019

6

If a man purchases a raffle ticket, he can win a first prize of Rs.5,000 or a second prize of Rs.2,000 with probabiliti…

Topic: NIMCET 2019

7

Let U and V be two events of a sample space S and P(A) denote the probability of an event A. Which of the following sta…

Topic: NIMCET 2019

8

Let \(f(x) = \begin{cases} \cos [x], & x\geq 0\\ |x| + a, & x< 0 \end{cases}\) where \([x]\) denotes the gre…

Topic: NIMCET 2019

9

Suppose A1, A2, ... 30 are thirty sets, each with five elements and B1, B2, ...., Bn are n sets each with three element…

Topic: NIMCET 2019

10

In a chess tournament, n men and 2 women players participated. Each player plays 2 games against every other player. Al…

Topic: NIMCET 2019

1

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

Topic: NIMCET 2019

2

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

3

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

4

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

5

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

6

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

7

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

Topic: NIMCET 2019

8

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

9

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

Topic: NIMCET 2019

10

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

Topic: NIMCET 2019