Let \(f(x) = \begin{cases} \cos [x], & x\geq 0\\ |x| + a, & x< 0 \end{cases}\) where \([x]\) denotes the greatest integer \(\leq x\). If f should be continuous at \(x = 0\) then a must be:
Previous 10 Questions — NIMCET 2019
Nearest first
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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
In a chess tournament, n men and 2 women players participated. Each player plays 2 games against every other player. Al…
Topic: NIMCET 2019
\(\vec{a}\) and \(\vec{b}\) are non-zero non-collinear vectors such that \(|\vec{a}| = 2\), \(\vec{a}\cdot \vec{b} = 1\…
Topic: NIMCET 2019
The $sin^2 x tanx + cos^2 x cot x-sin2x=1+tanx+cotx $, $x \in (0 , \pi)$, then x
Topic: NIMCET 2019
The position vectors of the vertices A, B, C of a tetrahedron ABCD are \(\hat{i} + \hat{j} + \hat{k}\), \(\hat{i}\) and…
Topic: NIMCET 2019
Equation of the tangent from the point (3,−1) to the ellipse 2x2 + 9y2 = 3 is
Topic: NIMCET 2019
If , then the values of A1, A2, A3, A4 are
Topic: NIMCET 2019
If x is real, then the minimum value of $\dfrac{x^2-x+1}{x^2+x+1}$is:
Topic: NIMCET 2019
Let $X_i, i = 1,2,.. , n$ be n observations and $w_i = px_i +k, i = 1,2,
,n$ where p and k are constants. If the mean o…
Topic: NIMCET 2019
The median AD of ΔABC is bisected at E and BE is extended to meet the side AC in F. The AF : FC =
Topic: NIMCET 2019
Next 10 Questions — NIMCET 2019
Ascending by ID
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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
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
If the mean deviation 1, 1+d, 1+2d, … , 1+100d from their mean is 255, then d is equal to
Topic: NIMCET 2019
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
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
The solution set of the inequality is
Topic: NIMCET 2019
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
If (1 + x – 2x2)6 = 1 + a1x + a2x2 + ... + a12x12,
then the value a2 + a4 + a6 + ... + a12
Topic: NIMCET 2019
If \(a\) and \(b\) are the greatest values of \(^{2n}C_r\) and \(^{2n-1}C_r\) respectively, then:
Topic: NIMCET 2019
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
