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NIMCET 2023 #642
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If $\vec{a}=\hat{i}-\hat{k}$, $\vec{b}=x\hat{i}+\hat{j}+(1-x)\hat{k}$ and $\vec{c}=y\hat{i}+x\hat{j}+(1+x-y)\hat{k}$, then $\begin{bmatrix}{\vec{a}} & {\vec{b}} & {\vec{c}}\end{bmatrix}$ depends on
NIMCET 2023 #643
If $\vec{a}, \vec{b}$ are unit vectors such that $2\vec{a}+\vec{b} =3$ then which of the following statement is true?
NIMCET 2023 #644
NIMCET 2023 #645
$\lim _{{x}\rightarrow1}\frac{{x}^4-1}{x-1}=\lim _{{x}\rightarrow k}\frac{{x}^3-{k}^2}{{x}^2-{k}^2}=$, then find k
NIMCET 2023 #646
NIMCET 2023 #647
NIMCET 2023 #648
NIMCET 2023 #649
Given to events A and B such that odd in favour A are 2 : 1 and odd in favour of $A \cup B$ are 3 : 1. Consistent with this information the smallest and largest value for the probability of event B are given by
NIMCET 2023 #650
NIMCET 2023 #651
A bag contain different kind of balls in which 5 yellow, 4 black & 3 green balls. If 3 balls are drawn at random then find the probability that no black ball is chosen
NIMCET 2023 #652
Between any two real roots of the equation $e^x sin x = 1$, the equation $e^x cos x = –1$ has
NIMCET 2023 #653
NIMCET 2023 #654
The maximum value of $f(x) = (x – 1)^2 (x + 1)^3$ is equal to $\frac{2^p3^q}{3125}$
then the ordered pair of (p, q) will be
NIMCET 2023 #655
The coefficient of $x^{50}$ in the expression of ${(1 + x)^{1000} + 2x(1 + x)^{999} + 3x^2(1 + x)^{998} + ...... + 1001x^{1000}}$
NIMCET 2023 #656
If ${{x}}_k=\cos \Bigg{(}\frac{2\pi k}{n}\Bigg{)}+i\sin \Bigg{(}\frac{2\pi k}{n}\Bigg{)}$ , then $\sum ^n_{k=1}({{x}}_k)=?$
NIMCET 2023 #657
NIMCET 2023 #658
If n1 and n2 are the number of real valued solutions x = | sin–1 x | & x = sin (x) respectively, then the value of n2– n1 is
NIMCET 2023 #659
NIMCET 2023 #660
A point P in the first quadrant, lies on $y^2 = 4ax$, a > 0, and keeps a distance of 5a units from its focus. Which of the following points lies on the locus of P?
NIMCET 2023 #661
If $\int x\, \sin x\, sec^3x\, dx=\frac{1}{2}\Bigg{[}f(x){se}c^2x+g(x)\Bigg{(}\frac{\tan x}{x}\Bigg{)}\Bigg{]}+C$, then which of the following is true?
NIMCET 2023 #662
Let a, b, c, d be no zero numbers. If the point of intersection of the line 4ax + 2ay + c = 0 & 5bx + 2by + d=0 lies in the fourth quadrant and is equidistance from the two are then
NIMCET 2023 #663
$\theta={\cos }^{-1}\Bigg{(}\frac{3}{\sqrt[]{10}}\Bigg{)}$ is the angle between $\vec{a}=\hat{i}-2x\hat{j}+2y\hat{k}$ & $\vec{b}=x\hat{i}+\hat{j}+y\hat{k}$ then possible values of (x,y) that lie on the locus
NIMCET 2023 #664
Let R be reflexive relation on the finite set a having 10 elements and if m is the number of ordered pair in R, then
NIMCET 2023 #665
NIMCET 2023 #666
The range of values of θ in the interval (0, π) such that the points (3,5) and
(sinθ, cosθ) lie on the same side of the line x + y − 1 = 0, is
NIMCET 2023 #667
Which of the following number is the coefficient of $x^{100}$ in the expansion of $\log _e\Bigg{(}\frac{1+x}{1+{x}^2}\Bigg{)},\, |x|{\lt}1$ ?
NIMCET 2023 #668
A real valued function f is defined as $f(x)=\begin{cases}{-1} & {-2\leq x\leq0} \\ {x-1} & {0\leq x\leq2}\end{cases}$.
Which of the following statement is FALSE?
NIMCET 2023 #669
A line segment AB of length 10 meters is passing through the foot of the perpendicular of a pillar, which is standing at right angle to the ground. Top of the pillar subtends angles $tan^{–1}$ 3 and $tan^{–1} 2$ at A and B respectively. Which of the following choice represents the height of the pillar?
NIMCET 2023 #670
If a vector having magnitude of 5 units, makes equal angle with each of the three mutually perpendicular axes, then the sum of the magnitude of the projections on each of the axis is
NIMCET 2023 #671
Bag I contains 3 red, 4 black and 3 white balls and Bag II contains 2 red, 5 black and 2 white balls. One ballsis transferred from Bag I to Bag II and then a ball is drawn from Bag II. The ball so drawn is found to be black in colour. Then the probability, that the transferred is red, is:
NIMCET 2023 #672
NIMCET 2023 #684
In a reality show, two judges independently provided marks based on the performance of the participants. If the marks provided by the second judge are given by y= 1+ x, where x is the marks provided by the first judge. Then for a participant
NIMCET 2023 #698
A circle touches the x–axis and also touches the circle with centre (0, 3) and radius 2. The locus of the centre of the circle is
NIMCET 2023 #712
A university is offering elective courses in Mathematics, Economics and Sociology. Each of its 100 undergraduate students has to opt for at least one of these electives. Course enrollment data showed that 47 students enrolled for Mathematics, 47 students enrolled for Economics and 57 students enrolled for Sociology. If 7 students enrolled for all three courses, how many students enrolled for exactly one course?
NIMCET 2023 #744
A computer producing factory has only two plants $T_1$ and $T_2$. Plant $T_1$ produces 20% and plant $T_2$ produces 80% of total computers produced. 7% of computers produced in the factory turn out to be defective. It is known that P (computer turns out to be defective given that it is produced in plant $T_1$) = 10P (computer turns out to be defective given that it is produced in plant $T_2$). where P(E) denotes the probability of an event E. A computer produced in the factory is randomly selected and it does not turn out to be defective. Then the probability that it is produced in plant $T_2$ is
NIMCET 2023 #745
The mean of 5 observation is 5 and their variance is 12.4. If three of the observations are 1, 2 and 6; then the mean deviation from the mean of the data is:
NIMCET 2023 #746
The perimeter of a $\Delta ABC$ is 6 times the arithmetic mean of the sines of its angles. If the side a is 1, then the angle A is
NIMCET 2023 #747
In an examination of nine papers, a candidate has to pass in more papers than the number of papers in which he fails in order to be successful. The number of ways in which he can be unsuccessful is
NIMCET 2023 #748
For a group of 100 candidates, the mean and standard deviation of scores were found to be 40 and 15
respectively. Later on, it was found that the scores 25 and 35 were misread as 52 and 53 respectively. Then the
corrected mean and standard deviation corresponding to the corrected figures are
NIMCET 2023 #749
Consider the following frequency distribution table.
| Class interval | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 | 70-80 |
| Frequency | 180 | $f_1$ | 34 | 180 | 136 | $f_2$ | 50 |
If the total frequency is 685 & median is 42.6 then the values of $f_1$ and $f_2$ are
NIMCET 2023 #750
The sum of infinite terms of decreasing GP is equal to the greatest value of the function $f(x) = x^3
+ 3x – 9$ in the
interval [–2, 3] and difference between the first two terms is f '(0). Then the common ratio of the GP is
NIMCET 2023 #751
If $f(x)=\lim _{{x}\rightarrow0}\, \frac{{6}^x-{3}^x-{2}^x+1}{\log _e9(1-\cos x)}$ is a real number then $\lim _{{x}\rightarrow0}\, f(x)$
NIMCET 2023 #752
NIMCET 2023 #753
The equation of the tangent at any point of curve $x=a cos2t, y=2\sqrt{2} a sint$ with $m$ as its slope is
NIMCET 2023 #754
If $\prod ^n_{i=1}\tan ({{\alpha}}_i)=1\, \forall{{\alpha}}_i\, \in\Bigg{[}0,\, \frac{\pi}{2}\Bigg{]}$ where i=1,2,3,...,n. Then maximum value of $\prod ^n_{i=1}\sin ({{\alpha}}_i)$.
NIMCET 2023 #756
If $\overrightarrow{{a}}$ and $\overrightarrow{{b}}$ are vectors in space, given by $\overrightarrow{{a}}=\frac{\hat{i}-2\hat{j}}{\sqrt[]{5}}$ and $\overrightarrow{{b}}=\frac{2\hat{i}+\hat{j}+3\hat{k}}{\sqrt[]{14}}$, then the value of$(2\vec{a} + \vec{b}).[(\vec{a} × \vec{b}) × (\vec{a} – 2\vec{b})]$ is
NIMCET 2023 #757
Let $\vec{A} = 2\hat{i} + \hat{j} – 2\hat{k}$ and $\vec{B} = \hat{i} + \hat{j}$, If $\vec{C}$ is a vector such that $|\vec{C} – \vec{A}| = 3$ and the angle between A × B and C is ${30^{\circ}}$, then $|(\vec{A} × \vec{B}) × \vec{C}|$ = 3 then the value of $\vec{A}.\vec{C}$ is equal to
NIMCET 2023 #758
Let A and B be sets. $A\cap X=B\cap X=\phi$ and $A\cup X=B\cup X$ for some set X, relation between A & B
NIMCET 2023 #759
If a, b, c, d are in HP and arithmetic mean of ab, bc, cd is 9 then which of the following number is the value of ad?
NIMCET 2023 #760
NIMCET 2023 #761
The locus of the mid-point of all chords of the parabola $y^2 = 4x$ which are drawn through its vertex is