Let $f(x)$ be a function defined by $f(x)=\begin{cases}4x-5,\ x\le2 \ x-\lambda,\ x>2 \end{cases}$ If $\lim_{x\to2} f(x)$ exists, then the value of $\lambda$ is
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Using the information from the figure, $\cos^{-1} x$ is equal to
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If $\sin(\alpha+\beta)=1,\ \sin(\alpha-\beta)=\frac{1}{2},\ \alpha,\beta\in\left[0,\frac{\pi}{2}\right]$ then the value…
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The range of the function $f(x)=\frac{2+x}{2-x},\ x\ne2$ is
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If $f(x)=x e^{x(1-x)}$, then $f(x)$ is
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The function $f(x)=x-[x]$ where $[,]$ denotes the greatest integer function is
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Let $P={\theta;\ \sin\theta - \cos\theta = \sqrt{2}\cos\theta}$ and
$Q={\theta;\ \sin\theta + \cos\theta = \sqrt{2}\sin…
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For any three sets $A, B$ and $C$ the set
$(A \cup B \cup C)\cap (A \cap B' \cap C')' \cap C'$ is equal to
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The tangent of the angle between the lines whose intercepts on the axes are respectively $a,-b$ and $b,-a$ is
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The equation of the circle whose radius is $5$ and which touches the circle
$x^2+y^2-2x-4y-20=0$ externally at the poin…
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The variance of $20$ observations is $5$. If each observation is multiplied by $2$, then the variance of the resulting …
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If the sum of $n$ terms of an AP is
$S_n=nR+\frac{1}{2}n(n-1)T$, where $R$ and $T$ are constants, then the common diffe…
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A man repays a loan of ₹ $3250$ by paying ₹ $20$ in the first month and then increases the payment by ₹ $15$ every mont…
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If the two positive numbers whose difference is $12$ and whose AM exceeds the GM by $2$, then the numbers are
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The coefficients of three consecutive terms in the expansion of $(1+x)^n$ are in the ratio $1:7:42$, then the value of …
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The number of words with or without meaning which can be made using all the letters of the word AGAIN. If these words a…
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Coefficient of variation of two distributions are $60$ and $70$ and their standard deviations are $21$ and $16$ respect…
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The equation of the normal to the curve $y=e^x$ at $(0,1)$ is
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