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JEE Advance 2015
Paper-2 2015
Question
Suppose that all the terms of an arithmetic progression (A.P.) are natural numbers. If the ratio of the sum of the first seven terms to the sum of the first eleven terms is 6 : 11 and the seventh term lies in between 130 and 140, then the common difference of this A.P. is
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Showing 18 questions
QJEE Main 20242024
Let f(x) = 3 $ \sqrt{\mathrm{x}-2}+\sqrt{4-\mathrm{x}}$ be a real valued function. If $\alpha$ and $\beta$ are respectively the minimum and...
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If the value of the integral $\int_{-1}^1 \frac{\cos \alpha x}{1+3^x} d x$ is $\frac{2}{\pi}$. Then, a value of $\alpha$ is
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QJEE Main 20242024
The area (in sq. units) of the region $S=\{z \in \mathbb{C} ;|z-1| \leq 2 ;(z+\bar{z})+i(z-\bar{z}) \leq 2, \operatorname{lm}(z) \geq 0\}$...
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QJEE Main 20242024
The area (in sq. units) of the region described by $\left\{(x, y): y^2 \leq 2 x\right.$, and $...
JEE MainMathematicsEasy
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QJEE Main 20242024
Let $f(x)=\int_0^x\left(t+\sin \left(1-e^t\right)\right) d t, x \in \mathbb{R}$. Then $\lim _{x \rightarrow 0} \frac{f(x)}{x^3}$ is equal to
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QJEE Main 20242024
The value of $\frac{1 \times 2^2+2 \times 3^2+\cdots+100 \times(101)^2}{1^2 \times 2+2^2 \times 3+\cdots+100^2 \times 101}$ is
JEE MainMathematicsEasy
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QJEE MAIN 20242024
Let ABC be an isosceles triangle in which A is at $(-1,0), \angle A=\frac{2 \pi}{3}, A B=A C$ and $B$...
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QJEE MAIN 20242024
If $\frac{d x}{d y}=\frac{1+x-y^2}{y}, x(1)=1$, then $5 x(2)$ is equal to :
JEE MainMathematicsEasy
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QJEE Main 20242024
Let $A=\left[\begin{array}{ll}1 & 2 \\ 0 & 1\end{array}\right]$ and $B=I+\operatorname{adj}(A)+(\operatorname{adj} A)^2+\cdots+(\operatorname{adj} A)^{10}$. Then, the sum of all the elements of...
JEE MainMathematicsEasy
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QJEE Main 20242024
Let three real numbers 𝑎, 𝑏, 𝑐 be in arithmetic progression and a +1, b, c +3 be in geometric...
JEE MainMathematicsEasy
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QJEE MAIN 20242024
The sum of squares of all possible values of $k$, for which area of the region bounded by the parabolas...
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QJEE Main 20242024
Let a relation R on N x N be defined as : $\left(x_1, y_1\right) R\left(x_2, y_2\right)$ if and only if...
JEE MainMathematicsEasy
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QJEE MAIN 20242024
Three points $\mathrm{O}(0,0), \mathrm{P}\left(\mathrm{a}, \mathrm{a}^2\right), \mathrm{Q}\left(-\mathrm{b}, \mathrm{b}^2\right), \mathrm{a}>0, \mathrm{~b}>0$, are on the parabola $y=x^2$. Let $S_1$ be the area of...
JEE MainMathematicsEasy
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QJEE MAIN 20242024
The lines $\mathrm{L}_1, \mathrm{~L}_2, \ldots, \mathrm{I}_{20}$ are distinct. For $\mathrm{n}=1,2,3, \ldots, 10$ all the lines $\mathrm{L}_{2 \mathrm{n}-1}$ are parallel to...
JEE MainMathematicsEasy
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Q JEE MAIN 20242024
Let $\vec{a}=\hat{\imath}+\hat{\jmath}+\hat{k}, \vec{b}=-\hat{\imath}-8 \hat{\jmath}+2 \hat{k}$ and $\overrightarrow{\mathrm{c}}=4 \hat{\imath}+\mathrm{c}_2 \hat{\jmath}+\mathrm{c}_3 \hat{\mathrm{k}}$ be three vectors such that $\vec{b} \times \vec{a}=\vec{c} \times \vec{a}$....
JEE MainMathematicsEasy
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QJEE Main 20242024
Let C be a circle with radius $\sqrt{10}$ units and centre at the origin. Let the line $x+y=2$ intersects the...
JEE MainMathematicsEasy
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QJEE Main 20242024
If $\lambda>0$, let $\theta$ be the angle between the vectors $\vec{a}=\hat{\imath}+\lambda \hat{\jmath}-3 \hat{k}$ and $\vec{b}=3 \hat{\imath}-\hat{\jmath}+2 \hat{k}$. If the vectors...
JEE MainMathematicsEasy
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QJEE Main 20242024
If the function $f(x)=\left\{\begin{array}{ll}\frac{72^x-9^x-8^x+1}{\sqrt{2}-\sqrt{1+\cos x}} & , x \neq 0 \\ \log _e 2 \log _e 3 & , x=0\end{array}\right.$...
JEE MainMathematicsEasy
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