List of top Mathematics Questions asked in JEE Main

If the value of $\frac{\cos^2 48^\circ - \sin^2 12^\circ}{\sin^2 24^\circ - \sin^2 6^\circ}$ is $\frac{\alpha + \beta\sqrt{5}}{\gamma}$ then value of $(\alpha + \beta + \gamma)$ (where $\alpha, \beta, \gamma \in \mathbb{N}$ and are in lowest form) :

If \[ \frac{\cos^2 48^\circ - \sin^2 12^\circ}{\sin^2 24^\circ - \sin^2 6^\circ} = \frac{\alpha + \sqrt{5}\,\beta}{2}, \] then the value of $(\alpha + \beta)$ is

The number of values of $x$ satisfying \[ \tan^{-1}(4x)+\tan^{-1}(6x)=\frac{\pi}{6}, \quad x\in\left[-\frac{1}{2\sqrt{6}},\,\frac{1}{2\sqrt{6}}\right] \] is

The value of \[ \int_{\frac{\pi}{2}}^{\pi} \frac{dx}{[x]+4} \] where $[\,\cdot\,]$ denotes the greatest integer function, is

Let $ M = \{1,2,3,\ldots,16\} $ and $ R $ be a relation on $ M $ defined by $ xRy $ if and only if $ 4y = 5x - 3 $. Then, the number of ordered pairs required to be added to $ R $ to make it symmetric is

Let $ A = \begin{bmatrix} 3 & -4 \\ 1 & -1 \end{bmatrix} $ and $ B = \begin{bmatrix} 29 & 49 \\1 & 2 \end{bmatrix} $. If $ (A^5 + B)\begin{bmatrix} x\\ y \end{bmatrix} = \begin{bmatrix} 0 \\ 0 \end{bmatrix} $, then find $ (x, y) $.

If all the words with or without meaning made using all the letters of the word "KANPUR" are arranged as in a dictionary, then the word at 440^th position in this arrangement is:

Let R = {(1, 2), (2, 3), (3, 3)}} be a relation defined on the set $ \{1, 2, 3, 4\} $. Then the minimum number of elements needed to be added in $ R $ so that $ R $ becomes an equivalence relation, is:

The value of $ (\sin 70^\circ)(\cot 10^\circ \cot 70^\circ - 1) $ is:

Suppose that the number of terms in an A.P. is $ 2k, k \in \mathbb{N} $. If the sum of all odd terms of the A.P. is 40, the sum of all even terms is 55, and the last term of the A.P. exceeds the first term by 27, then $ k $ is equal to:

Let $ a_n $ be the $ n $-th term of an A.P. If $ S_n = a_1 + a_2 + a_3 + \cdots + a_n = 700 $, $ a_6 = 7 $, and $ S_7 = 7 $, then $ a_n $ is equal to:

Suppose that the number of terms in an A.P. is $ 2k, k \in \mathbb{N} $. If the sum of all odd terms of the A.P. is 40, the sum of all even terms is 55, and the last term of the A.P. exceeds the first term by 27, then $ k $ is equal to:

Let a circle C pass through the points (4, 2) and (0, 2), and its centre lie on $3x + 2y + 2 = 0$. Then the length of the chord of the circle C, whose midpoint is (1, 2), is:

Let $ A(6,8) $, $ B(10\cos\alpha, -10\sin\alpha) $, and $ C(-10\sin\alpha, 10\cos\alpha) $ be the vertices of a triangle. If $ L(a,9) $ and $ G(h,k) $ be its orthocenter and centroid respectively, then $ 5a - 3h + 6k + 100\sin2\alpha $ is equal to _____ .

Let I be the identity matrix of order 3 × 3 and for the matrix $ A = \begin{pmatrix} \lambda & 2 & 3 \\ 4 & 5 & 6 \\ 7 & -1 & 2 \end{pmatrix} $, $ |A| = -1 $. Let B be the inverse of the matrix $ \text{adj}(A \cdot \text{adj}(A^2)) $. Then $ |(\lambda B + I)| $ is equal to _______

For a $ 3 \times 3 $ matrix $ M $, let trace(M) denote the sum of all the diagonal elements of $ M $. Let $ A $ be a $ 3 \times 3 $ matrix such that $ |A| = \frac{1}{2} $ and $ \text{trace}(A) = 3 $. If $ B = \text{adj}(\text{adj}(2A)) $, then the value of $ |B| + \text{trace}(B) $ equals:

The number of terms of an A.P. is even; the sum of all the odd terms is 24, the sum of all the even terms is 30 and the last term exceeds the first by $ \frac{21}{2} $. Then the number of terms which are integers in the A.P. is:

Let A, B, C be three points in the xy-plane, whose position vectors are given by $ \sqrt{3} \hat{i} + \hat{j} $, $ \hat{i} + \sqrt{3} \hat{j} $, and $ a\hat{i} + (1-a) \hat{j }$ respectively with respect to the origin $ O $. If the distance of the point C from the line bisecting the angle between the vectors $ \overrightarrow{OA} $ and $ \overrightarrow{OB} $ is $ \frac{9}{\sqrt{2}} $, then the sum of all possible values of $ a $ is:

Let $ P_n = \alpha^n + \beta^n $, $ n \in \mathbb{N} $. If $ P_{10} = 123,\ P_9 = 76,\ P_8 = 47 $ and $ P_1 = 1 $, then the quadratic equation having roots $ \alpha $ and $ \frac{1}{\beta} $ is:

Let $ T_r $ be the $ r^{\text{th}} $ term of an A.P. If for some $ m $, $ T_m = \dfrac{1}{25} $, $ T_{25} = \dfrac{1}{20} $, and $ \displaystyle\sum_{r=1}^{25} T_r = 13 $, then $ 5m \displaystyle\sum_{r=m}^{2m} T_r $ is equal to:

Let $ \langle a_n \rangle $ be a sequence such that $ a_0 = 0 $, $ a_1 = \frac{1}{2} $, and $ 2a_{n+2} = 5a_{n+1} - 3a_n $.n= 0,1,2,3.... Then $ \sum_{k=1}^{100} a_k $ is equal to:

Let $ A = \{-3, -2, -1, 0, 1, 2, 3\} $ and $ R $ be a relation on $ A $ defined by $ xRy $ if and only if $ 2x - y \in \{0, 1\} $. Let $ l $ be the number of elements in $ R $. Let $ m $ and $ n $ be the minimum number of elements required to be added in $ R $ to make it reflexive and symmetric relations, respectively. Then $ l + m + n $ is equal to:

Number of functions $ f: \{1, 2, \dots, 100\} \to \{0, 1\} $, that assign 1 to exactly one of the positive integers less than or equal to 98, is equal to:

Let the range of the function \[ f(x) = 6 + 16 \cos x \cdot \cos\left(\frac{\pi}{3} - x\right) \cdot \cos\left(\frac{\pi}{3} + x\right) \cdot \sin 3x \cdot \cos 6x, \quad x \in R \text{ be } [\alpha, \beta]. \] Then the distance of the point $(\alpha, \beta)$ from the line $3x + 4y + 12 = 0$ is:

The value of $ \cot^{-1} \left( \frac{\sqrt{1 + \tan^2(2)} - 1}{\tan(2)} \right) - \cot^{-1} \left( \frac{\sqrt{1 + \tan^2 \left( \frac{1}{2} \right)} + 1}{\tan \left( \frac{1}{2} \right)} \right) $ is equal to: