List of top Mathematics Questions asked in JEE Main

The number of ways, 5 boys and 4 girls can sit in a row so that either all the boys sit together or no two boys sit together is:
If the area of the region {(x,y):−1≤x≤1,0≤y≤a+e∣x∣−e−x,a>0} \{(x, y) : -1 \leq x \leq 1, 0 \leq y \leq a + e^{|x|} - e^{-x}, a> 0\} is e2+8e+1e, \frac{e^2 + 8e + 1}{e}, then the value of aa is:
If in the expansion of (1+x)p(1−x)q (1 + x)^p (1 - x)^q , the coefficients of x x and x2 x^2 are 1 and -2, respectively, then p2+q2 p^2 + q^2 is equal to:
Let x=x(y) x = x(y) be the solution of the differential equation: y=(x−ydxdy)sin⁡(xy), y>0 and x(1)=π2. y = \left( x - y \frac{dx}{dy} \right) \sin\left( \frac{x}{y} \right), \, y > 0 \, \text{and} \, x(1) = \frac{\pi}{2}. Then cos⁡(x(2)) \cos(x(2)) is equal to:
Three defective oranges are accidentally mixed with seven good ones and on looking at them, it is not possible to differentiate between them. Two oranges are drawn at random from the lot. If x x denotes the number of defective oranges, then the variance of x x is:
The area (in sq. units) of the region (x,y):0≤y≤2∣x∣+1,0≤y≤x2+1,∣x∣≤3(x, y) : 0 \leq y \leq 2|x| + 1, 0 \leq y \leq x^2 + 1, |x| \leq 3 is:
Let for some function y=f(x) y = f(x) , ∫0xtf(t) dt=x2f(x),x>0\int_0^x t f(t) \, dt = x^2 f(x), x>0 and f(2)=3 f(2) = 3 . Then f(6) f(6) is equal to:
What is the sum of the infinite series S=∑n=0∞13n S = \sum_{n=0}^{\infty} \frac{1}{3^n} ?
Let Tn−1=28T_{n-1} = 28, Tn=56T_n = 56, and Tn+1=70T_{n+1} = 70. Let A (4cos⁡t,4sin⁡t)(4\cos t, 4\sin t), B (2sin⁡t,−2cos⁡t)(2\sin t, -2\cos t), and C (3rn−1,rn2−n−1)(3r_n - 1, r^2_n - n - 1) be the vertices of a triangle ABC, where tt is a parameter. If (3x−1)2+(3y)2=a(3x - 1)^2 + (3y)^2 = a, is the locus of the centroid of triangle ABC, then aa equals:
The number of different 5 digit numbers greater than 50000 that can be formed using the digits 0, 1, 2, 3, 4, 5, 6, 7, such that the sum of their first and last digits should not be more than 8, is:
If the equation of a circle is 4x2+4y2−12x+8y=0 4x^2 + 4y^2 - 12x + 8y = 0 , what is the radius of the circle?
What is the solution to the differential equation dydx=yx \frac{dy}{dx} = \frac{y}{x} with the initial condition y(1)=2 y(1) = 2 ?
Let the equation of the circle, which touches x-axis at the point (a,0) (a, 0) and cuts off an intercept of length b b on y-axis be x2+y2−cx+dy+e=0 x^2 + y^2 - cx + dy + e = 0 . If the circle lies below x-axis, then the ordered pair (2a,b2) (2a, b^2) is equal to:
Let A (x,y,z)(x, y, z) be a point in xyxy-plane, which is equidistant from three points (0, 3, 2), (2, 0, 3) and (0, 0, 1). Let B (1,4,−1)(1, 4, -1) and C (2,0,−2)(2, 0, -2). Then among the statements:
(S1): ABC is an isosceles right angled triangle, and
(S2): the area of △ABC\triangle ABC is 922 \frac{9\sqrt{2}}{2} .
The value of cos⁡(sin⁡−1(−35)+sin⁡−1(513)+sin⁡−1(−3365)) \cos \left( \sin^{-1} \left(-\frac{3}{5}\right) + \sin^{-1} \left(\frac{5}{13}\right) + \sin^{-1} \left(-\frac{33}{65}\right) \right) is:
Two numbers k1k_1 and k2k_2 are randomly chosen from the set of natural numbers. Then, the probability that the value of ik1+ik2i^{k_1} + i^{k_2} (where i=−1i = \sqrt{-1}) is non-zero equals:
Let Tr T_r be the rth r^{th} term of an A.P. If for some m m , Tm=125 T_m = \frac{1}{25} , T25=120 T_{25} = \frac{1}{20} , and ∑r=125Tr=13 \sum_{r=1}^{25} T_r = 13 , then 
5m∑r=m2mTr is equal to: 5m \sum_{r=m}^{2m} T_r \text{ is equal to:}  
For the function f(x)=ln⁡(x2+1) f(x) = \ln(x^2 + 1) , what is the second derivative of f(x) f(x) ?
The relation R={(x,y):x,y∈Z and x+y is even} R = \{(x, y) : x, y \in \mathbb{Z} \text{ and } x + y \text{ is even} \} is: 
Find the value of the integral ∫0π2sin⁡2(x) dx \int_0^{\frac{\pi}{2}} \sin^2(x) \, dx .
If f(x)=2x2x+2 f(x) = \frac{2^x}{2^x + \sqrt{2}} , x∈Rx \in \mathbb{R}, then ∑k=181f(k82)\sum_{k=1}^{81} f\left(\frac{k}{82}\right) is equal to:
If the image of the point (4,4,3) (4, 4, 3) in the line x−12=y−21=z−13 \frac{x-1}{2} = \frac{y-2}{1} = \frac{z-1}{3} is (a,β,γ) (a, \beta, \gamma) , then a+β+γ a + \beta + \gamma is equal to:
Let f:R→R f: \mathbb{R} \to \mathbb{R} be a function defined by f(x)=(2+3a)x2+(a+2a−1)x+b,a≠1 f(x) = \left( 2 + 3a \right)x^2 + \left( \frac{a+2}{a-1} \right)x + b, a \neq 1 . If f(x+y)=f(x)+f(y)+1−27xy, f(x + y) = f(x) + f(y) + 1 - \frac{2}{7}xy, then the value of 28∑i=15f(i) 28 \sum_{i=1}^5 f(i) is:
Let A=[aij] A = [a_{ij}] be a square matrix of order 2 with entries either 0 or 1. Let E E be the event that A A is an invertible matrix. Then the probability P(E) P(E) is:
Let (2,3) (2, 3) be the largest open interval in which the function f(x)=2log⁡e(x−2)−x2+ax+1 f(x) = 2 \log_e (x - 2) - x^2 + ax + 1 is strictly increasing, and (b,c) (b, c) be the largest open interval, in which the function g(x)=(x−1)3(x+2−a)2 g(x) = (x - 1)^3 (x + 2 - a)^2 is strictly decreasing. Then 100(a+b−c) 100(a + b - c) is equal to: