Practice questions
88551 published questions with worked solutions.
- If f(x) = cases (p+1)x + x x , & x < 0 q, & x = 0 x + x^2 - x x^ 3/2 , & x > 0 cases is continuous at x = 0, then the ordered...
- If the coefficients of x^2 and x^3 are both zero, in the expansion of the expression (1 + ax + bx^2)(1 - 3x)^ 15 in powers of x,...
- If the circles x^2 + y^2 + 5Kx + 2y + K = 0 and 2(x^2 + y^2) + 2Kx + 3y - 1 = 0, (K ∈ R), intersect at the points P and Q, then...
- The sum 3 1^3 1^2 + 5 (1^3 + 2^3) 1^2 + 2^2 + 7 (1^3 + 2^3 + 3^3) 1^2 + 2^2 + 3^2 + up to 10th term is:
- Let f: R R be differentiable at c ∈ R and f(c) = 0. If g(x) = |f(x)|, then at x = c, g is:
- If Q(0, −1, −3) is the image of the point P in the plane 3x − y + 4z = 2 and R is the point (3, −1, −2), then the area (in sq....
- If dx (x^2 - 2x + 10)^2 = A ( ^ -1 ( x-1 3 ) + f(x) x^2 - 2x + 10 ) + C where C is a constant of integration then:
- The line x = y touches a circle at the point (1, 1). If the circle also passes through the point (1, −3), then its radius is:
- The value of _0^ 2 [ 2x(1 + 3x)] ,dx, where [t] denotes the greatest integer function is:
- Let A(3, 0, −1), B(2, 10, 6) and C(1, 2, 1) be the vertices of a triangle and M be the midpoint of AC. If G divides BM in the...
- If the system of linear equations x + y + z = 5, x + 2y + 2z = 6, x + 3y + λz = μ, (λ, μ ∈ R), has infinitely many solutions,...
- The number of 6 digit numbers that can be formed using the digits 0, 1, 2, 5, 7 and 9 which are divisible by 11 and no digit is...
- If for some x ∈ R, the frequency distribution of the marks obtained by 20 students in a test is: | Marks | 2 | 3 | 5 | 7 |...
- If a_1, a_2, a_3, , a_n are in A.P. and a_1 + a_4 + a_7 + + a_ 16 = 114, then a_1 + a_6 + a_ 11 + a_ 16 is equal to:
- Let f(x) = e^x - x and g(x) = x^2 - x, ∀ x ∈ R. Then the set of all x ∈ R, where the function h(x) = (f∘g)(x) is increasing, is:
- If the line x − 2y = 12 is tangent to the ellipse x^2 a^2 + y^2 b^2 = 1 at the point (3, - 92 ), then the length of the latus...
- In a communication system operating at wavelength 800 nm, only one percent of source frequency is available as signal bandwidth....Not in JEE or NEET syllabus
- The magnetic field associated with a light wave is given, at the origin, by B = B_0[ (3.14 10^ 7 )ct + (6.28 10^ 7 )ct]. If this...
- A rod of mass 'M' and length '2L' is suspended at its middle by a wire. It exhibits torsional oscillations; If two masses each of...
- A series AC circuit containing an inductor (20 mH), a capacitor (120 μF) and a resistor (60 Ω) is driven by an AC source of 24...