Mathematics questions
18011 published questions with worked solutions.
- A plane passing through the points (0, −1, 0) and (0, 0, 1) and making an angle 4 with the plane y − z + 5 = 0, also passes...
- If the tangent to the curve, y = x^3 + ax - b at the point (1, −5) is perpendicular to the line, −x + y + 4 = 0, then which one...
- If the fourth term in the Binomial expansion of ( 2x + x^ _8x )^6 (x > 0) is 20 8^7, then a value of x is:
- The area (in sq. units) of the region A = (x, y) : x^2 y x + 2 is:
- If _ x 1 x^2-ax+b x-1 = 5, then a + b is equal to:
- The locus of the centres of the circles, which touch the circle, x^2 + y^2 = 1 externally, also touch the y-axis and lie in the...
- The number of real roots of the equation 5 + |2^x - 1| = 2^x(2^x - 2) is:
- A spherical iron ball of radius 10 cm is coated with a layer of ice of uniform thickness that melts at a rate of 50 cm^3/min....
- The sum 1 + 1^3+2^3 1+2 + 1^3+2^3+3^3 1+2+3 + + 1^3+2^3+3^3+ +15^3 1+2+3+ +15 - 1 2 (1+2+3+ +15) is equal to:
- If the plane 2x - y + 2z + 3 = 0 has the distances 1 3 and 2 3 units from the planes 4x - 2y + 4z + = 0 and 2x - y + 2z + = 0,...
- Let f(x) = _e( x), (0 < x < ) and g(x) = ^ -1 (e^ -x ), (x 0). If α is a positive real number such that a = (f g)'( ) and b = (f...
- The angles A, B and C of a triangle ABC are in A.P. and a : b = 1 : 3. If c = 4 cm, then the area (in sq. cm) of this triangle is:Not in JEE syllabus
- Minimum number of times a fair coin must be tossed so that the probability of getting at least one head is more than 99% is:
- Let λ be a real number for which the system of linear equations x + y + z = 6, 4x + y - z = - 2, 3x + 2y - 4z = -5 has infinitely...
- If z and w are two complex numbers such that |zw| = 1 and (z) - (w) = 2 , then:
- The smallest natural number n, such that the coefficient of x in the expansion of (x^2 + 1 x^3 )^n is ^nC_ 23 , is:
- The sum of the real roots of the equation vmatrix x & -6 & -1 2 & -3x & x-3 -3 & 2x & x+2 vmatrix = 0, is equal to:
- If 5x + 9 = 0 is the directrix of the hyperbola 16x^2 - 9y^2 = 144, then its corresponding focus is:
- The area (in sq. units) of the region bounded by the curves y = 2^x and y = |x + 1|, in the first quadrant is:
- If the line ax + y = c, touches both the curves x^2 + y^2 = 1 and y^2 = 4 2 ,x, then |c| is equal to: