List of top Mathematics Questions

If $f: R \rightarrow S $ defined by $ f(x)=\sin x-\sqrt{3} \,\cos\,x+\,$ 1, is onto, function then S = ?
The graph of the function $y = f(x) $is symmetrical about the line $x = 2$, then
The unit vector which is orthogonal to the vector $3\widehat{i} + 2\widehat{j} + 6\widehat{k}$ and is coplanar with the vectors $ 2\widehat{i} + \widehat{j} + \widehat{k}$ and $\widehat{i} + \widehat{j} + \widehat{k}$ is
If three natural numbers from $1$ to $100$ are selected randomly then probability that all are divisible by both $2$ and $3$, is
Area of triangle formed by the lines $ x + y = 3$ and angle bisectors of the pair of straight lines $x^2 - y^2 + 2y = 1$ is
If the line $2x+\sqrt6y=2$ touches the hyperbola $x^2-2y^2=4$, then the point of contact is
If f(x) is differentiable and $\int_0^{t^2}x f(x) dx =\frac{2}{5}t^5,$ then $f\bigg(\frac{4}{25}\bigg)$ equals
The sides of a triangle are in the ratio $ 1 : \sqrt 3 : 2 $, then the angles of the triangle are in the ratio
If one of the diameters of the circle $x^2 + y^2 - 2x - 6y + 6 = 0$ is a chord to the circle with centre (2,1), then the radius of the circle is
If $^{n-1}C_r =(k^2 -3) \, ^nC_{r+1}$then k belongs to
Given both $\theta and \phi are acute angles and sin \theta=\frac{1}{2}, cos \phi=\frac{1}{3},$ then the value of $\theta+\phi $ belongs to
If y is a function of x and $\log (x + y) = 2xy$, then the value of y ' (0) is
An infinite GP has first term x and sum 5, then x belongs to
If one root is square of the other root of the equation $x^2+px+q=0,$ then the relation between p and q is
If $\omega (\ne 1)$ be a cube root of unity and $(1 + \omega^2)^n = (1 + \omega^4)^n,$ then the least positive value of n is
The vector sum of two forces is perpendicular to their vector differences. In that case the forces
A train can travel 20\(\%\) faster than a car. Both start from the point A at the same time and reach point B 75 km away from A at the same time. On the way, however, the train lost about 12.5 minutes while stopping at the stations. The speed of the car is
The length of the longest rod that can be placed in a room which is 12 m long 9 m broad and 8 m high is
Two trains of equal length are running on parallel lines in the same direction at 46 km and 36 km per hr. The faster train passes the slower train in 36 sec. The length of each train is
In a 800 m race around a stadium having the circumference of 200 m, the top runner meets the last runner on the 5th minute of the race. If the top runner runs at twice the speed of the last runner, what is the time taken by the top runner to finish the race?
The remainder when 784 is divided by 342 is
A dairyman pays Rs. 6.4 per litre of milk. He adds water and sells the mixture at Rs. 8 per litre, thereby making 37.5\(\%\) profit. The proportion of water to milk received by the customers is
A bicycle originally costs Rs 100 and was discounted 10\(\%\). After three months it was sold after being discounted 15\(\%\). How much was the bicycle sold for?
Wheels of diameters 7 cm and 14 cm start rolling simultaneously from X and Y, which are 1980 cm apart, towards each other in opposit directions. Both of them make same number of revolutions per second. If both of them meet after 10 seconds, the speed of the smaller wheel is
A bag contains Rs. 216 in the form of one rupee, 50 paise and 25 paise coins in the ratio of 2:3: 4. The number of 50 paise coins is