List of top Mathematics Questions

The domain of definition of the function $y = \frac{1}{\log{10} ( 1 -x)} + \sqrt{x + 2}$ is

Which of the following functions is periodic?

The centre of the circle passing through the point (0, 1)and touching the curve $y = x^2 at (2,4)$ is

AB is a diameter of a circle and C is any point on the circumference of the circle. Then,

The largest interval for which $ x^{12} - x^9 + x^4 - x + 1 > 0 $ is

There exist a function f (x), satisfying $f (0) = 1, f'(0) = -1, f (x) > 0$ for all x, and

The area bounded by the curves y = f (x), the X-axis and the ordinates x = 1 and x = b is (b - 1 ) sin (3b + 4). Then, f (x) is equal to

If A and B are two independent events such that $P(A) > 0,$ and $P(B)\ne 1$, then $P(\overline{A}/ \overline{B})$ is equal to

The scalar $\overrightarrow{A}.[(\overrightarrow{B}+\overrightarrow{C})\times(\overrightarrow{A}+\overrightarrow{B}+\overrightarrow{C})]$ eqy=ual

Eight chairs are numbered 1 to 8. Two women and three men wish to occupy one chair each. First the women choose the chairs from amongst the chairs marked 1 to 4 and then the men select the chairs from amongst the remaining. The number of possible arrangements is

The value of the definite integral $\int _0^1 (1+e^{-x^2}) dx \, is$

The equation $\frac{x^2}{1-r}-\frac{y^2}{1+r}=1,|r|<1$ represents

Ten different letters of an alphabet are given, Words with five letters are formed from these given letters. The number of words which have at least one of their letter repeated is

The value of the expression \(^{47}C_4+ \displaystyle \sum^5_{j = 1} , ^{52-j}C_3\) is

Two events A and B have probabilities 0.25 and 0.50, respectively. The probability that both A and B occur simultaneously is 0.14. Then, the probability th a t neither A nor B occurs, is

The probability that an event A happens in one trial of an experiment, is 0.4. Three independent trials of the experiments are performed. The probability that the event A happens at least once, is

Two circles $ x^2 + y^2 = 6$ and $ x^2 + y^2 - 6x + 8 = 0$ are given. Then the equation of the circle passing through their points of intersection and the point (1, 1) is

Given positive integers $r >1, n > 2$ and the coefficient of $(3r)th$ and $ (r + 2)th $ terms in the binomial expansion of $(1 + x)^2n$ are equal. Then,

Both the roots of the equation $(x-b)(x-c)+(x-a)(x-c)+(x-a)(x-b)=0$ are always

If $tan \theta=-\frac{4}{3},$ then $sin \theta$ is

Factorise : (i) 12x ² – 7x + 1 (ii) 2x ² + 7x + 3 (iii) 6x ² + 5x – 6 (iv) 3x ² – x – 4.

Prove that cos² 2x-cos² 6x = sin 4x sin 8x

Identify the numerical coefficients of terms (other than constants) in the following expressions: 
(i) 5 – 3t² 
(ii) 1 + t + t² + t³ 
(iii) x + 2xy + 3y 
(iv) 100m + 1000n 
(v) – p²q² + 7pq 
(vi) 1.2 a + 0.8 b 
(vii) 3.14 r² 
(viii) 2 (l + b) 
(ix) 0.1 y + 0.01 y²