List of top Mathematics Questions

The average of nine consecutive natural numbers is 25. Find the smallest number.

Pipes A and B can fill a tank in 25 hours and 10 hours respectively. Pipe A was opened and after half an hour pipe B was also opened. In how much time the tank got filled?

A quadrilateral ABCD has diagonal AC of length 28 cm. If the perpendiculars drawn from vertices B and D to AC are 30 cm and 21 cm respectively, then find its area.

Akhil is two times as efficient as Vinod and Kamal is three time as efficient as Vinod. They worked together and received ₹ 5,700 for doing the work. Find the share of Kamal in the money received.

Given below are two statements:
Statement I: Line of regression of y on x is the line which gives the best estimate for the value of y for any specified value of x.
Statement II: Line of regression of x on y is the line which gives the best estimate for the value of x for any specified value of y.
In the light of the above statements, choose the correct answer from the options given below:

A man invests some money partly in 8% stock at 105 and partly in 12%, stock at 90. In what ratio should he invest the money to have equal dividends?

See the adjacent figure and find the value of ∠A in the semicircle

See the adjacent figure and find the value of ∠A in the semicircle

Let S = \(\{z \in C-\{i,2i\}:\frac{z^2+8iz-15}{z^2-3iz-2}\in R\}\) if \(\alpha-\frac{13}{11}i\in S, a \in R-{0}\), then \(242\alpha^2\) is equal to ____.

Let $P$ be the plane, passing through the point $(1,-1,-5)$ and perpendicular to the line joining the points $(4,1,-3)$ and $(2,4,3)$. Then the distance of $P$ from the point $(3,-2,2)$ is

If the functions $f(x)=\frac{x^3}{3}+2 b x+\frac{a x^2}{2}$ and $g(x)=\frac{x^3}{3}+a x+b x^2, a \neq 2 b$ have a common extreme point, then $a+2 b+7$ is equal to:

If \(A=\frac{1}{2}\begin{bmatrix}1 & \sqrt{3} \\ -\sqrt{3} & 1\end{bmatrix}\), then :

Given below are two statements about a normally distributed data.
Statement I : 95.45% of the occurrences will lie between \(\bar {X}±3σ\).
Statement II : 68.27% of the occurrences will lie between \(\bar {X}±1σ\).
In the light of the above statements, choose the correct answer from the options given below:

Let the shortest distance between the lines $L: \frac{x-5}{-2}=\frac{y-\lambda}{0}=\frac{z+\lambda}{1}, \lambda \geq 0$ and $L_1: x+1=y-1=4-z$ be $2 \sqrt{6}$ If $(\alpha, \beta, \gamma)$ lies on $L$, then which of the following is NOT possible?

3, 8, 13, ......,373 are in arithmetic series. The sum of numbers not divisible by three is

In the equation \(y_i = β_0+β_1.X_1+ε_1, \ β_0\) stands for

Let \(a,b,c>1,a^3,b^3 \text{ and } c^3\) be in A.P., and \(log_ab, log_ca \text{ and } log_bc\) be in G.P. If the sum of first 20 terms of an A.P., whose first term is \(\frac{a+4b+c}{3}\) and the common difference is \(\frac{a−8b+c}{10}\) is −444, then abc is equal to:

For the system of linear equations\(\alpha x+y+z=1, x+\alpha y+z=1, x+y+\alpha z=\beta\) which one of the following statements is NOT correct ?

In what ratio must a grocer mix tea leaves costing Rs.600/kg and rs.650/kg. So that by selling the mixture at Rs.682/kg, he gains 10%?

Given A, B, C represents angles of a ⃤ AB and cosA + 2 cosB + cosC = 2 and AB = 3 and BC = 7 then cosA – cosC is?

Which one of the following is more useful and effective for a quick visualization of a limited amount of information?

Match List I with List II :

List I (Method)		List II (Characteristic)
(A)	Mean	(I)	Identify what is most common
(B)	Median	(II)	Based on sound mathematics
(C)	Mode	(III)	Square-root of the variance
(D)	Standard deviation	(IV)	Divides into 2 equal parts

Choose the correct answer from the options given below:

The tangents at the point $A (1,3)$ and $B (1,-1)$ on the parabola $y^2-2 x-2 y=1$ meet at the point $P$ Then the area (in unit $^2$ ) of $\triangle PAB$ is :-

Ravi invested certain sum on simple interest. He invested two-third of his sum at 7% p.a and the remaining at 8% p.a. In 3 years he earned ₹1320 as interest. Find the sum invested by him (in ₹).

If sec 5 A = Cosec A, then the value of A is

Let αx=exp(x^βy^γ) be the solution of the differential equation 2x²ydy−(1−xy²) dx = 0, x>0 , y(2)=\(\sqrt {log_e2}\). Then α+β−γ equals :