List of top Mathematics Questions

In a triangle ABC, with the usual notations, \(\angle B = \frac{π}{3}\), \(\angle C = \frac{π}{4}\). If D divides BC internally in the ratio 1:3, then \(\frac{sin\angle BAD}{sin\angle CAD} =\)

The element in the third row and the second column in the inverse matrix of a matrix \(\left[ \begin{array}{ccc}1 & 3 & 3 \\ 3 & 1 & 3 \\ 3 & 3 & 4\end{array} \right]\) is

If \(y = tan^{-1}\sqrt{\frac{1+sin2x}{1-sin2x}}\), then \(\frac{\text{d}y}{\text{d}x}\) at \(x = \frac{π}{6}\) is

If \(A = [\begin{array}{cc}3 & 1 \\ -1 & 2\end{array}]\), \(C = [\begin{array}{cc}7 & 3 \\ 0 & 6\end{array}]\) and \(AB = C\), then the inverse of matrix B is

The equation of the line passing through the point of intersection of the lines \(x+2y+6 = 0\) and \(2x-y = 2\) and making an intercept 5 on the y-axis is

The equation of the common tangent touching the circle \((x-3)^2+y^2 = 9\) and the parabola \(y^2 = 4x\) above the X-axis is

If \(\underset{x\rightarrow \infty }{lim}\frac{(2x-1)^{19}\cdot (3x+2)^{11}}{(6x-5)^{30}} = 2^a\cdot 3^b\), then \(a+b =\)

The dual of the statement pattern \((p∧\sim q)⟶(q∧\sim p)\) is equivalent to

The angle between the tangents drawn from the origin to the circle \((x-7)^2+(y+1)^2 = 25\) is

The line \(x+y = 3\) intersects the pair of straight lines \(x^2-3xy+y^2 = 0\) at points A and B. Then the co-ordinates of the mid-point of AB are

If \(33θ = π\), then the value of \(cosθcos2θcos4θcos8θcos16θ\) is

If 6 boys and 3 girls are to be seated in a row for a photograph, then the probability that the end seats are occupied by the girls and no two girls are side by side is

If \(sec4θ-sec2θ = 2\), then \(θ =\)

A bag contains 23 balls, of which 7 are identical. The number of ways of selecting 12 balls from the bag is....

The approximate value of \((0.007)^{\frac{1}{3}}\) is

If \(x\), y, z are the sides of a right angled triangle, where z is the largest side, then \(\frac{1}{log_{x+z}y}+\frac{1}{log_{z-x}y} =\)

If \(ω\) is a complex cube root of unity, then the value of \(sin[π(ω^{10}+ω^{23})-\frac{π}{4}] =\)

The area of the shaded region is ... sq.units.

Two pipes A and B can fill a tank in 12 minutes and 15 minutes respectively while a third pipe C can empty the full tank in 20 minutes. All the three pipes are opened in the beginning but pipe C is closed 6 minutes before the tank is filled. In what time will the tank is full?

In a 700 m race, A reaches the finishing point in 30 seconds & B reaches in 35 seconds. By how much distance A beats B?

A man can row a boat in still water at the rate of 17 km/hr. He finds that it takes him thrice as long to row upstream of a river as to row downstream of the same river. The speed of of the stream is,

If \(53 \equiv y \pmod 6\), then the possible values of \(y\) are:-

A tin container contains 50 litres of cow milk. From this container 5 litres cow milk was taken out and replaced with soya milk. This process was repeated further two more times. How much cow milk is there in the container now?

Which of the following properties are not correct for three real numbers a, b and c?

A. If \(a > b\) and \(b > c\), then \(a < c\)
B. If \(a > b\), and \(c < 0\), then \(ac < bc\)
C. If \(a > b\), and \(c < 0\), then \(a \div c < b \div c\)
D. If \(a > b\) and \(c > 0\), then \(a \div c < b \div c\)

Choose the correct answer from the options given below:

Match the LIST-I with LIST-II

	LIST-I		LIST-II
A.	Row matrix	I.	\(\begin{bmatrix}1 & 0 & 0\\0 & 2 & 0\\0 & 0 & 3\end{bmatrix}\)
B.	Scalar matrix	II.	\(\begin{bmatrix}1\\2\\3\end{bmatrix}\)
C.	Column matrix	III.	\(\begin{bmatrix}1 & 2 & 3\end{bmatrix}\)
D.	Diagonal matrix	IV.	\(\begin{bmatrix}2 & 0 & 0\\0 & 2 & 0\\0 & 0 & 2\end{bmatrix}\)

Choose the correct answer from the options given below: