List of top Mathematics Questions asked in AP EAPCET

In \( \triangle ABC \), coordinates of A are (1, 2). If the equations of the medians through B and C are \( x+y=5 \) and \( x=4 \) respectively, then the area of \( \triangle ABC \) (in sq. units) is

Let A be the resulting point after the point (4, 1) undergoes the following transformations successively:
i. reflection in the line \( y=x \)
ii. translation through a distance of 2 units along the positive direction of X-axis.
If the axes are rotated through an angle of \( \frac{\pi}{4} \) about origin in the positive direction, then the coordinates of the point A are

The straight line which is parallel to X-axis and passing through the intersection of the lines \( ax+2by+3b=0 \) and \( bx-2ay-3a=0 \), \( (a,b)\neq(0,0) \) is

If the slope of one of the lines \( 2x^{2}-17xy+by^{2}=0 \) is 16 times the slope of another line, then the angle between this pair of lines is

The square of the distance from the origin to the point of intersection of the pair of lines \( ax^{2}-xy-3y^{2}-5x+20y-25=0 \) is

The locus of the centre of a circle of radius 2 which rolls on the outside of the circle \( x^{2}+y^{2}+3x-6y-9=0 \) along its circumference is

From a set containing four positive numbers and four negative numbers, four numbers are chosen at random and they are multiplied. The probability that the obtained product is positive is:

From a group of 10 men and 5 women, a four-member committee which includes at least one woman is to be formed. Then the probability for the committee thus formed to have more women than men is:

Three numbers are chosen at random from \{1, 2, ..., 10\}. The probability that the minimum of the chosen numbers is 3 or their maximum is 7, is

A dice is thrown twice. If getting a number greater than four is considered a success, the variance of the probability distribution of the number of successes is

If the mean and variance of a random variable X having binomial distribution are 4 and 2 respectively, then \( P(X=2)= \)

From a pack of 52 playing cards, one card was found missing. From the remaining cards, two cards are drawn at random and found to be spade cards. The probability that the missing card is a spade card is

If M is the foot of the perpendicular drawn from \( P(1,2,-1) \) to the plane passing through the point \( A(3,-2,1) \) and perpendicular to the vector \( 4\overline{i}+7\overline{j}-4\overline{k} \) then the length of PM is

Consider the following statements:
Statement - I: The variance of the first n even natural numbers is \( \frac{n^{2}-1}{4} \)
Statement - II: The difference between the variance of the first 20 even natural numbers and their mean is 112
Which of the following is correct?

A vector \( \vec{a} \) has components \( 2p \) and \( 1 \) with respect to a rectangular Cartesian system. This system is rotated through a certain angle about the origin in the positive direction. If with respect to the new system, \( \vec{a} \) has components \( p+1 \) and \( 1 \), then the values of \( p \) are:

Let \( \overline{a}=4\overline{i}+3\overline{j} \) and \( \overline{b} \) be two vectors in XOY plane, and let \( \overline{a} \) be perpendicular to \( \overline{b} \). Then a vector \( \overline{c} \) in the same plane having projections 1 and 2 respectively on \( \overline{a} \) and \( \overline{b} \) is:

If \( \overline{a}=\overline{i}+\overline{j}+\overline{k} \), \( \overline{a}.\overline{b}=1 \) and \( \overline{a}\times\overline{b}=\overline{j}-\overline{k} \), then \( \overline{b}= \)

O is the origin, \( \overline{OP} \) and \( \overline{OR} \) are vectors making angles \( 45^{\circ} \) and \( 135^{\circ} \) respectively with the positive direction of x-axis, \( |\overline{OP}|=3 \) and \( |\overline{OR}|=4 \). M is the midpoint of PQ in the rectangle OPQR. If OM meets the diagonal PR at T, then \( \overline{OT}= \)

If the lengths of the sides of a triangle a, b, c \( (a>b>c) \) are in arithmetic progression and the greatest angle is twice the smallest, then a: b: \( c= \)

If \( u=log_{e}[tan(\frac{\pi}{4}+\frac{\theta}{2})], \) then \( sinh~u= \)

If the angles of a triangle are in the ratio 4: 1: 1, then the ratio between its largest side and its perimeter is

In \( \Delta ABC \), if \( A+B=120^{\circ} \), \( a=\sqrt{3}+1 \) and \( b=\sqrt{3}-1 \), then \( A:B= \)

Match the items of List - I with those of List - II: \[ \begin{array}{ll} \text{List - I} & \text{List - II} \\ \hline \text{A) } Tan^{-1}3+Tan^{-1}x=Tan^{-1}8 \implies x= & \text{I) } \frac{\sqrt{5}}{3} \\ \text{B) } Sin^{-1}x-Cos^{-1}x=\frac{\pi}{6} \implies x= & \text{II) } \frac{1}{5} \\ \text{C) } sin^{-1}\frac{4}{5}+2~Tan^{-1}\frac{1}{3}= & \text{III) } \frac{\sqrt{3}}{2} \\ \text{D) } tan(Sec^{-1}\frac{1}{x})=sin(Tan^{-1}2), x>0 \implies x= & \text{IV) } \frac{\pi}{2} \\ & \text{V) } \frac{\pi}{3} \end{array} \] The correct match is:

Statement I: If \( x\in(0,\frac{\pi}{2}) \) and \( cos~3x+cos~x=cos~2x \), then \( x=\frac{\pi}{4} \) or \( \frac{\pi}{3} \)
Statement - II: If \( sin~x~sin~2x=cos~x~cos~2x-1 \), then \( x=\frac{n\pi}{3},n\in Z \)
Which of the following options is correct?

Assertion (A): \( cos^{2}5^{\circ}+cos^{2}10^{\circ}+cos^{2}15^{\circ}+...+cos^{2}85^{\circ}=\frac{17}{2} \)
Reason (R): If \( A+B=90^{\circ} \), then \( cos^{2}A+cos^{2}B=1 \)
Then, which one of the following is True?