class 11

Math

Algebra

Fundamental Of Mathematics

There are n urns each containing (n+1) balls such that ith urn contains i white balls and (n+1-i) red balls.

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Contrapositive of the statement. If the squares of two numbers are equal then the numbers are equal is (A) If the squares of two numbers are equal then the numbers are equal (B) If the squares of two numbers are not equal then the numbers are not equal (C) If two numbers are not equal then the square of the numbers are not equal (D) If squares of two numbers are equal then the numbers are to equal

Tangents are drawn from the point (17, 7) to the circle $x_{2}+y_{2}=169$, Statement I The tangents are mutually perpendicular Statement, lls The locus of the points frorn which mutually perpendicular tangents can be drawn to the given circle is $x_{2}+y_{2}=338$ (a) Statement I is correct, Statement II is correct; Statement II is a correct explanation for Statementl (b( Statement I is correct, Statement I| is correct Statement II is not a correct explanation for Statementl (c)Statement I is correct, Statement II is incorrect (d) Statement I is incorrect, Statement II is correct

If $(A+⊕B)∧(AΘB)=A∧B$ what should be proper symbol in place of $⊕$ and $Θ$ to hold the equation (a) $∧$ and $∨$ (b) $∧$ and $∧$ (c) $∨$ and $∨$ (d) $∨$ and $∧$

$((p∧q)∨(p∨q))∧(p∧q)$ is equivalent to (A) $p∧q$ (B) $p∧q$ (C) $p∨q$ (D) $p∨q$

Let O(0,0), P(3,4), Q(6,0) be the vertices of the triangle OPQ. The point R inside the triangles OPQ is such that the triangles OPR, PQR, OQR are of equal area. The coordinates of R are (1) $(34 ,3)$ (2) $(3,32 )$ (3) $(3,34 )$ (4) $(34 ,32 )$